3022
J . Phys. Chem. 1992, 96, 3022-3029
Enhanced AI+ Binding Energies of Some Azoles. A Theoretical Study of Azole-X+ (X = Na, K, AI) Complexes M. Alcami, 0.M6, and M. Yfiiez* Departamento de Quimica C-XIV, Universidad AutBnoma de Madrid, Cantoblanco, 28049 Madrid, Spain (Received: July 5, 1991) HartreeFock calculations with the 3-21G(*)and 6-3 lG* basis have been performed to investigate the structure and energetics of Na+-, K+-, and APazole complexes. Structures have been fully optimized at the 3-21G(*)level. The structures of azole-Al+ complexes resemble closely those of the corresponding protonated species while those of Na+ and K+ complexes are similar to those found upon Li+ association. Na+- and K+-bridgedstructures, when the azolic system presents two neighbor nitrogens having lone pair electrons, are particularly stable with respect to Li+-bridged systems. This implies that Li+ vs Na+ (or K+) binding energies follow two different linear correlations. For those cases where Na+ and K+ are single coordinated a good linear correlation between their binding energies and the proton affinities is found. A similar behavior is observed when AI+ binding energies are considered. The former correlation obeys a quite simple electrostatic model, which is not fulfilled by AI+ association energies. Our topological analysis of the complexes' charge density shows that the AI+-azole interaction has a nonnegligible covalent character, which involves the low-lying empty p orbitals of AI+. These interactions are responsible for the enhanced stability of some AI+ complexes, as for instance, AI+-imidazole, which presents a stability very close to that of the Li+-imidazole system.
Introduction The intrinsic basicity of a molecule is defined by its binding energy to a reference acid in the gas phase, and it is not uncommon to find that the basicity trends along a given family of compounds change from one reference acid to another. A typical example is provided by methylamines, which present a relative ordering of basicity for protonation which is different from that for lithiation.' In our research on the gas-phase basicity of different organic bases we have lately focused our attention on the behavior of azoles and azines as typical polydentate base^.^-^ Actually, we have shown that the presence of several basic centers within the same cyclic structure is responsible for the enhanced Li+ binding energies exhibited by some triazoles, tetra~oles,~ and some azine^.^ As a further step toward a better understanding of the gas-phase basicity of azoles, we have carried out in the present work a theoretical study of the different complexes between the azoles and Na+, K+, and Al+. The first two monocations have been chosen because the azoles are components of several enzymes and pharmaceuticals and they may be used as model systems to probe the coordination chemistry of alkali-metal ions with nucleic acid bases6and to examine cation-selective transport through biological In this respect, the information provided here complements that presented in ref 3 on the corresponding azole-Li+ complexes. Accordingly, one of the objectives of the present study is to investigate whether bridging structures similar to those found for Li+ complexes are stable when the reference acids are Na+ or K+. We shall try also to establish the possible relationships between Li+, Na+, and K+ binding energies to the azoles and to characterize, using a topological analysis of the electronic charge density, the corresponding ion-molecule interactions. We have also considered of interest to include Al+ in this study. AI+, as with Na+ or K+, is a closed-shell monocation, but its electronic core is more polarizable than that of Na'; on the other hand, it presents low-lying empty p orbitals which may lead to (1)Woodin, R. L.;Beauchamp, J. L. J. Am. Chem. SOC.1978,100,501. (2)M6, 0:;de Paz, J. L. G.; Yiiiez, M. J. Phys. Chem. 1986,90,5597. (3)Alcamj, M.;M6, 0.;YBiiez, M. J. Phys. Chem. 1989,93,3929. (4)Alcami, M.; M6.0.; Yiiiez, M.; Anvia, F.; Taft, R. W. J. Phys. Chem. 1990,94,4795. (5) Alcami, M.; M6, 0.;de Paz, J. L. G.; YBiiez, M. Theor. Chim. Acta 1990,77, 1. (6)Sletten, E.;Stogard, A. J. Mol. Struct. (THEOCHEM) 1987,153, 288. (7)Pedersen, C. J. J . Am. Chem. SOC.1967,89,7017. (8) Izatt, R. M.; Nelson, P. P.; Rytting, J. H.; Haymore. 8. L.; Christensen, J. J. Am. Chem. SOC.1971,93, 1619.
