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Formalisms suitable for calculating the rate of electron exchange between transition metal complexes in aqueous solution are reviewed and implemented in conjunction with ab initio quantum chemical calculations which provide crucial off-diagonal Hamiltonian matrix elements as well as other relevant electronic structural data. Rate constants and activation parameters are calculated for the hex-aquo Fe2 +-Fe3+ system, using a simple activated complex theory, a non-adiabatic semi-classical model which includes nuclear tunnelling, and a more detailed quantum mechanical method based on the Golden Rule. Comparisons are made between calculated results and those obtained by extrapolating experimental data to zero ionic strength. All methods yield similar values for the overall rate constant (a 0.1 L/(mol-sec)). The experimental activation parameters (δHd and δSd) are in somewhat better agreement with the semi classical and quantum mechanical results than with those from the simple activated complex theory, thereby providing some indication that non-adiabaticity and nuclear tunnelling may be important in the Fe2+/3+ exchange reaction. It is concluded that a model based on direct metal-metal overlap can account for the observed reaction kinetics provided the reactants are allowed to approach well within the traditional contact distance of 6.9 a. 6 figures, 7 tables.

The mechanistic conundrum is commonly posed by the intrinsic structural disconnect between a bimolecular (reactive) intermediate that is fleetingly detected spectroscopically in solution versus that rigorously defined by isolation and X-ray crystallography. We resolve this ambiguity by the combined experimental and theoretical application of the solvent media probe to the transient (1:1) precursor complex in the simplest chemical reaction involving direct adiabatic electron transfer (ET) among various donor/acceptor pairs. Of particular help in our resolution of such an important ET problem is the characterization of the bimolecular precursor complex as Robin-Day class II (localized) or class III (delocalized) from either the solvent-dependent or the solvent-independent response of the diagnostic intervalence absorption bands for the quantitative evaluation of the electronic coupling elements. The magnitudes of these intracomplex bindings are confirmed by theoretical (ab initio and DFT) computations that derive from X-ray structures and Marcus-Hush theories. Most importantly, the experimental solvent-induced ET barriers evaluated from the intervalence absorption bands are also quantitatively verified by the calculated outer-shell reorganization energies to establish unambiguously the intimate interconnection between the loosely bound bimolecular intermediate identified concurrently in solution and in the solid state.

The paramagnetic [1:1] encounter complex ( TCNE ) 2 - is established as the important precursor in the kinetics and mechanism of electron-transfer for the self-exchange between tetracyanoethylene acceptor (TCNE) and its radical-anion as the donor. Spectroscopic observation of the dimeric complex ( TCNE ) 2 - by its intervalence absorption band at the solvent-dependent wavelength of λIV ∼ 1500 nm facilitates the application of Mulliken–Hush theory which reveals the significant electronic interaction extant between the pair of cofacial TCNE moieties with the sizable coupling of HDA = 1000 cm−1. The transient existence of such an encounter complex provides the critical link in the electron-transfer kinetics by lowering the classical Marcus reorganization barrier by the amount of HDA in this strongly adiabatic system. Ab initio quantum-mechanical methods as applied to independent theoretical computations of both the reorganization energy (λ) and the electronic coupling element (HDA) confirm the essential correctness of the Mulliken–Hush formalism for fast electron transfer via strongly coupled donor/acceptor encounter complexes.

Fluorescence of fac-AlQ3 (Q=8-quinolinolato), mer-AlQ3, mer-Al(mQ)3 (mQ=4-methyl-8-quinolinolato), and BeQ2 were investigated with electronic structure calculations. The molecular structure of the first singlet excited state (the emission state) was optimized with the ab initio “configuration interaction with single excitations” (CIS) method. Ab initio CIS and semiempirical “Zerner’s intermediate neglect of differential overlap” (ZINDO) methods were used to calculate the emission energies (ΔE) and also the corresponding absorption energies. Although the ab initio CIS method overestimated the experimental value of ΔE by 1.09–1.16 eV, the ZINDO method reproduced it to a reasonable accuracy (within 0.26 eV). The optimized excited-state structure has an interesting feature in that one of the equivalent ligands distorts appreciably, while the thers keep their ground-state structures. As a result the highest occupied and the lowest unoccupied molecular orbitals (HOMO and LUMO) are localized on the distorted lig...

