DISSERTATIONES CHIMICAE UNIVERSITATIS TARTUENSIS
2
THEORETICAL STUDY 
OF GAS-PHASE ACID-BASE 
EQUILIBRIA
by
Peeter Burk
TARTU 1994
DISSERTATIONES CHIMICAE UNIVERSITATIS TARTUENSIS
2
ilQb%
THEORETICAL STUDY 
OF GAS-PHASE ACID-BASE 
EQUILIBRIA
by
Peeter Burk
TARTU 1994
The thesis Mill be defended on April 21, 1994 at 14.00 in thp 
room 204 in the Main Building of University of Tartu, ülikooli
18, EE2400 Tartu, Estonia.
Secretary of the Council: Л * Tuulleets
The permanent address of the author is Institute of Chemical 
Physics, University of Tartu, Jakobi 2, EE240C Tartu, Estonia.
© Peeter Burk, 1994
Ouaifutilist* h»ppelis-alus«li*t* ttukaalud« 
teoreetiline uurimine.
Peeter Burk 
Kokkuvõte
Gaasifaasxlised happelis-aluselised tasakaalud on viimasel 
paarikümnel aastal tõusnud füüsikalise orgaanilise keemia 
tähelepanu keskpunkti, kuna nad võimaldavad uurida asendaja ja 
rektsioonitsentri vahelist vastasmõju tingimustes, kus keskkonna 
(solvendi) mõju on välistatud. See võimaldab ülalnimetatud 
vastasmõju olemuse ja mehhanismi uurimist, samuti avaneb uudne 
võimalus selgitamaks solvendi mõju lahuses toimuvatele 
protsessidele.
Viimastel aastatel on kiiresti kasvanud ka kvantkeemiliste 
arvutuste kasutamine mitmesuguste keemiliste probleemide 
uurimiseks, kuna sellised arvutused annavad sageli kasulikku 
lisainformatsiooni uuritavate molekulide ja ioonide struktuuri ja 
laengujaotuse kohta, võimaldades nii paremini mõista uuritavate 
süsteemide käitumise fundamentaalseid seaduspärasusi ning 
võimaldavad uurida ka süsteeme, mis on eksperimentaalselt raskesti 
käsitletavad.
Käesolevas töös on kvantkeemilisi arvutusi rakendatud 
gaasifaasiliste happelis-aluseliste tasakaalude uurimiseks. On 
teostatud poolempiirilise PM3 meetodi testimine gaasifaasiliste 
prootonafiinsuste ja deprotoneerimisentalpiate arvutamiseks.
Kasutades poolempiirilisi ja ab initio arvutusmeetodeid on 
uuritud mitmesuguste tugevate hapete ja aluste omadusi (energiad, 
geomeetriad, laengujaotused) ning nende võimalikku prototroopset 
tautomerismi. Põhinedes nendel arvutustel on välja pakutud uute 
rekordilist aluselisust või happelisust omavate ühendite loomise 
võimalused.
3
Contents
List of Publications............................................. 5
1. Introduction................................................... 6
2 . Literature overview............................................ 8
2.1.Evaluation of different methods for calculating gas 
phase proton affinities and deprotonation enthalpies...... 8
2.2.Applications of molecular orbital calculations
to study of the acid-base equilibria...................... ll
3.Results and discussion........................................ 15
3.1. Critical test of the PM3 method for calculating
gas-phase (intrinsic) proton affinities................... 15
3.2 Theoretical Study of Structure and Basicity of
Some Alkali Metal Oxides, Hydroxides and Amides...........16
3.3.Theoretical Study of Prototropic Tautomerism and 
Acidity of Tris(fluorosulfonyl)methane and
hexafluoroacetylacetone....................................18
3.4.Superacidity of Neutral Brönsted Acids in Gas Phase— 20
Acknowledgements................................................ 22
References.......................................................23
4
List of Publications
The thesis consists of the review and the six articles listed 
below. They are referred in the text by Roman numerals I-VI. The 
review summarizes and supplements the articles.
I. Peeter Burk and Ilmar A.Koppel
An a mi and PM3 study of hexafluoroacetylacetone.
J.Mol.Struct. (Theochem), 1993, 2 8 2 ,  277.
II. Peeter Burk and Ilmar A.Koppel
Critical test of PM3 calculated gas-phase acidities.
Theor. Chim.Acta, 1993, 86, 417.
III. Peeter Burk, Koit Herodes, Ivar Koppel and Ilmar Koppel 
Critical test of PM3 calculated proton affinities.
Int. J. Quant. Chein. : Quant. Chem. Symposium, 1993, 2 7 ,  633.
IV. Peeter Burk, Ilmar A. Koppel and Juri Tapfer
Theoretical study of structure and basicity of some alkali metal 
oxides, hydroxides and amides. 
int. J . Quant. Chem., submitted.
v. Peeter Burk, Ilmar A. Koppel, Jüri Tapfer, Frederick Anvia and 
Robert W. Taft
Theoretical Study of Prototropic Tautomerism and Acidity of 
Tris(fluorosulfonyl)methane.
J.Mol. Struct. (Theochem), submitted.
VI.Peeter Burk, Ilmar A. Koppel, Ivar Koppel, Lev M. Yagupolskii 
and Robert W. Taft
Superacidity of neutral brönsted acids in gas phase. PM3 study.
J .Comp.Chem. , submi11ed.
5
2
1.Introduction
Proton transfer reactions are among the most extensively 
studied of simple chemical reactions. Over many decades, the 
careful scrutinity of such processes in solutions has provided much 
insight into the nature of substituent-reaction center interactions 
and into the role of the solvent in directing molecular stability 
and reactivity. The interpretation of results from these studies 
(in solution), however, has not always been straightforward, since 
the acidity or basicity of the compound could be modified by the 
solvent so that experimentally observed thermochemical quantities 
may differ from those that can be attributed strictly to intrinsic 
molecular properties.
In the past two decades, several experimental techniques such 
as high-pressure mass spectrometry [1,2], flowing afterglow [3] and 
Fourier transform ion cyclotron resonance spectrometry [4] has 
provided an accurate set of thermochemical data for acidities and 
basicities of organic and also inorganic compounds in gas phase. 
Since then, there have been a increasing interest in using such 
information to distinguish intrinsic molecular acidities and 
basicities from the chemical effect of solvation, and to interpret 
the thermochemistry of proton transfer and bonding [5].
At the same time, in recent years quantum chemical 
calculations have become a widely used tool for investigation of 
wide range of problems [6]. Both ab initio and semiempirical self- 
consistent field molecular orbital calculations are often used. If 
these methods can be used to calculate gas phase (intrinsic) 
acidities and basicities with sufficient accuracy, it would be of 
great value, while such calculations can be carried out much faster 
and supposedly at much less cost than experiments. Such 
calculations are also not limited by the physical properties of the 
samples (stability, vapor pressure, etc.) or the availability of 
sufficient number of reference compounds. Although PA calculations, 
at present, have been carried out mostly on neutrals and anions, it 
should be possible to calculate the proton affinities of radicals,
6
a quantity that is quite difficult to obtain experimentally.
Besides of serving as another "experimental" method for 
determining the thermochemical parameters, theoretical calculations 
provide also structural information on ions and can be used 
quantitatively to determine the difference in energy for 
protonation or deprotonation of two different sites in the same 
molecule. A more detailed understanding can be gained by examining 
various electronic energy components, for example, using the 
Bader's "atoms in molecule" method [7] . Finally, more detailed 
information about the intrinsic nature of the proton affinity can 
be determined from theory, for example, the separation of chemical 
and physical effects (e.g., zero-point energy differences), thus 
enabling us to get better understanding of chemical and physical 
processes lying behind the acid-base equilibria.
7
2 *
2.Literature overview
As it was already mentioned above, quantum chemical molecular 
orbital calculations have become very widely used tool for 
investigating gas-phase proton transfer equilibria. Publications on 
this field can be divided roughly into two classes: 1. works, which 
investigate the usability of certain methods for calculating 
gas-phase deprotonation enthalpies and proton affinities, and 2. 
works, where such calculations are used to study some aspects of 
acid-base equilibria. However, it must be mentioned, that 
practically in all publications of latter class also the 
verification of usability of applied calculation methods is given. 
Short overview of recent publications of both classes is given 
below.
2.1.Evaluation of different methods for calculating 
gas phase proton affinities and deprotonation enthalpies
Chandrasekhar, Andrade and Schleyer showed, that UNIX) is quite 
good for estimating acidities with average error near 10 kcal/mol 
[8]. However, they noticed also that the ordering of acidities of 
some compounds (e.g. methanol and ethanol) is not given correctly 
and MNDO geometries have also deficiencies.
Dewar and Dieter have carried out a systematic study of 
reliability of PM3 calculated proton affinities and deprotonation 
enthalpies [9] . They have shown, that with a few exceptions the 
errors in calculated proton affinities of bases and deprotonation 
enthalpies of acids are comparable with those in the calculated 
heats of formation of corresponding neutral molecules. The average 
errors in calculated proton affinities and deprotonation enthalpies 
were 6.0 and 8.2 kcal/mol respectively.The main reported problem 
involves anions in which the charge is largely concentrated on one 
atom.
Very similar results for AMI predicted deprotonation 
enthalpies of large collection of C-H acids were reported by Kass
8
[10] . The use of empirical correction, which reduces the average 
unsigned error to 4.2 kcal/mol was proposed.
Catalan et al. have found [11], that the AMI method doesn't 
handle correctly the effect of adjacent lone pairs on the relative 
basicity of pyridazine and pyrimidine, and on the relative 
gae-phase acidity of pyrazole and imidazole. At the same article it 
was also found that INDO method handles these effects correctly.
Good starting point for choosing adequate ab initio method for 
studies of gas-phase acid-base equilibria is given by Hehre, Radom, 
Schleyer and Pople [6] and by Dixon and Lias [5]. Authors stress, 
that for comparison of calculated and experimental numbers 
corrections for differential zero-point energies and to uniform 
temperature are needed, as uncorrected values often differ from the 
corrected ones by 5 kcal/mol or more, primarily as a consequence of 
differing number of reactant and product molecules in 
(de)protonation reactions. It was shown, that for successful 
reproduction of experimental absolute proton affinities at least 
6-31G* basis set must be employed. It is concluded, that for 
calculation of absolute acidities (more precisely, deprotonation 
enthalpies) basis sets which incorporate diffuse functions are 
required, and the use of 3-21+G* and 6-31+G* basis sets for such 
calculations is encouraged. This conclusion agrees with earlier 
works of Chandrasekhar et al. [8] and Kollmar [12], where it was 
established, that inclusion of diffuse AOs in basis sets of modest 
size (3-21G, 4-31G) improves th'e description of acidity more than 
use of correlation corrected calculations with very extended basis 
sets. However, Hehre et al. also state [6], that for calculations 
of relative proton affinities, deprotonation enthalpies and effects 
of remote substitutions on acid and base strength even the minimal 
STO-3G basis set reproduces the majority of experimental data 
accurately.
Koppel, Mõlder and Palm have carried out ab initio 
calculations of proton affinities and deprotonation enthalpies 
using various basis sets (STO-3G, 3-21G, 4-31G, 6-31G*, 3-21+G,
4-31+G) and with the 6-31G** basis set using fourth order
9
3
Möller-Plesset perturbation theory [13]. They showed, that the fit 
with experiment can be substantially improved by using empirical 
corrections based on linear regression between calculated and 
experimental values.
Extensive study of the basis set dependencies of proton 
affinities of carbonyl bases calculated both at Hartree-Fock level 
and using MP2 and MP3 levels of correlation have been carried out 
by Del Bene [14-16] . At the ST0-3G level differences in both 
absolute and relative proton affinities from their experimental 
values were too large. Quantitatively correct results were found 
for relative proton affinities at the 4-31G level. Remarkably good 
agreement in the relative and absolute proton affinities was found 
6-31G', 6-31G** and 6-311G’* basis sets, especially when the MP2 and 
MP3 were used.
In a later work [17] Del Bene and Shavitt have used 6- 
31+G(2d,2p) basis set to study the influence of different basis 
sets and electron correlation methods like many-body (Moller- 
Plesset) perturbation theory at second, third and fourth order; the 
linearized coupled-cluster method; the averaged coupled-pair 
functional; configurational interaction with all single and double 
excitations; and configurational interaction with all single and 
double excitations with the Davidson and Pople corrections on 
proton affinities and deprotonating energies. All calculations were 
carried out at MP2/6-31+G** geometries. The basis set superposition 
error was evaluated using counterpoise correction. It was shown, 
that MP2 values for the protonation and deprotonation energies are 
always the lowest, while the CISD values are often highest. The 
results of various correlation methods agree with each other within 
2 kcal/mol for almost all protonation energies and within 2-7 
kcal/mol for deprotonation. The protonation and deprotonation 
energies computed with various methods generally agree with 
experimental values to about 1%. It was shown, that the 
counterpoise correction is quite big for even such large basis sets 
as 6-31+G** and 6-311+G(2d,2p) - ranging from 4.1 to 4.6 and from 
2.0 to 2.8 respectively. The inclusion of counterpoise correction
10
generally improves the agreement between different basis sets and 
correlation methods.
Eades et al. have carried out two studies on proton affinities 
of N-bases [18,19]. It was shown that at the DZ+d level 
qualitatively accurate relative proton affinities can be obtained 
at Hartree-Fock level.
Nicholas et al. have recently carried out the study of the 
effects of basis set size on the calculated structure and acidity 
of some compounds which mimic the zeolites [20] . They have come to 
conclusion, that TZ+d level of theory is required for prediction of 
geometry, while the trends in proton affinities and deprotonation 
enthalpies can be predicted at DZ level.
DeFrees and McLean have demonstrated [21], that ab initio 
molecular orbital theory at the MP4/6-3ll++G(3df,3pd) level yields 
proton affinities for small neutral and anionic bases to within 2 
kcal/mol of accuracy. The usefulness of MP4/6-311++G(2d,2p) and 
MP2/6-311G** theoretical models for bigger systems is pointed out.
Pople and coworkers represented recently two methods for 
accurate calculation of energetic properties of molecules - Gl [22] 
and G2 [23] . They have found [23] , that these methods yield the 
proton affinities consistently within 2.5 kcal/mol of experimental 
values. This statement was later confirmed by Smith and Radom [24] .
2.2.Applications of molecular orbital calculations 
to study of the acid-base equilibria
Berthelot and coworkers have studied the gas-phase basicity of 
biologically interesting molecules such ar nicotines, nicotinic 
acid derivatives, etc. [25]. They used AMI method to predict the 
site of protonation and found, that nornicotine and nicotine 
protonate preferentially on the five membered ring amino nitrogen, 
while for methyl nicotinate and nicotineamide the pyridine nitrogen 
appears clearly as the favored site of protonation.
Benedetti and coworkers calculated AMI proton affinities for 
prazosin analogues (2-substituted 4-amino-6, 7-dimethoxy derivatives
11
3*
of quinazoline, guinoline and isoquinoline) [26] . these values were 
correlated with corresponding experimental basicity constants and 
al-adenoceptor binding affinities. The results confirm the crucial 
role of the N1 protonated form of these derivatives for a selective 
and productive binding with the a’ adrenergic receptor.
Ogretir and Kaninskan showed using ab initio calculations with 
minimal basis set, that the protonation of imidazo[4, 5-f ] quinolines 
take place at the pyridine nitrogen atom rather than at the 
imidazole nitrogen atom [27]. The preferred form of 
imidazo[4,5-f]quinolines was found to be the 3H form. A 
satisfactory correlation between experimentally obtained pKa values 
and computed electron densities at the protonation site was found.
Abboud and coworkers investigated the gas phase basicities of 
p-lactams and azetidines [28] at the 6-31G* level of theory. They 
showed, that in gas phase ß-lactams are weaker bases than acyclic 
amides, it was found, that both ß-lactams and acyclic amides are 
oxygen bases, but the gap between the nitrogen and oxygen intrinsic 
basicities is much smaller in the former. This is the result of the 
charge redistribution due to the hybridization changes at the 
carbonyl carbon, which are well described by the topological 
analysis of the corresponding charge densities. The cyclization 
effects of proton affinities of amines were found to be almost 
negligible.
Sabio and Topiol calculated at 4-31G* and MP2/4-31G* level of 
theory the basicities of several N-methyleformamidine analogues to 
find out whether these compounds can serve as H2-receptor agonists 
[29], where the simultaneous domination of N3-H tautomeric form 
and lower basicity than that of N- (3 - aminopropyl) formamidine is 
required.
Tang et al. [30] calculated within the charge density 
topological approach the -Vp values of nonbonded charge 
concentrations of methylamines and some other nitrogen bases. Very 
good linear relationship between those values and gas phase 
basicities of studied molecules was found.
Shambayati et al. have used ab initio calculations of basicity
12
of silyl ethers as inquiry into the nature of silicon-oxygen 
interactions [31].
Tunon, Silla and Tomasi [32] calculated the basicities of 
various methylamines both in vacuo and solution using the 6-31G* 
basis set. Polarizable continuum model of solvent was used for 
calculations in solution. It was shown, that correlation effects 
are very important in order to have a good estimation of the 
inductive effect produced by methyl substitution.
Gordon, Damrauer and Kremp have studied gas-phase acidities of 
silanols and their sulfur analogues [33] using ab initio 
calculations with up to 6-3l++G(2df,2p) basis sets to asses 
ß methyl and ß-ethyl substitution effects and demonstrated, that 
such effects are very small both in silanols and thioles.
Siggel and Thomas [34] have investigated the anomalous gas 
phase acidity of formic acid using ab initio calculations at 
6-31+G* level. They showed, that the anomalously high acidity of 
formic acid in gas phase when compared with to that of acetic, 
propionic and butyric acids, arises because replacement of hydrogen 
by alkyl group in carboxylic acid gives a rise to an unusually high 
change in the potential at the acidic proton in the neutral acid 
and a smaller change in the relaxation that occurs when the proton 
is removed. Analysis of the charge distribution in these molecules 
shows that there is a significant charge transfer from the alkyl 
group to the carboxyl group - especially to the carboxyl carbon.
Fleicher et al. [35] performed ab initio molecular orbital 
calculations of both the *H NMR chemical shifts and deprotonation 
energies of wide variety of small hydroxyl containing inorganic and 
organic molecules, some of which is are the models of surface 
oxygen groups in zeolites, to check whether the postulated 
property-reactivity relationship between the chemical shift of the 
hydroxyl proton and its acidity exists. It was found, that this is 
not the case for the general set of studied systems. That was 
attributed to the non-constant and non-negligible contributions to 
the chemical shift by the X-0 bond and the lone pairs of oxygen.
Abboud et al. have carried out a comparison of intrinsic
13
4
reactivities of thiocarbonyl and carbonyl compounds using ab initio 
calculations at HP and MP2 levels with different basis sets and 
also AMI calculations [36] . it was shown, that all investigated 
thiocarbonyl compounds are sulfur bases. Experimental data on both 
thiocarbonyl and carbonyl compounds were correlated and the 
features found were rationalized in terms of the interactions 
between the MOs of the parent compound and substituent using 
topological analysis of charge densities.
Ventura et al. performed high-level ab initio calculations 
using basis sets with several diffuse and polarization functions 
and including correlation energy through MP2 theory on the 
different possible structures of formo- and acetohydroxamate anions 
to determine their preferred conformations in gas-phase [37]. It 
was found, that in gas phase both acids behave as HH acids rather 
that OH acids.
Komornicki and Dixon [38] have performed a set of large scale 
ab initio molecular orbital calculations on proton affinities of 
Na, CO, COj and CH* to establish very accurate proton affinities for 
each of those molecules. The influence of basis set superposition 
error was also studied. Authors claim, that they have obtained 
final proton affinities at the chemical accuracy (the errors are 
supposed to be less than l kcal/mol) . Good agreement with recently 
revised absolute proton affinity scale is reported.
Smith and Radom [24] used G2 level of theory to calculate 
proton affinities for 31 small molecules to evaluate different 
competing proton affinity scales. Calculated proton affinities were 
in good agreement with those of Lias et al. [39]. It was found, 
that various experimental proton affinity scales can be 
substantially reconciled, if the currently accepted value of the 
proton affinity of isobutene, used as an absolute standard in 
several of the experimental determinations, is adjusted downwards 
by 2-5 kcal/mol. Recent experimental results [40].
14
3.Result* and discussion
3.1. Critical taat of the PX3 method for calculating 
gaa-phaae (intrinsic) proton affinities
In order to test the usefulness of the PM3 method for 
calculating proton affinities the calculations for a wide range of 
acids and bases (175 acids and 119 bases) for whom the 
corresponding experimental quantities are known were carried out. 
The species to be calculated were chosen so that they covered wide 
ranges on the acidity (314.3 - 421.0 kcal/mol) and basicity (63.6 - 
240.6 kcal/mol) scales and represented also a wide variety of 
different classes of acids and bases: hydrocarbons, amines, 
anilines, aldehydes, ketones, nitriles, alcohols, phenols, etc.; 
nitro-, fluoro-, cyano-, etc. substituted acids and bases, etc. 
Numerical results of these calculations as well as results of 
statistical analysis of calculated and experimental acidities and 
baeicities are presented in articles [II] and [III].
Prom those results one can conclude that PM3 method can in 
many cases provide an useful and rather satisfactory quantitative 
estimate of gas-phase acidities and basicities. However, one has to 
keep in mind that the average errors are rather big (more than 8 
kcal/mol) and in many cases even bigger. Besides to random errors 
there seem to be also the systematic ones for some classes of 
compounds, as characterized by the non-zero intercept, non-unity 
slope and good correlation for these series (see Table 3 in [II], 
Table 2 in [III] and Table 2 in [VI]. It should be mentioned that 
for bases and acids the deviations from the onity slope are to the 
different sides - acids have slope 1.1 while for the bases the 
corresponding value is 0.8. Similar behavior is earlier noted also 
for aJb initio calculated proton affinities [13] . It should also be 
noted that using the empirical correction, especially for certain 
claeses of compounds, the acidities and basicities can be estimated 
much more accurately.
15
4*
The comparison of results from PM3 calculations and ab initio 
calculations shows, that the better fit with experiment can be 
achieved only using 6-31G* (6-31+G* for deprotonation enthalpies) 
or higher basis sets (frequently using corrections for electron 
correlation effects at the post Hartree-Fock level), which makes 
the use of PM3 method for investigating of larger systems (with 50- 
100 atoms) quite feasible. When one compares the reliability of PM3 
calculated basicities and acidities with the results of ami 
calculations, it could be concluded, that for the prediction of the 
acidities both methods are roughly of the same quality and also 
share the same deficiencies: big errors for small anions and also 
for relatively big and bulky anions. For the calculation of 
basicities the AMI method seems somewhat superior. At the same 
time, the PM3 method can be an useful tool for investigation of 
proton transfer equilibria of hypervalent compounds of second row 
elements, for whom the AMI method is not very reliable [41,42].
3.2 Theoretical Study of Structure and Basicity of 
Some Alkali Metal Oxides, Hydroxides and Amides
Gas-phase proton affinities and geometries of Li20, LiOH, 
LiNHj, Na20, NaOH, NaNHj, K30, KOH and KNHj were found [IV] using 
ab initio (TZV*, SBK* and 3-21G* or 6-31G* basis sets) calculations. 
The proton affinities, geometries and charge distributions, 
obtained using these basis sets were considerably consistent. So 
one can conclude, that all used basis sets are equally good for 
that sort of calculations and SBK* basis set as computationally 
most efficient should be suggested for investigation of similar 
systems.
Our calculations confirm the experimentally established 
superiority of intrinsic proton affinities of alkali metal oxides 
over their hydroxylic counterparts. Also the extremely high 
basicity of alkali metal amides, often used in organic synthesis as 
highly effective deprotonating agents, was confirmed. The 
calculated (SBK* basis set) and experimental proton affinities are
16
collected in Table l.
Table 1.
Me PA(calculated) PA(experimental)J
Me20 MeOH MeNH2 Me20 MeOH
Li 299 .9 250 . 5 276 . 8 285.9 2 3? 8
Na 340 . 8 246 . 7 297.0 306.7 272 . 6
К 370 . 3 287.1 314 . 0 318.2 262.9
Ref.l in [IV]
The difference between calculated and experimental proton 
affinities is considerable (mean average error is more than 25 
kcal/mol), but there is good correlation between the above 
mentioned proton affinities. The latter fact enables us to predict 
the proton affinities of LiNH2, NaNH2 and KHN2 to be 257.0, 271.9 
and 284.5 kcal/mol respectively.