0022-3654/92/2096-3022$03.00/0
some peculiarities in the corresponding azole-Al+ interactions. Actually, we have recently shown? for a wide set of organic bases, that their Al+ complexes present structures quite different from the corresponding Li+ complexes as a result of an efficient interaction between the base lone pairs and the empty p-orbitals of the Al+ cation. In this paper we shall show that this mechanism is also responsible for the enhanced stability of some azole-Al+ complexes which are found to be almost as stable as the corresponding Li+ complexes. On the other hand, although there is a considerable number of papers on Li+, Na+, and K+ complexes,I0 the information on Al+ basicities, both experimental and theoretical, is scarce. We are only aware of the experimental studies of Hodges et al.," Uppal and Staley,I2 Chowdhury and Wilkins,I3 Weber et al.,14and Bouchard et a1.I5and the theoretical work of Smith et a1.I6 To our knowledge, Al+ binding energies of azoles have not been reported in the literature so far.
Computational Details Gradient techniques were used to determine the geometrical structures of the complexes of azoles with Na+, K+, and Al+ at the Hartree-Fock level of theory, using the 3-21G(*) basis set'' in order to include polarization functions in the second- and (9)Alcaml, M.; Mb, 0.;Yiiiez, M. J. Mol. Struct. (THEOCHEM) 1991, 234, 357. (IO) See, for instance: Davidson, W. R.; Kebarle, P. J. Am. Chem. SOC. 1976,98,6133. Woodin, R. L.;Houle, F. A,; Gcddard, W. A,, 111 Chem. Phys. 1976,14,461. Kollman, P. Chem. Phys. Lett. 1978,55, 5 5 5 . Smith, S. F.; Chandrasekhar, J.; Jorgensen, W. L. J. Phys. Chem. 1982,86,3308. Del Bene, J. E.; Frisch, M. J.; Raghavachari, K.; Pople, J. A,; Schleyer, P. v. R. J. Phys. Chem. 1983,87,73.Latajka, Z.; Scheiner, S. Chem. Phys. Lett. 1984,105,435;Chem. Phys. 1985,98,59.Ikuta, S. Chem. Phys. Lett. 1985, 116,482;Chem. Phys. 1985,95,235;Chem. Phys. 1986,108,441.Impey, R. W.; Sprik, M.; Klein, M. L. J. Am. Chem. SOC.1987,109,5900. Sletten, E.; Stogard, A. J. M o l . Strucf. (THEOCHEM) 1987. 153,289. Portmann, P.; Maruizumi, T.;Welti, M.; Badertscher, M.; Neszmelyi, A,; Simon, W.; Scheiner, S. J. Chem. Pretsch, E. J. Chem. Phys. 1987.87,493. Latajka, Z.; Phys. 1987,87, 1194. Guo, 8. C.; Conklin, B. J.; Castleman, A. W., Jr. J . Am. Chem. SOC.1989,Ill, 6506. Larrivee, M. L.; Allison, J. J. Am. Chem. SOC.1990,112,7134. ( 1 1 ) Hodges, R. V.; Armentrout, P. B.; Beauchamp, J. L. Int. J . Muss. Spectrom. Ion Phys. 1979,29,375. (12)Uppal, J. S.;Staley, R. H. J. Am. Chem. Soc. 1982,104,1029;1982, 104,1235; 1982,104, 1238. (13)Chowdhury, A. K.; Wilkins, C. L. I n f . J. Mass. Spectrom. Ion Processes 1988,82,163. (14)Weber, M. E.;Elkind, J. L.; Armentrout, P. B. J. Chem. Phys. 1986, 84, 1521. (15) Bouchard, F.; Hepburn, J. W.; McMahon, T.B. J. Am. Chem. SOC. 1989,1 1 1 , 8934. (16)Smith, S. C.;Chandrasekhar, J.; Jorgensen, L. J. Phys. Chem. 1983, 87, 1398. (17)Pietro, W. J.; Francl, M. M.; Hehre, W. J.; De Frees, D. J.; Pople, J. A,; Binkley, J. S. J. Am. Chem. Soc. 1982,104,5039.Dobbs, K. D.; Hehre, W. J. J. Compur. Chem. 1986,7, 359.
