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Quantum Chemical Investigation of the Electric Field Effect on Activation Barriers for Electrochemical Transformations of Organic Compounds Victor V. Lobanov and Vladimir I. Bogillo* Institute of Surface Chemistry, National Academy of Sciences, Prospekt Nauki 31, 252022 Kiev, Ukraine Received June 16, 1994. In Final Form: February 26, 1996X The MINDO/3 method was used to study the effect of intensity and vector direction of the external electric field on activation barriers of unimolecular reactions which are possible in electrochemical transformations of simple organic compounds: orientation of molecules and radical anions, heterogeneous electron transfer to adsorbed molecules, dissociation of radical anions, cations, and molecules, inversion of anions, free radicals, and neutral molecules, cis-trans isomerization, and chair-boat conformational transition in molecules. The electronic and spatial structure of the molecules, free radicals, and ions, the height of the activation barriers of their reorientation, dissociation, isomerization, and conformational transition, and the configurational stability to change as affected by the field in the range 0.01-0.05 au are determined. Obtained data permit one to theoretically ground different effects under organic compound adsorption on the electrode surface, changes in stereochemistry of the products of alkyl halide electroreduction, and some properties of chemically modified electrodes possibly affected by electrode potential gradient.
Introduction Over the last 40 years there has been great theoretical and experimental interest in the influence of electric field on the structure and reactivity of molecules and ions localized nearby solid surfaces and on the mechanisms of the interface reactions.1-6 Such influence is exhibited in the UHV processes of field adsorption, dissociation, and desorption from surfaces of metals or semiconductors,1,6-14 on the surfaces of heterogeneous oxide catalysts,15-19 especially in the zeolite cavity,20-24 in interface reactions proceeding in the double electric layer of solid elec* To whom correspondence should be addressed. X Abstract published in Advance ACS Abstracts, August 1, 1996. (1) (a) Beckey, H. D. Z. Naturforsch., A 1962, 17a, 1103. (b) Beckey, H. D. Z. Naturforsch., A 1964, 19a, 71. (2) (a) Tyutyulkov, N. Rep. Bulg. Acad. Sci. 1958, 11, 295; (b) 1959, 12, 129. (3) Wisseroth, K. Chem.-Ztg. 1976, 100, 380. (4) Block, J.; Moentack, B. L. Z. Naturforsch., A 1967, 22, 711. (5) Copeland, R. F. J. Phys. Chem. 1971, 75, 2967. (6) Kreuzer, H. J. In Physics and Chemistry of Solid Surfaces VIII; Vanselow, R., Ed.; Springer: Berlin, 1990. (7) Kreuzer, H. J. Surf. Sci. 1991, 246, 336. (8) Tomanec, D.; Kreuzer, H. J.; Block, J. H. J. Phys. (Paris) 1986, 47, C2-139. (9) Kreuzer, H. J. J. Phys. (Paris) 1988, 49, C6-3. (10) Wang, L. C.; Kreuzer, H. J. J. Phys., Colloq. 1989, 50, C8-53. (11) Kreuzer, H. J.; Wang, L. C. J. Chem. Phys. 1990, 93, 6065. (12) Block, J. H.; Kreuzer, H. J.; Wang, L. C. Surf. Sci. 1991, 246, 125. (13) Madenach, R. P.; Abend, G.; Mousa, M. S.; Kreuzer, H. J.; Block, J. H. Surf. Sci. 1992, 266, 56. (14) (a) Bragiel, P. Surf. Sci. 1992, 266, 35. (b) Grundler, W. Surf. Sci. 1992, 266, 137. (c) Grundler, W. Ultramicroscopy 1992, 42-44, 191. (15) Zagradnik, R. J. Mol. Catal. 1993, 82, 265. (16) Pancir, J.; Zagradnik, R. Helv. Chim. Acta 1978, 61, 59. (17) Pancir, J.; Haslingerova, I. Collect. Czech. Chem. Commun. 1980, 45, 2474. (18) Sauer, J.; Fiedler, K.; Schirmer, W.; Zagradnik, R. In Proceedings of the 5th International Conference on Zeolites; Rees, L. V. C., Ed.; Heyden: London, 1980. (19) Nakatsuji, H.; Hayakawa, T.; Yonezawa, T. J. Am. Chem. Soc. 1981, 103, 7426. (20) Rabo, J. A.; Angell, C. L.; Kasai, P. H.; Schomaker, V. Discuss. Faraday Soc. 1966, 41, 328. (21) Sankararaman, S.; Yoon, K. B.; Yabe, T.; Kochi, J. K. J. Am. Chem. Soc. 1991, 113, 1419. (22) Rabo, J. A.; Gajda, G. J. Catal. Rev.sSci. Eng. 1989, 31, 385. (23) Rabo, J. A.; Kasai, P. H. Prog. Solid State Chem. 1975, 9, 1.