The oxides and hydroxides of alkali metals were found to be 
linear. Corresponding cations were planar, as well as were the 
neutral amides. The cations of latter species were tetrahedral. 
This is obviously caused by the strong coulombic repulsion forces 
between hydrogen and metal atoms, which both bear rather big 
positive charges both in neutrals and cations as evidenced by 
Mulliken population analysis. The latter also shows big negative 
charges on oxygen and nitrogen atoms. These facts evidence that the 
Me-О or Me-N bonds are fairly ionic and the high basicity of title 
compounds is mainly caused by coulombic stabilization due to the 
interaction of proton with the highly negatively charged 
protonation center (oxygen or nitrogen atom).
Our later PM3 calculations on phosphazenes indicate, that such 
high basicity values are accessible also for organic neutral 
Brönsted bases. So, for the below presented simple P4 phosphazene
17
5
NH, NH NH, NH,
I I I I
H jN ---P =  N---- P ---- N =  P ----N =  P ---- NHj
KIfwtTj j шПП»2  Mшnj  nШrij
the predicted proton affinity is 281 kcal/mol. That is by ca 30 
kcal/mole more than that of 7-methyl-1,5,7-triazabicyclo[4.4.0]dec- 
5-ene, which has the highest proton affinity (250.8 kcal/mol) 
reported [43] so far in the literature.
3.3.Theoretical Study of Prototropic Tautomeriam and 
Acidity of Tria(fluorosulfonyl)methane and 
hexafluoroacetylacetone
Recently it was suggested [44] , that the high acidity of 
perfluorosulfonyl compounds may be affected by the prototropic 
tautomerism. Tris-fluorosulfonylmethane was chosen as a model for 
such systems, and the ability of different molecular orbital 
calculation methods (PM3, ab initio at STO-3G* and 3-21G* levels) 
to describe prototropic tautomerism was studied in article [V].
It was shown, that PM3 method totally fails to describe 
energetics of prototropic tautomerism of (FSOJjCH. At the same time 
it predicts the geometries of both the neutral sulfo form and its 
anion in good agreement with experiment. Both ab initio methods 
used predicted in accordance with experiment that the sulfone form 
is more stable than enol form. The conformity between calculated 
and experimental geometries was also satisfactory.
The gas-phase deprotonation enthalpy of (FS02)3CH was 
calculated. The analysis of changes in charge distribution upon 
deprotonation indicate, that the high acidity of this compound is 
caused by strong charge delocalization in its anionic form.
Keto-enol tautomerism, acidity and intramolecular hydrogen 
bonding of hexafluoroacetylacetone was studied in article [I] using
18
semiempirical AMI and PM3 methods without and with the inclusion of 
limited configuration interaction. It was shown, that both used 
semiempirical models were able to reproduce the experimental data 
at least qualitatively (with the preference of enol form) only when 
Cl was taken in account. Using this approach it was shown in 
accordance with experiment that the most stable conformation of 
hexafluoroacetylacetone is cyclic hydrogen-bonded enol form. The 
geometry found for that conformation, however, differs remarkably 
from that found experimentally [45]: the hydrogen bond 0--H-0 was 
found to be nonlinear and also nonsymmetric. On the basis of recent 
experimentally reestablished geometry of hexafluoroacetylacetone 
analogue acetylacetone we consider that our geometry may be more 
proper and the experimental re-examination of 
hexafluoroacetylacetone geometry is needed.
The hydrogen bond energy was found to be 4.5 kcal/mol and the
0 - --H and О - - -О distances were 2.09 and 2.86 A respectively using 
AMI method. The proton transfer potential curve was found to have 
two minima separated by the barrier, which height was predicted to 
be 24.1 kcal/mol.
Based on the above facts it was suggested that the 
hexafluoroacetylacetone is rather O-H than C-H acid, which 
dissociates according formula
19
5*
The gas-phase deprotonation enthalpy of hexaf luoroacetylacetone was 
found to be 318.8 kcal/mol, what is in satisfactory agreement with 
experimentally found value 311.2 kcal/mol.
3.4.Superacidity of Neutral Brõnated Acids in Qas 
Phase
Previous results and the analysis given in Refs.4-7 in [VI] 
evidence that three major kinds of substituent effects i.e.,
1. field/inductive effect (P) ,
2. л-electron acceptor (resonance) effects (R), and
3. substituent polarizability (P) effect,
determine the gas-phase acidity of neutral Brönsted superacids. For 
all of those three influencing factors the acidity increases for AH 
acids are due to much stronger substituent stabilizing interactions 
with the deprotonated protonization center of A (e.g., O', N', С', 
etc..) than with the protonated reaction center in AH (e.g., OH, 
NH, CH, etc..).
Therefore, the simplest strategy to develop progressively more 
acidic superacid systems would be the synthesis of molecules which, 
along with the acidity site (C-H, 0-H, N-H, S-H, etc..), include 
(several) highly dipolar superacceptor and strongly polarizable 
substituents which form very extensive, strongly conjugated system 
with the anionic protonization center of A‘.
Very strong increase in acidities is expected for compounds 
where sp2 oxygen is replaced by NS02CF3 group (Yakupolsii1s 
principle) . In the present work PM3 calculations of many 
potentially superacidic neutral Br&nsted acids designed according 
this principle were carried out.
The geometries of known superacidic systems were reproduced 
quite good, so the PM3 method can be recommended for the studies of 
that kind. Charge distribution, predicted by PM3 for hypervalent 
compounds is however unreliable, because due to the lack of d- 
orbitals "hypervalent" atoms of these molecules must bear big 
formal charge to give needed number of formal bonds.
20
From the geometries of analyzed superacids it can be concluded 
that the most stable conformations are determined by the resonance 
interaction which requires the coplanarity of certain molecular 
fragments. This resonance stabilization seems to be rather strong 
and sometimes dominates over the electrostatic repulsion between 
closely located trifluoromethyl groups.
The possibility of creating new, more acidic superacids by 
continuous replacement of spJ oxygens with NS02CF, groups was 
proposed.
21
6
Acknowledgement*
The present study has been performed at the Institute of 
Chemical Physics, formerly Department of Analytical Chemistry, of 
Tartu University. The calculations have been performed also on the 
computers of Computational Center of Tartu University, Estonian 
Biocenter and Office of Academic Computing at University of 
California, Irvine, USA.
First of all I want to thank my doctoral advisor Professor 
Ilmar Koppel for continuous support and assistance throughout the 
years of our collaboration.
I also want to thank the staff of above mentioned 
computational division for providing computer time and continuous 
help throughout of years performing current work. Much of this work 
would have been impossible without the day-to-day work of the 
computer staff of Estonian Biocenter, and the financial support 
from Soros Foundation, who provided the necessary computer 
networking facilities for accessing the computing resources 
unavailable in Tartu.
Let me also thank Toomas Tamm, Ivar Koppel, Koit Herodes and 
Juhan Põldvere for providing help and support in the everyday 
computing environment and for many stimulating discussions.
I am very thankful to Professor Jose-Luis Abboud for the warm 
hospitality and many fruitful discussions during my stay in 
Institute of Physical Chemistry, CSIC, Madrid, in the framework of 
EC Tempus JEP 06125-93 project.
And, last but not least, there has been a continuous support 
and encouragement from my family, who have understood my problems 
and needs during all these years.
These studies have been supported in part by Estonian Science 
Foundation. *
22
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7
Journal o f  Molecular Structure (Theochem), 282 (1993) 277-282 277
0166-1280/93/J06.00 ©  1993 -  Elsevier Science Publishers B.V. All rights reserved
An AMI and PM3 study of hexafluoroacetylacetone
Peeter Burk, Ilmar A. Koppel*
Department o f Analytical Chemistry, Tartu University, EE2400, Jakobi 2, Tartu, Estonia 
(Received 16 April 1992; in final form 30 September 1992)
Abstract
The AMI and PM3 methods with the inclusion of a limited configuration interaction (Cl) approach were used 
to study the stabilities of the tautomers of hexafluoroacetylacetone (HFAA). It was found that the most stable 
tautomer is the hydrogen bonded cyclic asymmetric enol form, the energy of which is lower than that of any keto 
tautomer by at least 2.5 kcal т о Г 1 with the AMI model and 0 9 kcal т о Г 1 with the PM3 model. It was shown that 
HFAA should be an О - H  acid. The intramolecular hydrogen bond energy is4 .5 k ca lm o r' with the AMI model 
and 4.8 kcal т о Г 1 with the PM3 model. It was shown that proton transfer from one oxygen atom to the other is 
controlled by the double minimum potential curve and the correspondig energy barrier height is 24.1 kcal т о Г 1 
with the AMI model and 27.4 kcal т о Г 1 with the PM3 model.
Introduction electron-diffraction measurements [6] indicate that 
the HFAA molecule forms a planar symmetric 
Hexafluroracetylacetone (HFAA) is a simple, a ring, from which it can be deduced that proton 
highly acidic [1] /З-diketone, which is most widely transfer is controlled by a single minimum poten­
known for its ability to form rather stable and tial curve. However, the most recent gas-phase 
specific chelate-type complexes with many cations electron-diffraction measurements of the HFAA 
[2]. Members of the /З-diketone family are charac­ analogue acetylacetone [7] support the conclusion 
terized by keto-enol tautomerism in both the gas that the molecular skeleton is planar but asym­
and liquid phases. It has been suggested [3,4], that metric and the hydrogen atom involved in the 
in both phases the enol tautomer generally pre­ hydrogen bond may be located out of the mol­
dominates due to the extra stabilization of a ecular plane (in the case of acetylacetone the 
strong intramolecular hydrogen bond and reso­ angle of rotation of OH around the С —О bond is 
nance interaction. ca. 26°).
Despite numerous theoretical and experimental Another question is the evaluation of the 
studies neither the details of the electronic structure hydrogen bond strength. The hydrogen bond in 
nor the geometry of HFAA itself or its chelates /З-diketone enol tautomers is strong and was 
seem to have been established with reasonable deduced from the very short О ■ ■ • О distance 
accuracy. Thus whether there is a centred or non­ (2.38-2.55 A) [6,8-10] found in these compounds, 
centred hydrogen bond and whether a single or in contrast with the usual value of ca. 2.7-3.0Ä  in 
double minimum potential curve controls the other hydrogen-bonded systems such as acid and 
proton transfer from one oxygen atom to the other water dimers [11-13].
are hotly debated issues [5]. The earlier gas-phase While sophisticated high level ab initio calcu­
lations are too expensive, especially when geo­
* Corresponding author metry optimization is carried out, the most recent
278 P. Burk and I.A . Koppel/J. Mol. Struct. (Theochtm ) 282 (1993) 277- 282
semiempirical methods AMI [14] and PM3 [15] Calculations were performed on a MicroVAX II 
have been shown to evaluate molecular geometries computer. All the geometries of the various con­
and hydrogen-bond strengths well [16,17] and formations of HFAA were fully optimized at 
within an acceptable computation time, thus the limited configuration interaction (Cl) level 
making calculations on large compounds feasible. using standard procedure: no restrictions were 
In the present study we used the AMI and PM3 imposed. For this purpose 36 configurations, 
approaches to investigate HFAA in both its keto arising from the two highest cccupied and the 
and enol tautomeric form, with special emphasis on two lowest virtual orbitals, were included in each 
the determination of the minimum-energy mol­ calculation. Although it has been pointed out 
ecular geometries o f all possible conformations of [19] that adoption of such a method (semiempirical 
neutral HFAA and its cation. The hydrogen bond method with Cl) leads to calculation of twice 
strength and barrier, the potential energy curve the correlation energy (because the electron corre­
governing the proton transfer process, and the lation effects are partially included in the par­
gas-phase acidity were calculated. At the same ameterization of the method) we included Cl 
time a comparison between theoretical and experi­ because it improves the calculated enthalpies 
mental results could give useful indications as to of formation (using the AMI model without Cl 
the reliability of the method used. the most stable keto and enol tautomers had 
practically the same heat o f formation, while with 
Methods Cl the most stable enol tautomer was approxi­
mately 2.5 kcal mol-1 lower in energy than any 
The морде 6.0 package from the Quantum keto tautomer, which agrees with the experimental 
Chemistry Program Exchange [18] was used. results).
CH, CFj CFj
HFAA-1
CF3 С
I I
CFj CFj
HFAA-6 HFAA-7 HFAA-8
Fig. 1. Calculated conformations of neutral hexafluoroacetylacetone.
7 *
/>. Burk and I.A. KoppeliJ. МЫ. Struct. (Theochem) 282 (1993) 277-282 279
чг. сгГС<'си> С ^ о  o ^ Ĉ CH> C X
Fig. 2. Calculated conformations of tbe hexafluoroacetylacetone anion.
R calta and discussion lated, being separated by a CH2 group; in the latter 
the C =C  and C = 0  double bonds are conjugated so 
Three keto and five enol tautomers and the pro­ that the enol tautomer is resonance stabilized and 
ton transfer transition state of neutral HFAA were forced to planarity by both conjugation and the 
taken into account (see Fig. 1). In the estimation of presence of a hydrogen bond.
the gas-phase acidity of HFAA the geometries and The planarity o f the cis-diketo isomers might 
heats of formation of all the conformations of the be perturbed by the repulsion between the two 
deprotonated form were also calculated. Three cal­ oxygen atoms (HFAA-1) or by the steric hin­
culated conformations of deprotonated HFAA drance between the two trifluoromethyl groups 
(HFAN) are shown in Fig. 2. For all enol tauto­ (HFAA-3). An analogous situation may occur in 
mers calculations were also done for conforma­ the case of cis-cnol conformations without a hydro­
tions where the O -H  bond is rotated by 180° in gen bond.
order to avoid premature completion of calcu­ In fact HFAA-1 was found to be almost planar 
lations of the local minimum. In the tables and when using PM3 parameterization. It should be 
figures only the most stable conformations are mentioned that AM! could not locate an energy 
presented. minimum corresponding to HFAA-2 when geo­
The diketo structures differ from the enol struc­ metry optimization was started from this struc­
tures mainly in the position of the two double ture; the result was the geometry o f the most 
bonds: in the former the two C = 0  groups are iso­ stable keto tautomer (HFAA-1). The results of
T atle 1
Results of the calculation on the HFAA keto structures
HFAA-1 HFAA-2 HFAA-3 HFAA-3
PM3 AMI PM3
AMI PM3
Bond length (A)
R(C=0) 1.221 1.202 1.207 1.232 1.212
R( C -F ) 1.370 1.349 1.348 1.371 1.348
R (C -H ) 1.129 1.113 1.113 1.138 1.116
Д (С1-С2) 1.569 1.590 1.586 1.569 :.5S>5
Л( C 2-C 3) 1.494 1.504 1.513 1.498 1.516
z 'C 2-C 3-C 4=0* (deg) 39.9 0.5 166.8 176.4 178.0
A tf (kcal mc I 1J -370.9 -377.5 -374.9 -354.6 -363.8
pb (D) 2.012 1.727 2.311 2.28! 2.279
* The carbon atoms in Fig. I are numbered from left to right.
bCalculated using AMI or PM3 without Cl at the geometries calculated with ЛМ1 or PM3 with Cl.
P. Burk and I.A. Koppel/J. Mol. Struct, ( Theochem) 282 (1993) 277-282
Table 2
Results of the AMI calculation on the HFAA enol tautomers
HFAA-4 HFAA-5 HFAA-6 HFAA-7 HFAA-8
Bond length (A)
Ä (C=0) 1.236 1.229 1.223 1.231 1.291
A(C-O ) 1.2 SO 1.357 1.361 1.350 1.291
Л (О -Н ) 0.978 0.972 0.972 0.972 1.248
R(C4-C5) 1.566 1.572 1.577 1.566 1.551
Ä(C3-C4) 1.445 1.450 1.459 1.352 1.403
Ж С 2-С З) 1.356 1.357 1.356 1.446 1.404
« (C I-C 2 ) 1.550 1.544 1.543 1.569 1.550
Ä (C -F) 1.370 1.370 1.369 1.369 1.370
Я (С -Н ) 1 105 1.106 1.108 1.113 1.097
/С 2 -С З -С 4 -О а (deg) 0.1 176.0 129.2 0.8 1.2
А Н  (kcal mol“ 1) -373.4 -368.2 -  368.6 -369.1 -349.2
/‘b (D) 0.828 4.310 3.949 0.679 0.295
‘ The carbon atoms in Fig. 1 are numbered from left to right.
Calculated using AM i or PM3 without Cl at the geometries calculated with AMI or PM3 with Cl
the calculalions on the keto tautomers are pre- symmetrical. The results o f the calculations on the
sen ted in Table 1. enol tautomers are presented in Tables 2 and 3.
The structures of the HFAA-4 and HFAA-5 The heats of formation for all the calculated
enol tautomers are planar, while HFAA-6 is non- tautomers are presented in Tables 1 to 3. It can
planar. The transition state HFAA-8 is planar and be seen that in the case of both AM 1 and PM3
Table 3
Results of the PM3 calculation on the HFAA enol tautomers
HFAA-4 HFAA-5 HFAA-6 HFAA-7 HFAA-8
Bond length (Ä)
R{ C = 0 ) 1.222 1.210 1.205 1.210 1.279
Ä(C-O ) 1.338 1.349 1.351 1.341 1.280
Л (О -Н ) 0.967 0.951 0.950 0.956 1.183
«(C 4-C 5) 1.575 1.589 1.585 1.560 1.556
Ж С З-С 4) 1.453 1.461 1.474 1.354 1 405
Ä(C 2-С З) 1.362 1.358 1.356 1.463 1.404
Я(С1 -С 2) 1.552 1.554 1 549 1.590 1.556
Ä (C -F ) 1.349 1.349 1.349 1.349 1.350
Л (С -Н ) 1.097 1.102 1.101 1.104 1.095
/С 2 -С З  -С 4 -0 *  (deg) 1.1 176.5 121.2 2.8 2.0
А Н  (kcalmol-1) -378.5 -373.2 -376.9 -374  4 -351.1
/‘Ь (D) 0.359 4.312 4.339 0.716 0.480
* The carbon atoms in Tig. I are numbered from left to right.
bCalculated using AMI or PM3 without Cl at the geometries calculated with AMI or PM3 with Cl.
8
P. Burk and I.A . Kopptl/J. Mol. Struct. (Theochem) 282 (1993) 277-282 281
Table 4
Results of the calculation on the HFAA anions
HFAN-2
AMI PM3
Bond length (A) 
A(C=0) 1.241 1.225 1.246 1.229 1.253 1.235
*(C—F) 1.374 1.354 1.372 1.354 1.374 1.353
Я (С -Н ) 1.098 1.093 1.099 1.095 1.113 1.102
Л(С1-С2) 1.591 1.612 1.572 1.588 1.582 1.596
Ä(C2-C3) 1.399 1.404 1.401 1.408 1.398 1.405
/С 2 -С 3 -С 4 = 0 *  (deg) 0.1 0.5 175.9 176.7
Д # (к с а 1 т о Г ') -433.5 -439.0 -431.5 -422.4
3.907 4.212 3.688
“ The carbon atoms in Fig. 2 are numbered from left to right.
4Calculated using AMI or PM3 without Cl at the geometries calculated with AMI or PM3 with Cl.
the most stable tautomer is the enol having an and geometries of the most stable anions are pre­
intramolecular hydrogen bond (HFAA-4). The sented in Table 4. The conformation HFAN-4 is 
energy of HFAA-4 is lower than that of any keto much more unstable than the others (its heat of 
tautomer by at least 2.5kcalт о Г 1 with the AMI formation is -403.7 kcal mol "1 with AMI and 
model and by 0.9 kcal т о Г 1 with the PM3 model. -405.2 kcal т о Г 1 with PM3. Thus, because the 
The enol tautomer with a hydrogen bond was most sUbie conformation of neutral HFAA is the 
found to be antisymmetrical. This does not hydrogen bonded cyclic enol (HFAA-4) and the 
agree with the experimentally determined geo­ most stable HFAA anion is HFAN-1, it can be 
metry, but on the basis of calculations [20] and concluded that HFAA is an O -H  acid. The depro­
experiments [7] bn the HFAA analogue, acetylace- tonation energy (acidity) (DPE) of HFAA was 
tone, we consider that further experimental inves­ calculated as
tigation of the HFAA structure will agree with the DPE =  Д Я (Н +) +  ДЛ(А п") -  ДЯ(АпН)
results of our calculations. The distance between 
oxygen atoms was 2.86A with AMI and 2.65A where Д Я( An~) is the calculated heat of formation 
with PM3. The hydrogen bond length was 2.09 A of the HFAA anion, ДЯ(АпН) is that for neutral 
with AMI and 1.83 A with PM3. This also agrees HFAA, and Д Я (Н +) it the heat of formation of a 
with both calculated [20] and measured [7] values proton (in the caae of PM3 the calculated value 
for acetylacetone. (353.6 kcal mol-1) was used, while in the case of 
On the basis of the total energy, and in agree­ AMI the experimental value (367.2kcal m o l '1) 
ment with experimentally determined keto-enol was used, because AMI gives a very poor estimate 
equilibrium [3,4], enol forms prevail over the cor­ of the heat of formation of a proton). The DPE was 
responding diketo conformers. found to be 318.8 kcal т о Г 1 with AMI and 
In the case of anions, the most stable one is the 293.1 kcalmol-1 with PM3, which is in reasonable 
symmetrical conformation HFAN-1, which would agreement with the experimentally determined 
be expected because this conformer corresponds to value of 311.2 kcal т о Г 1 [1].
the most stable enol conformer (HFAA-4) and also The hydrogen bond energy, which was found as 
to the keto conformation (HFAA-1). The energies the difference between the energy of HFAA-4 and
282 P. Burk and I.A. KoppeltJ . Mol. Struct. (Theochem) 282 (1993) 277-282
the energy of the HFAA-4 analogue with the O -H  Both the AMI and PM3 methods were able to 
bond rotated by 180°, was 4.5 k ca lm o r1 with the reproduce the experimental data at least quali­
AMI model and4.8 k c a lm o r1 with the PM3 model. tatively only when Cl was taken into account.
On the basis of the results obtained here, and 
in agreement with suggestions in the literature References
[5,20], the hydrogen atom implied in the hydrogen 
bridge can transfer from an oxygen atom of the 1 I.A. Koppel, R.W. Taft, F. Anvia, D.D. DesMarteau, 
asymmetrical cis-enol tautomer to the other pos­ L.M. Yagupolskii. Yu.L. Yagupplskii, N.V. Ignat'ev, 
N.V. Kondratenko, A.Yu. Volkonskii and V.M. Vla­
ition via a transition state (HFAA-8). The proton sov, J. Am. Chem. Soc., in press.
transfer potential curve was calculated assuming 2 M.L. Morris, R.W. Moshier and R.E. Sievers, Inorg. 
that this process is slow enough for geometry Chem., 2(1963)411.
relaxation [20]. The curve shows two minima 3 J. Burdet and M. Rogers, J. Am. Chem. Soc., 86 (1964) 
separated by an energy barrier, the height of 2105.4 G. Allen and R.A. Dwek, J. Chem. Soc. B, 1 (1966) 161.
which (calculated as the difference between the 5 J. Emsley, Struct. Bonding Berlin, 57 (1984) 147.
energies of the transition state (HFAA-8) and 6 A.L Andreassen, D. Zebelman and S.H. Bauer, J. Am. 
the asymmetrical hydrogen bonded enol form Chem. Soc., 93 (1971) 1148.
(HFAA-4)) is 24.1 k c a lm o r1 in the AMI model 7 K. Jijima, A. Ohnogi and S. Shibata, J. Mol. Struct., 156(1987) 111.
and 27.4 kcal т о Г 1 in the PM3 model. 8 A.H. Lowery, C. George, P.D. Antonia and J. Karle, J 
Am. Chem. Soc., 93 (1971) 6399.
Conclusion* 9 S.L. Baughcum, R.W. Duerst, W.F. Rowe, Z. Smith 
and E.B. Wilson, J. Am. Chem. Soc., 103 (1981) 6296.