0 1992 American Chemical Society
The Journal of Physical Chemistry, Vol. 96, No. 7, 1992 3023
Al+ Binding Energies of Some Azoles
k 1
X:
6b
XzH, L( No, K, PI
H,LI, No, K, N
x:u
X: H. Lo,&, K . A I
M
X = L1.Na.K
A
Ila
13
14
H.LI. M.H.AI
X : 4, Li. k , K , A
‘2
X = H . AL
X
5
I8
11
X
a
LI,PJo,+
:
AI
X = tl, AI
tI AI
21
20
19
18b
Ib
LI, Na.K X
x - tq
IOb
IO
9
8
1
X-H. Y
5
L
3
2
‘ I I H,Li. 4 1
210
X = N3.K
21b
X:H
Figure 1. Neutral azoles and their X+ (X = Na, K, and Al) complexes included in this study.
third-row atoms. These optimized geometries were then used for single-point calculations at the 6-3 1G* levelL8with the only exception being K+ complexes, for economic reasons. These calculations will be denoted hereafter as 6-3lGS//3-21G(*). All these calculations have been carried out by using the Gaussian 86 series of programs.I9 The geometries and total energies of the neutral bases were taken from refs 2 and 3. The complete set of systems included in this work has been schematized in Figure 1. Since one of the aims of this paper is to compare Na+, K+, and Al+ complexes with Li+ and H+complexes, we have also indicated in Figure 1 which (18) Hariharan, P. C. Pople, J. A. Chem. Phys. Left. 1972, 66, 217. Francl, M. M.; Pietro, W. J.; Hehre, W. J.; Binkley, J. S.;Gordon, M. S.;De Frees, D. J.; Pople, J. A. J. Chem. Phys. 1982, 77, 3654. (19) Frisch, M. J.; Binkley, J. S.;Schlegel, H. B.; Raghavachari, K.; Melius, C. F.; Martin, R. L.; Stewart, J. J. P.; Bobrowicz, F. W.; Rohlfing, C. M.; Kahn, L. R.; DeFrees, D. J.; Seeger, R.; Whiteside, R. A.; Fox, D. J.; Fleuder, E. M.; Pople, J. A. Gaussian 86; Carnegie Mellon Quantum Chemistry Publishing Unit: Pittsburgh, PA, 1984.
Li+ and protonated species are stable. Na+, K+, and Al+ binding energies were obtained by subtracting from the energy of each complex the sum of the energies of the neutral base and the corresponding metal cation. The effect of the basis set superposition error (BSSE) was estimated by means of the counterpoise method of Boys and BernardLzo To analyze some of the peculiarities of the interaction between the neutral azoles and the metal monocations, we shall discuss the topological characteristics of the electronic density, p, of each complex and those of its laplacian, V 2 p . As has been shown by Bader,2’-23the laplacian of p identifies regions of space wherein the electronic charge of a given system is locally concentrated (V2p < 0) or depleted ( V z p > 0). In the first case there is a covalent (20) Boys, S. F.; Bernardi, F. Mol. Phys. 1970, 19, 553. (21) Bader, R. F. W.; Essen, H. J . Chem. Phys. 1984,80, 1943. (22) Bader, R. F. W.; MacDougall, P. J.; Lau, C. D. H. J. Am. Chem. SOC.
1984, 106, 1594.
(23) Wiberg, K. B.; Bader, R. F. W.; Lau, C. D. H. J. A m . Chem. SOC.
1987, 109, 985.
3024 The Journal of Physical Chemistry, Vol. 96, No. 7, 1992 CHART I
u t
A
I
Alcami et al. TABLE I: p (e/au3) and V2p (e/aus) at the N-X+ (X = Na, AI) Bond Critical Points of Nonbridged Complexes' Na+ AI' complex 2
4 8 13 14 20
interaction, while in the second there is a closed-shell interaction such as in ionic bonds, hydrogen bonds, or van der Waals complexes. To complete this topological description we have located the bond critical points (i.e., points in which the electronic charge density has one positive curvature along the bond and two negative curvatures in the other directions) corresponding to the new bond formed in the complex. Finally, it should be mentioned that the correlation and zeropoint vibrational energy (ZPVE) corrections were not taken into account for economic reasons. Nevertheless, we can reasonably assume that, as for other bases,24inclusion of electron correlation would not significantly change relative Na+, K+, or Al+ binding energies. On the other hand, ZPVE corrections for Na+ complexes, for instance, are more than 5 times smaller than for protonated specie^,^^*^^ but more importantly, they are practically constant along a homologous series of compounds such as the one considered in this study.