S0743-7463(94)00480-4 CCC: $12.00
trodes,25-34 and in some electron transfer reactions.35,36 From these studies it follows that an applied electric field induces a large change in the distance of bonds formed between surface atoms and ionic or molecular adsorbates, shifts of the bonds’ vibrational frequencies,25 a decrease of the Wiberg index, electronegativity, hardness, and pseudohardness of surface atoms,14a changes in the charge state of adsorbed particles, the binding energy, and possibly even the orbital configuration of the adsorbate,13 polarization and ionization of atoms and molecules in the zeolite crystal,23,24 a change in ionization potential and electron affinity of the molecules, shifts in the electronic transitions and vibrational frequencies of adsorbate bonds, and a change in reactivity.16,17 These effects clearly can be manifested by the action of a strong electric field with intensity varied from 0.005 to 0.06 au (0.01 au ) 5.2 × 107 V cm-1).11-13,25-29 The electrochemistry of organic compounds is one of the areas in which such influences can occur. The progress of understanding physical phenomena at metal-solution (24) Kasai, P. H.; Bishop, R. J. ACS Monogr. 1976, 171, 350. (25) Bagus, P. S.; Pacchioni, G. Electrochim. Acta 1991, 36, 1669. (26) Pacchioni, G.; Cogliandro, G. Surf. Sci. 1991, 255, 344. (27) Bagus, P. S.; Nelin, C. J.; Muller, W.; Philpott, M. R.; Seki, H. Phys. Rev. Lett. 1987, 58, 559. (28) Bagus, P. S.; Nelin, C. J.; Hermann, K.; Philpott, M. R. Phys. Rev. B 1987, 36, 8169. (29) Bagus, P. S.; Nelin, C. J.; Muller, W.; Philpott, M. R.; Seki, H. Phys. Rev. Lett. 1987, 58, 559. (30) Schuhmann, D. Electrochim. Acta 1987, 32, 1331. (31) Becka, A. M.; Moller, C. J. J. Phys. Chem. 1992, 96, 2657. (32) Finklea, H. O.; Hanshew, D. D. J. Am. Chem. Soc. 1992, 114, 3173. (33) Porter, M. D.; Bright, T. B.; Allara, D. L.; Chidsey, C. E. D. J. Am. Chem. Soc. 1987, 109, 3559. (34) (a) Stern, D. A.; Laguren-Davidson, L.; Frank, D. G.; Gui, J. Y.; Lin, C. H.; Lu, F.; Salaita, G. N.; Walton, N.; Zapien, D. C.; Hubbard, A. T. J. Am. Chem. Soc. 1989, 111, 877. (b) Philpott, M. R.; Glosli, J. N. Chem. Phys. 1995, 198, 53. (c) Philpott, M. R.; Glosli, J. N.; Zhu, S. B. Surf. Sci. 1995, 335, 422. (d) Xia, X.; Perera, L.; Essmann, U.; Berkowitz, M. L. Surf. Sci. 1995, 335, 401. (35) Lockhart, D. J.; Kirmaier, C.; Holten, D.; Boxer, S. G. J. Phys. Chem. 1990, 94, 6987. (36) (a) Franzen, S.; Goldstein, R. F.; Boxer, S. G. J. Phys. Chem. 1990, 94, 5135. (b) Gajdek, P.; Najbar, J.; Turek, A. M. J. Photochem. Photobiol., A: Chem. 1994, 84, 113. (c) Lao, K. Q.; Franzen, S.; Steffen, M.; Lambright, D.; Stanley, R.; Boxer, S. G. Chem. Phys. 1995, 197, 259. (d) Kharkats, Y. I.; Kuznetsov, A. M.; Ulstrup, J. J. Phys. Chem. 1995, 99, 13545.
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and metal-ultrahigh vacuum interfaces stemmed in substantial measure from the development of in-situ probe microscopic, X-ray scattering, and vibrational spectroscopic techniques.37a In line with the Gouy-ChapmanStern model, the electric field intensity at the outer Helmholtz plane of the double layer at the electrodesolution interface depends on the electrode potential, the dielectric permeability, and the ionic strength of the solution and ranges up to 0.01 au.37b,38 In the case of specific adsorption of ions, the field intensity is the sum of the above value for the charge density of specifically adsorbed ions divided by the integral capacity of space between the outer and inner Helmholtz planes of the double layer and it can be as large as 0.03 au.37b Also, the intensity of the nonuniform electric field near the solid rough surface exceeds the value of the flat surface, as F ) U/(Ar), where U is the outer potential difference and r is the radius of the divided crystallites or the roughness of the surface.39 Correct estimation of the electric field intensity on the different faces of the silver electrode was performed using the jellium model for explanation of the peculiarities of aliphatic alcohol adsorption from water on the several crystal faces of Ag electrodes in ref 40a. The inverse capacity of the inner Helmholtz layer due to solvent as estimated from a model of hard-sphere ions and dipoles against a wall on the basis of the “mean spherical approximation” equals approximately 0.716 nm,40b and the distance from the jellium edge of the “image plane” varies from 0.044 to 0.049 nm for different faces. The electric field orienting the adsorbed molecules on the different silver faces was obtained from the PartenskiiSmorodinskii equation40c and equals 0.013 au. At F < 0.01 au the change of the calculated quantum chemical parameters of molecules and ions reduces progressively with field intensity and the main effect of electric field action becomes the polarization of them. Molecules possessing the dipole moment µ and polarizability R gain additional energy in the electric field: ∆E ) µF + 0.5RF2. As a result of this process, molecules can take on a preferential orientation relative to the electrode surface and their adsorption energies will changes. At F < 0.001 au (or at F < kT) these polarization effects become negligibly small.5 The electronic and spatial structure of organic molecules and the products of their electrode reactions (radical ions and neutral radicals) placed in the electric field of the dense part of a double-electrode layer differs from the structure of these particles in solution. As a result, the activation barriers of their reactions with solution components will change and the composition of the organic compounds’ electrolysis products will differ from those of analogous reduction (oxidation) processes in solution. The electrode field induces orientation of solvent dipoles and reagent molecules on the solid surface. With conformation transitions being possible in molecules, the conformations with higher dipole moment are mainly formed on the electrode surface. The regioselectivity of the further reactions of the products of the electrode process (radical anions or radical cations) is determined by the conformation of the products on the electrode surface. However, (37) (a) Weaver, M. J.; Gao, X. Annu. Rev. Phys. Chem. 1993, 44, 459. (b) Bard, A. J.; Faulkner, L. R. Electrochemical Methods: Fundamentals and Applications; John Wiley & Sons: New York, 1980. (38) Carnie, S. L.; Chan, D. Adv. Colloids Interface Sci. 1982, 16, 81. (39) Block, J. H.; Czanderna, A. W. In Methods of Surface Analysis; Czanderna, A. W., Ed.; Elsevier Science Publishing Co.: Amsterdam, Oxford, New York, 1975; Vol. 1, Chapter 6. (40) (a) Foresti, M. L.; Aloisi, G.; Innocenti, M.; Kobayashi, H.; Guidelli, R. Surf. Sci. 1995, 335, 241. (b) Blum, I.; Henderson, D. J. Chem. Phys. 1981, 74, 1902. (c) Partenskii, M.; Smorodinskii, Ya. Sov. Phys. Solid State 1974, 16, 423.