10 W.S. Rowe, Jr., R.W. Duerst and E.B. Wilson, J. Am. 
It was found that the most stable tautomer of Chem. Soc., 98 (1976) 4021.
HFAA is the hydrogen bonded cyclic asymmetri­ 11 A. Almenningen, O. Bastiansen and T. Motzfeldt, Acta 
cal enol form. The energy of this tautomer is lower Chem. Scand., 23 (1966) 2849.
than that of any keto tautomer, by at least 12 J.L. Derissen, J. Mol Struct., 7 (1971) 67.
13 J.A. Odutola and T.R. Dyke, J. Chem. Phys., 72 (1980) 
2.5kcalmol-1 (AM I) or 0 .9k c a lm o r1 (PM3). It 5062.
was shown that HFAA preferentially dissociate* 14 M.J.S. Dewar and W. Thiel, J. Am Chem. Soc., 107 
as a rather strong O -H  acid. The intramolecular (1985) 3902.
hydrogen bond energy is 4.5 kcal т о Г 1 (AMI 15 J.J.P. Stewart, J. Comput. Chem., 10 (1989) 209
model) or 4.8 kcalmol-1 (PM3 model). Our calcu­ 16 G. Buemi, F. Zuccarello and A. Raudino, J. Mol. Struct., 164 (1988) 379.
lations show that the proton transfer from one 17 J.J.P. Stewart, J. Comput. Chem., 10 (1989) 221.
oxygen atom to another is controlled by the 18 J.J.P. Stewart, QCPE No. 445, Bloomington, IN, 1990.
double well potential curve and the corresponding 19 T. Clark, A Handbook of Computational Chemistry, 
energy barrier height is 24.1 k c a lm o r1 (AM I) or Wiley, New York, 1985, p. 356.20 G. Buemi and C. Gandolfo, J. Chem. Soc., Faraday 
27.4 kcalmol“ 1 (PM3). Trans. 2. 85 (1989) 215.
8*
Theor Chim Acta (1993) 86: 417-427 Theoretica
ChimicaActa
j*' Springer-Verlag 1993
Critical test of PM3 calculated gas-phase acidities
Peeter Burk and Ilmar A. Koppel
Department of Analytical Chemistry, Tartu University EE2400, Jakobi 2, Tartu. Estonia 
Received September 21, 1992/Accepted February 11, 1993
Summary. Gas-phase acidities have been calculated for 175 compounds using 
the PM3 semiempirical molecular orbital model. With some exceptions, PM3 
seems to be a useful tool for the investigation o f gas-phase acidities. The main 
problems encountered involve two rather different classcs o f acids: one which 
generates small anions (e.g., halide ions, hydride ion, etc.), in which the charge 
is localized on one atom, and, a second, represented by anions that contain bulky 
electron acceptor substituents characte.rized by an extensive negative charge 
delocalization. In some cases (anilines, amides, alcohols, and phenols) the 
average error in predicted gas-phase acidity can be significantly reduced by 
employing an empirically derived correction.
Comparison with AMI results shows that both methods are of roughly equal 
quality with the exception o f hypervalent molecules where PM3 is better (aver­
aged unsigned errors are 11.8 and 17.0kcal/mol for PM3 and AM I. respec­
tively).
Key words: Gas-phase acidities -  PM3 -  AMI
1 Introduction
In recent years quantum chemical calculations have become a widely used tool 
for the investigation o f a wide range o f problems [1]. Both ab initio and 
semiempirical self-consistent field molecular orbital calculations are often used. 
The widespread application o f  the semiempirical M INDO/3 [2]. M NDO  [3]. 
AMI [4], and PM3 [5] methods is due to the fact that they often give reliable 
answers, are easy to use, require relatively little computer time, and can handle 
large molecules.
Proton transfer reactions play a basic role in chemistry and in biochemistry. 
As a result, besides the gas phase basicities or proton affinities o f neutral bases, 
also numerous calculations o f gas phase acidities o f neutral Bronsted acids have 
appeared [ 1, 6, 7 and references therein]. These computations require the heats o f  
fomiation o f  the acid and the conjugated base, the latter being an anion for 
uncharged acids. It is known [1, 8], that qb initio methods require the addition o f  
diffuse orbitals in order to obtain reliable energies for anions. This requirement
41$ P. Burk and I. A. Koppel
further limits the size o f a molecule that can be calculated in a reasonable time. 
Semiempirical methods, at the same time, are reported to reproduce the energies 
of anions almost as well as for neutral molecules [ 4 ,6, 9-13]. Known exceptions 
are small anions with charge predominantly localized on a single atom, such as 
CH, and OH where the calculated energies are consistently too positive. This 
error is probably 114] due to failure to allow for orbital expansion accompanying 
large localized negative charge.
However, there have been only a few systematic investigations [1 ,6 , 
7. 11. 15-17] testing the reliability o f different methods for prediction o f gas- 
phase acidities and none dealing with the PM3 method. Therefore the current 
investigation was undertaken to evaluate the reliability o f the PM3 method for 
predicting gas-phase acidities.
A useful way to consider agreement between experiment and theory is to 
calculate the linear regression between the theoretical and experimental quanti­
ties and to calculate the mean difference (unsigned average error) between the 
experimental and theoretical quantities. The degree o f agreement between the 
two is then reflected by the slope and intercept o f the correlation line, the 
unsigned average error, the standard deviation from the correlation line and the 
correlation coefficient. The last two depend on the scatter o f the points about the 
correlation line. A slope different from  unity and a non-zero intercept imply 
systematic deviation between experiment and theory and means that the theoret­
ical values o f relative acidities will be systematically either too high or too low. 
A non-zero mean difference between theory and experiment reflects an overall 
bias in the absolute values o f the calculated acidity.
2 Method
The acidity (JW-K.iU) of compound HA was found as the heat o f reaction for the 
proton abstraction equilibrium to form the conjugate base A":
H A ^ H -  +  A" АНлЫ(Н А ) =  AHf (H  + ) +  ( 1)
where J t f ,(H ~ ) ,  ЛЯДН А), and AHf { A ") are the heats o f formation for 
proton, acid, and its conjugated anion. In case o f  proton the experimental heat 
of formation (367.2 kcal/inol [19]) was used instead o f the calculated value 
(353.6), because it improves the calculated acidities considerably. We acknowl­
edge that this is not quite a correct procedure, despite the fact that such a way 
was also used in earlier works on semiempirical calculations o f  acidities and 
basicities [6, 11].
The calculations were carried out on a M icroVAX II computer using the 
standard PM3 procedure, as implemented in the MOPAC 6.0 program package 
[20]. All geometries were fully optimized by minimizing the energy with respect 
to ail geometrical variables without using the aid o f  symmetry. In order to avoid 
premature completion o f calculations in local minimum, the calculations were 
carried out starting off from several different initial geometries.
3 Results and discussion
Acidities for 175 compounds, calculated using the PM3 method, are given in 
Table 1, along with corresponding experimentally measured values when avail-
9
Critical test of PM3 calculatcd gas-phasc acidities 419
Т*Ые 1. Comparison with experiment of PM3 heati of formation and acidities (kcal/mol)
calc AH{  exp error
-----------------------  ----------------------------- d / / ; (HA) in calc
HA A -  calc exp* error AHf ( HA)
C-H acids
Methane -1 3 .0 51.5 430.2 416.6 13.6 -17 .8 4.8
Ethane -18.1 31.7 415.5 421.0 -5 .5 -20.1
Propane -2 3 .6 14.8 404.1 419.0 -1 4 .9 -2 5 .0 1.4
Cyclopropane 16.3 60.2 409.7 412.0 -2 .3 12.7 3.6
/-Butane -2 4 .4 0.0 390.1 414.0 -23 .9 -32.1 7.7
Ethene 16.6 61.7 410.8 406.0 4.8 12.5 4.1
Propene 6.4 25.2 384.5 387.5 -3 .0 4.8 1.6
2-Methylpropene -2 .8 16.1 384.6 390.3 -5 .7 -4 .0 1.2
2-Methyl-1,3-butadiene 22.8 39.0 381.9 385.7 -3 .8 17.9
Cyclopentadiene 31.8 15.9 349.8 353.9 -4 .1 31.0
Ethyne 50.7 76.4 391.4 376.7 14.7 54.5 -3 .8
Propyne 40.2 64.2 389.7 381.1 8.6 44.6 -4 .4
1-Pentyne 40.2 54.5 380.0 379.8 0.2 34.4
/-Bu-acetylene 31.8 47.4 381.3 378.0 3.3 25.0
Phenylacetylene 74.7 86.8 377.8 370.7 7.1 73.1 1.5
Benzene 23.5 51.7 393.9 400.7 -6 .8 19.8 3.7
Toluene 14.1 18.5 370.1 380.8 -10 .7 12.0 2.1
1,4-Dimethylbenzene 4.8 8.7 369.6 381.9 -12 .3 4.3
Ethylbenzene 9.5 8.5 364.7 379.8 -15.1 6.9 2.5
i-Propylbenzene 4.9 -1 .2 359.6 379.0 -1 9 .4 1.0 3.9
Cycloheptatriene 46.4 43.1 362.3 375.2 -12 .9 43.7 2.7
Fluorene 49.0 27.7 344.4 353.3 -8 .9 44.9 4.1
9-Ph-fluorene 79.6 43.6 329.7 343.3 -13 .6 76.0b 3.6
Fluoradene 10.0 72.9 328.7 332.5 -3 .8
Diphenylmethane 43.0 26.8 349.5 363.6 -14.1 33.5 9.6
1,4-DiPh-cyclo-pentadiene 78.4 42.5 329.8 337.7 -7 .9 77.0b 1.4
CHjBr -5 .0 27.2 397.9 392.7 5.2 -9 .1 4.1
CHjCl -14 .7 20.7 401.1 396.0 5.1 —19.6 4.9
CH2Clj -17.1 -7 .9 374.9 374.6 0.3 -22 .9 5.8
CHC!3 -20 .9 -3 5 .2 351.4 357.1 -5 .7 -2 5 .0 4.1
C1CH2-acetylene 38.2 50.1 377.6 368.1 9.5 39.0b -0 .8
Cl-benzene 16.7 35.8 384.8 387.2 -2 .4 13.0 3.7
Nitromethane -15 .9 -43 .3 338.3 356.4 -18.1 -17 .9 2.0
Nitroethane -19 .7 -53 .3 332.1 356.0 -2 3 .9 -2 4 .4 4.7
2-Nitropropane -27.1 -61 .8 331.0 356.1 -25.1 -33 .2 6.1
Nitromethyl-/-butane -51.1 -68 .2 348.6 355.2 -6 .6 - 4 5 .2b -6 .0
/?iN02-toluene 5.1 -7 .7 352.9 362.9 —10.0 7.0 -1 .9
HCN 33.0 27.7 360.5 351.2 9.3 32.3 0.7
Cyanomcthane 23.3 28.5 370.9 372.9 -2 .0 18.0 5.3
Cyanoethane 18.5 17.1 364.2 375.0 -10 .8 12.3 6.3
2-Cyanopropane 13.4 6.1 358.4 375.2 -16 .8 5.8 7.6
Cyanocyclopropanc 52.2 53.7 367.2 375.4 -8 .2 44.0 8.2
2-Cyanopropene 41.0 42.6 367.4 370.7 -3 .3 31.0 10.0
/?CN-toluene 49.0 34.7 351.4 360.8 -9 .4
Cyanotoluene 43.2 28.6 351.1 351.9 -0 .8
PhCH(CN), 94.7 47.5 318.5 322.1 -3 .6
FCHjCN -13.1 -20 .5 358.3 369.2 -10 .9
Metoxycyanomethane -10 .2 -13 .7 362.1 371.8 -9 .7 — 8.0" -2 .2
m C F,-C6H4CH,CN -105.3 -138.2 332.8 341.9 -9 .1 -115.9” 10.6
420 P. Burk and I. A. Koppel
Table 1. (continued)
calc AHj ^  ̂ icid exp error 
J t f ^ H A ) in calc
HA A - calc exp‘ error
/'COCN-iolucnc 19.7 -2 .6 343.4 345.7 -2 .3 3.6b 16.2
Methyl other -46 .9 -5 .0 407.7 407.0 0.7 -4 4 .0 - 2 .9
Fthanal -44 .2 -39 .9 370.0 365.8 4.2 -3 9 .6 -4 .6
Propanal -47.1 -5 1 .4 361.5 365.3 -3 .8 -4 4 .8 -2 .3
Propanone -5 3 .0 -4 8 .6 370.0 369.1 0.9 -5 1 .9 -1 .1
Phenylmeihylketone -17 .7 -2 0 .2 363.2 361.3 1.9 -20 .8 3.1
BenAlmethylketoiw -2 3 .0 -43 .7 345.0 351.8 -6 .8 -2 3 .4 0.4
Ethylphenylketone -22 .8 -2 0 .6 358.9 360.5 -1 .6 -26 .1 3.3
MeCO-aeetylene 9.4 15.9 372.2 360.1 12.1 15.6 -6 .2
MeOCO-acetylene -2 9 .6 -2 6 .9 368.4 358.8 9.6 —24.0b -5 .6
4-M otho\yphon\lmcilnlketone -54.S -58 .5 362.0 362.8 -0 .8 -58 .3 3.5
Methyl acetate -9 2 .8 -92 .8 365.7 371.9 -6 .2 -9 8 .0 5.2
Dimethyl ethane-amide -5 2 .2 -4 9 .0 368.9 374.9 - 6 .0 -5 5 .9 3.7
Me.S -1 0 .4 2.3 378.4 393.2 -1 4 .8 -9 .0 -1 .4
PhSCH, 23.9 25.0 366.8 381.6 -14 .8 23.4 0.5
MeSOM, -10 .4 2.3 378.4 373.5 4.9 -3 6 .2 25.8
MeSO: Me -7 6 .2 -9 0 .6 351.3 365.8 -1 4 .5 -8 9 .0 12.8
/>SO.Me-toluene -5 1 .0 -7 1 .7 345.0 358.8 -13 .8 -6 5 .2 14.2
C F,SO : Me -207.7 -250.5 322.9 347.0 -24.1
C F jS O X H  =C H M e -192.8 -239 .0 319.5 343.3 -23 .8 — 222,0b 29.2
p SO, С F,-toluene -182.8 -217.7 330.8 347.4 -1 6 .6
Pyridine 30.4 48.2 383.5 391.9 -8 .4 33.0 -2 .6
Pyrimidine 38.0 43.6 371.4 383.3 -1 2 .4 47.0 -9 .0
M e,P -29 .8 -4 .3 391.2 391.3 -0 .1 -24.1 -5 .7
CH . = Se(M e)CH, 3.5 29.8 392.0 385.6 6.4 5.0 -1 .5
S. Me, -53 .5 -1 8 .7 400.5 397.0 3.5 -5 5 .7 2.2
N -H  acids
Ammonia -3 .1 38.3 407.1 403.6 3.5 -1 1 .0 7.9
Methylamine -5 .2 38.3 407.1 403.6 3.5 -1 1 .0 7.9
Methylamine -5 .2 21.7 392.6 403.3 -1 0 .7 -5 .5 0.3
Eihylamine -11.1 17.0 393.8 399.3 -5 .5 -1 1 .3 0.2
Dimethylamine - 8 .0 7.8 381.5 396.2 -1 4 .7 -4 .4 -3 .6
M e,SiNH: -57 .9 -4 1 .6 382.0 378.8 3.2
Aniline 21.3 14.3 358.7 366.4 -7 .7 20.8 0.5
/>CH,-aniline 12.1 4.7 358.3 367.3 -9 .0 14. Ib -2 .1
mCl-aniline 14.4 1.5 352.8 358.9 -6 .1 13.0b 1.4
/»Cl-aniline 14.4 1.2 352.5 360.4 -7 .9 13.0b 1.4
mOCH,-aniline 15.2 5.2 355.7 366.8 -11.1 12.9b 2.3
/>OCH,-aniline -15 .4 -25 .8 355.3 367.1 -1 1 .8 — 14.1b - 1 .3
/»CHO-a niline -1 3 .6 -34 .8 344.5 349.6 -5 .1 — 8 .lb -5 .4
/я NO,-aniline 12.5 -1 0 .4 342.7 352.3 -9 .6 15.0 -2 .4
/>NO: -aniline 10.7 -24.1 330.9 343.5 -1 2 .6 13.0 -2 .3
m SO; CF,-aniline -174.9 -202.7 337.9 346.9 -9 .0
/>SO; CF,-aniline -178.4 -209.5 336.1 338.6 -2 .5
Pyrrole 27.1 11.5 350.0 358.7 -8 .7 25.9 1.2
HCONH, -4 1 .8 -5 0 .5 357.0 359.9 -2 .9 -4 4 .0 2.1
PhCONH, -16.1 -2 8 .7 353.2 354.1 -0 .9 -2 4 .0 7.9
H .NCONHj -4 5 .8 -5 3 .8 357.7 362.6 -4 .9 -5 8 .8 13.0
C F,CO N H :* -196.2 -223 .8 338.1 343.8 -5 .7 —200.0b 3.8
Cl.CCONH. -5 5 .7 -81.1 340.3 343.2 -2 .9 —56.2b 0.4
9 *
Critical lest of PM3 calculated gas-phase acidities 421
Table 1. (continued)
calc AHf * exp error 
AH, (HA) in calc 
HA A - calc exp* error AH, (HA
HCONHMe -4 3 .7 -5 3 .0 356.3 360.4 -4 .1 —45.0b 1.3
Acetaminobenzene -2 2 .0 -4 7 .2 340.4 347.5 -7 .2 -3 0 .8 8.9
CF3CONHPh -165 .2 -209 .4 321.4 333.4 -1 2 .0 - 1 68.7b 3.6
O-H acids
Water -4 3 .4 -1 7 .5 401.6 390.7 10.9 — 57.8 4.4
Methanol -51.1 -3 7 .9 378.8 380.6 -1 .« -4 8 .2 -2 .9
Ethanol -5 8 .7 -44 .8 379.7 378.0 1.7 -56.1 -2 .6
Propanol -64.1 -5 1 .4 378.3 376.0 2.3 -60 .9 -3 .2
Isopropanol -65 .8 -5 4 .9 376.6 375.4 1.2 — 65.1 -0 .7
Isobutanol -6 7 .7 -5 6 .9 376.5 374.7 1.8 -67 .8 0.1
/•Butanol -65 .7 -5 4 .9 376.6 374.6 2.0 -7 4 .7 9.0
r-Bu-methanol -7 5 .5 -5 8 .8 382.3 372.6 9.7 — 76.0b 0.5
l-/-Bu-ethanol -7 9 .2 -64 .2 380.7 371.1 9.6 -8 3 .9 b 4.7
1-r-Bu-propanol -8 1 .2 -7 4 .0 372.8 370.0 2.8 —88.7b 7.5
1-f-Bu-isobutanol -8 9 .6 -76 .2 379.0 368.5 10.5 — 93.7»' 4.1
1-f-Bu-methanol -8 8 .2 -78 .9 375.0 366.4 8.6 — 99.2b 11.0
Phenylmethanol -2 2 .4 -1 8 .6 369-5 370.0 -0 .5 -23 .9 1.5
2-Methoxyethanol -92 .7 -8 3 .6 374.7 373.8 0.9 -8 7 .0 b -5 .7
Fj CHCH j OH -151.8 -155.6 361.9 366.4 -4 .5 —148.2b -3 .6
CF3CH(Me)OH -214.4 -231.5 348.5 360.3 -1 1 .8 — 216.3b 1.9
(CFj)jCHO H -360.6 — 398.1 328.2 344.9 -1 6 .7 -367 .0b 6.4
CFjC H jC H jO H -305 .6 -325.7 345.5 355.4 -9 .9 — 313.9 7.4
(CFj)jCOH — 516.6 -572.6 309.7 331.6 -2 1 .9 — 549.0b 32.4
EtjSiOH -133.2 -125.8 373.1 360.5 12.6 — 133.6b 0.4
Phenol -21 .7 -44.1 343.3 349.2 -5 .9 -23 .0 1.3
pMe-phenol -3 0 .9 -5 3 .9 342.8 351.6 -8 .8 -29 .9 -1 .0
/>iEt-phenol -35 .6 -56 .5 344.8 349.3 -4 .5 -3 4 .9 -0 .7
mF-phenol -65 .4 -94 .5 336.5 344.5 -8 .0 — 7l.0b 5.6
pCF}-phenol -180 .6 -219.1 327.2 337.2 -1 0 .0 -1 8 2 .8b 2 2
pCN-phenol 13.1 -25 .8 326.9 332.2 -5 .3 10.3b 2.8
»riNOj-phenol -29 .9 -68 .7 326.8 334.6 -7 .8 — 27.0b -2 .9
p N 0 2-phenol -31 .7 — 81.5 315.8 327.8 -1 2 .0 — 28.0b -3 .7
mCOMe-phenol -6 3 .0 -91 .5 337.2 342.5 -5 .3 -7 8 .5 15.7
m S02Me-phenol -8 5 .6 -121.5 329.9 336.1 -6 .2 — 105.9b 20.3
/jSOj C F ,-phenol -219.6 -275.7 309.6 322.6 — 13.0
CH3CH=NOH -2 .9 -14 .9 353.7 365.6 -1 1 .9 -4 .8 1.9
C4H j CH=NOH 30.6 3.4 338.5 352.9 -1 4 .4 25.8b 4.8
(СН j ), CCH=NOH -17 .5 -31.1 352.1 364.6 -1 2 .5 -3 2 .3 b 14.8
(C H ,)jC -N O H -11 .6 -24 .9 352.5 366.1 — 13.6 — 15.0b 3.4
EtjNOH -27 .7 -14 .8 378.6 370.6 8.0 -8 .6 b -19.1
Formic acid -90.1 -110.9 344.9 345.2 -0 .3 -90 .5 0.4
Acetic acid -99 .3 -119 .6 345.3 348.5 -3 .2 -103.3 4.0
Propanoic acid -104.3 -124.9 345.1 347.3 — 2.2 -107.0 2.7
/-BuCOOH -113.8 -129.6 349.9 344.6 5.3 — 122.0b 8.2
MeOCH2COOH -133.3 -154.3 344.7 341.6 3.1 — 132.9b -0 .4
FCH,COOH -139.7 -165.8 339.6 338.8 0.8 — 140. lb 04
CHF j COOH -186.6 -222.8 329.5 330.0 -0 .5 ~  196.9" 10.3
CF,COOH -244 .0 -290.4 319.3 322.7 -3 .4 -246.3 2.3
CFjCHjCOOH -254.9 -287.2 333.4 334.8 -1 .4 —259.3b 4.4
CICHjCOOH -101.3 -127.4 339.6 336.3 3.3 -104.0 2.7
422 P. Burk and I. A. Koppel
Table 1. (continued)
calc AH, ^W.cid exp error 
-------------------- A H ,(  HA) in calc 
HA calc exp* error AH , (HA)
CHCi-COOH -102.4 -135.1 333.0 327 3 5.7 -1 0 2 . lb -0 .4
Cl(CH; ),COOH -109 .0 . -135.0 339.7 345.4 -5 .7 - 1 19.7b 10.8
BrCH.COOll -89 ,6 -116.4 338.9 334.0 4.9 — 94.4b 4.8
MeCHBrCOOH -9 9 .0 -125.2 339.5 336.2 3.3 -103 .3b 4.2
EtCHBrCOOH -103.9 -130.4 339.2 336.4 2.3 — U4.0b 10.1
Benzoic acid -66 .2 -89 .7 342.2 338.3 3.9 -7 0 .3 4.1
pCH ,-benzoic acid -223.1 -254.9 333.9 332.4 1.5 -233 .3b 10.2
.'.'-DiCF:-benzoic acid -378.7 -416.8 327.7 324.4 3.3 — 391.3b 12.5
/iCN-ber.zoic acid -30 .0 -6 1 .4 334.3 328.5 5.8 — 37.8to 7.8
jiiNO; -benzck acid -66 .4 -97.1 335.0 329.5 5.5 — 94.3 27.9
/iNH.-betvoic acid -69 .2 -91 .5 343.4 341.1 2.3 — 70.0 0.8
»Ю Н-benzoic acid — 110.9 -136.3 340.3 337.9 2.4 — 1 i 2.3b 1.4
S-H acids
H; S -0 .9 -15 .9 350.8 351.2 -0 .4 —4.9 4.0
MeSH -5 .5 -22.1 349.1 356.9 -7 .8 — 5.5 0.0
EtSH -8 .4 -25 .2 348.9 355.2 -6 .3 -11 .1 2.7
/i-PrSH -13 .7 -31.1 348.3 354.2 -5 .9 -1 6 .2 2.5
/-PrSH — i 4.4 -28.1 352.0 353.4 -1 .4 -1 8 .2 3.8
//-BuSH — 24.5 -42 .3 347.9 353.7 -5 .8 -21 .1 -3 .4
i-BuSH — J6.0 -33 .5 348.2 353.1 -4 .9 -2 3 .3 7.3
/-B j SH -17 .8 -35 .7 347.8 353.0 -5 .2 -2 6 .2 8.4
/-BuCH; SH -24 .7 -43.1 347.3 351.7 -4 .4 -3 0 .8 6.2
Other acids
H; -13 .2 91.8 470.9 400.4 70.5 0.0е -1 3 .4
Me,SiH -37 .2 -50 .7 352.2 381.2 -2 9 .0 -3 9 .0 1.8
SiH4 13.1 -2 .8 349.8 372.3 -22 .5 8.0 5.1
PH, 0.2 -14 .5 351.0 370.9 -1 9 .9 1.3 -1 .1
HF -59 .7 -17.1 409.8 371.4 38.4 -65.1 5.4
HC! -20 .5 -5 1 .2 336.5 333.7 2.8 -22.1 1.6
HBr 5.3 -5 6 .2 305.7 322.4 -1 6 .7 -8 .7 14.0
HI 28.8 -6 4 .6 273.8 314.3 -40 .5 6.3 22.5
J -  from Ref. [ 19] 
b -  esiimated in Ref. (19] 
1 -  by definition
able. These particular compounds were chosen because they cover a wide range 
o f acidities for different classes o f  compounds (C -H , O -H , N -H , S -H  acids; 
alcohols, amines, anilines, phenols, hydrocarbons, etc., fluoro-, nitro-, cvano-, 
etc. substituted acids, etc.). In Table 2 the analogous results, calculated with 
AM I method, for 11 hypervalent compounds are presented.
