J . Phys. Chem. 1986, 90, 5597-5604 contributes independently to first order.38) It would be interesting to apply the present model to other Pt”-PtIv systems and also to the spectra of the mixed-metal Pd”-PtIv systems recently reported by Clark and CroudZ2where (3’8) Schatz, P. N., unpublished calculation.
5597
the unsymmetrical case (W’ # 0) is applicable. ~.
Acknowledgment. This work was supported by the S.E.R.C. (K.P. and P.D.) and by the National Science Foundation (P.N.S. and K.Y.W.) under Grants CHE8400423 and INT-8510077. We acknowledge many useful discussions with Professor S . B. Piepho and Dr. M. Kurmoo.
Protonation Energies and Tautomerism of Azoles. Basis Set Effects 0. M6, J. L. G. de Paz, and M. Yiiiez* Departamento de Quimica Fhica y Quimica Cubntica, Facultad de Ciencias, C-XIV, Universidad Autbnoma de Madrid, Cantoblanco, 28049 Madrid, Spain (Received: March 10, 1986)
The structure, protonation energies, tautomerism, and vertical ionization potentials of several azoles are investigated by ab initio calculations using different basis sets ranging from minimal to split valence plus polarization. Minimal basis tends to overestimate all N-N and C-N lengths considerably. Though, in general, 3-21G geometries are close to 6-31G structures, the former basis does not always correct the deficienciesof minimal basis. In general, 6-31G structures are in good agreement with the experimental ones. Azoles with more than one basic nitrogen protonate preferentially on “imidazo1ic”-rather than on ’pyrazo1ic”-type nitrogens. Minimal basis significantly overestimates absolute protonation energies, but the deviations observed for relative protonation energies are not always of the same sign. Both 3-21G and 6-31G absolute protonation energies are almost equal and much smaller than those obtained at the minimal basis level. The inclusion of polarization functions in the basis (6-31G*//6-31G calculations) leads to a further decrease in absolute protonation energies which depends on the degree of anisotropy of the charge distribution of the center which undergoes protonation. The relative stabilities of the tautomers change with the basis. These changes are particularly important for triazolium and tetrazolium cations, as well as for pyrazole and imidazole. For 1,2,4-triazoIes, tetrazoles, and 1H-pentazole Koopman’s theorem predicts the wrong ionization.
1. Introduction
Five-membered heteroaromatic compounds containing only nitrogen as heteroatoms and which can be considered as pyrrole derivatives-by progressive substitution of X H groups by +N-have received considerable attention’ because they constitute one of the principal families of heterocycles and present a quite rich chemistry. During the past 10 years we devoted some effort to the theoretical study of the gas-phase basicity of organic compounds. Recently, we have focused our attention on this family of azoles. Very little is known on the gas-phase basicity of these compounds and our first contribution* intended to offer some systematic information mainly on their intrinsic basicities and preferred protonation sites, by means of a b initio calculations carried out at scaled I N D O fully optimized geometriesS2 Throughout that analysis it was put in evidence that the gas-phase basicity of most of these compounds is directly affected by tautomeric equilibria involving different tautomers of either the nonprotonated or the protonated forms. Tautomerism is a delicate problem to be treated from a theoretical point of view, mainly due to the limitations of the S C F calculations themselves. Even when one has decided to use an a b initio method, the choice of the basis functions employed to expand the molecular wave functions can be crucial. Usually this choice is a compromise between quality and economy and, quite often, for large systems one becomes forced to use a minimal basis set. Although minimal basis sets present well-known limitations, their use seems to be justified when one attempts to obtain relative magnitudes. Beneath this reasoning is implicit the assumption that, for a given family of compounds, the errors induced by the finite character of the basis are about the same for each member (1) See, for instance: Schofield, K.; Grimmet, M. R.; Keene, B. R. T. The Azoles; Cambridge University: Cambridge, U.K., 1976; Comprehensive Heterocyclic Chemistry; Katritzky, A. R., Rees, C. W., Eds.; Pergamon: Oxford, 1984. (2) Catalan, J.; de Paz, J. L. G.; YBiiez, M.; Elguero, J. Chem. Sci. 1984, 24, 84.
of the family and therefore relative values will not change when the basis set is enlarged. This can be indeed the case (on qualitative grounds) when the calculated magnitudes (energies, proton affinities, etc) are well separated, but caution must be taken when we deal with small differences. It would be interesting, therefore, to know the limitations of small-sized basis sets to study relative protonation energies when, as for the compounds indicated above, one or more tautomeric equilibria are involved in the protonation process. In this paper we shall study the effects of systematically enlarging the basis set from a minimal to a polarized split-valence quality on the gas-phase basicities and tautomer stabilities of a representative set of azoles: pyrrole (l),imidazole (2), pyrazole (3), 4H-1,2,4-triazole (4), lH-1,2,4-triazole (5), 2H-tetrazole (6), 1H-tetrazole (7), lH-pentazole (S), and their corresponding protonated species (9-18). The particular problem of tautomer stability is interesting per se. Quite often, experimental results are contradictory as to which tautomer is the most stable one. Moreover, not always, relative gas-phase stabilities coincide with those observed in solution. Tetrazole is a suitable example: different microwave studies3t4 concluded that both tautomeric forms (6 and 7) are present in on mass the gas phase, while a more recent a n a l y ~ i s based ,~ spectrometric results, showed that only the 2 H tautomer is present in the gas phase. Furthermore, the 1 H tautomer seems to be dominant in dioxane, benzene, and D M F / H 2 0 s o l ~ t i o n s . ~ ~ ~ Regarding this particular problem, it should be mentioned that, when our work was under way, a theoretical study on the tautomerism of tetrazole was published.* Consequently, part of the (3) Bolton, K.; Brown, R. D.; Burder, F. R.; Mishra, A. J. Chem. SOC., Chem. Commun. 1971, 873. (4) Krugh, W. D.; Gold, L. P. J. Mol. Spectrosc. 1974, 49, 423. ( 5 ) Razynska, A.; Tempczyk, A.; Maslinski, E.; Szafranek, J.; Grzonka, Z . J . Chem. SOC.,Perkin Trans. 2 1983, 319. (6) Kaufman, M. H.; Ersenberg, F. M.; McEwan, W. S. J . Am. Chem. SOC.1956, 78, 4197. (7) Moore, D. G. W.; Whittaker, A. G. J. Am. Chem. SOC.1960,82, 5007.