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in contrast to the case for neutral organic molecules, the charge distribution data for atoms of these particles are unknown for unstable radical ions, and so we need quantum chemical computations for the stability of different orientations of radical ions in the electric field. The effects connected with the action of the electrode field gradient are often used to explain different peculiarities of the properties of chemically modified electrodes. These effects are connected with a decrease in stability of radical anions of nitroaromatic compounds generated electrochemically from molecules grafted to the surface of metal oxide electrodes as compared to the stability of the same radical anions which are generated in solution.41 The data on the dependence of anthraquinone’s propensity for two-electron reduction on its orientation on the electrode surface may also be explained using the hypothesis of the electrode field effect.42 In spite of the considerable number of studies dealing with the electrode field effect on the rate and direction of electrochemical reactions of organic compounds,43 it is rather difficult to separate experimentally the electrode field effect on these transformations from the effect of specific adsorption of these compounds and reactions of reagents and intermediates of electrochemical transformations with the material of the electrode surface. Thus, possible electrode field effects can be distinguished by means of the quantum chemical computations of its effect on activation barriers of model electrochemical reactions. The quantum chemical methods are widely used in organic electrochemistry to predict the structure and properties of adsorption complexes of organic compounds on electrode surfaces,44 the structure45 and activation barriers of dissociation of electrochemically generated radical anions,46a the direction of the attack and positional selectivity of nucleophile addition to electrochemically generated aromatic compounds’ radical cations,46b and the direction of protonation of aromatic hydrocarbons’ dianions.47 But all these computations, with the exception of those made in ref 47 using a very simple Huckel’s MO method and performed in refs 25-29 for some atoms, diatomic molecules, and ions by the ab initio method, do not allow for a possible effect of the electrode field on the electronic and spatial structure as well as on the reactivity of organic particles in the near-electrode space. If a sophisticated model of an electrochemical reaction is treated quantum chemically, the electrode field is adequately accounted for. In order to obtain a realistic theoretical description, an electric field operator must be incorporated into the Hamiltonian,16 or local point charges representing rather extensive neighbors of the reaction center must be taken into consideration.18 The method SCF MO LCAO in the valence approximation MINDO/3 was used in the present work to study the effect of the electric field intensity and vector direction on the structure of molecules and radical ions containing electrochemically active functional groups (halogen, nitro, carbonyl, and amino) and activation barriers of orientation of the particles, heterogeneous charge transfer, particle dissociation, inversion, and cis-trans isomerization on (41) Murray, R. W. Electroanal. Chem. 1984, 43, 191. (42) Sharp, M. Electrochim. Acta 1978, 23, 287. (43) Mayranovskij, S. G. In Voltammetry of Organic and Inorganic Compounds (Russian Edition); Mayranovskij, S. G., Ed.; Nauka: Moscow, 1985. (44) Nazmutdinov, R. R.; Kuznetsov, A. M.; Shannik, M. S. Elektrokhimiya 1986, 22, 897. (45) Eliving, P. J.; Pullman, B. Adv. Chem. Phys. 1961, 3, 1. (46) (a) Canadell, E.; Karafiloglou, P.; Salem, L. J. Am. Chem. Soc. 1978, 100, 287. (b) Yochida, K. Electrooxidation in Organic Chemistry; Wiley Interscience Publishers: New York, 1984. (47) Hoytink, C. J. Recl. Trav. Chim. 1957, 76, 885.
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the electrode surface. This method reproduces well experimental heats of formation of organic compounds, their polarizabilities, and the activation barriers of their uni- and bimolecular reactions.48-51 The self-empirical method with parameters based on the experimental heats of formation of organic compounds is best suited for the qualitative investigation of the electric field effect on the activation barriers of reactions of complex organic compounds. It should be particularly emphasized that the nonempirical quantum chemical methods are computation time consuming and in many instances lead to poor reproducibility of heats of large organic compound formation and their reaction activation barriers. For these reasons, the latter methods were applied in most cases only for study of the electric field effect on the reactions of the simple inorganic molecules and ions.25-29 Computation Method Computations were performed according to the program described in ref 53. The external field was simulated by the uniform electric field of an infinitely long plane condenser and was accounted for by adding the one-electron part of the Hamiltonian of the terms proportional to the field intensity to the diagonal matrix elements (∆µµ)
∆µµ ) zAF
(1)
where zA is the coordinate of the atom on which the atomic orbital µ is centered. The field vector lies along axis z of the molecular coordinate system. Due to the used approximation MINDO the additives in almost all nondiagonal matrix elements (∆µν) are equal to zero. The terms of the following kind differ from zero
∆µν ) χsnzeAχpz
(2)
where χns is the atomic orbital of s-kind with quantum number n, χpnz is the atomic orbital of p-kind (both orbitals are centered on one atom A), and zAe is the z-projection of the radius vector of the electron counted off from the atom nucleus A. After integration in the spherical system of coordinates with the origin on the atom nuclues A, we obtain
∆s,pz(n) ) 22n+1(2n + 1)(ζsζpz)n+1/2/x3(ζs + ζpz)2n+2
(3)
where ζs and ζpz are the effective charges of the nucleus (Slatter’s exponents). When considering charged systems in the external electric field, the origin of the molecular system of coordinates was placed at the mass center. The validity of this approach was justified in refs 54 and 55. Obtained heads of organic compound formation in our calculations at F ) 0 agree well with experimental values and those from ref 50. Methyl fluoride is the only molecule studied with an essential difference between the experimental (234 kJ mol-1 52), and calculated (214 kJ mol-1) heats of its formation from the elements. There are a number of points to be made. The interference of solvents and supporting electrolyte ions as well as field inhomogeneity within a Helmholtz inner layer is not sufficiently taken into account in the present model. To compare our simulations with experimental data, one has to include the ions and solvent molecules in simulations. This introduces a substantial difficulty into the treatment, since the potentials of ion/ surface and organic molecule/surface interactions are not known (48) Dewar, M. J. S. Chem. Br. 1975, 11, 95. (49) Jug, K. Theor. Chim. Acta 1980, 54, 263. (50) Bingham, R. C.; Dewar, M. J. S.; Lo, D. H. J. Am. Chem. Soc. 1975, 97, 1285. (51) Bischof, P. J. Am. Chem. Soc. 1977, 99, 8145. (52) JANAF Thermochemical Tables, PB-168370, Clearinghouse; U.S. Department of Commerse (National Bureau Standards): Washington, DC, Aug, 1965. (53) Lobanov, V. V. Zh. Strukt. Khim. 1985, 26, 128. (54) Hanson, G. R. J. Chem. Phys. 1962, 62, 1161. (55) Javanainen, J. Phys. Lett. 1981, 81A, 255.