The results of statistical (regression) analysis according to the formula:
^#udd(calc) =  a +  b ■ <dtfucid(exp) (2)
are presented in Table 3, where N  is the number o f points, АН™"д is minimal and 
maximal experimental gas-phase acidity in considered group; SAHaci(1 is 
the average unsigned error in acidities, R is the correlation coefficient, a  is the
1 0
Critical test of PM3 calculated gas-phase acidities 423
Table 2. Comparison with experiment of AMI heats c f  formation and acidities (kcal/mol) for 
hypervalent compounds
calc &Hj A Hocid exp error 
AH, (HA) in calc 
HA A - calc exp“ error AHf ( HA)
mSOjMe-phenol -82 .9 -115 .9 334.2 336.1 -1 .9 -105.9 23.0
p S 0 2Me-toluene -4 6 .6 -72 .8 341.0 358.8 -17 .8 -65 .2 18.7
MeSOjMe -70 .0 -9 4 .0 343.2 365.8 -2 2 .6 -8 9 .0 19.0
MeSOMe -8 .7 8.6 384.5 373.5 11.0 -  36.2 27.5
pSOjCFj-phenol -222.4 -282.7 307.0 322.6 -1 5 .6
CF3S 0 2CH =CH M e -193.8 -251.8 309.2 343.3 -34.1 -222.0 28.2
m  SOjCFj-aniline -177.1 -202.1 342.2 346.9 -4 .7
CFjSOjM e -204.3 -262.2 309.3 347.0 -37 .7
/7S02C F3-toluene -184.7 -277.5 324.3 347.4 -23.1
/jS 02C F3-aniline -186.5 -213 .6 340.1 338.6 1.5
a -  from Ref. [19]
Table 3. Results of statistical analysis of gas-phase acidities, calculated with PM3 method
N acid &AHa cjd a h R a V
All 175 314.3 421.0 8.2 -3 0 .4 1.1 0.903 11.2 7.3
All" 165 314.3 421.0 7.5 -4 .8 1.0 0.937 7.9 6.3
Allb 80 338.3 421.0 7.6 -8 .6 1.0 0.900 9.2 7.2
C-H acids 75 322.! 421.0 8.8 -33 .8 1.0 0.923 9.4 7.0
C-H acidsb 46 351.2 421.0 8.2 -8 .4 1.0 0.891 10.2 7.6
N -H  acids 25 333.4 403.6 7.2 -14 .3 1.0 0.975 4.7 3.6
N-H acidsb 10 347.6 403.6 7.8 -28 .9 1.0 0.977 5.0 3.1
Amines 5 378.8 403.6 7.5 110.6 0.7 0.691 8.7 7.7
Amides 8 333.4 362.6 5.1 -80 .6 1.2 0.979 2.8 1.7
Anilines 11 338.6 367.3 8.4 30.0 0.8 0.959 2.9 2.5
O-H acids 58 322.6 390.7 6.2 -36 .2 1.0 0.934 7.5 5.6
Alcohols 29 322.6 380.6 6.8 -113 .9 1.3 0.970 5.7 3.1
Carboxylic acids 22 322.7 348.5 3.2 53.3 0.8 0.897 3.2 2.9
Nitro-compounds 9 327.8 362.9 13.2 123.5 0.6 0.717 8.4 11.1
Diatomic hydrides 5 314.3 400.4 34.1 -410.3 2 2 0.995 8.5 2.4
Hypervalent comp. 10 322.6 373.5 11.8 -65 .8 1.1 0.895 9.1 6.3
Trifluoromethyl-sulfonyl
compounds 6 322.6 347.4 14.8 71.0 0.7 0.662 9.1 8.5
a -  without Si-H and P -H  acids, H2, C3H: . CH4. H: 0 . HF. and HCN 
b - compounds, calculated by Dewar [6] with AMI and used by us to compare AMI and PM3
standard deviation, and у is the average unsigned error, when is corrected
using formula:
= AH^ ~ a (3)
b
Table 4 gives the analogous results for AM ! calculated acidities from Ref. [6].
[II], and from this work.
424 P- Burk and I. A. Koppel
ТаЫг 4. Results of statistical analysis of gas-phase acidities, calculated with AMI method
V -J*H*• "че“к"* A UHseiUd 5AHKiü a b R a У
Al! 97 338.3 421.0 7.9 -2 8 .7 1.1 0.894 9.6 7.2
AH' SO 33S.3 421.0 8.2 -3 1 .6 1.1 0.892 10.1 7.4
C -H  acids 63 350.3 421.0 7.7 -25.1 1.1 0.894 9.5 6.8
C-H acids- 46 351.2 421.0 8.1 -1 9 .0 1.0 0.890 10.4 7.4
N-H acids 10 3517 403.2 6.7 -136.5 1.4 0.975 6.4 2.9
O-H acids 24 338.3 390.8 9.0 -87 .3 1.2 0.860 9.0 5.5
Hypervalent
compounds 10 322.6 373.5 17.0 -6 8 .9 1.1 0.740 16.5 11.5
J -  compounds, calculated by Dewar [61 with AMI and used by us to compare AMI and PM3
The average unsigned error in the heats o f formation for all 175 neutrals is
5.1 kcal/mol. This error is fairly typical for the PM3 method and is in keeping 
with what has previously been found [18]. Knowing that the heats o f  formation 
of the anions are reproduced more poorly, it is not surprising, that the calculated 
absolute acidities are not very reliable. At the same time, the average unsigned 
error in acidities of the same collection o f acids is 8 1 kcal/mol, compared with 
7.9 kcal/moi for AMI method obtained by us (Table 4) from analysis o f results 
of calculations for 97 compounds presented in Ref. [6] and [11]. But when we 
compare the results only for compounds calculated by both methods, the errors 
are 8.2 kcal/mol and 7.6 kcal/mol for AMI and PM3 respectively It should be 
mentioned that in case o f  PM3 nearly one third o f  calculated acidities have errors 
greater than 10 kcal/mol and more than half deviate more than 5  kcal/mol (see 
also Fig. I).
3:?0 3!0 300 380 -100 420 
Exp.
Fig. I. Calculated and experimental gas-phase acidities (kcal/mol) for all acids surveyed
10*
Critical test o f PM3 calculated gas-phase aridities 425
From Tables 1 and 2 it can be seen, that the behavior o f the five calculated 
diatomic hydrides (H 2, HF, HC1, HBr, HI) is quite different from that for the 
rest o f  the compounds. For these molecules the average error is as big as
34.1 kcal/mol, but when we use empirical correction according Eq. (3), the error 
reduces to 2.4 kcal/mol. It should also be mentioned, that in case o f  these 
compounds the slope o f the correlation line is 2.21 and intercept is -4 1 0 .4  which 
both display the largest'deviations o f these quantities from their ideal values, i.e. 
the unity slope and zero intercept.
For a few calculated Si-H  and P-H  acids and for acetylene, methane, water 
and HCN, the calculated values are also far from their experimental values. 
When these compounds are excluded from the statistical analysis, the average 
unsigned error reduces to 7.3 kcal/mol. The poor results for these acids can be 
attributed to the failure of methods from the M NDO  family to allow for orbita! 
expansion on atoms bearing large negative charge. The calculated heats of 
formation are expected to be, and are, too positive whereas the formal charge in 
an anion is largely concentrated on a single atom.
On the other hand, it should be mentioned that the PM3 tends to overesti­
mate the charge delocalization in a relatively bulky anions, such as (C H j^ C - . 
CF3SO2CH2, (C F 3)3CO“, etc., which results in too negative heats o f formation. 
In turn this leads to too high acidities for these acids. This can be also the reason 
for which the PM3 method and also A M I, as mentioned by Dewar [6]. mostly 
overestimate the stabilizing effect o f methyl and phenyl substitution at the 
anionic ccnter.
On the basis o f  the results o f  the overall correlation analysis, one can conclude 
that the errors in calculated acidities are not systematic, while the slope b o f  the 
correlation line is practically unity and the intercept a is also reasonably small. 
But such an inference turns out to be false, while examining the results o f  
correlation analyses obtained for different classes o f compounds (compare with 
Ref. [7], where the theoretical values for the slope b and intercept a were obtained 
for the simultaneous comparison of the calculated and experimental acidities of 
neutral and cationic Bronsted acids). It becomes evident that in many cares 
(amides, alcohols, and phenols) there are excellent correlations between calculated 
and experimental acidities with the intercept and slope considerably differing from 
theoretical (see Table 3). Sc, it can be concluded that overall good agreement with 
theoretical regression with zero intercept and unity slope is due to using in the 
same correlation several classes o f compounds. However, in different classes, 
correlated one by one, the differences from the theoretical correlation are iarge 
enough to decide that there are still remaining systematic errors.
The average unsigned error in calculated acidities for the carbon acids is
8.8 kcal/mol, which is comparble with that found by us for the AMI method 
(7.7 kcal/mol). But v/hen we compare the results only for compounds calculated 
by both methods, the errors are 8.1 kcal/mol and 8.2 kcal/mol for AMI and 
PM3, respectively.
The average unsigned errcr for acidities o f 26 nitrogen acids is 7.2 kcalm ol. 
That is slightly better than the overall average unsigned error and average 
unsigned error for C-H  acids and worse than that found by us for the AMI 
method (6.7 kcal/mol). When one compares the results only for compounds 
calculated by both methods, the errors are 6.7 kcal/mol and 7.8 kcal/mol for 
AMI and PM3, respectively.
The reasonable closeness o f the slope of correlation line and the intercept to 
the theoretical values is due to fact that in the same regression are amines.
426 P. Burk and I. A. Koppel
anilines, and amides. If we consider these classes o f  compounds separately, a 
different view appears. Amines have an average unsigned error o f  7.5 kcal/mol 
and a rather scattered correlation. At the same time, amides have an excellent fit 
with a slope and intercept different from expected ideal values. In case o f  
anilines. />-CF,SO:-aniline deviates considerably. After the exclusion o f this 
point a very good correlation with slope and intercept close to their theoretical 
values appears (see Table 3).
For the oxygon acids listed in Table 1 the average unsigned error in acidities 
is 6.2 kcal.mol. compared with 9.0 kcal/mol found by us using A M I. When we 
compare the results only for compounds calculated by both methods, the errors 
didn't change. The reasons for big errors in calculated acidities o f water and 
(C F ,),C O H  have already been discussed. The errors for oximes are also signifi­
cantly larger than those for the other compounds. Excluding water, (C F 3)3COH 
and oximes from the statistical analysis, the average unsigned error for the 
remaining 51 O-H acid falls to 5.2 kcal/mol. This value compares favorably with 
the corresponding error (4.4 kcal/mol) in ihc heals o f formation o f  the corre­
sponding neutrals and is only slightly larger than that o f  N -H  acids and smaller 
than C-H  acids. This is a bit surprising, as Dewar has reported that for the AMI 
method the acidities o f the oxygen acids are reproduced worse than C -H  and 
N -H  acids.
As in the case of N -H  acids, the different classes o f O -H  acids show different 
correlations between calculated and experimentally measured acidities. The 
correlation for the carboxylic acids is rather poor, while in case o f phenols and 
alcohols the fit is significantly better (see Table 2).
The average unsigned error o f nine calculated S-H  acids is 4.7 kcal/mol. 
However, no conclusions about effectiveness o f PM3 to estimate the acidities o f
S -H  acids can be made since a very narrow (351.2-356.9 kcal/mol) range o f 
experimentally measured acidities was available.
For the nitrosubstituted acids given in Table 1, the average unsigned error is
13.2 kcal/mol, which is too big compared with the overall average unsigned 
error. For the AMI model Dewar has attributed this mainly to the failure o f  
method to predict the heats o f formation rather neutrals than anions, which is 
supported by his calculation results. For the PM3 method, however, for nitro­
compounds, Stewart had reported a great improvement o f  calculated heats o f  
formation, which was also confirmed by us in this wo'k (average unsigned error 
is 6.4 kcal/mol). However, the errors in the calculated acidities o f  nitrosubsti­
tuted acids remain too big. It must be pointed out that all the calculated acidities 
for nitrocompounds are too high and the bigger errors are associated mostly 
with the small compounds.
For the calculated acidities o f  six trifluoromethylsulfonylsubstituted acids the 
average unsigned error is 14.8 kcal/mol, which is too large when compared with 
the overall error. At the same time we should not forget that we deal here with 
hypcrvalcnt compounds for which the reported [18] error o f calculated heats of 
formation of neutrals is 13.6 kcal/mol.
4 Conclusions
With a few exceptions, PM3 seems to be a useful tool for the investigation o f  
gas-phase acidities. The errors in calculated acidities (8.1 kcal/mol) are compara­
ble with those reported [18] in calcualted heats o f formation o f  the neutrals
11
Critical test of PM3 calculated gas-phase acidities 427
(7.8 kcal/mol). However, it should be mentioned that in case o f PM3 nearly one 
third o f calculated acidities have errors greater than 10 kcal/mol and more than 
half deviate more than 5 kcal/mol.
The main problems encountered involve relatively small, often diatomic, 
neutral hydrides whose anions are usually characterized by the charge localiza­
tion on one atom, as well as acids whose conjugated anions contain bulky 
electron acceptor substituents, capable to the extensive delocalization of the 
negative charge from the protonization center to the other regions o f the anions. 
Probably for the same reason the large errors accompany also the introduction 
of methyl and phenyl substituents at anionic centers.
In some cases (anilines, amides, alcohols, and phenols) the average error in 
acidity can be significantly reduced by employing an empirically derived correc­
tion.
Comparison with AM I results show that both methods are o f roughly equal 
quality with the exception of hypervalent molecules, where PM3 is clearly better 
(average unsigned errors are 17.0 and 11.8 kcal/mol for AM I and PM3, respec­
tively). Shortcomings o f both M NDO  family-based methods for the correct 
description o f hypervalent compounds are rather evident and another approach 
with proper inclusion o f <af-orbitals [21] is needed.
References
1. Hehre WJ, Radom L, Schlyer, PRv, Pople JA (1986) Ab Initio molecular orbital theory. Wiley. 
NY
2. Bingham RC, Dewar MJS, Loo DH (1975) J Am Chem Soc 97:1285
3. Dewar MJS, Thiel W (1977) J Am chem Soc 99:4899
4. Dewar MJS, Zoebisch EG, Healy EF, Stewart JJP (1985) J Am Chem Soc 107:3902
5. Stewart JJP (1989) J Comput Chem 10:209
6. Dewar MJS, Dieter KM (1986) J Am Chem Soc 108:8075 arid references therein
7. Koppel IA, Mölder UH, Palm VA (1985) Org React (Tartu) 21:3
8. Kollmar H (1978) J Am Chem Soc 100:2665
9. Bartmess JE, Burnham RD (1984) J Org Chem 49:1382
10. Bartmess JE, Caldwell G, Rozeboom D (1983) J Am Chem Soc 105:340
11. Kass SR (1990) J Comp Chem 11:94
12. Dewar MJS, Fox MA, Nelson DJ (1980) J Organomet Chem 185:157
13. Gordon MS, Davis LP, Burggaf LF, Damrauer M (1986) J Am Chem Soc 108:7889
14. Olivella S, Urpi F, Vilarrasa J (1984) J Comput Chem 5:230
15. Siggel MR, Thomas TD, Saethre LJ (1988) J Am Chem Soc 110:91
16. Koppel 1A, Comisarow MB (1980) Org React (Tartu) 17:498
17. Koppel 1A, Mölder UH (1981) Org React (Tartu) 18:42
18. Stewart JJP (1989) J Comput Chem 10:221
19. Lias SG, Bartmess JE, Liebman JF, Holmes JL, Levin RD. Mallard WG (I98S) J Phys Chem 
Ref Data 17, Suppl No. I
20. Stewart JJP (1983) MOPAC Program Package -  QPCE 455
21. Thiel W, Voityuk A A (1992) Theor Chim Acta 81.391
Critical Test of РмЗ-Calculated Proton Affinities
PEETER B U R K , KOIT H ERO DES, IVAR KOPPEL, 
and ILM AR KOPPEL
Institute o f  Chemical Physics, Tartu University EE2400, Jakobi 2, Tartu, Estonia
Abstract
Proton affinities have been calculated for 119 com pounds using the pm3 semiempirical molecular 
orbital model. pm3 seems to be not as good as am I for the calculation o f proton affinities. At the same 
time, it can be a valuable tool for investigation o f proton affinities, when a m  1 is not usable (for hypervalent 
com pounds o f second-row elem ents). © 1993 John Wiley & Sons, Inc.
Introduction
M olecular orbital calculations are carried out by an increasing number o f  chem ists 
on a widest range o f  problems. Both ab  in itio  and sem iem pirical self-consistent 
field m olecular orbital calculations are often used. The widespread use o f  the sem i­
em pirical M iN D O /3 [1], MNDO [2 ] ,  AM l [ 3 ] ,  and PM3 [4 ]  m ethods is due to the 
fact that they often give reliable answers, are easy to use, require relatively little 
com puter tim e, and can handle large m olecules.
Proton transfer reactions are widespread and o f  fundam ental im portance in 
chem istry and in biochem istry. Therefore, the knowledge o f  the proton affinities 
o f  neutral bases is essential. If these quantities could be calculated theoretically by 
som e quantum  chem ical procedure with sufficient accuracy, this w ould be a great 
value, while such calculations can be carried out m uch faster and supposedly at 
m uch less cost than experim ents. Such calculations are also not lim ited by the 
physical properties o f  the sam ples (stability, vapor pressure, etc.). As a result, nu­
m erous calculations o f  gas-phase (intrinsic) basicities ( or proton affinities) o f  neutral 
bases have appeared [ 5 -7  and references therein ].
H owever, there have been only a few system atic investigations [ 5 -1 0 ]  testing 
the reliability o f  different m ethods for prediction o f  proton affinities o f  neutral bases 
and none dealing with the reliability o f  the p m 3 m ethod on the large scale o f  co m ­
pounds. Therefore the current investigation was undertaken to evaluate the reliability 
o f  PM3 m ethod for predicting gas-phase proton affinities.
A useful way to com pare the experim ent and theory is to calculate the linear 
regression between the theoretical and experim ental quantities and to  calculate the 
m ean difference ( unsigned average error) between the experim ental and theoretical 
quantities. The degree o f  agreem ent between the tw o is then reflected by the slope 
and intercept o f  the correlation line, the unsigned average error, the standard de­
viation from correlation line, and the correlation coefficient. The last tw o depend
International Journal o f Quantum Chemistry: Quantum Chemistry Symposium 27, 633-641 (1993)
©  1993 John Wiley & Sons, Inc. CCC 0020-7608/93/010633-09
11*
634 BURK ET AL.
on the scatter o f  the points about the correlation line. A  slope different fro m  unity  
and a nonzero intercept im ply system atic deviation between experim ent and theory 
and m eans that the theoretical values o f  relative proton affinities will be system ­
atically either too high or too  low. A nonzero m ean difference between theory and 
experim ent reflects an overall bias in the absolute values o f  the calculated proton  
affinity.
M ethod
The proton affinity ( p a ) o f  com pound В was found as the heat o f  reaction for 
the proton addition equilibrium  to form the conjugate acid BH +:
B  +  H + * ± B H + P A ( B )  = AHf ( H +) + A H f { B ) - A H f ( B H + )  (1 )
where Д # / (  Я +), ДH / (  B) ,  and ДH j {  B H +) are the standard heats o f  formation  
for proton, neutral base and its conjugated acid, B H T. In the case o f  proton the 
experim ental heat o f  formation (3 6 7 .2  k ca l/m o l [11]) was used instead o f  the 
calculated value (3 5 3 .6 ) , because it im proves the calculated proton affinities con ­
siderably. W e acknowledge that this is not quite a correct procedure, despite the 
fact that such a way was also used in earlier works on sem iem pirical calculations 
o f  acidities and basicities [7 ,1 2 ] .
The calculations were carried out on MicroVAX II and v a x  8650 com puters 
using the standard p m 3 procedure, as im plem ented in the m o pa c  6 .0  program  
package [1 3 ]. All geom etries were fully optim ized by m inim izing the energy with 
respect to  all geom etrical variables without using the aid o f  sym m etry. In order to 
avoid premature com pletion o f  calculations by reaching som e local m inim um , the 
calculations were carried out starting off from several different initial geom etries.
Results and D iscussion
Proton affinities for 119 com pounds, calculated using p m 3 m ethod, are given in 
Table I, along with the corresponding “experim ental” values. These particular 
com pounds were chosen because they cover a wide range o f  basicities for different 
classes o f  neutral Bronsted bases (C -, О-, N-, S-, P-bases, alcohols, am ines, hydro­
carbons, etc.).
The results o f  statistical (regression) analysis o f  the relationship between the 
calculated, pa  (ca lc ) , and experim ental proton affinities, pa  (ex p ) according to for­
mula
И А (сэ\с) -  a +  b - P A ( e x p )  (2 )
are presented in Table II (see also Fig. 1), where N  is the num ber o f  points, PAmm 
is m inim al, and PAmax m axim al experim ental gas-phase proton affinity in a con­
sidered group; Дра is the average unsigned error in proton affinities, R  is the cor­
relation coefficient, a is the standard deviation, and у  is the average unsigned error, 
when PAca.c is corrected using formula
РМЗ-CALCULATED PROTON AFFINITIES 635
T a b le  I. Comparison with experiment o f  pm3 heats оГ formation and proton affinities (kcal/mol, 
experimental values from Refš. [I I), [15], and [16]).