Two independent methods are presented for the nonperturbative calculation of the electronic coupling matrix element (Hab) for electron transfer reactions using ab initio electronic structure theory. The first is based on the generalized Mulliken–Hush (GMH) model, a multistate generalization of the Mulliken Hush formalism for the electronic coupling. The second is based on the block diagonalization (BD) approach of Cederbaum, Domcke, and co-workers. Detailed quantitative comparisons of the two methods are carried out based on results for (a) several states of the system Zn2OH2+ and (b) the low-lying states of the benzene–Cl atom complex and its contact ion pair. Generally good agreement between the two methods is obtained over a range of geometries. Either method can be applied at an arbitrary nuclear geometry and, as a result, may be used to test the validity of the Condon approximation. Examples of nonmonotonic behavior of the electronic coupling as a function of nuclear coordinates are observed for Zn2OH2+. Both methods also yield a natural definition of the effective distance (rDA) between donor (D) and acceptor (A) sites, in contrast to earlier approaches which required independent estimates of rDA, generally based on molecular structure data.

Important energy quantities governing electron transfer (ET) kinetics in polar solutions (reorganization energy, Er, and net free energy change, ΔU) are evaluated on the basis of quantum-chemical self-consistent reaction-field (SCRF) models. Either self-consistent field (SCF) or configuration interaction (CI) wavefunctions are used for the solute, which occupies a molecular cavity of realistic shape in a dielectric continuum. A classical SCRF model together with unrestricted Hartree-Fock SCF wavefunctions based on the semiempirical PM3 Hamiltonian is applied to the calculation of the solvent portion of Er (denoted Es) for two different series of radical ion ET systems: radical cations and anions of biphenylyl/naphthyl donor/acceptor ( D A ) pairs linked by cyclohexane-based spacer groups and trans-staggered radical anions of the type (CH2)2m, m = 2–5. Results for Es based on two-configurational CI wavefunctions and an alternative reaction field (the so-called Born-Oppenheimer model, which recognizes the fast timescales of solvent electrons relative to those involved in ET) are also noted. Results for inner-sphere (i.e. intra-solute) reorganization, Ei, and for ΔU are also reported. The semiempirical Es results are quite similar to corresponding ab initio results and display the form of the two-sphere Marcus model for Es as a function of D A separation. Nevertheless, in the one case where direct comparison is possible, the calculated Es result is more than twice the magnitude of the estimate based on experimental ET kinetic data. To reconcile this situation, a generalized SCRF model is proposed, which assigns different effective solute cavity sizes to the optical and inertial components of the solvent response, using ideas based on non-local solvation models.

Ab initio calculations of transfer integrals (T[sub DA]) for long-range [pi]- and [sigma]-type electron transfer through saturated spacers linking donor (D) and acceptor (A) groups in several radical anion and cation systems have been carried out and analyzed in terms of additive superexchange models. The sensitivity of calculated results to orbital basis and wave function type has been carefully examined. The one-electron Koopmans' theorem approach, based on the neutral triplet diradical parent state and employing the split valence 3-21 G basis, provides generally reliable results. The minimal STO-3G basis is quantitatively useful in some cases, where it facilitates a compact perturbative analysis of the coupling in terms of competing pathways. For trans alkyl spacers containing one to seven CC bonds, reasonably good global exponential fits are obtained for fall-off of T[sub DA] with D-A separation even though the relative importance of different pathway types (hole, electron, and hybrid) changes markedly over the range of spacers. The calculated decay coefficients [beta][sub r] cover a range of approximately 0.5-0.9 A[sup [minus]1], being systematically greater for radical anions than for cations (by a factor of 1.1-1.7, depending on wavefunction type), consistent with similar findings by Jordan and Paddon-Row for radical cation and anionmore » systems involving norbornyl spacer groups. The behavior of calculated transfer integrals for spacers composed of bicyclo [1.1.1] pentane (bcp) and bicyclo [2.2.2] octane (bco) units is complex, including cases of nonmonotonic variation with number of units (1, 2, or 3), and global exponential fits were possible only for [pi]-transfer through the bcp spacers. 53 refs., 4 figs., 10 tabs.« less

Effective transfer integrals (T) have been evaluated for {sigma} and {pi} type electron and hole transfer in radical ion systems comprising methylene donor/acceptor groups linked by various saturated organic spacer groups. The T values have been calculated on the basis of ab initio self-consistent-field wave functions for the radical ion states, obtained either directly for the system of interest (Tscf) or from the associated neutral state via Koopmans` theorm (Tkt), and employing either minimal (STO-3G) or split-valence (3-21G) basis sets. T{sub kt} values have been decomposed into additive contributions from individual pathways, both through-space (T{sup TS}{sub KT}) and through-bond (T{sup TB}{sub KT}) using perturbation theory formulated by Ratner together with a localized orbital basis represented by natural bond orbitals (NBO`s) as defined by Weinhold et al. The overall coupling has been shown to arise from interference among a large number of competing pathways, none of which is strongly dominant. Nearest-neighbor pathways of the McConnell type are significant for transfer in some radical cation systems, but are frequently of very minor significance in comparison with lower-order superexchange pathways, often with contributions differing in sign from the overall T{sub KT} values. 59 refs., 5 figs., 8 tabs.