0022-3654/86/2090-5597%01.50/0 0 1986 American Chemical Societv
5598 The Journal of Physical Chemistry, Vol. 90, No. 22, 1986
1
2
M6 et al.
6
5
4
3
li 7
9
10
11
12
13
15
16
17
18
discussion to be presented here, relative to the preferred tautomer of tetrazole in the gas phase, has been already offered by Mazurek and Osmam8 However, since we are interested also in the gasphase basicity of this compound, a similar analysis of the stability of the four possible protonated forms (13, 14, 15, and 16)-not carried out in ref 8-must be performed. Accordingly, and for the sake of clarity, we have retained this compound in our discussion. Moreover, while the experimental evidence on tautomeric equilibria between neutral forms is relatively abundant, there is a complete lack of experimental information regarding protonated forms.
2. Computational Details The geometries of the azoles (1-8) and their corresponding protonated forms (9-18) were fully optimized at the STO-3G, 3-21G, and 6-3 1G levels by using a suitable gradient optimization proced~re.~ A geometry optimization at the 6-31G* level is completely beyond our computational capacity, but, in order to have an estimation of the effects of including polarization functions in the basis set, single-point calculations, using a 6-31G* basis at 6-31G optimized geometries (to be referred from now on as 6-31G*/ /6-31G), were performed for all species included in this study. Very frequently, tautomer stability is investigated by means of photoelectron spectroscopy; l o therefore, we have considered pertinent to present, in following sections, the corresponding orbital energies for the compounds studied, obtained at the highest level of accuracy (6-31G*//6-31G). However, since, as has been pointed out by Mazurek and Osman: Koopman’s theorem predicts the wrong ionization, at least for tetrazoles; we have also evaluated the two radical cations (u and T ) which can be obtained upon ionization of the corresponding neutral azoles. The corresponding RHF calculations for these open-shell systems were carried out by using a direct minimization technique involving a sequence of univariate searches.l’ For each case, we have employed the (8) Mazurek, A. P.; Osman, R. J. Phys. Chem. 1985, 89, 460. (9) Pulay, P. Applications of Electronic Structure Theory; Schaeffer 111, H. F., Ed.; Plenum: New York, 1977; p 153. Murthaugh, B. A.; Sargent, R. W. H. Comput. J . 1972,131, 185. Schegel, H. B. J. Comput. Chem. 1982, 3, 214. (IO) Palmer, M. H.; Simpson, I.; Wheeler, J. R. 2. Naturforsch. 1981, 36a, 1246.
optimized geometry of the corresponding neutral molecule. Therefore, the energy differences between the radical cations and the neutral systems can be taken as a measure of the corresponding vertical ionization potentials.
3. Geometries The optimized geometries obtained for the different basis sets employed have been summarized in Table I. The corresponding experimental parameters are also included for those cases where the microwave s t r ~ c t u r e s ~have ~ * ~been - ~ ~ resolved. Some particular points should be singled out for comment. In general, the STO-3G minimal basis set tends to noticeably overestimate the N-N and C-N bond lengths when compared to the 6-3 1G values. Moreover, these differences are not constant along this family of compounds. For instance, while the Nl-N2 bond length in pyrazole (3) is overestimated by 0.033 A, the same bond length is overestimated by 0.025 A in lH-1,2,4-triazole (5) and by 0.056 A in 2H-tetrazole (6). This results, in general, in a better agreement between the 6-31G optimized structures and the experimental ones. Going back to the Nl-N2 bond in pyrazole, for example, while its STO-3G optimized length is 1.384 A, that obtained at the 6-31G level is 1.35 1 A, in much better agreement with the microwave resultI4 (1.349 A). It should be noticed, however, the exceptional disagreement observed for the particular case of 1H- 1,2,4-triazole (5). The STO-3G optimized value for the Nl-N2 bond of this compound (1.388 A) is in much better agreement with the microwave assignment3 (which yields a surprisingly large value (1.38 l A)) than the 6-31G result (1.363 A). However, this latter value is in remarkably good accord with that reported by Jeffrey et al.,I5 obtained in a neutron diffraction experiment. (1 1) Program Gaussian-80. Binkley, J. S.;Witheside, R. A,; Krishna, R.; Seeger, R.; De Frees,D. J.; Schlegel, H. B.; Topiol, S.; Kahn, L. R.; Pople, J. A. Department of Chemistry, Carnegie Mellon University. IBM version by: Nuder, E. M.; Kahn, L. R. (12) Nygaard, L.; Nielsen, J. F.; Kircbheiner, J.; Maltesen, G.; Rastrup Andersen, J.; Sarensen, G. 0. J. Mol. Struct. 1969, 4, 49. (13) Christen, D.; Griffiths, J. H.; Sheridan, J. Z . Naturforsch. 1982,37a, 1378. (14) Nygaard, L.; Christen, D.; Nielsen, J. T.; Pedersen, E. J.; Snerling, 0.. Vestergaard, E.; Ssrensen, G. 0.J. Mol. Struct. 1974, 22, 401. (15) Jeffrey, G. A.; Ruble, J. R.; Yates, J. H. Acra Crystallogr., Sect. B 1983,839, 388.