Calc AHr PA Error
--------------------- Exp in calc
В BH+ Calc Exp Error Д Щ В ) ДНКВ)
Carbon bases
Methane -1 3 .0 228.9 125.2 132.0 -6 .8 -17.8 4.8
Ethane -18 .1 221.5 127.6 143.6 -1 6 .0 -20 .1 2.0
Ethene 16.6 222.5 161.4 162.6 -1 .2 12.5 4.1
Propene 6.4 197.3 176.3 179.5 -3 .2 4.8 1.6
1 -methylcylcohexene -1 4 .4 168.6 184.2 197.5 -1 3 .3 -1 0 .3 -4 .1
Benzene 23.5 212.5 178.2 181.3 -3 .1 19.8 3.7
Naphthalene 40.7 218.1 189.8 194.7 -4 .9 35.9 4.8
Toluene 14.1 197.5 183.8 189.8 -6 .0 12.0 2.1
Styrene 39.2 210.6 195.8 200.9 -5 .1 35.3 3.9
Hexamethylbenzene -2 0 .9 151.0 195.3 207:0 -1 1 .7 -2 1 .0 0.1
pMe-C»H4-C (M e)= C H 2 21.8 183.9 205.1 211.2 -6 .1
1,3,5-trimethoxybenzene -9 0 .8 73.6 202.8 220.0 -1 7 .2 -8 6 .7 -4 .1
Acetylene 50.7 263.9 154.0 153.3 0.7 54.5 -3 .8
Propyne 40.2 238.2 169.2 182.0 -1 2 .8 44.6 -4 .4
CO -1 9 .7 176.9 170.6 168.4 2.2 -2 6 .4 6.7
Nitrogen bases
n 2 17.6 237.2 147.6 118.2 29.4 0.0 17.6
Ammonia -3 .1 153.4 210.7 204.0 6.7 -1 1 .0 7.9
HNFj -1 1 .4 193.4 162.4 160.0 2.4 -1 6 .0 4.6
NFj -2 4 .4 201.7 141.1 136.9 4.2 -3 1 .0 6.6
Methylamine -4 .0 153.3 209.9 214.1 -4 .2 -5 .5 1.5
Ethylamine -1 2 .5 144.3 210.4 217.0 -6 .6 -1 1 .3 -1 .2
Propylamine -1 7 .7 138.5 211.0 217.9 -6 .9 -1 7 .3 -0 .4
Iso-propylamine -1 7 .3 135.1 214.8 218.6 -3 .8 -2 0 .0 2.7
Butylamine -2 1 .7 132.9 212.6 218.4 -5 .8 -2 2 .0 0.3
Iso-butylamine -2 3 .0 131.8 2! 2.4 21K.8 - 6 .4 -2 3 .6 0.6
/ert-butylamine -1 8 .7 125.7 222.8 220.8 2.0 -2 8 .9 10.2
Neopentylamine -2 6 .9 125.4 215.0 219.3 -4 .3 -3 1 .0 4.1
Cyclohexylamine -2 6 .0 125.8 215.4 221.2 -5 .8 -2 5 .0 -1 .0
2-aminonorbomane -9 .5 142.3 215.4 221.7 -6 .3 -8 .0 -1 .5
Etylideneamine 9.5 168.5 208.2 213.9 - 5 .7 2.0 7.5
Dimethylamine -5 .4 152.6 209.3 220.6 -1 1 .3 -4 .4 -1 .0
N-ethylmethylamine -1 3 .0 143.7 210.4 222.8 -1 2 .4 -1 1 .0 -2 .0
Diethylamine -2 0 .3 135.0 211.9 225.9 -1 4 .0 -1 7 .4 - 2 .9
Hydrazine 20.7 191.8 196.0 204.7 - 8 .7 22.8 -2 .1
1,2-diaminoethane -3 .9 146.4 216.8 225.9 -9 .1 -4 .3 0.4
1,3-diaminopropane -9 .3 138.9 218.9 234.1 -1 5 .2 -4 .2 -5 .1
3-aminopropan-1 -ol -5 6 .4 92.5 218.3 228.6 -1 0 .3 -5 2 .0 -4 .4
1,4-diaminobutane -1 7 .4 129.7 220.1 237.6 -1 7 .5 -1 3 .0 -4 .4
(CH,)2N(CH2),N(CH,)2 -2 6 .0 134.4 206.8 240.6 - 33.8
1,8-diaminonaphtalene 43.3 184.2 226.3 223.8 2.5 46.0 -2 .7
Trimethylamine -1 0 .9 155.6 200.7 225.1 -2 4 .4 -5 .7 -5 .2
N.N-dimethylethylamine -1 5 .9 143.2 208.i 227.5 -1 9 .4 -1 1 .0 -4 .9
N,N-dimethylmethylamine -2 0 .5 141.9 204.8 230.0 -2 5 .2 -1 7 .0 -3 .5
12 (Continued)
636 BURK ET AL. 
T ab le  I. (Continued)
Calc AHf PA Error 
Exp in calc 
В BH+ Calc Exp Error ДНКВ) ДНКВ)
Nitrogen bases
Tributylamine -5 8 .8 92.3 216.1 236.0 -1 9 .9 -5 3 .0 - 5 .8
N-methylformamide -4 3 .7 133.5 190.1 204.6 -1 4 .5 -4 5 .0 1.3
Aniline 21.3 175.1 213.4 209.5 3.9 20.8 0.5
Pyrrolidine -1 2 .0 144.8 210.5 225.2 -1 4 .7 -0 .8 -1 1 .2
Piperidine -1 6 .5 137.2 213.5 226.4 -1 2 .9 -1 1 .7 - 4 .8
2,2,6,6-tetramethyl-
piperidine -3 9 .7 105.4 222.1 231.7 -9 .6 -3 8 .0 -1 .7
1 -methylpyrrolidi ne -1 4 .6 143.7 208.9 228.7 -1 9 .8 -0 .5 -14 .1
1 -methylpiperidine -1 9 .3 136.2 211.7 229.7 -1 8 .0 -1 2 .0 -7 .3
Quinuclidine -13.1 142.9 211.2 232.1 -2 0 .9 -1 .0 -12 .1
l-asabicyclo[2,2,2]
-oct-2-ene 16.8 171.1 212.9 228.5 -1 5 .6 37.0 -2 0 .2
Pyridine 30.4 187.3 210.3 220.8 -1 0 .5 58.0 -2 7 .6
2-methylpyridine 21.1 174.7 213.6 225.0 -1 1 .4 23.7 -2 .6
3-methylpyridine 20.8 175.7 212.3 224.1 -1 1 .8 25.4 -4 .6
4-methylpyridine 20.8 175.1 212.9 225.2 -1 2 .3 24.8 -4 .0
Tetrazole 86.3 261.1 192.4 197.8 -5 .4 80.0 6.3
HCN 33.0 213.6 186.6 171.4 15.2 32.3 0.7
Acetonitrile 23.3 197.9 192.6 188.4 4.2 18.0 5.3
Butyronitrile 14.7 188.0 193.9 192.4 1.5 7.0 7.7
(C H b C = C (C N b 169.2 353.1 183.3 166.6 16.7 169.0 0.2
T richloroacetonitrile 18.5 201.5 184.2 175.7 8.5 20.0 -1 .5
FCN 6.5 196.0 177.7 163.0 14.7
T rifluoroacetonitrile -1 1 5 .0 78.6 173.5 164.1 9.4 -1 1 9 .4 4.4
(CNb 77.5 266.6 178.1 163.5 14.6 73.8 3.7
Oxygen bases
o 2 -4 .2 257.8 105.2 105.5 -0 .3 0.0 -4 .2
Water -5 3 .4 159.1 154.7 166.5 -1 1 .8 -5 7 .8 4.4
Methanol -5 1 .9 156.6 158.8 181.9 -23 .1 -4 8 .2 -3 .7
Ethanol -5 6 .9 143.9 166.5 188.3 -2 1 .8 -56 .1 -0 .8
2-methyl-2-propanol -7 1 .3 120.0 175.9 193.7 -1 7 .8 -7 4 .7 3.4
2,2-difluoroethanol -1 5 1 .8 64.7 150.8 175.2 -2 4 .4
(CFjbCOH -5 0 1 .0 -2 6 6 .6 132.7 163.0 -3 0 .3 -5 4 .9 0 48.0
(CFjbCHOH -3 6 0 .7 -1 32 .8 139.4 163.4 -24 .1 -3 6 7 .0 6.4
Methyl ether -4 6 .9 157.0 163.2 192.1 -2 8 .9 -4 4 .0 -2 .9
Ethyl ether -5 9 .6 135.9 171.7 200.2 -2 8 .5 -60 .1 0.5
ferf-butylmethyl ether -6 4 .4 116.5 186.3 202.2 -1 5 .9 -6 7 .8 3.4
ferf-butyl ether -7 5 .0 102.3 189.8 212.0 -2 2 .2 -8 7 .0 12.0
(CF3bO -3 8 1 .4 -1 3 4 .9 120.7 158.0 -3 7 .3
Carbondioxide -8 5 .0 139.5 142.7 130.9 11.8 -9 4 .5 9.5
Formaldehyde -34 .1 166.3 166.8 171.7 -4 .9 -2 6 .0 -8 .1
Acetaldehyde -4 4 .2 144.7 178.3 186.6 -8 .3 -3 9 .6 -4 .6
F2CO -1 38 .5 75.4 153.3 158.2 -4 .9 -1 5 3 .0 14.5
Hexafluoroacetone -3 3 8 .4 -1 0 5 .6 134.5 159.3 -2 4 .8 -3 3 4 .0 -4 .4
РМЗ-CALCULATED PROTON AFFINITIES 6 3 /
T a b le  I. (Continued)
Calc AHf PA Error 
Exp in calc 
В BH+ Calc Exp Error ДНКВ) ДНКВ)
Oxygen bases
CF3COC1 -1 9 4 .3 12.7 160.3 163.1 -2 .8
CFjCOOH -2 4 4 .0 -3 9 .8 163.0 171.1 - 8 .2 -246 .3 2.3
Methylacetate -9 2 .7 89.3 185.3 197.8 -1 2 .5 -9 8 .0 5.3
Acetylacetone -8 6 .9 91.5 188.8 206.9 -18 .1 -9 2 .0 5.1
Formamide -4 1 .8 128.3 197.1 198.4 -1 .3 -4 4 .0 2.2
Sulphurdioxide -5 0 .8 135.3 181.2 160.2 21.0 -7 0 .9 20.1
Dimethylsulfoxide -3 8 .6 117.2 211.4 210.9 0.5 -3 6 .2 -2 .4
Methylsulfonylbenzene -4 0 .6 111.8 214.8 194.8 20.0 -6 0 .6 20.0
c f 3s o 2n h 2 -2 0 7 .8 -1 1 .0 170.4 176.0 -5 .6
F2SO2 -1 8 4 .3 9.3 173.6 157.3 16.3
T rimethylphosphineoxide -8 1 .9 51.3 234.0 216.5 17.5
(C3H,hPO -1 0 1 .4 32.2 233.6 225.3 8.3
bis(dimethylamino>-
methylphophineoxide -85 .1 51.2 230.9 226.3 4.6
Diethylchloromethyl-
phosphonate -1 9 1 .9 -4 6 .6 222.0 211.2 10.8
T ri methyl phosphate -239 .1 -89 .1 217.2 212.5 4.7
Triethyl phosphate -250 .1 -8 4 .6 201.6 216.5 -1 4 .9 -2 8 4 .0 33.9
Hexamethylphosphoric -8 5 .0 53.7 228.5 227.4 1.1
Amide
Phosphor bases
Phosphine 0.2 117.2 250.3 188.0 62.3 1.3 -1 .1
Methylphosphine -9 .5 114.8 243.0 203.5 39.5 -4 .0 -5 .5
Dimethylphosphine -1 8 .5 112.8 235.9 216.5 19.4 -1 4 .0 -4 .5
T rimethylphosphine -2 8 .6 109.7 228.8 226.5 2.3
T riethylphosphine -3 5 .2 109.3 222.6 232.0 -9 .4 -5 4 .0 18.8
Phosphorustrifluoride -2 5 2 .2 -7 0 .4 185.5 164.4 21.1 -2 2 9 .0 -2 3 .2
Sulphur bases
H 2S -0 .9 175.6 190.7 171.1 19.6 -4 .9 4.0
Ethanethiol -8 .7 161.4 197.1 189.8 7.3 -11 .1 2.4
tert-butanethiol -1 3 .2 153.7 200.3 195.9 4.4 -2 6 .2 13.0
Methylsulfide -1 0 .4 159.4 197.4 199.1 -1 .7 -9 .0 -1 .4
Ethylmethylsulfide -1 4 .5 155.7 197.0 202.3 -5 .3 -1 4 .2 -0 .3
Propylsulfide -30 .1 135.3 201.9 206.3 -4 .4 -2 9 .9 -0 .2
Other bases
H 52.1 344.7 74.6 63.6 11.0 52.1 0.0
H2 -1 3 .4 215.2 138.6 101.2 37.4 0.0 -1 3 .4
н а -2 0 .5 184.2 162.5 128.0 34.5 -22 .1 1.6
HI 28.8 256.0 140.0 150.0 -1 0 .0 6.3 22.5
CF,Br -1 5 7 .9 93.6 115.7 137.5 -2 1 .8 -1 5 5 .0 -2 .9
CFjO -1 69 .2 51.6 146.4 136.0 10.4 -1 6 9 .7 0.5
12*
638 B U R K  ET AL.
T able II. Results o f statistical anlaysis o f  calculated (pm 3) and experimental proton affinities in terms
o f Eq. (2).
N PA™" pa" “ ДРА a b R a 7
All 119 63.6 240.6 12.9 28.3 0.8 0.884 14.9 12.8
All1 118 63.6 240.6 12.5 27.2 0.8 0.901 13.6 12.2
All2 60 130.9 237.6 11.2 14.4 0.9 0.937 8.7 7.4
Carbon
bases 15 132.0 220.0 7.8 9.4 1.0 0.962 6.8 5.8
Nitrogen
bases 51 118.2 240.6 11.7 73.5 0.6 0.931 6.6 7.8
Oxygen
bases 35 105.5 227.4 14.5 -12.7 1.0 0.875 16.0 12.8
Phosphor
bases 6 164.4 232.0 22.6 149.9 0.3 0.408 21.3 42.1
Phosphor
bases' 5 164.4 232.0 16.0 97.9 0.6 0.711 15.9 18.9
Sulphur
bases 6 171.1 206.3 7.0 144.1 0.3 0.889 2.0 5.2
' W ithout PHj.
2 Com pounds, calculated by Dewar [7] with AM I.
PA(exp)
Figure 1. Calculated and experimental proton affinities (kcal/m o l) for all bases surveyed.
РМЗ-C ALC U LATED  PR O TO N  AFFINITIES 639
P A S  =  PAakb “  (3 )
Table III gives analogous results for the statistical analysis o f  a m  1-calculated proton  
affinities ( from Ref. [ 7 ] ) .
The average unsigned error in the heats o f  form ation for all neutrals is 7.9 kca l/ 
m ol. This error is fairly typical for the pm 3 m ethod and is in keeping with what 
has previously been found [1 4 ]. At the sam e tim e, the average unsigned error in 
proton affinities o f  the sam e collection o f  bases is 12.9 k ca l/m o l, com pared with 
6 .0  k ca l/m o l for the AMl m ethod obtained by us from analysis o f  results o f  cal­
culations for 60 com pounds presented in Ref. [ 7 ]. But when we com pare the results 
only for com pounds calculated by both m ethods, the average unsigned error for 
the PM3 m ethod reduces to 11.2 k ca l/m o l, which is, however, still larger than the 
sam e quantity for the a m  1 m ethod. It should be m entioned that in the case o f  pm 3, 
nearly one fifth o f  calculated proton affinities have errors greater than 20 kcal /  m ol 
and m ore than half deviate m ore than 10 k c a l/m o l (see  also Fig. 1).
From Table I it can be seen that extrem ely large error (62.3 k ca l/m o l) conesponds  
to  P H 3. W hen the phosphine is excluded from the statistical analysis, the average 
unsigned error reduces to 12.5 k ca l/m o l. It should be m entioned that alongside 
with a big error in the calculated heat o f  form ation the pm 3 m ethod also gives an 
unrealistic charge distribution for phosphonium  cation— the calculated M ulliken  
charge on phosphor atom  is 2.42.
On the basis o f  the results o f  the overall correlation analysis one can conclude that 
in the calculated proton affinities there is also present a systematic error, as indicated 
by the nonunity slope o f  the correlation line b and by the nonzero intercept a.
Carbon Bases
T he average unsigned error in calculated proton affinities for the carbon bases is
7.8 k ca l/m o l, which is considerably higher than that found by us for am I m ethod  
(2.9 k c a l/m o l) . The correlation between experim entally found and calculated pro­
ton affinities seem s to be reasonably good as evidenced by the lack o f  the system atic
T a b l e  III. Results o f  statistical analysis o f proton affinities, calculated with a m  I method in terms o f
Eq. (2).
N pAmm рдша» ДРА a b R a 7
All 60 130.9 237.6 6.0 23.8 0.9 0.979 4.8 4.5
Carbon
bases 9 132.0 194.7 2.9 9.5 1.0 0.987 3.7 2.7
Nitrogen
bases 33 171.4 232.1 5.8 76.4 0.6 0.934 3.0 3.8
Oxygen
bases 12 130.9 202.2 6.9 38.9 0.8 0.948 5.4 5.4
640 BU R K  ET AL.
error (see results o f  correlation analysis in Table II), but the existence o f  big random  
errors makes one prefer the AM 1 m ethod for calculation o f  proton affinities o f  
carbon bases.
Nitrogen Bases
T he average unsigned error in calculated proton affinities for the nitrogen bases 
is 11.7 k ca l/m o l, which is again considerably higher than that found by us for A M l 
m ethod (5 .8  kcal /  m o l). H owever, it seem s that these errors are system atic for both  
m ethods while the slopes o f  correlation lines are 0.62 ±  0.04 and 0.63 ±  0.04 for 
pm 3 and a m I m ethods, respectively, and the application o f  em pirical correction  
reduces the errors in calculated proton affinities considerably (to  7.8 and 3.8 kcal/ 
m ol for pm3 and a m I m ethods, respectively). O nce again, the A M l m ethod seem s 
to be superior for the calculation o f  proton affinities o f  nitrogen bases.
Oxygen Bases
T he average unsigned error in calculated proton affinities for the oxygen bases 
is 14.5 k ca l/m o l, which similarly to  that o f  the carbon and nitrogen bases is still 
significantly larger than the average unsigned error that is found in the present 
work for a m I m ethod (6.9 k c a l/m o l) . As a rule, in case o f  alcohols, ethers, and 
carbonyl com pounds the predicted proton affinities are lower than the experimental 
values.
Phosphor Bases
T he average unsigned error in calculated proton affinities for the phosphor bases 
is 22.6 kca l/m ol. However, i f  we exclude from the com parison the extrem ely strongly 
deviating value for the phosphine (v ide supra), the unsigned average error reduces 
to 16.0 k ca l/m o l. Still, the statistical analysis (see  Table II) show s that there is prac­
tically no correlation between calculated and experim ental proton affinities, so  one  
m ust exercise extrem e caution, when using pm 3 for investigation o f  phosphor bases.
Sulphur Bases
T he average unsigned error in calculated proton affinities for the sulphur bases 
is 7.0 k ca l/m o l, which when com pared with the previous groups o f  bases is a 
surprisingly good result.
Conclusions
On the basis o f  the above results one can conclude that the РмЗ m ethod is not 
as good as a m  1 for the calculation o f  proton affinities o f  neutral Bronsted bases 
(see  Table II).  At the sam e tim e, it can be a useful tool for investigation o f  proton  
affinities, when the A M l  m ethod is not usable, e.g., for hypervalent com pounds o f  
second-row elem ents.
РМЗ-C ALC U LATED  PR O TO N  AFFINITIES 641
References
[ 1 ] R. С ..Bingham, M. J. S. Dewar, and D. H. Loo, J. Am. Chem. Soc. 97, 1285 ( 1975).
[2] M. J. S. Dewar and W. Thiel, J. Am. Chem. Soc. 99, 4899 (1977).
[3 ] M. J. S. Dewar, E. G. Zoebisch, E. F. Healy, and J. J. P. Stewart, J Am. Chem. Soc. 107, 3902 
(1985).
[4] J. J. P. Stewart, J. Com put. Chem. 10, 209 (1989).
[5] W. J, Hehre, L. Radom , P. v. R. Schleyer, and J. A. Pople, A b Initio  M olecular O rbita l theory  
(Wiley, New York, 1985).
[6 ] I. A. Koppel, U. H. Mölder, and V. A. Palm, Org. React. (T artu ) 21, 3 (1985).
[7] M. J. S. Dewar and K. M. Dieter, J. Am. Chem. Soc. 108, 8075 (1986).
[8] I. A. Koppel and M. B. Comisarow, Org. React. (T artu ) 17, 498 (1980).
[9] L A. Koppel and U. H, Mölder, Org. React. (T artu ) 18, 42 (1981).
[ 10] D. A. Dixon and S. G. Lias, in: M olecular S tructure an d  Energetics, Vol. 2, J. F. Liebman and A 
Greenberg, Eds. ( VCH Publishers, Deerfield Beach, 1987), p. 269.
{11] S. G. Lias, J. JE. Bartmess, J. F. Liebman, J. L. Holmes, R. D. Levin, and W. G. Mallard, J. Phys.
Chem. Ref. Data 17, Supplement No. 1 ( 1988).
[ 12] S. R. Kass, J. Com put. Chem. 11 , 94 (1990).
[ 13] J. J. P. Stewart, mopac  Program Package.— qcpe 455, (1983).
[ 14] J. J. P. Stewart, J. Com put. Chem. 10, 221 (1989).
[15] R. W. Taft, I. Koppel, F. Anvia, and J.-F. Gal, unpublished data.
[16] I. Koppel, U, Mölder, and R. Pikver, in: Electron an d  Proton Affinities o f  M olecules (in  Russian), 
G. A. Tolstikov, Ed. (Ufaa, 1991), p. 5.
Received July 6, 1993
1
THEORETICAL STUDY OF STRUCTURE AND BASICITY OP SOME ALKALI
METAL OXIDES, HYDROXIDBS AND AMIDES
Peeter Burk*, Ilmar A. Koppel* and Jüri Tapfer1* 
“institute of Chemical Physics, Tartu university, EE2400 Tartu, 
Estonia
b Computational Center, Tartu University, Liivi 2, BE2400 Tartu, 
Estonia
Abstract. Ab Initio (TZV*, SBK* and 3-21G* or 6-31G* basis 
sets) calculations were performed to predict the geometries and 
gas-phase proton affinities of LiaO, LiOH, LiNH,, Na,0, NaOH, 
NaNHj, KjO, KOH and KNH2.
Key words: alkali metal oxides, hydroxides and amides; 
proton affinities.
1 .introduction.
The oxides of alkaline metals are known to be the 
strongest bases in gas-phase [1,2]. Their reported proton 
affinities exceed by a very wide margin (by 45-60 kcal/mol) the 
similar quantity for the alkali metal hydroxides [2,3], usually 
considered the strongest existing bases, at least in the 
aqueous solution. However, till now very little is known about 
their geometry and electron structure. Surprisingly, the same 
refers also to the study of the geometry and electronic 
structure of the alkali metal hydroxides and amides. So the 
current investigation of these compounds was undertaken to gain 
some knowledge about above mentioned problems.
2 .Method.
All calculations were performed on IBM 4381 computer using 
'13 nov 1992' version of Gamess-US [4] program package. All 
calculations were executed with full optimization of geometry 
in respect of energy without aid of symmetry. The calculations 
were performed at RHF level using 6-31G* [5,6,7], TZV* [8,9,10]
2
and SBK* [11,12] basis sets, when available fcr elements 
considered, as implemented in Gamess program package. For the 
K,0, KOH and KNHj, where the 6-31G* set is not available, 
similar calculations were performed at 3-21G* [13,14] level. The 
results of calculations are presented in Tables I-IX where bond 
lengths (r) are given in A, angles (Z> in deg, dipole moments 
(ц) in D, charges (q) in a.u., total electronic energies (E) in 
hartrees and proton affinities (PA) in kcal/mol.
3.Discussion.
As a rule, all used basis sets give identical 
conformations of both neutrals and cations. Both oxides and 
hydroxides are found to be linear, while corresponding cations 
and the neutrals of amides are planar. Th.-i s is obviously caused 
by strong coulombic impact forces between hydrogen and metal 
atoms, which bear considerably big positive charges (see 
Mulliken charges ir Tables I IX) . As expected the cations of 
amides are tetrahedrical. The bond lengths and angles obtained 
with employed basis sets are also in good agreement with soma 
minor exceptions.