Figure 1. Dependencies of formation heats of organic molecules from elements on the angle (R) between the electric field vector and the C-Y bond (Y ) F, Cl, dO): 1, CH3Cl; 2, CH3CHdO; 3, CH3F; 4, (CH3)2CdO; 5, CH3CH2F. in most cases. The joint action of short-range field effects (chemical bond formation and cleavage) and of long-range field effects (homogeneous fields in molecular dimensions) is taken into consideration using the present approach.
Results and Discussion (i) Orientation of Molecules and Radical Anions. Most organic compounds dissolved in water and other solvents, which do not exhibit surface activity with the electrode material, undergo the reaction of charge transfer with the electrode being in the adsorbed state on its surface. Therefore in the first stage of electrochemical transformations, the molecule in solution diffuses to the electrode surface and is oriented on the external plane of its double electric layer. The molecular orientation on the electrode surface is affected both by the solution composition (solvent structure, pH of the solution, structure and concentration of background electrolyte, addition of surface active compounds) and by the electrode material properties (zero charge point, ability of electrode material to form donor-acceptor bonds with the solution components) as well as by the electrode potential. Most of the above-mentioned factors, as is shown from analysis of equations for double electric layer models on the electrode surface,37b,38,56,57 also determine the electric field intensity on this surface. Hence, with the exception of electrode properties, which determine its ability for donor-acceptor interaction with adsorbed molecules or ions, the action of all the other factors, in the first approximation, can be reduced to the effect of the electric field intensity of the double electrode layer on the particle orientation on the electrode surface. Figure 1 gives the heats of organic molecule formation in the gas phase as dependent on the angle between the electric field vector and the Y-C bond (Y ) F, Cl, CHdO) under the field intensity 0.02 au. These dependencies for asymmetric molecules, e.g., for CH3CHdO, are given for the azimuthal angles characterized by a minimum of the (56) Damaskin, B. B.; Krishtalik, L. I. Electrokhimiya 1984, 20, 291. (57) Krylov, V. S.; Damaskin, B. B.; Kir’yanov, V. A. Uspekhi Khimii 1986, 55, 1258.
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with the effect of the field intensity on the nuclear relaxation of the structure of the radical anions. The latter effect can be established from the reorientation of the activation energies using the Marcus equation58 for the activation energy at zero enthalpy, i.e., for the intrinsic barrier (E0q). We have calculated these values for the CH3F•- and CH3Cl•- reorientations and have found that their dependencies on the field intensity are well approximated by the following equations:
For CH3F•E0q ) 3731F1.55 (5 points; r ) 0.994) (4a) For CH3Cl•E0q ) 5994F1.47 (5 points; r ) 0.984) (4b)
Figure 2. Dependencies of formation heats of organic compound radical anions from elements on the angle (R) between the field vector and the C-Y bond: 1a, CH3Cl•- at 0.02 au; 1b, the same at 0.04 au; 2a, CH3CHdO•- at 0.02 au; 2b, the same at 0.05 au; 3a, CH3F•- at 0.02 au; 3b, the same at 0.04 au; 4, •- at 0.02 au. CH3NO•2 at 0.03 au; 5, CH3CH2F
heat. It is evident that such an orientation, when the more electronegative group Y is directed from the cathode, is the best orientation of molecules on the surface. The rise of field intensity leads to stabilization of this orientation, to an increase of C-Y bond length, and to the negative charge on the Y atom and the positive charge on the C atom of the C-Y bond being observed. The obtained optimal orientation of molecules in the cathode field coincides with the orientation of alkyl halides and carbonyl compounds suggested on the basis of the electrostatic views of Elving45 for electrochemical reduction of these compounds. In contrast to the orientation of the molecules in the field, the orientation of the radical anions, which are products of their one-electron reduction on the electrode, cannot be predicted from a comparison of the electronegativities of the C atom and the Y group. As follows from Figure 2, the most stable orientation in the field for radical anions formed from CH3CHdO, CH3NO2, (CH3)2CdO, and CH3CH2F is the same orientation as for the molecules, while for the CH3F•- and CH3Cl•- radical anions, that orientation is more stable when the Y group is turned to the cathode. The transition between these two orientations is connected with overcoming the activation barrier, whose height increases with the field intensity. One more example of the reaction of radical anion reorientation in the electric field, possessing a high activation barrier which does not coincide with the difference of energy of the two opposite orientations, is reorientation of the acetaldehyde radical anion. When the field intensity is increased from 0.02 to 0.05 au, the activation barrier height rises from 0 kJ mol-1 for the orientation at R ) 0° (orientation I) to 54 kJ mol-1 for the orientation at R ) 180° (orientation II). An increase of field intensity also leads to a decrease of the enthalpy of the transition from orientation I to orientation II of CH3F•- and CH3Cl•- radical anions and an increase of the reverse reaction enthalpy. The change of activation energy for these transitions upon enhancement of the field intensity may be connected both with the change of the enthalpy of these transformations and
where the E0q values are given in kilojoules per mole and F is given in atomic units; r is the correlation coefficient for the linear relation between the logarithms of E0q and F. Thus, the higher activation barrier of the CH3Cl•- radical anion reorientation as compared to that of CH3F•- is connected with the higher energy of nuclear relaxation for its structure in the course of transformation in the electric field. Experimental data59 indicate that, at the adsorption of alkyl halides on the negatively charged surface of mercury electrodes, molecules are oriented by the halogen atom to the electrode; i.e., there is an electrostatically unfavorable orientation. Suppose that there is a partial charge transfer from the electrode to the organic molecule under specific adsorption of alkyl halide on the mercury surface, so the stability of the experimentally observed orientation may be connected with the considerable contribution of the ionic structure of the radical anion of the alkyl halide (which is more stable in this orientation) to the total energy of the formation of the adsorption complex. The direction of the next attack of active particles (H+, ions of background electrolyte, and other compounds) from solution on the electrochemically active molecule or electrode reaction product in the near electrode space is determined by the orientation of these compounds on the electrode surface. Change of the reaction center of the compound is possible under the electric field effect in a definite orientation. The substrate atoms possessing maximum negative charges and large coefficients of the higher occupied molecular orbital are most probably attacked by the electrophilic reagents.60 When a particle is placed in the external electric field, the partial charges on atoms and orbital coefficients change, since the atom’s polarizability is different, depending on the field vector direction, and this may lead to the change of substrate reaction center. To illustrate this supposition, let us consider the data about the effect of the field intensity and vector direction on the charge distribution of the atoms of the nitromethane molecule and radical anion. These data are presented in Table 1. It is evident that the charge on the N atom of the molecule in orientations I and II weakly depends on the field intensity and vector direction, while in the radical anion it considerably increases with the field enhancement in orientation I and decreases in orientation II. The charges most considerably change in a molecule and radical anion on O and H atoms. The field (58) Marcus, R. A. J. Phys. Chem. 1968, 72, 891. (59) Frumkin, A. N.; Bagotskij, V. S.; Iofa, Z. A.; Kabanov, B. N. Kinetics of Electrode Processes (Russian Edition); Moscow University; Moscow, 1952. (60) Hudson, R. F.; Klopman, G. Tetrahedron Lett. 1967, 1103.