Protonation Energies and Tautomerism of Azoles The geometrical effects outlined above, reached their outermost consequences for 1H-pentazole (8), which is predicted to be a much “larger” cycle at the STO-3G level than at the 6-31G one, employed. since all ring bonds are noticeably larger if the former basis is C=C bond lengths, on the contrary, are underestimated at the STO-3G level (see, for instance, C4-C5 bond lengths for compounds 1, 2, and 3). This effect of the minimal basis set is quantitatively less important than that discussed for C-N and N-N bonds. Again, the 6-31G results are closer to the experimental values. It should also be noticed that the effects of enlarging the basis set on bond lengths are not regular. In some cases, the N-N and C-N bond lengths change very little in going from a STO-3G to a 3-21G basis set, the shortening of the bond being significant if the basis is further enlarged from 3-21G to 6-31G level (see, for example, the evolution of Nl-N2 bond lengths of compounds 3 and 7). In contrast, for compounds 4,6,and 8, the Nl-N2 bond shortens significantly in going from the STO-3G to 3-21G and from 3-21G to 6-31G levels. As a consequence, in these latter cases, the 3-21G values are almost an average of those obtained at the STO-3G and 6-31G levels, respectively. Furthermore, for compounds 5 and 8, Nl-N2 and N3-N4 3-21G bond lengths are even longer than those obtained at the STO-3G level, in remarkable disagreement with 6-31G results. Similar findings are observed when dealing with protonated species (see Table I). We can conclude, therefore, that the more economical 3-21G basis set, which has been specially designed16 for geometry and force-constant calculations, does not yield structures systematically close to those obtained at the 6-31G level. As we shall show in following sections there are some other significant discrepancies between both basis sets when we compare other molecular magnitudes. Basis set effects on endocyclic bond angles are also important. For instance, the endocyclic angle centered on N1 (the substituted ring nitrogen) is underestimated, at the STO-3G level, by about l o for compound 1, but it is overestimated by about 1.4O for compounds 2 and 3. The trend seems to be more regular when considering C N C endocyclic angles centered on nonsubstituted nitrogens or C N N angles, which are systematically underestimated, at the STO-3G level, by about 2.0’ or more. Similar effects, although smaller, are observed for protonated species. 4. Gas-Phase Basicities
The protonation energies of the azoles under investigation, obtained as the energy difference between the protonated and the unprotonated forms, are presented in Table 11. We have ratified our previous assignation2 of the most basic site of those azoles which present more than one basic center. In general, 1,2,4-triazoIes, tetrazoles, and 1H-pentazole protonate on “imidazolic” nitrogens rather than on “pyrazolic” ones. This qualitative result is independent of the size of the basis set used. The STO-3G basis significantly overestimates the corresponding absolute protonation energies, a fact which had been already pointed out by Del B e r ~ e ’ ~for , ’ ~a wide set of imino- and pyridine-type bases. It is interesting to note, however, that there is a remarkably good agreement between the values obtained at the 3-21G and 6-31G levels. The more economical 3-21G basis leads to protonation energies about 30 kcal/mol lower than those obtained at the STO-3G level. An almost identical decrease is attained when the 6-31G basis set is used. These changes are quantitatively similar when we disregard the compound or the basic center considered. The inclusion of polarization functions on the heavy atoms leads to a further decrease of absolute protonation energies. However, this effect does depend on the type of center which undergoes (16) Gordon, M. S.; Binkley, J. S.; Pople, J. A.; Pietro, W. J.; Hehre, W. J. J . Am. Chem. SOC.1982, 104, 2797. (17) Del Bene, J. E. J . Am. Chem. SOC.1977, 99, 3617. (18) Del Bene, J. E. J . Compuf.Chem. 1984, 5 , 381.
The Journal of Physical Chemistry, Vol. 90, No. 22, 1986 5599 SCHEME I
(--I
7i0 // I
H
5 protonation. In general, polarization effects seem to be stronger the lower the local symmetry at the center considered or the greater the difference between its electronegativity and that of the atoms directly bonded to it. Accordingly, polarization effects are more significant for (a) nitrogen atoms bonded to one carbon and to another nitrogen atom (as in pyrazole, 4H-1,2,4-triazole or N2 in lH-l,2,4-triazole) and (b) basic nitrogens bonded to two carbon atoms (as in imidazole or N 4 in lH-l,2,4-triazole). The results for N2 and N3 of 1H-tetrazole and for Iff-pentazole show little change due to the addition of polarization functions. This can perhaps be attributed to a much smaller anisotropy and a greater uniformity of the charge distribution within the basic nitrogen, which render polarization effects rather small for these particular cases. The most significant basis set effects appear when we consider relative protonation energies. As for absolute values, the minimal basis set usually overestimates them. For instance, whereas at the STO-3G leve! imidazole is predicted to be 18.4 kcal/mol more basic than pyrazole in the gas phase, this difference decreases to 13.1 kcal/mol when computed at the 6-31G*//6-31G level. Similarly, 1H-tetrazole is predicted to have, at the STO-3G level, a gas-phase basicity 6.9 kcal/mol higher than that of 2H-tetrazole, while this gap is only 3.8 kcal/mol at the 6-31G*//6-31G level. Nevertheless, the opposite situation is found for 1,2,4-triazoles: whereas the STO-3G basis predicts 4H- 1,2,4-triazole (4) to be 3.9 kcal/mol more basic than the 1 H tautomer, this difference increases up to 6.7 kcal/mol at the 6-31G*//6-31G level. As we shall discuss later, this is a direct consequence of the different description of the tautomers stability at both levels of accuracy. Moreover, lH-1,2,4-triazole ( 5 ) is predicted to be more basic than pyrazole (3) (by about 1.8 kcal/mol) at the minimal basis set level. The situation is reversed when a 6-31G basis set is used, and pyrazole appears to be 1.6 kcal/mol more basic than lH-1,2,4triazole. The inclusion of polarization functions in the basis set reinforces this tendency and this gap becomes 2.0 kcal/mol at the 6-31G*//6-31G level. Finally, as we have indicated at the beginning of this section, 1H- l ,2,4-triazole should protonate, undoubtedly, on the “imidazolic” nitrogen (N4). Consequently, both tautomers of 1,2,4-triazole (4 and 5 ) lead to a common cation upon protonation. Therefore, the difference between their protonation energies must be equal to the energy difference between both unprotonated tautomers (see Scheme I). Since, in this particular case (as we shall illustrate in the next section) tautomer stability is strongly basis set dependent, a measurement of the gas-phase proton affinity of these compounds would be particularly interesting. Unfortunately this is not the case for 1H- and 2H-tetrazoles, which, for the same reason (preferred protonation at the “imidazolic” nitrogen) do not yield the same cationic form upon protonation.
5. Tautomer Stabilities As indicated in the Introduction, the particular case of tetrazole has been recently discussed in the literature.8 We shall point out
5600 The Journal of Physical Chemistry, Vol. 90, No. 22, 1986
Mi5 et al.
? ? ?
? ? Y
I l l
235
R d d 4 4 4
? ? ? m
I l l e
.
...