Proton affinities, calculated at three different levels of 
theory are also considerably consistent. All calculations using 
different basis sets confirm the experimentally established 
superiority of the intrinsic (gas-phase) proton affinities of 
alkali metal oxides over their hydroxilic counterparts, as 
found by mass-spectrometric techniques [1] . Also, the 
calculations confirm the extremely high basicity of the alkali 
metal amides, often used in chemical synthesis as highly 
effective deprotonating agents. So one can conclude, that all 
three methods are equal in description of small molecules 
containing alkali metal atoms. That's not surprising while all 
used basie sets are very similar.
Nevertheless, ehe deviations from experimentally 
established proton affinities are considerable (average 
unsigned errors are 26.5, 30.1 and 27.4 kcal/mol for 6-31G*,
3
TZV* and SBK* basis sets respectively) . As it is mentioned in 
earlier works [15], the errors in ab initio calculated proton 
affinities have rather systematic than random nature. So there 
is quite good correlation between calculated and experimentally 
determined proton affinities for all compounds calculated. For 
example for SBK* basis set the slope of correlation line, 
intercept, correlation coefficient and the absolute mean 
difference between experimentally measured and empirically 
corrected calculated values are 1.35, -70.1, 0.9749 and 5.6. 
For other two basis sets these parameters are very similar. So 
using this correlation we predict the proton affinities of 
LiNH2, NaNH2 and KHN2 to be 257.0, 271.9 and 284.5 kcal/mol 
respectively.
The Mulliken charges at the metal and oxygen (nitrogen) 
atom in neutral species evidence (as expected) that the Me - 0  or 
Me-N bonds are fairly ionic. It means that the resulting 
Coulombic stabilization due to the interactions between the 
highly negatively charged protonation center (oxygen or 
nitrogen atom) and proton could be considered as a main 
contribution into the extremely high basicity of the title 
compounds. It is also interesting to mention that there are 
several truly good correlations between calculated proton 
affinities and Mulliken charges on different atoms in both 
neutrals and cations.
4.Conclusions.
It was shown that the alkali metal oxides and hydroxides 
are linear, while corresponding cations and also amides have a 
planar structure. The employed basis sets (6-31G* or 3-21G*, 
TZV* and SBK*) were %hown to be of the same quality for 
investigating of small alkali metal containing molecules (and 
corresponding cations) in both geometric and energetic aspect 
and the SBK* basis set can be recommended as the fastest.
The calculations confirm the much higher basicity of the 
alkali metal oxides relative to the alkali metal hydroxides.
4
However, for predicting proton affinities from results of 
calculations empirical corrections are needed. Using these 
corrections the most probable "experimental" proton affinities 
of LiNH2, NaNH2 and KHN2 were estimated to be 257.0, 271.9 and 
284.5 kcal/mol respectively. We hope that these theoretical 
predictions will be helpful in future experimental 
determinations of proton affinities of very strong bases.
References.
l .M. F. Butman, L.S.Kudin and K.S.Krasnov, Zh. Neorg. Khim. 29,  
2150 (1984).
2.5.G.Lias, J.E.Bartmess, J.F.Liebman, J.L.Holmes, R.D.Levin 
and W.G.Mallard, J.Phys.Chem.Ref.Data, 17 [Suppl. 1] (1988).
3.5.K.Searles, I.Džidiõ, P.Kebarle, J.Am.Chem.Soc., 91 ,  2810 
(1969) .
4.M.W.Schmidt, K.K.Baldridge, J.A.Boatz, J.H.Jensen, S.Koseki, 
M.S.Gordon, K.A.Nguyen, T.L.Windus, S.T.Elbert, QCPE Bulletin,
10,  52.(1990).
5.J.D.Dill, J.A.Pople, J.Chem.Phys. 62,  2921 (1975).
6 .M.M.Francl, W.J.Pietro, W.J.Hehre, J.S.Binkley, M.S.Gordon,
D.j.DeFrees, J.A.Pople, J.Chem.Phys. 77, 3654 (1982).
7.P.C.Hariharan, J.A.Pople, Theoret.Chim.Acta 2 8 ,  213 (1973).
8 .Т.н. Dunning, j.Chem.Phys. 55, 716 (1971).
9.A.D.McLean, G.S.Chandler, J.Chem.Phys. 72 ,  5639 (1980).
10.A.J.H. Wächters, J.Chem.Phys. 52,  1033 (1970).
11.W.J.Stevens, H.Basch, M.Krauss, J.Chem.Phys. 8 1,  6026 
(1984) .
12. .W. J. Stevens, H.Basch, M.Krauss, P.Jasien, Can. J.Chem. 70,  
612 (1992) .
13.J.S.Binkley, J.A.Pople, W.J.Hehre, J.Am.Chem.Soc. 10 2,  939
(1980) .
14.K.D.Dobbs, W.J.Hehre, J.Comp.Chem. 7, 359 (1986).
15.I.A.Koppel, U.H.Mõlder and V.A.Palm, Org.React.(Tartu) 21,
3 (1985).
5
Table I. Molecular Geometries, Dipole Moments, Mulliken Charges and Energetics
of Zix.0 and Li,OH*.
TZV* SBK* 6-31G*
Li,О Li,OH4 Li,О Li,OH* Li,0 Li,OH*
r(OLi) 1.598 1.742 1.619 1.791 1.614 1.758
r'OH) - 0.943 - 0.963 - 0.951
/LiOLi leO.O 137.7 180.0 144.5 180.0 140.1
ZLiOH 111.1 - 107.8 - 110.0
^HOLiLi - 179.9 - 180.0 - 180.0
H 0.001 2.312 0.0C1 2.079 0.001 2.228
q(Li) 0.455 0.818 0.412 0.700 0.484 0.799
q(O) -0.911 -1.073 -0.624 -0.777 -0.967 -1.058
q(H) - 0.438 - 0.378 - 0.460
В -89.7985 -90.2817 -16.1294 -16.6074 -89.7698 -90.2564
PA - 303.2 - 299.9 - 305.3
РД_,[1) 285.9 285.9 285.9
Table ZZ. Molecular Geometries, Dipole Moraente, Mulliken Chargee and Bnergetice 
of LiOH and LiOH,*.
TZV* SBK* 6-31G*
LiOH LiOH,* LiOH LiOH,* LiOH LiOH,*
r(OLi) 1.571 1.833 1.640 1.986 1.592 1.858
Г (OH) 0.931 0.944 0.949 0.965 0.938 0.954
ллон 180.0 126.2 179.9 127.6 180.0 126.8
Л Ш Л - 180.0 - 180.0 - 179.9
ß 4.154 3.326 4.977 4.027 4.314 3.479
q(Li) 0.618 0.928 0.535 0.861 0.612 0.898
q(o) -0.999 -0.970 -0.826 -0.718 -1.016 -0.943
q(H) 0.381 0.521 0.291 0.428 0.405 Õ.522
в -82.931490 -83.334951 -16.4959 -16.8950 -82.9032 -83.3093
PA - 253.2 - 250.5 - 254.8
PA^tl] - 239.8 - 239.8 - 239.8
6
ТаЫа III. Molecular Geometries, Dipole Moments, Mulliken Charges and Energetics 
of LiNH, and LiNH,\
TZV* ЧВК' 6-31G*
LiNH, LiNH, LiNH, LiNH,* LiNH, LiNH,4
r (NT i; 1.728 1.975 1.786 2.118 1. 750 2 . 0 0 2
_-(NH> 1 .0 0 2 1.004 1.019 1 . 0 2 0 1.005 1 . 008
i LiNH 127.4 113.3 128.1 113.9 127.4 113.2
.HJT,iH 180.0 1 2 0 . 0 180.0 1 2 0 . 0 179.9 1 2 0 . 0
4.530 3.850 5.074 4.32? 4.617 3 .968
q(Li) 0.563 0.875 0.361 0.761 0.535 0.851
q(N) -1.141 -1.132 0.730 -0.689 -1.130 -1.133
q(H) 0.289 0. 41Э 0.184 0.309 0.297 0.427
E -63 0618 -63.5081 -1 1 . 0 2 0 1 -j.1.4 703 - 63 . 0419 -63.4S06
PA 28?.1 - 276.8 - 281.6
Table IV. Molecular Geometries, Dipole Moments, Mulliken Charges and Energetics 
o f Na,0 and f’a2OH'.
TZV* SBK" 6 - 31G"
Na,0 N2,OH* Na-0 Na-OH Na,0 Na,C4*
r(ONa) 1 . 9 7 4 2.108 1.Э76 2.148 1.&S1 2.093
r(OH) - 0.945 - 0.962 - 0.950
ZNaONa 180.0 140.9 180.0 144.8 180.0 144.4
-NaOH 109.5 - 107.6 - 107.8
i-HONaNa 180.0 - 180.0 - 180.0
M 0.005 2.229 0.001 2.080 0.003 1.869
q(Na> 0.642 0.928 0.546 Э.838 0.505 0.816
q(C) -1.284 -1.231 -1.093 -1.010 -1.009 -1.042
q(H) - 0.374 - 0.334 - 0.410
E - 498.5302 -399.0756 -16.0011 -16.5449 -398.4858 -399.0358
PA - 342.3 - 340.8 - 345.2
PA^Jl] - 306.7 - 306.7 - 306.7
7
Table V. Molecular Geometries, Dipole Moments, Mulliken Charges and Energetice 
of NaOH and NaOR,.
TZV SBK‘ 6-31G*
tlaOH NaOH,* NaOH NaOfV NaOH NaOH/
r (ONa) 1.941 2.218 1.973 2.335 1.921 2.214
r (OH) 0.937 0.947 0.952 0.964 0.941 0.952
ZNaOH 180.0 126.6 180.0 127.9 179.8 127.2
ZHONaH 180.0 - 179 . 9 - 17&.9
ß 6.636 1.860 6.937 2.214 6.208 1.838
q(Na) 0 . 821 0.982 0. 720 0.949 0.696 0.925
q(0 ) -1.168 -0.935 -0.986 -0.775 -1.068 -0.930
q(H) 0 . 347 0.476 0.266 0.413 0.373 0.502
E -237.3174 -237.7518 -16.4477 -16.88214 -237.2725 -237.7155
PA 272 . 6 - 272.6 278.0
PA^tl] 246.7 - 246.7 - 246.7
Table VI. Molecular Geometries, Dipole Moments, Mulliken Charges and Energetics 
of NaNH2 and NaNH3*
TZV* SBK* 6-31G’
NaNH2 NaNHj* NaNHj NaNH,* NaNHj NaNHj*
r(NNa) 2.096 2.365 2.150 2.508 2 . 080 2.357
r (NH) 1.005 1.004 1 . 0 2 2 1.019 1.007 1.007
ZNaOH 127.7 113 .1 128.5 114 .2 127.8 113 .3
ZHNNaH 180.0 1 2 0 . 0 179.9 1 2 0 . 0 179.9 1 2 0 . 0
6.824 2.141 7.026 2.418 6.320 2.052
q(Naj 0.788 0.959 0.610 0.913 0.636 0.900
q(N) -1.313 -1.093 -0.935 -0.776 -1.180 -1.116
q (H) 0.263 0.378 0.162 0.288 0.272 0.405
E -217.4452 -217.9181 -10.9803 -11.4536 -217.4148 -217.8945
PA - 296.7 - 297.0 - 301.0
8
Table VII. Molecular Geometries, Dipole Moments, Mulliken Charges and Energetics 
of K ,0 and K,0*.
TZV* SBK* 3-21G*
KjO KjOlT K ,0 KjOIT KjO ICjOH*
r (OK) 2.329 2.501 2.257 2.476 2.268 2.440
r (OH) - 0.946 - 0.963 - 0.977
ZKOK 180.0 142.1 180.0 147.4 180.0 144.8
ZKOH - 109.0 - 106.4 - 107.6
ZHOKK - 180.0 - 180.0 - 180.0
l i 0.000 2.515 0.002 2.252 0.004 2.524
q(K) 0.747 0.954 0.564 0.877 0.801 0.930
q(O) -1.494 -1.253 -1.128 -1.060 -1.602 -1.255
q(H) - 0.346 - 0.307 - 0.396
E -1273.0763 -1273.6816 -15.9031 -16.4932 -1266.69Э8 -1267.2777
PA - 379.8 - 370.3 - 362.7
PA.4.UI - 318.2 - 318.2 - 318.2
Table VIII. Molecular Geometries, Dipole Moments, Mulliken Charges and Energetics
of KOH and KOH,*.
TZV* SBK' 3-21G*
KOH KOHj* KOH K0H2t KOH KOH2,
r (OK) 2.294 2.675 2.223 2.709 2.170 2 . 550
r(OH) 0.940 0.946 0.955 0.963 0.969 0.968
ZKOH 180.0 126.7 180.0 128.1 180.0 125.9
ZHOKH - 180.0 - 179.7 - 179.6
ß 8.339 1.256 8.432 1.514 6.802 1.154
q(K) 0.910 0.992 0.773 0.968 0.843 0.967
q(0 ) -1.240 -0.909 -1.026 -0.76 -1.234 -1 . 0 2 0
q(H) 0.330 0.459 0.253 0.399 0.452 0.526
E -674.6085 -675.0704 -16.4142 -16. 8 -671.1768 -671.6441
PA - 28? .9 - 287 1 - 293.3
W W H - 262.9 - 262.9 - 262.9
9
Table IZ. Molecular Geometries, Dipole Moments, Mulliken Charges and Energetics 
of KNtt, and KNiV •
KNHj KNHj* KNHj КИН,* KWH; KNHj*
r(KN) '*•. 486 2.858 2. bOl 2.919 2.395 2.802
r(NH) 1 008 1.003 1. 026 1.019 1.023 1.019
ZKNH 128 3 113.0 129.3 114 . 3 128.1 110.3
/НККН 140.0 120.0 180.0 120.0 180.0 120.0
M 8.943 1.602 9.126 1. 749 7.41 1.87
q(K) 0.913 0.987 0.956 0.839 0.933
q(N) -1.380 -1.074 -0.994 -0.767 -1.628 -1.193
q(H) 0.234 0.362 0.137 0.270 0.394 0.420
E -654.7325 -655.2343 -10.9404 -11.4407 -651.4155 -651.9260
PA - 314.9 - 314.0 - 320.4
О
p*
о
1
Theoretical Study of Prototropic Tautomeriem and Acidity of 
Trie(fluoroeulfonyl)methane 
Peeter Burk*, Xlmar A.Koppel*, Jüri Tapfer*, Frederick Anviac and 
Robert N.Taft'
* Institute of Chemical Physics, Tartu University, Jakobi 2, EE2400 
Tartu, Estonia
b Computational Center, Tartu University, Liivi 2, EE2400 Tartu, 
Estonia
c Department of Chemistry, University of California at Irvine, 
Irvine, California 92717, USA
The prototropic tautomerism and acidity of (FS02)3CH was 
studied at both the semiempirical (PM3) and ab initio (HF/ST0-3G* 
and 3-21G*) level. It was shown, that PM3 fails to describe the 
energetics of prototropic tautomerism, while giving the geometry of 
the sulfo form in good agreement with the experimental data. The ab 
initio calculations predict in accordance with the experiment, that 
the sulfone form is more stable than enol form. The conformity 
between calculated and experimental geometry was also satisfactory.
The gas phase acidity of (FS02)3CH was calculated and the 
factors which contribute to the extremely high gas phase acidity of 
the title compound were discussed.
2
1 .Introduction
Fluorosulfonyl and trifluoromethylsulfonyl substituted 
compounds such as (FS02)3CH 1, (FS02)2NH 2, (CF3S02)3CH 3 and 
(CF3S02) 2NH 4 are knovm as very strong acids in liquid phase. Recent 
gas-phase measurements s indicate, that at least some of them are 
relatively even stronger in the gas-phase exceeding the strength of 
such a commonly known strong acid as HI by many powers of ten.
However, there is very little known about these compounds. 
Only for a very few of them the geometries are established and even
less is known about their el•erctronic structure and relationsbetween geometry, electronic structure and chemical properties.
Recently it was suggested6 that the superacidic behavior of 
(CFjSOj) 2NH and (C4F,S02)2NH could be ascribed to the presence of the 
prototropic tautomerism according to the scheme presented on Fig.l. 
For (FS02) jNH such a tautomerism was indirectly suggested already 
in 1965 by J.K.Ruff2. However, such a prototropic tautomerism is 
very hard to investigate experimentally, while due to extremely 
strong acidity of the above mentioned molecules they exist in 
solutions in completely dissociated form.
In recent years the semiempirical calculations (MNDO7, AMI 8 
and PM3 methods*) have been widely used to investigate the 
prototropic tautomerism1011, geometries and energetics1 2 , 1 3 , 1 4 , 1 5 of 
medium-sized and large systems. The only one of them with declared1 6  
ability to reproduce and predict the properties of hypervalent 
molecules correctly is PM3, while the others are known to fail to 
describe such systems16.
The current investigation of (FS02)3CH was undertaken as one 
of the first steps in the investigation of the sulfonylsubstituted 
superacids to find out their geometry, electronic structure, 
prototropic equilibria and relationships between the abovementioned 
properties and extremely high intrinsic acidity of such compounds. 
Another aim of this study was to establish the usefulness of the 
PM3 method and ab initio calculations at ST0-3G* and 3-21G* levels
4
The energies and geometries for most stabile sulfone and enol 
forms as well as that of anion are presented in Tables 1-3. The 
corresponding conformations are presented on the Fig. 2 alongside 
with used numbering scheme for atoms.
The PM3 method predicts the hydrogen bonded enol form to be 
the most stabile one (27.8 kcal/mol more stable than the most 
stabile sulfone form) , while the experimental data1 ' 1 7 clearly 
indicates, that the sulfone form is at least predominant. The 
results of ab initio calculations at both ST0-3G* and 3-21G* level 
agree with experiment giving the sulfone form respectively 15.2 
and 3.5 kcal/mol more stabile.
The gas phase acidity of the title compound predicted by the 
PM3 method was found to be 261.3 kcal/mol when using the sulfone 
forms heat of formation for the calculation of acidity what doesn't 
agree with its predicted value 295 kcal/mol 5. Gas phase acidities 
found from results of ab initio calculations are 385.7 and 219.6 
kcal/mol respectively for STO-3G* and 3-21G* levels of theory. 
However, it should be mentioned, that such failure of predicting 
the absolute gas-phase acidities is common for the PM3 method in 
case of hypervalent molecules2 2 and peculiar also to ab initio 
calculations23.
The geometries of anion and sulfone form found both by PM3 and 
ab initio calculations at ST0-3G* and 3-21G* level are in excellent 
agreement with experiment. The bond lengths differ from the 
experimentally determined ones less than 0.05 angstroms (the only 
exception is S-C bond length in sulfone form found by PM3 method 
differing from experimental value by 0.08 angstrom*) and angles 
less than 5°.
The reasons for very high acidity of (FS02)3CH were 
investigated by means of Mulliken population analysis. In Tables 4 
and 5 are given total atomic charges and selected bond populations 
obtained by all three methods.
The interesting fact is that the PM3 method predicts the 
Mulliken charge on the sulphonyl sulphur to be nearly +2.5 in both 
neutral molecule and anion, what seems improbable. Also ab initio
for above mentioned tasks, while the title compound is the one of 
a few sulfonyl-containing superacids, for whom alongside with the 
geometry of anion in the crystal phase1 also the gas-phase geometry 
of neutral acid is properly established17.
2.Method
The first step of the calculations was carried out on MicroVAX
II computer using the standard PM3 procedure, as implemented in the 
MOPAC 6.0 program package18. All geometries were fully optimized by 
minimizing the energy with respect to all geometrical variables 
without using the aid of symmetry. All possible rotational 
conformations of sulfo and enol forms alongside with these of anion 
were studied. Then the most stabile conformations were calculated 
on the Convex 240 computer using Gaussian 92 1 9 program package at 
HF/STO-3G* and HF/3-21G* levels with full optimization of geometry.
The acidity (AH,cld) of compound HA was found as the heat of 
reaction for the proton abstraction equilibrium to form the 
conjugate base A':
HA~H'+A- ^Hacid(HA)=liHf(Ht)+^Hf(A-)-AHf(HA) (1)
where ДНГ(Ю, ДН,(НА) and AHf(A) are the heats of formation for 
proton, acid and its conjugated anion. In case of the PM3 method 
the experimental heat of formation for proton (365.7 kcal/mol so) 
was used instead of the calculated value (353.6), because it 
improves the calculated acidities considerably. We acknowledge that 
this is not quite a correct procedure, despite the fact that such 
a way was also used in earlier works on semiempirical calculations 
of acidities and basicities21.
4
3.?.esulte and discussion
The energies and geometries for most stabile sulfone and enol 
forme as well as that of anion are presented in Tables 1-3. The 
corresponding conformations are presented on the Pig. 2 alongside 
with used numbering scheme for atoms.
The PM3 method predicts the hydrogen bonded enol form to be 
the most stabile one (27.8 kcal/mol more stable than tha most 
stabile sulfone form), while the experimental data1 1 7  clearly 
indicates, that the sulfone form is at least predominant. The 
results of ab initio calculations at both ST0-3G' and 3-21G’ level 
agree with experiment giving the sulfone form respectively 15.2 
and 3.5 kcal/mol more stabile.
The gas phase acidity of the title compound predicted by the 
PM3 method was found to be 261.3 kcal/mol when using the sulfone 
forms heat of formation for the calculation of acidity what doesn't 
agree with its predicted value 295 kcal/mol 5. Gas phase acidities 
found from results of ab initio calculations are 385.7 and 279.8 
kcal/mol respectively for ST0-3G’ and 3-21G* levels of theory. 
However, it should be mentioned, that such failure of predicting 
the absolute gas-phase acidities is common for the PM3 method in 
case of hypervalent molecules2 2 and peculiar also to ab initio 
calculations23.
The geometries of anion and sulfone form found both by PM3 and 
ab initio calculations at ST0-3G* and 3-21G* level are in excellent 
agreement with experiment. The bond lengths differ from the 
experimentally determined ones less than 0.05 angstroms (the only 
exception is S-C bond length in sulfone form found by PM3 method 
differing from experimental value by 0.08 angstroms) and angles 
less than 5°.
The reasons for very high acidity of (FS02)3CH were 
investigated by means of Mulliken population analysis. In Tables 4 
and 5 are given total atomic charges and selected bond populations 
obtained by all three methods.
The interesting fact is that the PM3 method predicts the 
Mulliken charge on the sulphonyl sulphur to be nearly +2.5 in both
5
neutral molecule and anion, what seems improbable. Also ab initio 
calculations at 3-21G* level give very big charges. So, as it is 
noted already earlier24, most reliable charges were obtained at STO- 
3G* level. Hence, the further discussion bases on the charge 
distribution obtained at this level of theory. Also it should be 
mentioned, that the changes in Mulliken charges upon deprotonation 
are very similar for all three methods. The only considerable 
difference is the fact that the PM3 method estimates the change of 
Mulliken charge on carbon athom to be much higher (0.41)than both 
ab initio methods (0.09 and 0.08).
The most notable feature in the changes of total atomic 
charges upon deprotonation is its uniformity. These changes vary 
from -0.09 at carbon atom to -0.05 on the sulphur atom which 
indicates very strong and uniform charge delocalization in 
tris(fluorosulfonyl)methane's anion. This delocalization is 
undoubtly the main reason for extremely high acidity of title 
compound.
The changes in bond populations calculated from Jfcilliken 
population analysis exhibit somewhat bigger changes upon 
deprotonation. So the C-S bond populations rises notably (0.2 
units) while S-F and S-0 bond populations lover slightly (0.03 and
0.02 units respectively). This, alongside with the fact, that the 
biggest changes in total atomic charges (excluding carbon atom as 
deprotonation center) take place on oxygen atoms, suggests that 
alongside with induction also resonance stabilization takes place.
This is of course disputable while all six S-0 bonds are by no 
means coplanar. However, recent investigations by Mezey2 5 of N- 
sulfonylsylfilimines indicates, that whereas in carbon compounds 
the prerequisite for optimum conjugation is a rather strict 
geometrical condition of exact or near coplanarity of the 
participating carbon atoms, the geometrical conditions are much 
more relaxed for third-row atoms if valence-shell d orbitals are 
involved in bonding. Further investigations in this direction were 
undertaken by the present authors and will be discussed elsewhere.