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Table 1. Partial Charges on the Atoms of the Nitromethane Molecule and the Radical Anion in the External Electric Field particle charges at particle orientation in the field
atom
F ) 0 au
F ) 0.01 au
F ) 0.02 au
F ) 0.03 au
F ) 0.04 au
F ) 0.05 au
N O C H3 H1dH2
1.113 -0.562 -0.159 0.059 0.055
1.114 -0.597 -0.168 0.084 0.082
1.114 -0.632 -0.174 0.109 0.108
1.119 -0.666 -0.185 0.133 0.132
1.119 -0.700 -0.190 0.157 0.157
1.122 -0.733 -0.199 0.183 0.180
N O C H3 H1dH2
1.113 -0.562 -0.159 0.059 0.055
1.114 -0.526 -0.150 0.32 0.028
1.115 -0.488 -0.139 0.004 -0.002
1.117 -0.448 -0.127 -0.026 -0.034
1.125 -0.406 -0.113 -0.059 -0.069
1.128 -0.361 -0.097 -0.095 -0.107
N O C H3 H1dH2
0.798 -0.757 0.006 -0.133 -0.077
0.779 -0.794 -0.004 -0.093 -0.048
0.762 -0.829 -0.016 -0.055 -0.016
0.747 -0.862 -0.030 -0.019 0.013
0.742 -0.895 -0.048 0.014 0.040
0.739 -0.926 -0.068 0.045 0.068
N O C H3 H1dH2
0.798 -0.757 0.006 -0.133 -0.077
0.825 -0.721 0.006 -0.167 -0.111
0.855 -0.681 0.009 -0.229 -0.151
0.980 -0.660 0.013 -0.228 -0.270
1.027 -0.550 0.018 -0.226 -0.359
1.034 -0.506 0.024 -0.260 -0.393
intensity growth induces a decrease of negative charge on the O atom of a molecule and radical anion in orientation I and an increase of this charge in orientation II. Charge variations on the atoms, depending on the vector direction and intensity of the field, lead to such a situation that if, the field being absent, weak positive and negative charges (0.01), respectively, are located on the CH3 and NO2 groups of the molecule, then, at F ) 0.05 au in orientation II, the charge on the CH3 group reaches 0.344 while in orientation I its charge is negative (-0.406). When passing to the radical anion, the absolute value of CH3 group charges increases in orientation I (-1.022) and decreases in orientation II (0.113). Thus, the field being absent or not in orientation II, the attack of a positively charged particle, for example, H+, on the nitromethane molecule and radical anion is most advantageous for the negatively charged NO2 group while the CH3 group will be the reaction center for the electrophilic attack on the molecule and radical anion in orientation I in the electric field. (ii) Charge Transfer from Electrode to Molecule. The molecules which have achieved the Helmholtz external plane of the electrode double layer take part in this stage of the electrochemical transformation. Such a reaction rate should be affected either by the field on the metal electrode surface or by that created by specifically adsorbed ions in the dense part of the double layer. As is shown above, the energies of both the initial molecule and the radical anions, formed as the reaction result, depend on the intensity and vector direction of the electric field. The rate of charge transfer from an electrode to a molecule, being in the adsorbed state, with formation of a reduction product capable of electrode adsorption is determined by the change of the activation free energy for this process (∆Gq).57 Allowing for the fact that ∆Gq ) ∆Eq - TδSq, where ∆Sq is the change of reagent entropy in the transition state and ∆Eq is the reaction activation energy, and using the Polanyi equation for connecting the latter value with reaction enthalpy, we obtain the following expression for the reaction activation energy
Eq ) E0q + R∆He
(5)
where E0q is the reaction intrinsic barrier at Eq , ∆He and R is the charge transfer coefficient (0 e R e 1). The
Figure 3. Dependencies of adiabatic electron affinities of CH3Y compounds (Y ) F, Cl, NO2) on the electric field intensity. The angle between the C-Y bond and the field vector R ) 180° (orientation II). a, CH3NO2; b, CH3Cl; c, CH3F.