.
r - r - m
W W W N N N 4 4 4
N
? ? ? W
N
W
. . . W
W N H
N N N 4 4 4
W N
A
4
0 4
0 4
? ? ? S
r-r-r-r0
0
0
0
4 4 4 4
w m m m
0
4
0
4
0
4
0
4
N
4
.... 4
4
O
I l l
4
0 4
0 4
0 4
o
4 d
4
???'I
o
a
4 0 d 4
m
0
4
0
4
0
. . . .
m o o r -
0
4
4
4
4
. . . .
m 0
4
4
s
0
4
m
0
4
s
0
4
? ? ? ' I ? ? 4?
w m m m 0 4
0 4
r
-
0 4
m
I - W W I -
0 4
~
9 9 9 9 4
4
4
4
0 4
0 4
f - w w r 4
4
4
4
m m m m r - w w r -
4
4
4
4
4
o r - m f -
m w w r -
9 9 9 9 4
4
4
4
4
m m s m
m w w r -
9 9 9 9 9 9 9 9 4
4
4
4
4 s m w ~ m w c t o o o
3 3 3
o
m
o
m
ct44
ctctctrc
0
0
0
m 4 4 m m w w r -
4
4
4
4
4
w w I I I I m 9 9 9 4 4 4
m m m m ~m m w
d m m m "W
P i 0 0 0
m r - m o
4
0
0
4
4
4 4 4 4
I l l
4
? ? ? ?
4
4 4 4 4
I I
m f - m o m f - r - r -
s m m s w w w w
? ? ? ? 4
4
4
4
4 4 4 4
. . .
I I
4 4 4
I I
O m o N W m
O
4 0 0 0
4 0 0
4 0 0
? ? ?
4 0 0
? ? ?
I I
? ? ?
I 1
? ? ?
.
I I
I I
m m w
m w m
. . .
4 4 4 4
w m f - 0 )
4
4
4
4
N
O
O
N
4
4
4
4
? ? ? ?
? ? ?
.
4 4 4
o m N m O
N
f - m m
m w m
m
W
4 f - f -
W
4 4 4
m w 4 r l o m
m
m o m
? ? ?
? ? ? ?
? ? ?
4
4
4
m m d m m w m
N
o f - w
s m f -
w f - w
4
0"
4 ? ?
? ? ? ?
4
m s m N m w
? ? ?
O
4 4 4 4
9 9 9
m s m ( Y m m
? ? ? ?
S ? ? ?
4 0 0 4 4
m w w
s m m m N m w m
o f - f - m
4 4 4 4
m r v s
I I
w m 4 s
w o m w 4
m m 0 m 0 4 4 0 4
4 4 0
4 4 4 4
4
0 4
?'I?
4 4 4 4 4
0 4
m m w
4
s o w w "
0 4
I I I
4
m m m m 4
4
0 4
I I I I
4
f - m r - s s m m w 4
4 0
0 4
4 4 4
. . . .
0 4
I l l
m l - w m m m
? ? ? ?
W
? ? ? ?
w m r -
m r - r - r -
0 4
4
I I I I 9 9 9 4 4 4
0
0 4
I l l 4 m m m m m
4 s m r m w w w
? 9 9 ? 9 9 9 9 ? ? ? P i 0 0 0
0 4
W W W I -
N
4 0
? ? S
9 9 9 9 9 9 9
N
4 0
mr-a3
D D W W
m
W
m w w
0 4
. . . .
4 0
4
. . . m. m* m .
4 0
? ? ?
m m w
4 0
m m m
.
0 4
W 0
N o r -
0 4
4
I I I I
0 4
.
I l l
9 9 9 9
4
r - m w w r - w w r -
d m w s m w w m
9 3 9 9 3 9 9 9
o r - m r w w w r -
9 9 9 9
0 4
? ? 4
w
0 4
4 4
w w m
0 4
wm m m m
I
4 4
4 ? ?
m r - r - w 0 4
m m m o o m
8 g 8 4 4 4
Y ? ? ? ? ' ?I ? m m w m m m w w
4
...
4 4 4 4
? ? ?
0 4
4
\ o r - W 0 4 0 4 0 4
0 4 0 0
I l l
0 4
0 4
4
0
r0 - 0 m m0 r 0 -
I l l
4
0
o w - o 0
I l l
m a m 0 0 0
0 4
? ?1? N o o w
4 m m o 4 0 0 4 4 4 4 w 0
I I
4
. . . . . . . .
0 4
I l l
b u r -
W
m m m m
r-r-r-r-
I I
?I?? ? ? ?
W F W W 0 0 0 0 4
I l l
A d d N N N
W N
? ? ? ? ? ? ?' I
r - m m r 0 4
u m m
?'I? o m m
m
m m m
0 4
?'I?
3 3 a
w
33:
1 1 1
I l l
N
I l l
m
N 4 4 3 W
N
r
N r J N 4 4 4
? ? ?
4
4
4
4
m w m
? ? ?
4 4 4
m N o m
4 4 0
m i - 4
o m m S ? ? 4
4
4
The Journal of Physical Chemistry, Vol. 90, No. 22, 1986 5601
Protonation Energies and Tautomerism of Azoles
4 ?
4 9 9
N
N N N
r l m 4
N
4
m w w 4
9 1 I-*
4
I l l
4
I l l I l l
N N 4 4
m m
3 3 ? 9 ?
m
3 3 3
o m 4
4
N
4
4
0
I l l W
411
? ?
I'I
Y ? ?
I l l
I l l
I l l
I l l
I l l
'9?
I Y ' I
cy.??
23
3 3 3
3 3 3
4
'I?
?
0 4
4 4 4
m m
4 0 0
0 4
4
? ?
4
4
w w w
0
4
0
4
0
4
4Fl
0 0 0 4 - 4 4
wrw w
mON^ w w
m w
o m m
0 4
F r - F 0 4
0 4
0 4
w w w 0
0
0
4 4 4
m e m w m w
9 9 3 9 9 9 A A A F l 4 4
W r - F 0 0 0 4 4 4
0 4 0 4 4 4 4
4
4
m m e 0 0 0
? ? ?
?'9?
? 4 ?
4
4 0 4
4 0 0
w e e 4
4
4 4 4
4
4
4
4
4
4
m w F m w w
O
w
o
o
r-er-
w
m
e
F
0
Lncvw
m e m m w w
o w m w o m
I l l
.