We present calculations for various properties of the ground and excited states of several arylamine-substituted acridinium ion systems that have been studied experimentally. Using ab initio and semiempirical quantum mechanical methods together with the generalized Mulliken-Hush (GMH) model, we examine the excitation energies, dipole moment shifts, and electronic coupling elements for the vertical charge shift (CSh) processes in these systems. We also examine solvent effects on these properties using a dielectric continuum reaction field model. The results are in generally good agreement with available experimental results and indicate that there is strong electronic coupling in these systems over a wide range of torsional angles. Nevetheless, the initial and final cationic states remain reasonably well-localized over this range, and thus TICT state formation is unlikely in these systems. Finally, a version of the GMH model based on Koopmans' Theorem is developed and found to yield coupling elements generally within a factor of 2 of the many-electron GMH for a sample acridinium system, but with overestimated adiabatic and diabatic dipole moment differences.

Ab initio RHF molecular orbital calculations are carried out for several hydrate clusters of Fe2+ and Fe3+, using a double-zeta valence atomic orbital basis set and an effective core potential for inner shell electrons, and comparison is made with all-electron results at the monohydrate level. The calculations are shown to give a good quantitiative account of the solvent shell radii and breathing vibration frequencies for the hexahydrates. The large decrease (∼0.15 A) in going from Fe2+(H2O)6 to Fe3+(H2O)6 is related to the interaction of the ag (4s) and ϵg (3d) Fe valence orbitals with the ligand 2p-orbitals, with little π antibonding character found for the tg orbitals. The expansion of the 3d orbitals in the Fe2+ ion, relative to the Fe3+, is also noted and discussed in connection with the change in solvent shell size for the two complexes. The charge transfer from the ligands involves mainly a depletion of the hydrogen atom electrons, implying increased acidity for the first-shell water molecules.

Electronic Hamiltonian matrix elements between initial and final zeroth order states associated with electron exchange in the hexa‐aquo Fe2+/Fe3+ redox system have been calculated in terms of self‐consistent field (SCF) ab initio wave functions. The face‐to‐face and apex‐to‐apex approach geometries of the quasioctahedral reactants have been modeled, respectively, by the [Fe(H2O)3–Fe(H2O)3]5+ cluster (S6 symmetry) and the [Fe(H2O)–Fe(H2O)]5+ cluster (D2h symmetry). For the latter cluster, the Condon approximation has been tested and found to be accurate to within ∼1 cm−1 for the important range of inner‐shell FeO distances. The calculations employ ab initio effective core potentials for inner‐shell electrons and explicitly include all metal and ligand valence electrons. Due to weak 3d–3d overlap, the energy‐preferred SCF solutions are charge localized (i.e., symmetry broken: S6→C3 and D2h→C2v). The present results for the interpenetrating face‐to‐face approach geometry are quite similar to earlier results based on a crystal‐field model, implying an electronic transmission factor 〈κ〉 of ∼1/5 at the most probable reactive encounter separation (5.3 A). The alternative apex‐to‐apex approach geometry is found to be less kinetically favorable. Attempts to fit calculated values of the electronic matrix elements to functions of the form Pn(r)rm exp(−αr) for the range r∼5–8 A, where r is the Fe⋅⋅⋅Fe separation in A and Pn(r) is a polynominal, yield values of α ranging from 0.8 to 2.4 A−1, depending on the values of n and m, the orientation of reactants, and the model employed for the ligands. The calculated matrix elements are found to be rather insensitive with respect to variation of certain features of the SCF wave functions.