enthalpy of charge transfer (∆He) between the adsorbed reagent and the electrode depends on the adiabatic electron affinity of the reagent in the electric field of the electrode. Figure 3 presents the calculated dependencies of the adiabatic electron affinity of CH3Y (Y ) F, Cl, NO2) molecules placed in orientation II on the electric field intensity. It is evident that the increase of field intensity induces a decrease of the molecule’s electron affinity in orientation II. Since the dependencies of the formation heats for the reagents and the electrode reaction products in the electric field on the angle between the field vector and the C-Y bond (Figures 1 and 2) are nonlinear, this also leads to nonlinear dependencies of electron affinity on the angle between the field vector and the C-Y bond under constant field intensity, in particular, to its decrease
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under the value of the angle corresponding to the saddle point of the activation reorientation curve of the radical anions. The other factor which is affected by the intensity and vector direction of the field is the reaction intrinsic barrier (E0q). This value is determined by the reorganization energy of the external and internal coordination spheres of the reagents.61 The latter depends on the change of the bond force constants, their lengths, and the valence angles under the transition from reagent to electrode reaction product. For example, change of the C-Cl bond length under methyl chloride reduction at F ) 0 is 0.026 nm, while at F ) 0.05 au in orientation II it equals 0.012 nm. The intensity and vector direction of the field also exert an effect on bond force constants and on the following change of frequencies of the bond valence vibrations. Thus, the field intensity being increased from 0 to 0.05 au, the frequency of the C-Cl bond valence vibration in the CH3Cl molecule in orientation II decreases from 807 to 646 cm-1, and for the radical anion this change is from 478 to 171 cm-1. This value of the radical anion in orientation I changes from 478 to 623 cm-1. Therefore, the intensity and vector direction of the field also affect the value E0q and the overall reaction rate. The electrode field effect on the rate of the charge transfer reaction may be experimentally observed if the molecules are adsorbed or chemically bound on the electrode surface in an orientation unfavorable for the next charge transfer reaction and if we compare the rate constants of this process with those for the charge transfer process performed from the favorable molecule orientation, fixed to the electrode surface. An example of such a reaction is the dependence of the ability of anthraquinone molecules bonded to the electrode for two-electron reduction on their orientation on the electrode surface.40 The unfavorable orientation for the charge transfer between the adsorbed molecule and the electrode may also be achieved at high electrode surface coverage by adding the surfactant molecules into the solution. (iii) Dissociation of Neutral Molecules and Ions. The dissociation reactions of solvent and electrochemically active molecules and intermediates as well as products of electrode reactions have common organic electrochemistry. If the reaction layer thickness does not exceed that of the diffusion layer of the electrode (i.e., they proceed near the electrode), the kinetics and equilibria of such reactions should be affected by the electrode field. Radical anions formed under one-electron reduction of alkyl halides are unstable, and their dissociation is possible in the following directions:
Alk-Y•- f Alk• + Y-
(6a)
Alk-Y•- f Alk- + Y•
(6b)
The former corresponds to that suggested free radical mechanism of alkyl halide reduction,45 while the latter (with regard to the high electron affinity of the halogen atom) formally corresponds to a carbanionic reduction mechanism (SN2). Our calculations have shown that the activation barriers of the dissociation reactions and the composition of the reaction products, when radical ions are placed in the external electric field, considerably depend on their initial orientation with respect to the field vector and its intensity. Figure 4 present the dependencies of the activation barriers of the dissociation of some molecules and ions on the field intensity. For CH3Y•- (Y ) Cl, F, CH2F) radical anions in orientation II, when the (61) Marcus, R. A. J. Chem. Phys. 1965, 43, 679.
Figure 4. Dependencies of activation energies of particle dissociation on the intensity of the electric field. The angle between the C-Y bond and the field vector R ) 0 (orientation I) and R ) 180° (orientation II). The particles orientation is given in brackets. 1, CH3Cl•- (II); 2, the same (I); 3, CH3CH2F•(II); 4, CH3F•- (II); 5, the same (I); 6, (CH3)2OH+ (II); 7, H2O•+ (II); 8, H2O (II).
field intensity is increased, the activation barrier of dissociation sharply decreases. As is evident from the analysis of the charge distribution in the activated complexes under elongation of the C-Y (Y ) F, Cl) bond, the CH3 radical (or the C2H5 radical under CH3CH2F•anion radical dissociation) and the halogen anion are the main reactions products. As follows from Figure 4, in the case of radical anions oriented by a halogen atom to the cathode surface under field intensities up to 0.02 ÷ 0.03 au, the dissociation activation barrier grows as compared to that for the reaction at F ) 0. This fact may be explained by dissociation of radical anions into CH3- and Y• particles. Formation of such products is confirmed by the observed dependencies of the charge on Y in radical anions on the C-Y distance. Localization of an additional electron on the CH3 fragment at fields equal to 0.03 au is due to high-energy consumption. But at higher fields, these energy consumptions, which are due to the difference of electron affinity of the CH3 radical and the Y atom, are compensated by the field action and are accompanied by the potential curve bend. At high intensities the height of the dissociation activation barriers for radical anions in this orientation decreases with field growth. Table 2 gives the calculated coefficients of the equation which approximates the activation energy dependencies of the particle dissociation on the field intensity. It is evident that under radical anion dissociation from orientation I the activation barrier’s sensitivity to the change in field intensity much exceeds that under dissociation from orientation II. So orientation I is shown to be more stable in the electrode field for CH3Y•- (Y ) F, Cl) radical anions. Radical anions in this orientation either may be reoriented after overcoming the activation barrier or may dissociate with carbanion formation. Reorientation from I to II and dissociation with formation of a CH3 radical is more advantageous at relatively low fields, as the reorientation barrier height is lower than the dissociation
Electric Field Effect on Activation Barriers
Langmuir, Vol. 12, No. 21, 1996 5177
Table 2. Coefficient of the Equation Eq ) a exp(bF) Approximating the Dependencies of Particles’ Dissociation Activation Energies (Eq) on the Electric Field Intensity (F)
a
particle
dissociation products
range of field intensity change, au
a
b
dEq/dF at F ) 0.03 au
CH3Cl•CH3Cl•CH3CH2F•CH3F•CH3F•H2O (CH3)2OH+ H2Oo+
CH3o, ClCH3-, Cl• CH3CH2o, FCH3o, FCH3-, F• H+, OH(CH3)2O, H+ H+, OHo
0-0.05 0.02-0.05 0-0.02 0-0.05 0.03-0.05 0.03-0.05 0-0.04 0.02-0.05