0 4
4
Y ? ?
m 0 4
W 0 4
W 0 4
e
0 4
4
4
...
m h l m
m m 4 w
o
3 3 3 4 4 4
4
o
I l l
I I I
I l l
I l l
I I I
9 4 9 4 3 3 9 9 9 9 9 I l l 4 4 4 4 4 4 4 " e
.
0 4
4
o m 0 1
o m 0
w w rw-
m o m
4
m m m 0 0 0
4 ? ?
? ? 4
4
6 6 S 8 8 6 4 4 4 4 4 4
w w m o m m w w I l l m9 9 ? ? 9 9 9 9 ? 4 4 0 4 4 4 - 4 4 4
4
m m e 0 0 0
5 4 ' 1 ? ? ?
I I I
w w
4
4
0
4
4
? ? ?
4'9'1 ? ? ?
4
4
4901
? ?
? ?
4
4 0 0 4 4 4
0 4
0
0
4
? ? 4
m m F
?? ? ?I ' 'I1 4 5 9 4 ' 9
m m
4 4 4
4
0 0 F l 4
4
?'I? e m m A d d N N N N N N 0"
? ?
4
N N 4 4 3 I l l
? 4 ?
94'9 'I??
4
Y ? ?
m m I l l m 333
4 0 0
0 0 0 - 4 4 4 4 4 4
0
I l l
0 4
0
0 4
0
I l l
??'9
0
'I?
m w w
I l l
Q
0
cam
cnm
I l l
? S 4
4 4 4
4 4
m o mI ?
4
m c o w
w m 0 0
0 4
m w e
4"
4
W
I l l
m a 0
mvl I l l c9n 9 9 4 4 4
I l l
- 0 4 - 4 0
...
0
0
0
4 4
? ? 9 301 4 9 4 9 4 3 ? 4 4 0 4 4 0
e l m o m
w m w m w w
"r-
4 0
Fit44
4
hlln
h l m w
e l - m
r-wr-
? ?
? ? ?
? ? ?
3 94: 9 9 9 9 9 9 9 9 9 9 9 9 4 4 4 4 4 0 4 4 4 4 4 d
? ?
? ? o
m
- 4 0
3 9 9 m
o
m
4-40
m o m
? ? ? 4
I l l
I l l
I l l
0
w o m 4
4
0
m c y e
- 4 0 I l l e 9 9 3 I I I 4 4 4
m o m
m r - 0 w o o
w
o m 4
"4
o
o
n
m o o d o c n m
m m w e 4 4
c n w w
m m w m o m
4 - 4
- 4 - 4 4
4
4
4
m m m
? ?
? ? ?
4 ? ?
lnr-
4
4
? ?
4
4
4
4
In*
d a m F l o w
w o o
o m m
? ? ?
- 4 - 4 - 4
- 4 - 4 - 4
4 - 4 - 4
- 4 - 4 - 4
? ? ?
m m m m
c n w m
m l n h l
? ? ?
1 ? ?
4
4 - 4 4
? ? 4
m
o
o
-
N
I n N F V )
- 4 m 4 m m m
- 4 4
4 - 4 4
- 4 4 4
? ?
3 3 " I
I
m w
? ? ?
4 4 ?
? ? ?
r - w w
l z w m
a w l w e 4
" O d
- 4 - 4 . 4
4 - 4 4
-4-4-45
4
4
4
4
4
4
4
? ? ?
o
m
4 ? ?
m
m w o
z. z. s.
O
m o m m a r -
o m m w o c n
. . .
4
4 1 - m m w w m m m
4 - 4
e 4 0
m m m
4
. . .
- 0 4
e "
4
? ?
- 4 0
4
4 4
cnco
4
4
? ? ?
" e
w m e
. ; .
cncn
? ? ?
4 4 4
4
d m m
4 4 - 4
4
4
F l o w
4 4 ?
4
4
ez:
~
5602
The Journal of Physical Chemistry, Vol. 90, No. 22, 1986 SCHEME I1
TABLE 11: Absolute Protonation Energies (kcal/mol)
azole
protonated‘ 6-31Ga// center STO-3G 3-21G 6-31G 6-31G
imidazole (2) pyrazole (3) 4H-l,2,4-triaiole (4) IH-1,2,4-triazole (5)
N3 N2 N3-N4 N2 N4*
2H-tetrazole (6)
N2
IH-tetrazole (7) IH-pentazole (8)
N3* N5 N2 N3 N4* N2 N3*
283.4 265.0 270.7 249.1 266.8 222.3 244.2 225.3 225.7 244.6 251.1 200.3 223.4
248.9 233.4 237.9 219.3 234.1 193.0 213.1 196.1 195.1 212.1 218.7 170.5 191.8
247.0 232.6 236.6 217.3 231.0 192.2 211.9 194.0 194.8 212.7 217.0 170.2 192.0
240.1 227.0 23 1.8 214.1 225.1 190.4 209.6 192.1 193.7 211.3 213.4 170.9 191.6
The asterisk indicates the most basic position.