6
4.Conclusions
The above presented facts show clearly that PM3 should not be 
used to investigate the keto-enol tautomerism at least when the 
aulfonyl group is involved-
From the other hand it must be stated, that PM3 gives good 
prediction of bond lengths and angles, when the conformation of 
investigated molecule is known or'predictable.
The analysis of changes in charge distribution upon 
deprotonation of trisfluorosulfonylmethane indicate, that its high 
acidity is caused by strong charge delocalization in anion form 
both by field inductive and resonance interaction mechanisms.
5.Acknowledgments
We are indepted for the support in part of the Gaussian 92 
calculations by the Irvine Office of Academic Computing (UCI) and 
Molecular Solvometric Inc. for support of the work reported herein.
6 .References
1.G.Klötter, H.Pritzkow and K.Seppelt, Angew. Chem.,Int.Ed.Engl., 
1980, 19, 942.
2.J.K.Ruff, Inorg.Chem., 1965, 10, 1446.
3.L.Turowsky and K.Seppelt, Inorg.Chem., 1988, 27, 2135.
4. J. Foropoulus, Jr. and D.D.DesMarteau, Inorg.Chem., 1984, 23, 3720.
5.1.A.Koppel, R.W.Taft, F.Anvia, Shi - Zheng Zhu, Li-Quing Hu, Kuang- 
Sen Sung, D.D.DesMarteau, L.M.Yagupolskii, Yu.L.Yagupolskii, 
N.V.Ignat'ev, N.V.Kondratenko, A.Yu,Volkonskii, V.M.Vlasov, 
R.Notario and P.-C.Maria, J.Am.Chem.Soc., in the press
6 .1.A.Koppel, R.W.Taft, F.Anvia, N.V.Kondratenko, L.M.Yagupolskii, 
Zh.Org.Khim., 1992, 28, 1764.
7.M.J.S.Dewar, W.Thiel, J.Am. Chem.Soc., 1977, 99, 4899.
8 .M. J.S.Dewar, E.G.Zoebisch, E.F.Healy and J.J.P.Stewart, 
J.Am.Chem.Soc., 1985, 107, 3902.
9.J.J.P.Stewart, J.Comput.Chem., 1989, 10, 209.
10.O.A.Ivashkevich, P.N.Gaponik, A.O.Koren, O.N.Bubel,
7
E.V.Fronchek, Int. J. Quant. Chem., 1992, 43 ,  813.
11.J.G.Contreras, J.3.Alderete, J.A.Gnecco, Theochem, 1991, 83,  
195.
12.K.Ohta, Bull.Chem.Soc.Jpn. , 1992, 65, 2543.
1?.M.A.Palafox, Theochem, 1991, 82, 161.
14.j.Frau, J.Donoso, F.Munoz, F.G.Blanco, Theochem, 1991, 83,  205.
15.F.E.Romesberg, D.B.Collum, J.Am.Chem.Soc., 1992, 114, 2112.
16.J.J.P.Stewart, J.Сотриt.Chem., 1989, 10, 221.
17.J.Brunvoll, M.Kolonits, C.Bliefert, K.Seppelt and I.Hargittai, 
J. Mol.Struct. , 1982, 78, 307.
18.J.J.P.Stewart, QCPE No.4*5, 1990.
19.M.J.Frisch, G.W.Trucks, M.Head-Gordon, P.M.W.Gill, M.W.Wong, 
J.B.Foresman, B.G.Johnson, H.B.Schlegel, M.A.Robb, E.S.Replogle, 
R.Gomperts, J.L.Andres, K.Raghavachari, J.S.Binkley, C.Gonzalez, 
R.L.Martin, D.J.Fox, D.J.Defrees, u.Baker, J.J.P.Stewart, and 
J.A.Pople, Gauseian92, Revision C, Gaussian Inc., Pittsburgh PA, 
1992.
20.S.G.Lias, J.E.Bartmess, J.F.Liebman, J.L.Holmes, R.D.Levin and 
W.G.Mallard, J.Phys.Chem.Ref.Data, 1988, 37, Supplement No.l
2 1 .M.J.S.Dewar and K.M.Dieter, J.Am.Chem.See., 1986, 108, 8075.
22.P.Burk and I.A.Koppel, Theor. Chim. Acta, in the press.
23.W.J.Hehre, L.Radom, P.v.R.Schleyer and J.A.Pople, Ab initio 
Molecular Orbital theory. J.Wiley, NY, 1986.
24.1.A.Koppel and ü.Mõlder, Org. React. (USSR), 1981, 67, 396.
25.P.G.Mezey and H.Flakus, Theochem, 1989, 186, 117.
Table 1. Geometry of the most stabile conformation of
tris(fluorosulfonyl)methanes sulfonyl form.
PM3 STO-3G* 3-21G* EExp.
C-S 1.874Ä 1 . 844Ä 1 . 7 9 i A 1 . 8 3 l A
C-H 1 .1 2 0 Ä 1 . 0 9 7 A 1 . 0 8 3 A
F-S 1.551Ä 1.55 8A 1.542Ä 1 . 5 5 8 A
S-01 1.405Ä 1 . 4 4 4 A 1 . 4 C6 A 1 . 4 1 6 A
S-0a 1.413A 1 . 4 4 5 A 1 . 4 0 7 A 1 . 4 1 6 A
H-C-S 103.2° 1 0 9 . 5 ° 107.1°
C-S-F 100.e° 9 6 . 0 ° 96.4° 9 7 . 4 °
C-S-O1 110.9° 1 0 8 . 3 ° 109.8° 1 0 9 . 6 °
c-s-o* 106.3° 1 0 7 . 4 ° 107.6°
H-C-S-S 120.0° 120.0° 120.0°
H-C-S-F 39 .4° 4 2 . 8 ° 38.6° 4 1 .  0 “
H-C-S-O1 1 1 2 .8 ° 1 1 . 3 ° 1 1 1 .8 °
H-C-S-O2 -108.3° - 1 1 0 . 7 ° -110.3n
E -332.200 - 1 9 5 4 . 9 1 2 6 4 3 -1968.460018
kcal/mol a . u . a.u.
Dipole 3.751D 3.658П 4.064D
moment
Table 2. Geometry of the most stabile conformation of
tris(fluorosulfonyl)methanes enol form.
PM3 STO- 3G* 3 -21G*
1 . 7 3 9 A 1 . 6 9 6 A 1. 687Ä
c-s2 1 . 7 7 1 A 1 . 7 5 0 Ä 1.
1 . 642Ä 1 . 6 9 9 A 1. 668Ä
S'-F 1 . 5 4 7 A 1 . 5 5 8 A 1. 542Ä
S2-F 1 . 5 5 4 A 1 . 5 6 5 A 1. 547A
S3-F 1 . 5 1 7 A 1 . 5 5 9 A 1. 533А
1 . 4 1 6 A 1 . 4 4 7 A 1. 4 06A
1 . 4 6 8 A 1 . 5 1 7 A 1. 445A
1 . 4 1 8 A 1 . 4 4 вА 1. 4 10A
1 . 4 3 2 A 1 . 4 4 7 A 1. 416A
1 . 3 9 7 A 1 . 445A 1. 402Ä
s3-o6 1 . 6 3  8 A 1 . 5 1 6 A 1. 503A
0 . 9 7 2 A 1 . 170A 1. 037A
S'-C-S2 1 1 6 . 1 ° 1 3 3 . 9° 1 1 8 . 0 °
1 2 5 . 2 ° 110  . 7° 1 2 0 . 1 °
C-S1-? 1 0 5 . 6 ° 1 0 5 . .1° 1 0 4 . 6 °
C-S2-F 1 0 3 . 6 ° 1 0 0 . 1° 1 0 1 , 8 °
C-S3-F 1 1 0 . 9 ° 1 04 . . 3 ° 1 0 5 . 0 °
C-S'-O1 1 1 3 . 6 ° 1 15 . 0° 1 1 1 . 7 °
C-S'-O2 1 0 5 . 5 ° 10 6 . . 9 ° 1 0 7 . 4 °
c-s2-o3 1 1 1 . 6 ° 1 08 . . 3° 1 1 0 . 9 °
c-s2-o4 1 0 6 . 5 ° 1 08 . . 0 ° 1 0 6 . 2 °
c-s3-o5 1 2 0 . 3 ° 116 . . 5 ° 1 2 0 . 0 °
C-S3-0s 1 1 0 . 2 ° 106 . . 3 ° 1 0 6 . 7 °
1 1 8 . 4 ° 108 . 0 ° 1 1 9 . 1 °
11 . 4 ° 2 . 2 °
E - 3 6 0 . 9 -1954.8884 -1968.4553
kcal/mol a.u. a.u.
pole moment 3 . 1 2 1 D 3.204D 4.159D
ЫЫ
оо
CОD
я
о о о о X CO
X
CO CO О о ои
и и CO CO CO CO CO о CO
CO CO о
10
Table 3. The most stabile conformation of
tris(fluorosulfonyl)methyl anion.
PM3 STO-3G* 3-21G* Exp.
C-S 1 . 7 1 6 Ä 1 . 7 1 6 A  1 . 6 8 3 Ä  1 .  7Ä
F-S 1 . 5 7 9 Ä 1.57 8A 1 . 5 6 3 A  
S-O1 1 . 4 4 2 A 1 . 4 5 3 A  1 . 4 1 9 A
S-O2 1 . 4 4 9 A 1 . 4 5 4 A  1 .42ЗА 
S-C-S 120.0° 1 2 0 .0 ° 120.0° 
C-S-F 1 0 4 . 9 ° 1 0 2 .0 ° 1 0 2 . 5 °  
C-S-O1 1 1 4 . 5 ° 1 1 3 . 0 °  1 1 4 . 7 °  
C-S-O2 112.2° 1 0 8 . 3 °  1 0 8 . 1 °  
S-C-S-S 1 7 9 . 7 ° 1 8 0 . 0 ° 1 8 0 . 0 °  1 8 0 . 0 °
S-C-S-F 3 0 2 . 0 ° 2 1 .  7° 1 2 . 5 °  
C-S-F-O1 1 1 3 . 2 ° 1 1 1 . 5 °  1 1 2 . 5 °  
C-S-F-O2 - 1 0 8 . 3 ° 1 0 8 . 3 ° -110.6°
E - 4 3 6 . 6 ■ 1 9 5 4 . 2 9 7 8 8 8 - 1 9 6 8 ’. 0 1 5 8 2 0
kcal/mol a.u. a.u.
Dipole 2.892D 2.904D 1.722D
moment
Table 4. Net atomic charges, calculated from Mulliken
population analysis.
Neutral (sulfone form) Anion
PM3 STO-3G* 3-21G* PM3 STO-3G* 3-21G*
H С. 197 0.119 0.391
с -1.538 -0.062 -1.324 -1.952 -0.152 -1.404
s 2.444 0.449 1.651 2.442 0.397 1.673
F -0.327 -0.059 -0.337 -0.361 -0.119 -0.379
O1 -0.818 -0.199 -0.492 -0.871 -0.278 -0.567
0 J -0.852 -0.209 -0.512 -0.890 -0.283 -0.593
Table 5. Bond populations, calculated from Mulliken 
population analysis.
Neutral (sulfone form) Anion
PM3 STO-3G* 3-21G* PM3 STO-3G* 3-21G'
C-H 0.489 0.735 0.593
C-S 0.165 0.624 0.054 0 . 2 0 1 0.822 0.178
S-F 0.420 0.593 0.466 0.419 0.565 0.476
S-0A 0.739 1.029 1. 049 0.708 1.014 1.094
S-O2 0 . 727 1 . 026 1. 044 0.698 1 . 0 1 0 1.039
12
н
I
0II  H1 0II 0II  01
SII —  N - - SII- C F л3 ^ = —  F3C II II
0 0 0 0
Figure 1. Suggested prototropic tautomerism of (CF,SOj) 2NH.
Ill
Figure 2. The most stabile conformations of tris(fluoro­
sulf onyl) methanes sulfonyl form (I), enol form (II) and anion (III).
«Л
II
z
(1Л
1
SUPERACIDITY OF NEUTRAL BRÖNSTED ACIDS IN GAS PHASE.
PM3 STUDY.
Peeter Burk*, Ilmar Koppel*, Ivar Koppel*,
Lev M. Yagupolskiib and Robert W. Taftc
* Institute of Chemical Physics, Tartu University,
EE2400 Tartu, Estonia
b Institute of Organic Chemistry, Academy of Sciences of 
Ukrainian Republic, Kiev, Ukraine 
° Department of Chemistry, University of California at Irvine, 
Irvine, California 92717, USA
Abstract.
PM3 calculations of potentially superacidic neutral Brõnsted 
acids were carried out. It was shown, that PM3 method can be used 
to predict the gas-phase acidities of very acidic compounds only if 
the empirical corrections are made. Very strong acidifying effect 
is predicted for substitution of sp2 oxygen by =NS02CF3 group. The 
possibility of further increase of acidities of such compounds by 
further stepwise substitutions of =0 by =NS02CF3 has been predicted. 
The geometries of known superacidic systems are reproduced quite 
well, so the PM3 method can be recommended for studies of that 
kind. The geometries of several superacidic systems were analyzed.
1 .Introduction.
The name "superacid" was first used by J.B.Conant in 1927 [l] 
for the acid systems more acidic than the traditional mineral 
acids. Superacid media, much more acidic (H0 > -30) than anhydrous 
sulfuric acid (H0 = -12) were created by O.A.Olah and coworkers
[2 ] , which was important progress in developing new superacid 
systems.
Unfortunately, due to the substantial experimental and 
theoretical difficulties, besides the knowledge of some acidity 
function of the neat Brõnsted acid (AH) or related conjugated
2
superacid system, far less quantitative and practically not self- 
consistent information is available on the pK, values of strong or 
superstrong mineral or organic Brönsted acids, referred to their 
dilute solutions in water, nonaqueous solvent, or gas phase as 
standard state.
The intrinsic gas-phase equilibrium acidity (AG) scale (see
[3]), where AG refers to the following proton transfer equilibrium
AH-A +Я*
for various neutral Brönsted acids includes more than 700 weak, 
moderately strong, or relatively strong acids whose AG varies from 
415 kcal/mol to 315 kcal/mol, i.e. more than 70 pK, units. 
Recently, this scale was further extended [4] from AG=318 kcal/mol 
to AG=284 kcal/mol to involve many very strong Brönsted acids off 
different structure.
Previous results and the analysis given in Refs.4-7 evidence 
that three major kinds of substituent effects i.e.,
1. field/inductive effect (F),
2. я-electron acceptor (resonance) effects (R), and
3. substituent polarizability (P) effect,
determine the gas-phase acidity of neutral Brönsted superacids (see 
also Ref.9). For all of those three influencing factors the acidity 
increases for AH acids are due to much stronger substituent 
stabilizing interactions with the deprotonated protonization center 
of A' (e.g., O', N', C, etc..) than with the protonated reaction 
center in AH (e.g., OH, NH, CH, etc..).
Therefore, the simplest strategy to develop progressively more 
acidic superacid systems would be the synthesis of molecules which, 
along with the acidity site (C-H, O-H, N-H, S-H, etc..), include 
(several) highly dipolar superacceptor and strongly polarizable 
substituents which form very extensive, strongly conjugated system 
with the anionic protonization center of A .
It should be kept in mind [4,6-9] that no simple pattern for 
the influence of the above mentioned three major kinds of
substituent effects on the acid strength of neutral Brõnsted acids 
is expected because of the interdependence of the contributions for 
the F, P, and R-effects for the strongly electron-withdrawing, 
acceptor substituents, at least for some reaction series. So, 
increasing я-electron acceptor effects can decrease the P- and F- 
effects of the given substituent due to the increasing reduction of 
the negative charge of the anionic center. In its turn, the R 
effects could be significantly decreased by steric repulsion and 
non-coplanarity effects. All these phenomena lead to some, 
sometimes rather significant, reduction of the acidities expected 
on the grounds of the substituent effect additivity principle.
Proceeding from the above described principles several new 
families of superstrong Brõnsted acids could be anticipated.
A particular attention should be called on the derivatives 
with a new family of superstrong electron-withdrawing substituents 
[10,11], generated according to Yagupolskii's principle by the 
replacement by the =NS02CF3 group of an sp2 oxygen atom(s) bonded to
S,P or I-systems.
Only a few physical and chemical properties of these novel 
compounds have been studied so far, whereas the theoretical study 
of their electronic structure, reactivity and applications is 
practically absent. Due to the involvement of hypervalent fragments 
(CFjSOj, FS02, C1VI1, etc.) the theoretical investigation of the 
structure and reactivity of more conventional superacids 
( (CF3S02) 3CH, (FS02) 3CH, HC104, FSO3H, etc.) is also on its initial 
phase.
2 .Methods.
In recent years the semiempirical calculations (MNDO [12] , AMI 
[13] and PM3 [14] methods) have been widely used to investigate the 
properties of medium-sized and large systems. The only one of them 
with declared [15] ability to reproduce and predict correctly the 
properties of hypervalent molecules is PM3, while the others are 
known to fai1- to describe such systems.
In the present work an attempt to study the electronic
4
structure and acidity of a wide range of potentially superacidic 
molecules - neutral Brönsted acids - was undertaken using the 
semiempirical PM3 method. Calculations were carried on MicroVAX II 
and VAX 8650 computers using the MOPAC 6.0 [16] program package. A 
full optimization of the structures of neutral molecules as well as 
their conjugated anions was used throughout this work.
The deprotonation enthalpy -(DPE) of compound HA was found as 
the heat of reaction for loss of a proton to form the conjugate 
base:
HA+H*+A~ DPE(HA) =ДHf(H') +ДHf(A') -HHf(HA)
where AHf(H*), AHf(A ) and ДН((НА) are the heats of formation for 
proton, acid and acids anion. In case of proton the experimental 
heat of formation (365.7 kcal/mol [3]) was used instead of 
calculated value (353.6), while it improves the calculated 
deprotonation enthalpy considerably, we understand, that this is 
not a quite correct procedure, but such a way was also used in 
earlier works on semiempirical calculations of acidities and 
basicities [17,18,19] of wide variety of molecules.
3.Results and discussion.
Calculated deprotonation enthalpies (DPE) for several 
potentially superacidic substances alongside with several reference 
acids (CH4, NHj, H30, etc.) are presented in Table 1. when 
available, also the experimentally measured acidities (AG°) are 
given.
The results of statistical (regression) analysis of the 
relationship between the calculated deprotonation enthalpies and 
experimental gas-phase acidities according to formula
DPE (calc) =a +b-DPE (exp) (2)
are presented in Table 2, where N is the number of points, STDV is 
the average unsigned error in proton affinities, R is the 
correlation coefficient, о is the standard deviation and 5  is the
average unsigned error, when DPEc,lc is corrected using formula
bpCc. = - Р~ саь' ~ а (3 ]
It is not the most correct way to compare deprotonation enthalpies 
with gas-phase acidities as they must differ by TAS°, but this 
approach was selected as it saves a lot of computer time and the 
TÄS° values for many of the acids studied center at 7.0 kcal/mol
[4] .
As it can be seen, the correlation between calculated and 
experimentally measured acidities should be considered as fair 
(R2=0.9194 and STDV=12.7), which is comparable to the similar 
results for the wide range of acids 0.903 and 11.2 [18]. However, 
at closer look one can see that at the acidity scale region below 
340 kcal/mol, which is most important for current work, the 
correlation is rather bad (R2=0.7613 and STDV=12.9) and continues 
to become even worse when we are omitting regions of lower acidity 
(see Table 2) . It is not surprising, as these highly acidic 
compounds contain highly electronacceptor substituents', their 
anions are usually relatively bulky, whereas the PM3 method is 
reported to overestimate the stabilization energies of such anions 
[18] and, hence, also the acidity of their conjugated neutral 
acids. This statement is confirmed by constantly growing slope when 
going down in Table 2.
At the same time it can be said that the errors are some ways 
systematic, as for a series of substitutions in methane or ammonia 
with common substituent the correlation is very good (see 
trifluoromethyl-, trifluoroacetyl- and trifluoromethylsulfonyl- 
substituted acids in Table 2). In all these correlations also the 
corresponding parent acids (methane or ammonia) are included. So if 
the acidities of some members of the series are known, the 
acidities for the others can be predicted.
In a qualitative accordance and by analogy with the earlier 
experimental results, Table 1 shows that the introduction of the
6
"conventional" strong polarizable electron-acceptor groups (CN, 
N02, CFjSOj, fso2) immediately at the deprotonation center of the 
studied CH-, NH-, OH- and SH acids, or in the aromatic ring 
attached to the protonation center, increases by many powers of ten 
the acidity of their unsubstituted parents. The calculated AHf(AH) 
values obey roughly the same non-additivity and partial additivity 
trends as found for the experimentally measured values in Ref. 4.
In case of OH, NH and SH aliphatic Brõnsted acids FM3 
reproduces the experimental acidity of these compounds with a 
satisfactory precision. However, especially in case of sulfonyl- 
containing substituents, this method greatly overestimates the 
stability of the corresponding anions and therefore leads to very 
significantly overestimates acidities of those compounds. The 
largest deviation (49 kcal/mol) is noticed for (CF3S02)3CH whereas, 
as a rule, differences in the calculated and measured acidities for 
different acids range from 10-40 kcal/mol.
From the compounds listed in Table 1 probably the most acidic 
is 4,7,10-CF3S03 substituted fluoradene, for which on grounds of the 
additivity rule, an AG value ca 229 could be predicted assuming 
that all three CF3S02 substituents in the fluoradene ring display 
the same acidifying substituent effect as para-CF3S02 group in 
p-CF3S02CeH4CH3 (AG=340.7 kcal/mol) as compared with toluene itself 
(AG=373.7 kcal/mol), i.e. 33 kcal/mol per one CF3S02 group or
3 *33=99 kcal/mol assuming 100% additive effect (AG for 
unsubstituted fluoradene is 324.9 kcal/mol). Assuming ca 60% 
fractional additivity correction this value becomes ca 260-265 
kcal/mol. However, much higher acidity could be expected for
4, 7,10-fluoradene derivative with supersubstituents CF3S(0) (NS02CF3) 
or CF3S (NS02CF3) 2.
Enormous acidifying effect of supersubstituents CF3S0(N802CF3) 
or CF3S (N802CF3) j, as compared with the trifyl group, on the acidity 
of H20, NH3 and methane could be seen from the Table 3.
The effects of replacement of sp2 oxygen in various S02, SO, 
NO, =CO, etc. containing acids by NS02CF3 group could be seen from 
Table 4. One can see that the present calculations predict in most
cases extremely significant increases (up to 47 kcal/mol) of the 
acidity of compounds in which =0 is replaced by =NS02CF3 or =NS02F 
group. Tables 1 and 4 show that,similar very substantial increases 
(up to 50 kcal/mol) of the acidity are also predicted for such 
organic and inorganic superacids as CF3S03H, FSO-.H, H0N02, H2S04, 
(CF,S03) 2NH. On can see (Table l), that in the case of the latter 
molecule, the replacement of all four oxygen atoms by =NS02CF3 group 
is predicted by the PM3 approach to lead to the acidity in the 
range of 240 kcal/mol.
As each such replacement includes also two new sp2 oxygens 
into molecule, further replacements of =0 by =NS02CF3 are possible 
with subsequent increase of acidity. One must of course consider, 
that with each such replacement the increase in acidity will 
diminish so that at some point the plateau will be achieved, where 
further substitutions will not increase the acidity.
Somewhat confused is the situation in case of the replacement 
of -0 atoms in the perchloric acid by NS02CF3 groups. The first 
NS02CF, leads to some modest (by 3.4 kcal/mol) increase of the 
acidity of the parent acid. The PM3 calculations of 
H0C1(0) (NSO.CFj) 2 and H0C1(NS02CFJ 3 as neutral Brönsted acids show 
that to those hypothetical compounds correspond two different 
potential minima. The first ones evidently correspond to the 
structures given above. One can see from Tables 1 and 4 that in 
both cases also the modest increases of the acidity upon 
consecutive introduction of =NS02CF3 groups into the molecule of 
perchloric acid is expected. The second minimum on potential curve, 
however, corresponds to much lower energy (by 160-170 kcal/mol) and 
to the structures where intramolecular spontaneous proton transfer 
to =NS02CF3 group occurs. The formation of "internal" ion pair seems 
to stabilize the AH form of the neutral acid even to a such extent 
that it's formation enthalpy is lower than that of the anion, A .
