J. Phys. Chem. 1985,89, 1581-1592 administered by the American Chemical Society, for financial support of the U S . efforts, and to the Australian Research Grants Scheme for support of the Australian efforts. The U.S.-Australian collaboration has been made possible by the US.-Australian Agreement for Scientific and Technical Cooperation, funded by the National Science Foundation and the Australian Research Grants Scheme. W.D.L. thanks the Adolph C. and Mary Sprague
1581
Miller Institute for Basic Research in Science for a postdoctoral fellowship, and D.B.M. acknowledges fellowship support from the Procter & Gamble Co. Professor T. M. Dunn has been most 0 and in allowing helpful in discussions concerning ~ 3 anharmonicity us to use his determinations of the vJ0 frequencies. We thank G. M. Nathanson and G. M. McClelland for providing us with a preprint of their fluorescence polarization study.
ARTICLES Theoretical Analysis of Proton Transfers in Symmetric and Asymmetric Systems H. Z. Cao, M. Allavena, 0. Tapia; and E. M. Evleth* E.R. du C.N.R.S.,No. 271, Dynamique des Interactions MolZculaires, Tour 22, Universitd Paris VI, 75230 Paris Cedex 05, France, and The Swedish University of Agricultural Sciences, Uppsala, Sweden (Received: January 13, 19831
A series of symmetric and asymmetric proton-transfer systems are analyzed at the ab initio SCF level by using four different basis sets. It is shown that for anionic systems the 4-31+G diffuse basis set is still insufficient to quantitatively estimate the reaction energies for asymmetric systems. The symmetric and asymmetric proton transfers are analyzed within the context of single- and double-well potential energy surface models by using a modification of the Marcus equation. The Marcus parameters for the application of asymmetric double-well equations are obtained from ab initio calculations of the symmetric systems. In this case, the 4-31+G basis set is considered adequate. It is shown where one can expect single- or double-well surface behavior in asymmetric systems based on an analysis of the symmetric systems. Comparison is also made between these treatments and thme complexation energies obtained from simple dipole-polarizability ion-molecule potentials. Comparison with experimental data is made, especially in the area of deuterium-exchange mechanisms. Limitations of our particular form of the Marcus equations are found to occur.
Introduction The goal of this article is to theoretically characterize the various energy parameters involved in the proton transfers of a series of symmetric and asymmetric systems. A longer range goal is to develop a systematic understanding of the theoretical origins of condensed-phase slow proton transfers in carbon acids.' Because of the difficulty of separating the entropic and enthalpic terms involved in solvent-solvent and solvent-solute reorganization in the various possible stages involved in condensed-phase protontransfer systems, the study presented here will deal only with gas-phase processes. A thorough theoretical understanding of gas-phase systems will provide the basis for future work in condensed-phase systems. The theoretical methods used here for rationalizing proton-transfer systems are twofold. The systems will be quantitatively characterized by using a b initio methods. Next, the ab initio energy parameters will then be systematically interrelated in order to obtain a broad understanding of protontransfer processes. This intercorrelation will be effected by using Marcus theory.2 Marcus theory has been generally used in analyzing the kinetic behavior of various electron, proton-, and atom-transfer s y ~ t e m s l -and ~ provides a convenient framework for rationalizing surface behaviors of seemingly unrelated systems. Gas-phase proton transfers differ from their condensed-phase counterparts in several important ways. First of all, with some important exception^,^ gas-phase transfers are rapid and occur with high efficiencies if the overall enthalpy change is nearly zero or negativee6 The rapid nature of gas-phase transfers is easily rationalized by assuming that the potential-energy surfaces are inverted (Figure 1) and that the transition state, TS, for the The Swedish University of Agricultural Sciences.