only that the relative stability of 2H-tetrazole with respect to the 1 H tautomer evaluated at the 6-31G*//6-31G level (see Table 111) is identical with the one reporteds from 6-31G**//6-31G calculations. This seems to indicate that, for these molecules, tautomer stability is not specially sensitive to the inclusion of polarization functions on the hydrogen atoms. 1H- 1,2,4-Triazole(5) is predicted to be the most stable tautomer in the gas phase at all levels of accuracy, although the larger basis predicts an energy gap between both tautomers almost twice that obtained at the minimal basis set level (see Table 111). Basis set effects are particularly important for triazolium ions, where the energy difference between both tautomers (11 and 12) decreases from 17.6 kcal/mol (STO-3G result) to 1 I .O kcal/mol (6-31G*//6-31G value). More striking is the behavior of tetrazolium cations, where the relative stability of the most stable tautomer (14) is strongly basis set dependent and varies from 28.4 to 21.4 kcal/mol, while that of forms 13 and 15 are very little affected by enlarging the basis set. Something similar can be said of pentazolium ions. In summary, one may conclude that the variations discussed in the previous section for relative protonation energies arise basically from a quite different description of the relative stability of the cationic forms depending on the character of the basis set used. This is an important conclusion, since it has been shown,I9 for a great variety of organic bases, that substituent effects on gas-phase proton affinities come primarily from interactions in the charged forms. The relative stability of the pair pyrazole-imidazole also deserves some attention. Imidazole is predicted to be the most stable isomer at all levels of accuracy considered here, but its relative stability is underestimated by a factor of 2.0 at the STO-3G level (see Table 111). However, in contrast with our findings for triazolium and some tetrazolium ions, the relative stabilities of pyrazolium and imidazolium cations do not change significantly when the basis set is enlarged. Therefore, in this particular case, the variations observed in the relative basicities of these two compounds, upon enlarging the basis set, are a consequence of a different description of the neutral species, namely at the minimal basis level. Another problem is the tautomer stability in solution, where solute-solvent interactions can be crucial. These interactions should depend strongly on the polarity of the molecule, which changes appreciably from one tautomeric form to another (see Table IV). It can be seen, for instance, that the less stable tautomer of tetrazole in the gas phase presents a dipole moment more than twice that of the most stable form. Since according to the theoretical estimations, the energy gap between both tautomers is quite small, it is reasonable to expect the former to be the most (19) Taagepera, M.;Summerhays, K. D.; Hehre, W. J.; Topsom, R. D.; Pross, A.: Radom, L.; Taft, R. W. J . Org. Chem. 1981, 46, 891. Pross, A,; Radom, L.; Taft, R. W. J . Org. Chem. 1980, 45, 818. Reynolds, W. F.; Modro, T. A.: Mezey, P. G . ;Skorupowa, E.: Maron. A. Can. J . Chem. 1980. 58, 412.
M6 et al.
(--J I
H ..
/t \N I
H 15
stable species in solution, in agreement with the experimental e~idence.~,’ Something similar is found for 1,2,4-triazoles. The less stable tautomer (4) in the gas phase has a dipole moment twice that of the most stable one (5). However, in this case, the energy gap between both forms is larger than that found for tetrazoles. Hence, very likely, solutesolvent interactions might not be able to invert the stability pattern in solution. It is also evident, from Table IV, that there is a fairly good agreement between our calculated dipole moment and the experimental ones3,4,12,13,20 for those compounds whose dipole moment has been measured in the gas phase. One might expect, therefore, our values for 4H- 1,2,4-triazole and 1H-pentazole to be a good estimation of the corresponding (unknown) experimental ones. 6. Protonation Energies vs. N1, Orbital Energies
Several theoretical models have been proposed to predict gas-phase protonation energies. Among them, linear relationships between gas-phase proton affinities and the 1s orbital energy of the protonation center have been a ~ p l i e d ~ l -with ~ ’ success to a wide set of organic bases. It has been also pointed outz4that both protonation energies and 1s orbital energies are very sensitive to details of local bonding at the basic center. These details change considerably from one compound to another in the family of azoles we are considering here. As a consequence there does not exist a good linear relationship between both magnitudes, but a very rough correlation. Nevertheless, if one considers different active centers of a given compound one might reasonably expect their 1s orbital energies to reflect their intrinsic basicities, provided this constancy of hybridization is fulfilled. That is the case for N2, X 3 of 6 and N2, N 4 of 7. The endocyclic angles centered on these four positions are about equal ( N 106.4’), a fact which can be taken as an indication of an almost equal hybridization at those centers. Accordingly, their intrinsic basicities are linearly correlated (see Table V) to their N,, orbital energies. A similar relationship can be obtained when the charge density of the acidic hydrogen in the corresponding protonated forms (qH+in Table V ) is used as a measure of the intrinsic basicity of a given center.** (20) Kirschhoff, W. H. J . Am. Chem. Sor. 1967, 89, 1312. (21) Martin, R. L.; Shirley, D.A. J . Am. Chem. SOC.1974, 96, 5299. (22) Davis, D.; Rabalais, W. J . Am. Chem. SOC.1974, 96, 5303. (23) Mills, B. E.; Martin, R. L.; Shirley, D. A . J . Am. Chem. SOC.1976. 98, 2380. (24) Catalin, J.; Yiiiez, M. J . Chem. Soc., Perkin Trans. 2 1979, 1627. (25) Catalin, J.; Md, 0.;Ptrez, P.; Yiiiez, M. J . Am. Chem. SOC.1979, 101, 6520. (26) Brown, R. S.; Tse, A. Can. J. Chem. 1980, 58, 694. (27) Lee, T. H.; Jolly, W. L.; Bakke, A. A,; Weiss, R.; Verkade, J. G . J . Am. Chem. SOC.1980, 102, 2631. (28) Del Bene, J. E. J . Am. Chem. SOC.1978, 100, 1673. Hehre, W. J.; Taagepera, M.;Taft, R. W.; Topsom, R. D. J . Am. Chem. SOC.1981, 103, 1344. Gribov, L. A.; Sawin, S. B.; Reichstat, M. M.; Orlov, M. Yu. J . Mol. Sirucr. 1982, 88, 171.
The Journal of Physical Chemistry, Vol. 90, No. 22, 1986 5603
Protonation Energies and Tautomerism of Azoles
TABLE III: Total Energies (ETin au) of Different Tautomers and Relative Stabilities" (AI3 in kcal/mol) STO-3G
3-21G
6-31G
tautomerb
ET
AE
ET
AE
2 3 4 5 6 7 11 12 13
-221.98199 -221.97726 -237.73364 -237.73989 -253.47273 -253.47207 -238.16502 -238.13690 -253.86194 -253.87216 -253.83172 -253.82695 -269.52794 -269.56460
6.7.
-223.5491 1 -223.52552 -239.42198 -239.42802 -255.2671 8 -255.26875 -239.80104 -239.77746 -25 5.60663 -255.61725 -255.57963 -255.57477 -271.38094 -271.41487
14.8*
14 15 16 17 18
3.9* 0.41' 17.6* 22.0 28.4* 3.0 23.0'
3.8* 1.o* 14.8* 20.1 26.7* 3.0 21.3*
ET -224.70975 -224.69051 -240.66 100 -240.66962 -256.59256 -256.59124 -241.03769 -241.01574 -256.93026 -256.93112 -256.90161 -256.89880 -272.78561 -272.82031
6-31G*//6-31G
AE
ET
AE
12.1*
-224.81316 -224.79244 -240.79117 -240.80 192 -256.15403 -256.75134 -241.16052 -241.14300 -257.08800 -257.09149 -257.06009 -257.05741 -272.98 182 -273.01478
13.0'
5.4* 0.82* 13.8* 19.7 24.0* 1.8 21.7.