The disappointing fact is that for the compounds containing 
the hypervalent sulphur PMi predicts the Mulliken charge on the 
sulphur to be nearly +2.5 in both neutral molecules and anions, 
what is improbable and also contradictory wit}) our ab initio
8
calculations results at ST0-3G* and 3-21G* level, where the charges 
on sulphonyl sulphur vary near the 0.8-0.9 and 1.6-1.65, 
respectively [20]. However, this is predictable, as PM3 model uses 
currently only s and p orbitals [18] , so the sulphur atom must bear 
charge +2 to give "four" bonds. Thus no proper analysis of electron 
structure of above mentioned acids and conjugated anions can be 
made based on the PM3 charge distribution.
In many cases also the possibility of prototropic tautomerism, 
which lowers the acidity of corresponding compound should be 
considered. So it is established both experimentally [21] and 
computationaly [2 2 ] that hexafluoroacetylacetone exists 
predominantly in enol form. Also direct and indirect [4,23,24] 
suggestions about possible prototropic tautomerism in 
fluorosulfonyl- and trifluorosulfonyl compounds are made.
However, this rather intriguing question remains unanswered 
for further studies, as PM3 method is shown to be unusable for 
investigation of tautomeric equilibria in sulfonyl compounds [2 0 ] 
and even for trifluoroacetyl compounds at least limited Cl is 
needed in framework of AMI or PM3 methods for qualitative 
description of keto-enol tautomerism [22]. Further study of these 
phenomena using more sophisticated computational methods is in 
progress in our laboratory.
In Table 5 geometries of several calculated acids and their 
conjugated anions are given alongside with corresponding 
experimental data. As it can be seen, the PM3 method reproduces the 
geometries of presented compounds quite well, which generally seems 
to be the strongest point of PM3 method. Based on this we believe 
that the geometries of other investigated compounds are also 
correctly predicted. Calculated geometries of several interesting 
compounds are presented in Tables 4-5.
The geometries of trifluoromethylsulfonyl substituted methanes 
are presented in Table 6 . Some interesting geometrical properties 
of these compounds are discussed below on the example of 
(CF3S02)3CH. The central carbon atom and three sulphur atoms in 
anion are located on the same plane as found experimentally by
erystallographic study of hydrate of its K-salt [25]. Also the 
trend of oxygen atoms in both anionic and neutral form to be as 
close as possible to the plane, defined by the central carbon atom 
and sulphur atoms, can be expected (resonance stabilization). 
Somewhat surprising is the prevalation of this trend over the 
repulsion between CF3 groups, as in both anion and neutral 
molecule of (CF3SOa),CH the CFjSOj groups are oriented so that the. 
perfluoromethyl groups are cis to each other (in the same side of 
the above-mentioned S,C,S,S plane), while the oxygen atoms are on 
the other side of the plane. It is also somewhat surprising that 
the hydrogen atom in neutral tris-trifluoromethylsulfonylmethane is 
on the same side with perfluoromethyl groups. The differences in 
energies between different conformers are, however, not too big - 
the heats of formation of conformations, where one or more 
trifluoromethylsulfonyl groups are rotated 180° around S-C bonds is 
only ca 5-10 kcal/mol higher fox' both neutral and anion. Also, in 
comparison with the experiment [25], the rather long calculated C-S 
bond length (mote than 2.00A) between the sulphur and carbon atom 
of trifluoromethyl group should be noted (the experiment gives
0.1-0.15 ntr. shorter values). Similar trends can be found also in 
other trifluoromethylsulfonyl substituted compounds.
In Table 5 the geometries of sulphuric acid and its 
derivatives obtained by stepwise substitution of double-bonded 
oxygen atoms with =NSO,CF3 groups according to Yagupolskii’s 
principle as well as corresponding anions are given. In case of 
(HO) 2S (=NSOsCF3) 2 we once more see the strong influence of resonance 
to the molecular structure. In both neutral and anionic forms the 
C-S -N-3=N=S - С skeleton ir. close to planar, in case of neutral the 
S=0 bonds of substituent are also coplanar with parent's S-0 bonds. 
As in above-mentioned case of (CF3SGj) 3CH the C-S bonds are found to 
be rather long and trifluoromethylsulfonyl groups tend to be rather 
cis than trans. However, in (HO) ,ß (0) =NS02CF3 molecule the above- 
mentioned trend to position S= 0  bonds in the same plane don't hold. 
But despite this the hydrogen atoms and trifluoromethyl groups are 
in cis position.
10
Conclusions.
It was shown, that PM3 method can be used to predict the gas- 
phase acidities of many new very acidic compounds. However, 
quantitative predictions could be made only on assumption that the 
empirical corrections are made.
Very strong acidifying effect is predicted for substitution of 
sp3 oxygen by =NSO;CF3 group in a wide variety of acids (sulfonic 
acids, ketones, aldehydes, nitric and nitrous acids, imides, etc.) . 
The possibility of further increase of acidities of such compounds 
by further stepwise substitutions of *0 by =NS0,CF, was predicted.
The geometries of the known superacidic systems were 
reproduced quite well, so the PM3 method can be recommended for 
studies of that kind. Charge distribution, predicted by PM3 method 
for hypervalent compounds is, however, not reflecting the real 
picture due to the lack cf the inclusion of d- orbitals, so that 
"hypervalent" atoms of these molecules must bear big formal charge 
to give needed number of formal bonds.
From the geometries of analyzed superacids it can be 
concluded, that the most stable conformations are predominantly 
determined by the resonance interactions which require the 
coplanarity of certain molecular fragments. This resonance 
stabilization seems to be rather strong as it often overpowers even 
the electrostatic repulsion between closely located trifluoromethyl 
groups.
For the further quantitative study of the electronic 
structure, geometry and reactivity of hypervalent superacids 
internal shortcomings of PM3 approach are rather evident and 
another approach with the inclusion of d-orbitals is needed [26].
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Table 1. Calculated heats of formation, deprotonation 
entalpies and exprimental gas-phase acidities of investigaed 
compounds.
Acid DPE AHf (AH) ДН,(А) Д G°
C-H acids
CH4 430.2 -13 . 0 51.5 408.5’
CHjNO 355.1 7.0 -3 .6
CH3CN 370.9 23.3 28.5 364. 0b
CH2 (NC) 2 334.6 64.4 33 .3 328. 3*
CH (NC) j 308.4 109.2 51.9 294c
CF3CH3 376. 3 -172.3 -161. 7 370,4C
(CF3 )2CH2 339 . 0 -326.7 -353 .4 343.9b
(CF3)3CH 310.1 -478.4 -533. 9 326. 6 b
(CF3) 3CCH3 352 . 4 -483.0 -496. 3
CF3COCH3 346.1 -199 .2 -218 .8 342 . 1*
(CFjCO) 2CH2 306.9 -379.7 -438 .5 310.3b
(CF3CO) 3CH 287.0 -554.3 -633 .0 300.6b
(СН3СО)зСН 329.2 -129.1 -165. 6 328.9b
(CF,CO) 2CHCF3 289 . 5 -528.9 -605 .1 305.0b
fso2ch3 339. 8 -128.9 -154 .9
(FSOj) 2CH2 287.4 -236.6 -314 .9 307.3b
( fso2) 3ch 261.3 -332.2 -436. 7
FS (0) (=NS0,CF3) CH3 318.1 -28.5 -76. 1
CF,S02CH3 323 . 4 ' -207 . 8 -250. 1 339.8*
(cf3so2) 2ch2 268. 5 -390.4 -487. 6 301. 5b
(CF3S02) 3CH 240 . 4 -552.4 -677 .7 289. 0b
CF.SOjNNCHj 307 . 6 -171.2 -229. 3 299c
CH3COCN 349 . 3 -5.9 - 2 2  .3 338°
CF]S0;N=C (CN) CH3 306.8 -156.5 -215.4
(CF,S02) 2chcn 275.2 208 . 0 128. 1
CFjSOjCH (CN) 2 278 . 1 112 . 4 -199 .9 280*
14
Table 1. (Continued).
Acid DPE ÄHf (AH) ДН£(А) AG°
CF3SO (NSOjCFj) CH3 301.2 -361.1 -425.6
CF3S (NSOjCF3) 2CH3 284.7 -517,0 -598.0
CSHSCH(CN) j 318.3 94.6 47.2 314.3b
CSF5CH(CN) 2 298.5 -105.6 -172.8 303.6b
C«H5CH(S03F) 2 287.1 -199.1 -277.7 307.0b
CeHsCH (SOjCF3) 2 269.6 -350.8 -448.0 298.2b
2,4,6- 266.0 -458.7 -558.4
(CF3S02) 3CeH3CH (CN) 2
fluoradene 328.6 109.9 72.8 324.9C
4,7,10- 278.6 -473.1 -560.2
(CF3S02) 3f luoradene
(CN)2C=C(CH3 )CH(CN) 2 285.4 208.0 128.1
pentafluorocyclo- 308. 0 -174.5 -232.3
pentadiene
pentacyanocyclo- 264.4 -737.9 -839.3
pentadiene
N-H acids
NH3 407.1 -3.1 38. 3 396. la
CF3NHj 353 . 0 -166.6 -179.3
(CF3)2NH 317.4 “325.0 -373.3 324.3b
(CF3 )3CNH2 333 . 0 -472.6 -505.2 350 . lb
CF3CONHj 335.9 -196.2 -226.0 336.7b
(CF3CO) jNH 301.5 -378.6 -442.8 307 . 5b
2,4,6-NOj aniline 300 . 5 0 . 0 -65.2
2,4,6-CF3S02 aniline 291.5 -559.2 -633.4 304.8b
2,4,6-FS02 aniline 303.2 -328.0 -390 . 5 307 . 2b
FS02NH2 331. 3 -130.9 -165.3
(fso2) 2nh 296.4 - 261.8 -331.2 301.2b
cf3so2nh2 317.0 -207 . 8 -256.5 321. 3a
(cf3so2) 2nh 278.4 -412.9 -500.1 291. 8 *'
CF,S0(NS02CF3 )NH2 293 . 5 -364.3 -436.5
15
Table 1. (Continued).
Acid DPE ÄHf (AH) ДН, (A ) AG°
CFjS (NSOjCF-,) ,NHj 280.8 -521.0 -605.9
[CF,S (NgOjCFj) 2] ;NH 240 .5 -1026.0 -1151.2
ON-WHj 342.1 20.4 -3.1
CFjSO.NNNH, 302 .1 -156.0 -219.5
CF.SOjNHCOL'F, 287.7 - 392.1 -470.1 298.2b
PhS02NH2 340.6 -43 .4 -6 8 . 5 333.2b
PhSOfNSO^CFJ NH2 312 .2 -203.7 -257.2
PhS (NSOX'F,) . NH, 307.4 -233.2 -291.5
2,3,4,5- 262.6 -717.9 -821.0
tetratrifyipyrrole
O-H acids
H20 401 . 6 -53.4 -17.5 384.1'
FOH 364.9 -29.2 -30.0
CF*OH 332.2 -222.7 -256.3 340.7d
(CF,),COH 309 . 7 -516.6 -572.6 324. 0b
CFjCSOH 296.0 • 159 .2 -228.9
CF,COOH 319.3 -244.0 ■ 290.4 316.3b
(CN) jCCOOH 297. 3 32.0 -36.3
C.FsCOGH 326.8 -272 . 3 -311.1 316.6b
C6FsOH 312.9 -231.3 -284.0
2,4,6- 292.3 -637.5 710.0
(cf,so2) ,c6h,so3oh
2,4,6- 307 . 8 -624 . 8 -682.7
(CF,S02) ,Ci;HX’OOH
2,4,6 • (NOJ3CsH2OH 284.7 -41.2 -1 2 2 . 2 302.8b
fso2oh 318.4 -.186.4 -233 . 7 299 . 8 *
FSO (NSOjCFj) OH 289 . 5 -339.3 -415 .5
FS (NSOXF,) .OH 269.2 -488.7 -585.2
(CF.) -,CSO;.OH 292 . S -566 3 - 639 .2
CF^O.OH 302.4 -260.3 -323 . 5 299 . 5b
CF jSO (NSO,CF,) OK 2 79 7 -412.5 -498 . 5
A
CO
огч
Table 1. (Continued).
Acid DPE ДНГ (AH) AHf (A ) \G°
CF3S(NS02CF3) 2oh 266.3 -566.1 -665.5
ONOH 336.1 -13.3 -42 .9 330 . 5
CFjSOjNNOH 294 . 3 -182.2 -253.6
H2S04 324.0 -188.1 -229.8 302.2®
NCSOjH 314.1 -90.9 -142.6
CLS03H 303.6 -135.5 -197.6
HjSO, 324. 0 -188.1 -229.8 ? 0 2 .2 ®
h2so3=nso2cf3 292.3 -342.2 -415.7
h2so2 (=nso2cf3 ) 2 273 .2 -495.5 -588.0
HOCIOj 264 . 0 -26.4 -128.0
H0C102=NS02CF3 260.6 -216.9 -322 . 0
H0C10(=NS02CF3 ) 2 414.2 -565.4 -517.0
HOCIO (=NS03CF3) 2f 253.5 -405.2 -517.0
H0C1(=NS02CF3 ) 3 430.2 -777.3 -712 .9
HOC1 (=nso2cf3) 3f 252 .4 -599 . 8 -712 . 9
hono2 310.0 -38. 0 -93.3 317. Й"
hono(=nso2cf3) 282 . 3 -197.2 -280.6
H0N(=NS02CF3) 2 261.9 -353.7 -457.5
(CN)3COH 317 . 0 73.6 24 . 9
(CN)2C=C(CN)OH 294 .1 84 . 7 13 . 1
FSH 335 . 3 -40 .4 -70.7
CF3SH 320 . 0 -137.5 -183.2
(CF3)3CSH 306. 7 -446.0 -505.0
CF3COSH 314 . 8 -178.0 -228.9 312 . 5b
HC1 348.79 -20.5 -51.2 328 . 0a
HI 272 . I9 28.8 -64 . 6 309.3a
HBr 304.09 5 . 3 -56.2 318 . 2a
HF 408 . 39 -59 . 7 -17.1 371.4a
a from Ref.3; b from Ref. 4; c predicted in Ref.4; d from Ref.5;
* from Ref.24; f energies, corresponding to second minima on 
potential surface, discussed in text; 9 from Ref. 18
17
Table 2. Results of statistical analysis of calculated 
deprotonation enthalpies and experimental gas-phase acidities in 
terms of Eq. (2).
n STDV a b R2 a b
All acids 54 12.7 -85.5 1.23 0.919 14.6 8.7
Acids with 44 12.5 -91.4 1.24 0.761 15.2 9.3 
AG<340
Acids with 39 13.0 -97.2 1.24 0.691 15.8 9.6 
AG<330
Acids with 30 14.2 -102.4 1.26 0.531 17.1 10.7 
AG<320
Acids with 23 16.6 -109.5 1.27 0.301 18.9 16.4 
4G<310
Acids with 9 16.8 -266.4 1.88 0.514 22.3 8.9
AG<300
CF3 subst. 12 11.9 -110.0 1.31 0.948 11.3 5.9 
acids
CF3CO subst. 8  9.3 -104.1 1.31 0.997 3.6 2.0 
acids
CN subst. 9 9.7 -69.3 1.21 0.977 6.2 3.6
acids
CF3S02 subst. 5 29.6 -193.0 1.52 0.997 6.3 2.4 
methanes
CF3S02 subst. 4 9.7 -78.2 1.22 0.999 1.2 0.6 
ammonias
Table 3. Comparision of acidifying effect of CF3S02,
CF3S0(=NS02CF3) and CF3S (=Ns02CF3) 2 substituents on H20, NH3 and CH4.
Substituent XOH XNH2 XCH3
H 401.6 407.1 430.2
CF3S02 302.4 317.0 323.4
CF3S0(NS02CF3) 279.7 293.5 301.2
CF3S(NS02CF3 ) 2 266.3 280.8 284.7
18
Table 4. The effect of replacement of spa oxygen by =NS02CF3
group in various oxygen containing acids.
DPE DPE ADPE
(X=0) (X=NSOaCF3)
FSO (X) CH3 339.8 318.1 21.7
CFjSO (X) CH, 323.4 301.2 2 2 . 2
CF3eX (NSOaCF3) CH3 301.2 284.7 16.5
CH3NX 355.1 307.6 47.5
CHjCXCN 349.3 306.8 42.5
ONNHj 342.1 302.1 40.0
CFjSO (X) NHj 317.0 293.5 23.5
CF3SX (NS02CF3) 293.5 280.8 12.7
PhSO(X)NHj 340.6 312.2 28.4
PhSX (NSOjCFj) NH2 312.2 307.4 4.8
CF3CXOH 319.3 283.8 35.5
FSO (X) OH 318.4 289.5 28.9
FSX(NS02CF3)0H 289.5 269.2 20.3
CF3S0(X)OH 302.4 279.7 22.7
CFjSX ( NSOjCFj ) OH 279.7 266.3 13.4
XNOH 336.1 294 . 3 41.8
(HO)aSO(X) 324.0 292.3 31.7
(H0)2SX(NS02CF3) 292.3 273 .2 19.1
H0C102(X) 264.0 260.6 3.4
HOCIO(X) (NS02CF3) 260 .6 414 .2 -153.6
HOCIO(X) (NSOjCFj) 260.6 253 .5 7.1
H0C1X{NS02CF3)2* 414.2 430.2 -16.0
HOC1X (NSOjCFj) 2* 253.5 252.4 1 .1
HONO(X) 310.0 282.3 27.7
H0NX(NS02CF3) 282.3 261.9 20.4
* using energies, corresponding to second minima on potential 
surface, discussed in text
Table 5. Calculated and experimental geometries of some 
investigated acids (bond lenghts (R) in A, angles (A) in degrees).
Calc. Exp. Calc. Exp.
(CF3) 3CHa (CF3 )3C0Hb
R(C-H) 1.117 1 . 1 1 0 R(C-C) 1. 589 1. 566
R(C-C) 1.566 1. 537 R(C-F) 1. 345 1.335
R(F-C) 1. 347 1. 334 R(C-O) 1.391 1.414
A(C-C-C) 109 . 2 112 . 9 A(C-C-F) 113 . 0 1 1 0  . 6
A(C-C-F) 112 . 3 110 . 9 A(C-C-C) 108 . 4 110 .4
A(H-С С) 109 . 8 105 . 8 A(C-C-O) 112 . 3 108 . 5
H;>SCV HCLO,d
R(O-H) 0. 947 0 . 970 R(CL-O) 1 . 645 1. 635
R (S 0) 1  . 6 6 8 1 . 574 R (CL=0) 1.455 1 . 408
R(S=0 ) 1. 407 1. 422 A(0=CL=0) 1 0 1 . 6 1 1 2  . 8
A(H-O-S) 117 . 6 108.5 A(0=CL-0) 104 . 8 105 . 8
A(O-S-O) 97 . 9 101.3 FS02NH2e
A (0=S=0) 107 .4 123.3 R(N-S) 1.742 1  . 610
A(0-S=0) 107 . 3 108 . 6 R(S-F) 1.560 1. 560
A(H-0-S=0) 20 . 9 2 0 . 8 R(S=0) 1.425 1.412
A(H-O-S-O) -89 . 9 -90.9 R(N-H) 1 . 0 0 0 1 . 0 2 0
(CF3C0)2CH2f A(N-S-F) 1 0 0  . 0 99 . 0
R(HC-C) 1.362 1.407 A(0=S=0) 108 . 8 123 .4
R(C-C) 1. 552 1. 546 (FSG2) ,CHe
R(C-O) 1 . 280 1.259 R(C-S) 1. 874 1. 831
R(C-F) 1 . 349 1. 337 R(S-F) 1. 551 1. 558
A(OC-C-C) 111 . 7 115 . 2 R (S O) 1. 409 1. 416
А (НС' C- 0) 124 . 2 126 . 4 A(C-S-F) 1 0 0  . 8 97 . 4
A (НС C-C) 117.6 119 . 7 A(C-S-O) 1 1 1 . 0 109 . 6
A(C C-F) 112 . 5 1 1 0  . 6 A(S-C-S) 115 . 0 1 1 1 . 1
20
Table 5. (Continued).
Calc. Exp. Calc. Exp.
CFjSĈ OH5 CF3COOHh
R(S-C) 2 . 0 0 2 1.833 R (C- F) 1.348 1.325
R(F-C) 1.351 1. 332 R(C-C) 1.568 1. 546
R(S=0) 1.401 1.418 R(C=0) 1.208 1.192
R(S-O) 1.662 1. 558 R(C-O) 1.344 1.353
R(O-H) 0.949 0.960 R(O-H) 0.952 0.960
A(S-C-F) 113.7 110.3 A(C-C=0) 127.1 326.8
A(C-S-O) 96.8 102.3 A(C-C-O) 1 1 2 . 0 1 1 1 . 1
A(0-S=0) 107. 5 109.9 A(C-O-H) 148. 0 107.0
A(S-O-H) 118.1 115.0 A(C-C-F) 113 .1 109.5
A(F-C-C=0) 1.5 17.3
a Experimental geometry from Ref. 25
b Experimental geometry from Ref. 26
c Experimental geometry from Ref. 27
d Experimental geometry from Ref. 28
* Experimental geometry from Ref. 29
f Experimental geometry from Ref. 20
9 Experimental geometry from Ref. 30
h Experimental geometry from Ref. 31
21
Table 6. Selected geometrical parameters of neutrals and 
anions of the trifluorosulfonyl substituted methanes.
CP,SO,CH, (CF,SOj) jCHj (CFjSOj ) ,CH
Parameter Neutral Anion Neutral Anion Neutral Anion Bxp.
anion*
R (C-S) 1.769 1.538 1.812 1.620 1.872 1.722 1.69
1.73
R(S-CF) 2.012 2.123 2.010 2.053 2.020 2.040 1.84
1.90
R(C-F) 1.351 1.357 1.351 1.354 1.351 1.352 1.3C
1.34
R'S=0> 1.428 1.483 1.414 l.*52 1.411 1.436 1.43
1.44
R(C-H) 1.101 1.084 1.117 1.1J0 1.148
A(0=S-C) 112.0 116.9 111.3 118.2 112.6 116.5 109
110
A (01=S-C) 112.0 116.9 110.8 113.6 110.8 113.4 107
1 0 Q
A(F-C-S) 114.3 115.7 114.3 115.2 114.3 115.2 107
108
* from Ref. 25
Table 7. Selected geometrical parameters of neutrals and 
anions of the CF3S02N= substituted sulphuric acids.
H2SO« H3SO, ( =NSOjCF,) HjSO, ( =NSOaC F .) 2
Par Neutral Anion Neutral Anion Neutral Anion
R(O-H) 0.947 0.945 0.950 0.948 0.952 0 949
R (S-O) 1.668 1.718 1.660 1.691 1.661 1.682
R(S=0) 1.407 1.478 1.401 1.443 1.436
R (S=N) 1.585 1.675 1.567 1.630
R(S=N') 1.567 1.646
R(N-S) 1.681 1.627 1.694 1.657
R(N*- S ') 1.694 1.649
R(S'=0) 3 .415 1.417 1.410 1.440
R(S'=01) 1.415 1.417 1.414 1.434
R(S-C) ' 2.007 2.050 2.007 2.031
R(C-F) 1.351 1.354 1.351 1.354
A(H-O-S) 117.6 113 . 7 117.2 114.,6 116.2 115.2
A(O-S-O) 97.9 99.3 98.9
A(0=S=0) 107 . 4 115.6
A(0-S=0) 107.3 103. 7 109. 7 118._ 2 105.0
A(H-0-S=0) 20.9 60.5 31.9 65..2
A(N=S-0> 105.0 113..0 111.6 107.1
A(N'=S'-0) 105.6 100.5
A(N=S=0) 111.5 116..3 109.5 110. 8
A(N=S=01) 113 .8 110.3 115.3
A(N'=S'=0) 109.5 114.1
A(N'=S'=0') 110.3 114.5
A(N=S-C) 93.8 100,.0 97.6 101.8
A(N’=S-C) 97.4 97.0
TÜ 94. 56. 150. 6,52. 6,0.