215.4 286.2 285.0 349.5 441.5 1160.1 623.4 521.0
-163.5 -19.7 -17.0 -49.2 -7.7 -13.8 -21.9 -19.8
-261 -3122 -2909 -3930 -2698 -10582 -7078 -5696
Correlation coefficients are given for the linear relation ln
kJ mol-1
Eq
activation energy from orientation I. For example, for CH3Cl•- at F ) 0.05 au, the reorientation activation energy is 103.5 kJ mol-1 and dissociation is possible from orientation I. Since the electric field intensity on the external plane of the double layer grows upon shift of the electrode potential from its zero charge point and at enhancement of the background electrolyte concentration,56 and SN2 mechanism of alkyl halide reduction is more probable at high cathode potentials in concentrated electrolyte solutions. The correlation dependencies between the reduction potentials of these compounds and the Hammet or Taft coefficients of the substituents show the existence of negative charge on the carbon atom of alkyl or aryl halides in the reaction transition state.62 These data agree with the carbanion or free radical mechanism. We have found that in orientation II up to the field intensity 0.02 au the C atom in CH3Cl•- has positive charge. As it does in orientation I, while the field intensity is increased from 0.03 to 0.05 au, this atom acquires a negative charge which rises from 0.004 to 0.085. Thus, the electrode field effect on the charge of the C atom in the transition state of C-Hal bond reduction occurring in accordance with the free radical mechanism may cause positive values of the reaction coefficients in the mentioned correlations. The electrode field effect on the dissociation kinetics of electrochemically generated radical anions may be experimentally found if the lifetime of these radicals does not exceed 1 × 10-7 s,63 which is close to the limit of electrochemical methods for studying fast reaction kinetics in solutions. However such effects may be observed if the initial molecules are strongly adsorbed or chemically bound to the electrode surface. In this case one can observe a decrease in the stability of the radical anions, formed from the adsorbed molecules, as compared to the stability of particles generated in solution. This supposition may be proved by the data on the lower stability of nitroaromatic radical anions and the pyrazoline radical cation, immobilized on the oxide electrode surface, as compared with the behavior of analogs of these radical ions in solution.41 The protonation and deprotonation processes can serve as one more example of electrochemical reactions whose activation barriers are affected by the electrode surface field. The dependence of deprotonation rate constant on the electric field intensity is connected, using the Bronsted equation, with the dependence of acid dissociation equilibrium constants on the field intensity.64 This dependence is determined by the Onsager equation, which does not account for the effect of the structure of the dissociated (62) Sense, J. W.; Burton, F. G.; Nichol, S. L. J. Am. Chem. Soc. 1968, 90, 2595. (63) Parker, V. D. Adv. Phys. Org. Chem. 1983, 19, 131. (64) Arzumaniantz, E. A.; Gurevich, Yu. Ia.; Harkatz, Yu. I. Elektrokhimiya 1988, 24, 471.
correlation coefficienta 0.926 0.958 0.992
0.997
) ln a + bF
acid on the derivative of the dissociation free energy with field intensity. It is evident from Figure 4 that the activation barriers for deprotonation of different particles, such as the dimethyloxonium ion, a radical cation, and a molecule of water, decrease with growth of the field intensity, and the derivative of dissociation activation energy with field intensity, as follows from Table 2, depends on the structure of the particles. The value of the derivative is, probably, determined by the charge distribution on the atoms and the difference of product structure from the initial particle structure in the electric field. The electric field of high intensity (up to 5 × 106 V cm-1) created on the surface of ion-exchange membranes can lead to anomalously high values of current passing through these membranes.65 The observed effect can be related to the increase in water dissociation into H+ and OH- as affected by the membrane surface field. Our estimates show that the dissociation rate constant of H2O increases by 2.5 × 105 times on the anion-exchanged membrane surface, and it increases by 20 times on the bipolar membrane surface. Using equation coefficients from Table 2, which describes the dependence of the water dissociation activation energy on the field intensity, we shall obtain that such a decrease in the dissociation rate constant may be due to the action of the field with intensity 6.7 × 106 V cm-1 for anion-exchanged membranes and 1.7 × 106 V cm-1 for bipolar membranes. The calculated field intensities agree with their estimates on the surface of these membranes, given in ref 65. (iv) Inversion, Cis-Trans Isomerization, and Conformational Transition. Alkyl radicals, formed in the electrochemical reduction of alkyl halides, which occurs according to a free radical mechanism, can further accept an electron from the cathode with carbanion formation. In the following stage this anion interacts with a proton from a solvent molecule, with a hydrocarbon being formed. When optically active alkyl halides are subjected to electrolysis, the formed hydrocarbons can both retain their configuration and manifest inversion or complete racemization. The stereochemical result of the electrode reaction is determined by the ratio of the rates of heterogeneous electron transfer, carbanion diffusion from the electrode surface, inversion of radical or carbanion, and protonation of inverted or noninverted carbanions in solution.66 As is shown above, the activation barrier and so the rate of some of these transformations may be affected by the field intensity on the electrode surface. To explain alkyl halide electrolysis stereochemistry, it is supposed that the configuration stability of the formed radical and carbanion of the hydrocarbons and, thus, the inversion rate of these particles depend on the potential gradient at the electrode surface.67 (65) Simons, R. Electrochim. Acta 1984, 29, 151. (66) Butin, K. P. Uspekhi Khimii 1971, 40, 1058.
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Figure 6. Dependencies of heats of formation of 1,2-difluoroethylene isomers from elements on the double angle (γ) formed by the planes passing through the F-C-C-H and H-C-C-F bonds at different electric field intensities.
Figure 5. (a) Dependencies of the methyl radical (1) and methyl anion (2) heat formation on the angle (β) between the C-H bond and the direction of the single electron orbital of the radical or the occupied pz orbital of the carbanion at different field intensities: a, 0 au; b, 0.02 au; c, 0.04 au. (b) Dependencies of ammonia heat formation on the angle (β) between the N-H bond and the direction of the n orbital of the N atom at different field intensities, in atomic units.
We have studied the effect of electric field intensity on the inversion barriers of radical and carbanion, formed under electrolysis of methyl halides: CH3o and CH3- as well as the NH3 molecule. The dependencies of the particle heat formation on the angle (β) between the C-H or N-H bond and the direction of the single electron orbital of the radical, the occupied pz orbital of the carbanion or the n (67) Nonaka, T.; Ota, T.; Odo, K. Bull. Chem. Soc. Jpn. 1977, 50, 419.