6.1* 1.7* 11.0* 19.2 21.4* 1.7 20.7*
"The asterisk indicates the most stable tautomer. We include results for imidazole and pyrazole, although they are not real tautomers. TABLE I V Calculated (6-316*//6-316) Dipole Moments in Debyes
compd
P'
1.85 3.84 2.42 5.99 2.90 2.23 5.63 4.10
1 2 3
4 5 6
7 8
(1 .74)b (3.67)c (2.21)" (2.72)c (2.19)' (5.30)'
'Experimental values are given within parentheses. Reference 12. cReference 13. "Reference 20. CReference3. JReference 4. TABLE V N1,Orbital Energies (E,,) and Charge Density at the Proton in the Acidic Form of Some Azoles (6-316*//6-316 Level)
azole
center
E I S au ,
4H-1,2,4-triazole (4) lH-1,2,4-triazole (5)
N3-N4 N2 N4 N2 N3 N5 N2 N3 N4
-15.58126 -15.60214 -15.55600 -1 5.67997 -15.61729 -15.63941 -15.67067 -15.64992 -15.60356
2H-tetrazole (6) 1H-tetrazole (7)
qH+ 0.5124 0.5157 0.5203 0.4865 0.4975 0.4975 0.4886 0.4867 0.4992
E,* kcal/mol 231.8 214.1 225.1 190.4 209.6 192.1 193.7 211.3 213.4
These correlations are not followed by N 5 of 6 and N 3 of 7 because the hybridization at these nitrogens is different from that exhibited by the remaining basic centers, as revealed by the values of the endocyclic angles centered on these two positions (1 10So and 102.4', respectively). Moreover, the intrinsic basicity of N 5 of 6, is surprisingly low while that of N3 of 7 is surprisingly high. The explanation of this finding can be as follows: 2H-tetrazole (6) yields, upon N5 protonation, the cationic form 15. This cation can be also obtained by protonation of 1H-tetrazole (7)on its less basic position (N2). Consequently, the difference between the protonation energies associated to both processes must be equal to the relative stability of both neutral tautomers (see Scheme 11). Since 2H-tetrazole is only 1.7 kcal/mol more stable than 1H-tetrazole, the intrinsic basicity of N 5 of the former must be 1.7 kcal/mol smaller than that of N 2 of the latter and, therefore, much smaller than what should be expected. A similar reasoning would explain why the intrinsic basicity of N 3 of 1H-tetrazole is surprisingly high (1.6 kcal/mol greater than that of the most basic position (N3) of 2H-tetrazole).
7. Vertical Ionization Potentials As indicated in section 2, photoelectron spectra are frequently used to study the relative abundance of different tautomeric forms'0 of these kinds of compounds. Quite often, also, calculated molecular orbital energies help to carry out the assignation of the bands of the corresponding spectra.29 In Table VI we have
collected these molecular orbital energies, evaluated at the 631G*//6-31G level, for all compounds under study. It is clear that for all azoles considered here, the H O M O is always of a-symmetry (a", a2, or b,). However, Mazurek and Osmans pointed out that, for tetrazole, a-ionization does not lead to the most stable radical cation; Le., Koopman's theorem predicts the wrong ionization. To study this particular point we have evaluated the corresponding vertical ionization potentials, following the procedure outlined in section 2. The values so obtained at the STO-3G and 6-31G levels are presented in Table VII. It should be noticed that for pyrrole, imidazole, and pyrazole a-ionization leads indeed to the most stable radical cation. However, that is not so for 4H-1,2,4-triazole, tetrazoles, or 1Hpentazole, where the u vertical ionization potential is systematically smaller than the ?r one at the 6-31G level. For lH-1,2,4-triazole, our results predict u- and a-radical cations to be equally stable. It must be also remarked that STO-3G basis set considerably underestimates vertical ionization potentials1° and that, for some specific cases (1H-tetrazole and pentazole), it predicts the wrong ionization. Also, the stability of the radical cation of pyrrole obtained upon u-ionization is considerably underestimated at this level of accuracy. In summary, according to our 6-31G results, and with the exception of pyrrole, imidazole, and pyrazole, the first ionization potential observed for azoles must correspond to nitrogen lone-pair ionizations, since, as shown in Table V, these are the a-orbitals of higher energy. This result seems to indicate that for those azoles with two or more basic nitrogens, the interactions between the corresponding lone-pair orbitals30lead to a considerable destabilization of at least one of them, making u-ionization more favorable than a-ionization. For 1,2,4-triazoles, our results show that the antisymmetric c ~ m b i n a t i o n(LPN-) ~~ is always less stable than the symmetric one (LPN+). For tetrazoles and 1H-pentazole symmetric and antisymmetric combinations cannot be defined rigorously because there are interactions between three or more lone-pair orbitals. However, we have found that, to a good approximation, the lone-pair orbitals of 1H-pentazole can be considered namely as symmetric and antisymmetric combinations of symmetrically equivalent lone pairs. Those of higher energy correspond, basically, to the symmetric and antisymmetric combinations of the lone pairs centered on N3 and N4. Those of lower energy come, essentially, from the interaction between the lone pairs centered on N 2 and N5, respectively. This result is not surprising because the in(29) See,for instance: Van den Ham, D. M. W.; Van der Meer, D. J . Electron Spectrosc. Relat. Phenom. 1973, 2, 247. Van den Ham, D. M.; Van der Mecr, D.; Feil, D. Ibid.1974,3,479. Van den Ham, D. M. W.; Beerlage, M.; Van der Meer, D.; Feil, D. Zbid. 1975, 7, 33. Kluge, G.;Kania, G.; Achenbach, F.;Lippmann, E.; Novak, I.; Klasinc, L. Int. J . Quantum Chem. Quantum Biol. Symp. 1983, IO, 339. (30) Hoffmann, R.;Imamura, A.; Hehre, W. J. J . Am. Chem. SOC.1968, 90, 1499.
5604
The Journal of Physical Chemistry, Vol. 90, No. 22, 1986
M6 et al.