proton-transfer step between the two hydrogen-bonded complexes, R . The possible C1 and C2, is below the energy of the (1) (a) Eigen, M. Angew. Chem., Znt. Ed. Engl. 1964,3, 1-19. (b) Eigen, M.; Kruse, W.; Maass, G.; Meyer, L. React. Kinet. 1964, 2, 287-318. (c) Kresge, A. J. Acc. Chem. Res. 1975, 18, 354-360. (d) Reutov, 0. A.; Beletskaya, I. P.; Butin, K. P. "CH Acids"; Pergamon Press: New York, 1978. (e) Hihbert, F. "Chemical Kinetics, Proton Transfer"; Bamford, C. H., Tipper, C. F. H., Eds.; North-Holland Amsterdam, 1977; Vol. 8, pp 97-196. (2) (a) Marcus, R. A. J . Phys. Chem. 1968, 72,891-899. (b) Albery, W. J. Annu. Rev. Phys. Chem. 1980, 31, 227-263. (3) (a) Magnoli, D. E.; Murdoch, J. R. J. Am. Chem. SOC.1981, 103, 7465-7469. (b) Murdoch, J. R. Ibid. 1982,104, 588-600. (c) Murdoch, J. R.; Magnoli, D. E. Zbid. 1982,104,2782-2789. (d) Murdoch, J. R.; Magnoli, D. E. Ibid. 1982, 104, 3792-3800. (e) Donnella, J.; Murdoch, J. R. Ibid., in press. (4) Saunders, W. H. Jr. J . Phys. Chem. 1982, 86, 3321-3323. (5) (a) For a recent review see: Moylan, C. R.; Brauman, J. I. Annu. Rev. Phys. Chem. 1983,34,187-215. (b) Mackay, G. I.; Rakshit, A. B.; Bohme, D. K. Can. J. Chem. 1982,60,2594-2605. (c) Olmstead, W. N.; Brauman, J. I. J . Am. Chem. Soc. 1977, 99, 4219-4228. (d) Meyer, F. K.; Pellerite, M. J.; Brauman, J. I. Helv. Chim. Acta 1981, 64, 1058-1062. (e) Jasinski, J. M.; Brauman, J. I. J . Am. Chem. SOC.1980, 102, 2906-2913. (6) For a selected list of examples see: (a) Betowski, J.; Payzant, J. D.; Mackay, G. I. Bohme, D. K.; Chem. Phys. Lett. 1975, 31, 321-324. (b) Tanaka, K.; Mackay, G. I.; Bohme, D. K. Can. J . Chem. 1978,58, 193-204. (c) Olmstead, W. N.; Lev-On, M.; Golden, D. M.; Brauman, J. I. J . Am. Chem. SOC.1977,99,992-998. (d) Mackay, G. I.; Lien, M. H.; Hopkinson; A. C.; Bohme, D. K. Can. J . Chem. 1978,56, 131-140. ( e ) Bohme, D. K.; Mackay, G. I.; Tanner, S. D. J. Am. Chem. SOC.1979,101,3724-3730. (f) Mackay, G. I.; Tanner, S. D.; Hopkinson, A. C.; Bohme, D. K. Can. J. Chem. 1979,57, 1518-1523. (g) Tanner, S.D.; Mackay, G. I.; Bohme, D. K. Ibid. 1979, 57, 2350-2354. (h) Hopkinson, A. C.; Mackay, G. 1.; Bohme, D. K. Zbid. 1979,57, 2996-3004. (i) Lias; S. G.; Shold, D. M.; Ausloos, P. J. Am. Chem. SOC.1980,102,2540-2548. u) Mackay, G. I.; Schiff; H. I.; Bohme, D. K.; Can. J . Chem. 1981.59, 1771-1778. (k) Bohme, D. K.; Mackay, G. I. J. Am. Chem. Soc. 1981, 103, 2173-2175. (I) Ausloos; P.; Lias, S. G. Ibid. 1981, 103, 3641-3647.
0022-3654/85/2089-1581$01.50/0 0 1985 American Chemical Society
Cao et al.
1582 The Journal of Physical Chemistry, Vol. 89, No. 9, 1985 A+H% - .- - - - - - - - - . -
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c2 Figure 1. Schematic representation of single-well (i) and double-well (ii) potential-energy surfaces. Single-well surfaces show only two energy parameters, Eo, the reaction energy, and E,, the well depth for the complex formed. The inflection point indicates that the surface has a conceptual relationship to a double-well surface in which two complexes, C1 and C2, occur. In a double-well surface there are two additional energy parameters possible, E,,, for forming the first complex, and Ept. the barrier for passing from C1 to C2.