orbital of the N atom in ammonia, at different field intensities were computed. Figure 5 demonstrates the calculated curves of the inversion transitions of these particles under the field absence and with the intensities 0.02 and 0.04 au. It is evident that the activation barriers of the inversion of these particles must depend on the field intensity. The highest stability in the field is evidently peculiar to the particle configurations in which the single electron orbital of the radical, the occupied pz orbital of the carbanion or the n orbital of the N in ammonia, is directed away from anode and the C-H bonds of the radical and the carbanion or the N-H bonds of ammonia are directed toward the negatively charged electrode surface. The configuration stability of these particles decreases in the series carbanion > ammonia > methyl radical. On the basis of these calculations one can suppose that the configuration stability of the particles will increase when affected by the field created by the cations of the background electrolyte and will decrease, for example, under carbanion solvation, i.e. at the transition from tight to separated ion pairs in the solution. Thus, the change of field intensity on the electrode surface induced by the change in electrolysis potential, the concentration and content of background electrolyte, and the structures of the solvent and the electrode surface, as the result of the change in the rate of inversion of the intermediate of electrode reactions, can lead to the difference in stereochemistry of the electrolysis products. This is confirmed by the numerous experimental data presented in ref 66. One more type of unimolecular reaction, with the activation barrier being supposedly affected by the electrode surface field, is the alkene cis-trans isomerization process. The dependencies of the heats of formation of 1,2-difluoroethylene isomers from elements on the double angle (γ) formed by the planes passing through the F-C-C-H and H-C-C-F bonds at different electric field intensities are exhibited in Figure 6. The curves of the conformational transition were calculated when the
Electric Field Effect on Activation Barriers
external field was absent or its intensities were 0.02 and 0.04 au. The transition from trans to cis form without the field needs the overcoming of an activation barrier of 180 kJ mol-1. When the cis isomer is oriented by hydrogen atoms toward the negatively charged electrode surface in the field 0.02 au, this barrier decreases to 50 kJ mol-1, but when the isomer is oriented toward the same surface by fluorine atoms, the barrier increases to 210 kJ mol-1. The decrease of the activation barrier to zero for the electrostatically favorable orientation of the cis isomer and further growth of the barrier to 222 kJ mol-1 under orientation of the cis isomer by halogen atoms toward the cathode surface are observed at enhancement of the field intensity up to 0.04 au. The observed rise of the 1,2-dibromoethylene cis isomer yield under the cathode reduction of the tetrabromethane gosh conformer under the decrease of reduction potential (isomer yield reaches almost 100% of the theoretical one) is explained by the decrease of the electrode process rate and by superposition of the trans-cis conformation transition.68 The data of the present study about the dependence of the activation barrier of the analogous transformation on the field intensity prove the simpler proceeding of such a transition in the near-electrode space. Furthermore, the increase of the cis-trans stilbenediol isomer ratio under the increase of benzyl reduction potential in neutral media observed in ref 69 easily may be explained by the higher stability of the formed cis isomer or by the decrease of the barrier of the trans-cis transition in the electrode field. Also, the electric field of the electrode can affect the rates of possible conformation transitions. The chairboat transition of the dioxane molecule in the external electric field can be an example of such transitions studied by the method SCF MO LCAO in the CNDO/2 valence approximation.70 The field being absent, the chair conformation with a zero dipole moment is more stable and transition to the boat conformation requires the overcoming of an activation barrier equal to 53 kJ mol-1, but when the electric field is 0.02 au, the boat conformation possessing a large dipole moment proves more stable and the barrier height of this transition decreases to 13 kJ mol-1. Analogous effects of the electrode field action on the conformational transition barriers may be expected for other electrolysis processes of the cyclic compounds. Under these conditions the following stereochemical result of solution component addition to the electrode reaction products is determined by these product conformations, which are more stable in the field. The quantum chemical calculations with regard to the electric field are necessary for prediction of such conformations. Conclusion It follows from quantum chemical calculations that the vector direction and intensity of the external electric field (68) Markova, I. G.; Feoktistov, L. G. Elektrokhimiya 1969, 5, 1095. (69) Vincenz-Chodakowska, A.; Grabovski, Z. R. Electrochim. Acta 1964, 4, 789. (70) Lobanov, V. V.; Alexankin, M. M. Zh. Strukt. Khim. 1979, 20, 181.
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exert a considerable effect on the activation barriers of unimolecular reactions which are possible in the electrolysis processes of organic compounds. It is shown that such an orientation, when the more electronegative group of a molecule is directed away from the negatively charged electrode, is the most advantageous orientation in the electric field of CH3F, CH3Cl, CH3CH2F, CH3CHdO, and (CH3)2CdO compounds. For radical anions formed under reduction of these molecules, with the exception of CH3F•and CH3Cl•-, optimal orientation coincides with that observed for the molecules, while for the mentioned radical anions of alkyl halides the more stable orientation is when the halogen is turned toward the cathode. The transition between the two orientations of these radical anions is connected with overcoming the activation barrier conditioned by the high energy of nuclear relaxation of the reorientation process in the electric field. It is shown that the field effect on the rate of heterogeneous charge transfer from an electrode to the molecule oriented on the electrode surface can be connected with the change of adiabatic electron affinity and reorganization energy (intrinsic barrier) under the field effect. The direction and height of the dissociation barriers of alkyl halide radical anions are determined by their orientation on the electrode surface and by the field intensity. The activation barriers of deprotonation of the dimethyloxonium ion, a radical cation, and a molecule of water decrease with the rise of the field intensity. The sensitivity of the activation barrier height to a change in the field intensity depends on the structure of the particles. The height of the activation barrier of inversion of the carbanion, the methyl radical, and the ammonia molecule depends on the intensity and the vector direction of the external electric field. The configuration stability of these particles increases with field intensity. The height of the activation barrier of 1,2-difluoroethylene trans-cis isomerization decreases with field growth under orientation of the cis isomer by hydrogen atoms toward the cathode surface and increases under the reverse orientation. The field growth also leads to a decrease of the activation barrier of the chair-boat conformational transition of the dioxane molecule. A comparison of the results for activation barriers of organic reactions in the electric field with experimental data on stereochemistry, adsorption and electrolysis products of alkyl halides, properties of chemically modified electrodes, and ion-exchange membranes shows a necessity to estimate the reactivity of the initial molecules and the intermediate products of the electrochemical reactions in the electric field to explain the dependencies of the distribution of the products of organic compound electrolysis, the electron acceptor ability and stability of the products of the electrode reaction of chemically modified electrodes, and the regularities of the adsorption of organic molecules on electrolysis conditions. It is likely that the present results can be used also to explain the peculiarities of several unimolecular chemical reactions accomplished on the surface of metals or their oxides. LA9404806