Results and Discussion 1. Structures. For the sake of conciseness we are not going to discuss in detail the optimized structures of the complexes under study, which are included as supplementary material. However, several structural features deserve some comments. The complexes azole-Na+ and azole-K+ are quite similar to the azole-Li+ complexes. In general, they yield bridging structures when the system presents two neighboring nitrogen atoms having a lone pair of electrons. The only exception to this general behavior is represented by lH-tetrazole (17), where the complex in which the metal cation bridges N2 and N 3 is not stable, and the only stable species correspond to that in which the bridging takes place between N 3 and N 4 (18). A similar result was reported in ref 3 for a lH-tetrazoleLi+ complex, and the explanation offered there can be generalized to the case of Na+ and K+. There is however a dissimilarity between the behavior of Li+ with respect to Na+ and K+ regarding 2H-tetrazole (19), since the latter yield a bridge structure (214 which is not stable when the metal cation is Li+. The high stability of Na+- and K+-bridged structures with respect to Li+ ones will be discussed later. Another important result, as shown in Figure 1, is that the structures of Al+ complexes resemble that of the corresponding protonated species rather than that of Li+, Na+ or K+ complexes. A similar finding has been reported recently9 for a quite different set of nitrogen, oxygen, and fluorine bases. We have also investigated the possibility of *-face attachment by considering structures where the metal cation lies above the molecular plane, yielding a pyramidal coordination (see Chart I) similar to those r e p ~ r t e d ~for~ slithium ~ ~ isodicyclopentadienide, lithium cyclopentadienide, and other lithium derivatives. This has been carried out for lH-tetrazole (17) as a suitable model system and for Li+ and Al+ as reference acids. In both cases, we have found that the configuration of Chart I evolves without activation barrier to yield structures 18. We have also found that when the metal cation is forced to be above the mo(24)Del Bene, J. E.; Frisch, M. J.; Raghavachari, K.; Pople, J. A,; Schleyer, P. v. R. J. Phys. Chem. 1983, 87, 73. (25)Ikuta, S.Chem. Phys. 1984, 108, 441, (26)Meot-Ner (Mautner) M.;Liebman, J. F.; Del Bene, J. E. J. Org. Chem. 1986,51, 1105. (27)Paquette, L. A.; Bauer, W.; Sivik, M. R.; Buhl, M.; Feigel, M.; Schleyer, P. v. R. J. Am. Chem. SOC.1990, 112, 8776. (28)Buhl, M.; Hommes, N. J. R.; Schleyer, P. v. R.; Fleischer, U.;Kutzelnigg, W.J. Am. Chem. SOC.1991, 113, 2459.
P
0.032 0.034 0.030 0.031 0.032 0.028
V2P 0.217 0.226 0.197 0.207 0.216 0.183
P
0.056 0.059 0.049 0.052 0.055 0.045
V2P 0.320 0.345 0.242 0.278 0.308 0.195
"Values obtained at the 6-31G*level.
lecular plane, the stationary point (not a minimum) found corresponds to a structure where the metal cation is, on average, 2.3 A away from the nitrogens, but which lies 40.0 kcal/mol above the global minima corresponding to structures 18. This is in clear contrast with the coordination ability of neutral Li with cyclopentadienide and related compound^.^^^^^ In these cases, the exo-face coordination of Li is the consequence of an ion-pair interaction between Li+ and the corresponding molecular anion. In our case, the interaction is between Li+ and a neutral azolic system. As we shall show later, this interaction is essentially electrostatic, the ion-dipole term being the dominant one. Since the azolic dipole moment lies always in the plane of the molecule, it is not surprising to find that the configurations where the metal cation lies in that plane correspond to the global minima of the potential energy surface. It is also something well established that protonation of azoles produces significant changes in the structure of the azole ring. If one takes as an example imidazole (3), the endocyclic angle centered at the basic center (N3) opens considerably upon protonation and simultaneously the N1