TABLE VI: Orbital Energies (eV) Evaluated at the 6-316*//6-316 Level 2
1
4
3
-7.95 (a2) -9.15 (b,) -14.09 (al, LPN) -14.83 (b2)
-8.68 (a”) -10.59 (a”) -1 1.56 (a’, LPN) -15.51 (a’)
-9.26 (a”) -9.81 (a”) -12.20 (a’, LPN) -15.31 (a’)
-15.19 (b,)
-16.09 (a”)
-15.71 (b2) -16.01 -19.96 -20.71 -21.46 -26.47 -28.18 -34.98
(a,) (a,) (b,) (al) (b,) (a,) (az)
5
-16.04 (a’)
-10.05 (az) -11.55 (b,) -1 1.67 (bz, LPN-) -12.94 (a,, LPN’) -17.06 (bl)
-10.30 (a”) -11.19 (a”) -12.01 (a’, LPN-) -13.68 (a’, LPN’) -16.38 (a’)
-16.41 (a’)
-16.34 (a”)
-17.17 (bz)
-16.51 -20.69 -21.66 -22.47 -27.43 -31.55 -36.37
-16.68 -20.18 -21.73 -22.44 -28.48 -29.89 -37.29
-17.53 -21.44 -22.90 -23.30 -30.01 -33.05 -33.08
(a’) (a’) (a’) (a’) (a’) (a’) (a’)
(a’) (a’) (a’) (a’) (a’) (a’) (a’)
(a,) (al) (b2) (al) (b2) (a,) (al)
-17.24 (a”)
-11.49 (a”) -12.32 (a”) -12.83 (a’, LPN) -12.85 (a’, LPN) -15.55 (a’, LPN) -18.41 (a”)
-17.51 -21.07 -22.69 -23.64 -30.57 -32.47 -38.51
-18.69 -21.50 -24.08 -25.24 -32.45 -34.59 -41.21
-18.53 -21.92 -24.21 -24.75 -32.77 -34.13 -40.81
(a’) (a’) (a’) (a’) (a’) (a’) (a’)
Symmetric and antisymmetric combinations of LPO’s centered on N3 and N4, respectively. LPO’s centered on N 2 and N5, respectively.
TABLE VII: Calculated Vertical Ionization Potentials (eV) basis STO-3G
6-31G
compd
L?
k
L?
k
1
19.2 6.70 7.42 7.3 1 7.52 8.42 8.42 9.12
5.6 6.30 6.40 7.82 7.59 8.05 8.62 8.88
12.49 0.52 9.16 9.19 9.42 10.34 10.25 11.53
7.00 7.85 8.33 9.50 9.41 10.81 11.01 11.75
2 3 4
5 6
7 8
teraction between these two lone pairs (on N 2 and N5) and the azolic hydrogen contributes to stabilize them with respect to those centered on N 3 and N4. Finally, it should also be noticed that our calculated vertical ionization potentials for tetrazoles are smaller than those reported by Mazurek and Osmam8 This difference arises from our using a direct minimization method in the R H F calculations of the corresponding radical cations, obtaining for these species total energies about 0.2 eV lower than those reported by these authors.
8. Conclusions From our results we can draw the following conclusions: Optimized geometries of azoles are quite sensitive to the quality of the basis set used to expand the molecular wave function. Minimal basis tends to considerably overestimate N-N and C-N bond lengths, although these overestimations are, quantitativeiy, different for the different compounds. Though, in general, 3-21G geometries are close to those obtained at the 6-31G level, the more economical split-valence basis does not always correct the deficiencies of minimal basis. In general, the agreement between 6-3 1G optimized geometries and experimental microwave structures is fairly good. Azoles which present more than one basic nitrogen protonate preferentially on “imidazo1ic”- rather than on “pyrazo1ic”-type nitrogens.
7
6
-11.39 (a”) -12.21 (a”) -12.76 (a’, LPN) -13.69 (a’, LPN) -15.71 (a’, LPN) -18.09 (a’) (a”) (a’) (a’) (a’) (a’) (a’) (a’)
(a’) (a’) (a’) (a’) (a’) (a’) (a’)
8 -13.10 (b,) -12.15 (a2) -13.68 (a,, LPN’)“ -14.21 (bz, LPN-)“ -14.84 (b2, LPN-)~ -17.73 (a,, LPN+)~ -19.85 (b,) -22.63 (a,) -25.87 (bz) -26.47 (a,) -35.36 (a,) -36.06 (b2) -43.12 (al)
Antisymmetric and symmetric combinations of
Minimal basis significantly overestimates absolute protonation energies. However, the effects on relative protonation energies are not always of the same sign. 3-21G and 6-31G basis yield very similar absolute protonation energies (about 30 kcal/mol smaller than those obtained at the STO-3G level). The inclusion of polarization functions in the basis set leads to a further decrease of absolute protonation energies. This decrease depends on the characteristics of the center which undergoes protonation, and it is greater when the anisotropy of its charge distribution is greater. Variation of relative proton affinities with the basis is mainly a consequence of basis set influence on relative stabilities of protonated tautomers. The couple imidazole-pyrazole is an exception since, in this case, it is the relative stability of the neutral isomers which appears as specially sensitive to the quality of the basis. 2H-Tetrazole is predicted to be more stable than 1H-tetrazole in the gas phase, in agreement with previous findings.8 Very likely, however, lH-tetrazole is the predominant tautomer in solution due to its high polarity. lH-l,2,CTriazole is more stable, in the gas phase than 4H1,2,4-triazole. The energy gap between both tautomers is much larger than that found for tetrazoles. Accordingly, it is reasonable to expect the 1 H tautomer to be also the predominant species in solution. For 1,2,4-triazoles, tetrazoles, and 1H-pentazole Koopman’s theorem predicts the wrong ionization, since for these compounds the a-radical cation is more stable than the one produced upon a-ionization. Vertical ionization potentials are considerably underestimated at the minimal basis set level.
Acknowledgment. This research has been partially supported by the CAICYT project No. 91 3/8 1. All calculations have been performed at the UAM/IBM and CCUAM Centers, Madrid. Registry No. 1, 109-97-7; 2, 288-32-4; 3, 288-13-1; 4, 63598-71-0; 5, 288-88-0; 6, 100043-29-6; 7, 288-94-8; 8, 289-19-0; 9, 17009-90-4; 10, 17009-91-5; 12, 16842-36-7; 13, 16969-97-4: 16, 103692-65-5; 17, 103692-66-6.