existence of C1, TS, and C 2 implies that the surface has double-well structure with kinetic processes occurring as described in eq 1. In principle, the characterizable energies for these A H B ~t (AH--B) @ (A--H,--B) s (A--HB) @ R c1 TS c2 A H B (1)
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processes are Ealand Ea2,the well depths of C1 and C2 with respect to reactants (R) and products (P); Ept,the proton-transfer barrier; and EO, the overall enthalpy change. For symmetric transfers, Eo = 0 and Eal = Ea2. It is also possible that the symmetric transfer surface has single-well structure, in which case Eal = Ea2 = E,, and E , = 0. It should be noted that Figure 1 and eq 1 represent ideal behavior. It is possible to imagine real situations in which the most stable complexes in the system do not have hydrogen-bonded structures or that the proton donor or acceptor has several available exchange sites. In these cases, a number of complexes and transition states will have to be taken into account in any kinetic or theoretical scheme. Unfortunately, the experimental information available for symmetric and asymmetric proton-transfer systems is limited to E, and Eo The E, values will be those of the most stable complex (C2 according to the convention used in Figure 1 (ii)), and no quantitative proof is available that a particular system has either single- or double-well surface behavior. However, deuterium-exchange kinetics8 of asymmetric systems having several exchangeable hydrogens can be interpreted by using the assumption of double-well structure. In addition, estimations of E,,, v a l ~ e s ~have ~ ~been ~ d made using RRKM theory assuming that the overall reaction efficiency can be calculated from the ratio of the observed rate constants and those estimated from the ADO approximation. However, since efficiencies calculated in this manner can be greater than unity,8c the method is subject to unknown error. Modern a b initio methods, using large basis sets and correlatively corrected? are capable of providing near-ther(7) (a) Kabarle, P. Annu. Rev. Phys. Chem. 1977, 28, 445-476. (b) Bartness J. E.; Scott, J. A.; McIver, R. T. Jr. J. Am. Chem. SOC.1979, 101, 6064-6056. (c) Mmt-Ner, M. Ibid. 1984, 106, 1257-1264, 1265-1272. (8) (a) Meot-Ner, M.; Lloyd, J. R.;Hunter, E. P.; Agosta, W. A.; Field, F. H. J. Am. Chem. Soc. 1980,102,4672-4676. (b) Grabowski, J. J.; Dupuy, Bierbaum, V. M. Ibid. 1984, 105,2565-2571. (c) Squires, R. R.; C. H.; Bierbaum, V. M.; Grabowski, J. J.; DuPuy, C. H.; Ibid. 1983, 105,5185-5192.
F i 2. Atom numbering conventions used in the calculations presented in the various tables. In all cases a linear hydrogen bond is imposed. Certain additional restraints are also imposed in the cases of vi and vii.
mochemical accuracy for the surface features of small systems. However, for larger systems these levels of treatment may be financially prohibitive. The calculations presented here will test the levels at which reasonably quantitative results can be obtained. We will also provide the framework in which future results can be treated as methodological improvements occur. 11. Technical Details A . Basis Sets. Four different basis sets were employed in these studies in order to explore their relative values. The basis sets employed were (i) 4-31G, (ii) 6-31G*, (iii) 4-31+G, and (iv) 6-31+G*. The +G notation indicates the presence of 2s,2p heavy atom diffuse components necessary to treat anionic systems. These basis sets are approximately DZ, DZP, TZ, and TZP in character having 9, 15, 13, 19 CGTOs per heavy atom. The parameters used here are those reported in the literature.i@-12 All SCF and gradient calculations were performed by using MONSTERGAUSS.13 The geometry optimizations were performed with the symmetry restraints indicated in Figure 2 and the appropriate tables. The various energy parameters shown here are computed directly from the S C F values without any zero-point, thermodynamic, correlation, or basis set superposition error corrections. Finally, on several occasions S C F convergence could not be immediately effected on the complex structures using the diffuse bases. This could usually be effected by first performing a calculation using larger exponents for the diffuse orbitals and then using these MOs for initiating calculations having the literature value exponents.1° B. Correlation Energy Estimations. Although we will argue that correlation energy corrections should be relatively minor for geometry-optimized E,, E,,,,and E" values computed using proper basis sets, we performed an exhaustive study on the system CH