The electronic structure of metal cluster–ethylene complexes has been investigated by carrying out ab initio bonding pair‐correlated, self‐consistent field, and configuration interaction (CI) calculations on the NiC2H4 and Ni2C2H4 species. The π‐NiC2H4 and π‐Ni2C2H4 cluster complexes are found to be bound, the former only with CI, while diσ‐Ni2C2H4 has only a repulsive Ni2–C2H4 ground state potential curve. The bonding in the π‐type cluster complexes can be described as follows: The metal atom configuration is 3d94s1 with the 4s hybridized (by the metal 4p) away from the ethylene molecule, thereby allowing the π orbital to form a dative σ bond with the metal atom. The bonding interaction is promoted by the presence of a second nickel atom behind the first one, leading to a 4s orbital electron deficiency of the bonded nickel atom and thus making this nickel atom a better electron acceptor. Back donation from the occupied metal 3d into the ethylene π* molecular orbital also takes place to some extent, and t...

Hartree–Fock, GVB, and configuration interaction calculations were performed for diatomic nickel using an ab initio effective core potential. A basis set specifically optimized for the 3D state of atomic nickel is found to be far superior to the more common basis obtained from the 3F atomic state. Correlation effects are found to be significant in determining the bond energy. In particular, the two electrons of the s–s bond must be appropriately correlated. In addition, correlation effects which one would interpret as being principally intra‐atomic in character are found to have a marked effect on the molecular properties. The theoretically predicted bond dissociation energy (De) of 43.4 kcal/mol is significantly lower than the experimental estimate of 55±5 kcal/mol. However, molecular partition functions calculated using the present results indicate that the experimental value should be revised downward to a value of ∼46±5 kcal/mol, in good agreement with our calculations. An interatomic distance of 4.27...

Atomic and molecular electronic stopping powers for medium energy protons (≈ 10 keV-10 MeV) have been calculated using the binary-encounter approximation in conjunction with (1) either an energy or maximum impact parameter cut-off based on minimum excitation energies; and (2) ab initio electronic speed distributions. The maximum impact parameter approach yields good agreement with experiment for inert gases and closed-shell polyatomic molecules comprised of first-row atoms.

Calculated electron-transfer matrix elements (H/sub if/) for redox processes of the type ML/sub 6//sup 2 +/ + ML/sub 6//sup 3 +/ reversible ML/sub 6//sup 3 +/ + ML/sub 6//sup 2 +/ (M = Fe, Co, or Ru; L = H/sub 2/O or NH/sub 9/ have been analyzed in terms of various orbital concepts. The matrix elements are based on ab initio wave functions for model supermolecule clusters of the type (ML/sub n/ ...L/sub n/M)/sup 5 +/, with n = 1 or 3. The many-electron H/sub if/ quantities are analyzed as effective one-electron expressions of the type H/sub if/ proportional to (lambda')/sup 2/h/sub LlLr//sup c/, where lambda' is the metal-ligand covalency parameter and h/sub LlLr//sup c/ is a local one-electron matrix element for ligand orbitals in contact in the transition state. The data for apex-to-apex approach of reactants yield an excellent linear least-squares fit (r/sup 2/ = 0.996) and imply a value of approx. 5000 cm/sup -1/ for h/sub LlLr//sup c/, thus showing that significant coupling can occur in the absence of formal bonding between reactants.

Single crystal neutron diffraction studies are reported for cubic dinitrogen tetroxide (space group Im3; Z = 6). The crystals were grown from NO2 vapor in situ on the diffractometer by precise cryostatic control. The lattice parameter, measured at seven temperatures, increases from 7.6937(6) A at 20 K to 7.7925(6) A at 140 K. The nuclear positional and thermal parameters were refined using diffraction data (sin ϑ/λ⩽0.79 A−1) measured at 20, 60, and 100 K. Final fit indices R(F2) are 0.028, 0.034, 0.037, respectively. The observed N–N bond length and O–N–O angle are invariant between 20 and 100 K at values 1.7562(±4) A and 134.46(±6)° with individual e.s.d.’s of 0.001 A and 0.1°. The observed N–O bond length increases linearly from 1.1855(9) A at 100 K to 1.1893(5) A at 20 K; the extrapolated zero‐point value is 1.191 A. Ab initio self‐consistent field calculations using a two‐configuration wave function which allows partial occupation of the σ* MO (antibonding with respect to the two nitrogens) yields a r...

Ab initio SCF and CI calculations are reported for the sulfur nitride, SN, and disulfur dinitride, S2N2, molecules. Calculations on SN, varying the internuclear distance, are performed using a variety of basis sets to determine a suitable basis for S2N2. The total energy, internuclear distance, and force constant of SN are reported for several choices of basis. Extended basis computations on S2N2 are performed, and midbond polarization functions are found to contribute significantly to a description of the ground state, affecting the higher MO’s and the charge density. A prominent feature of the virtual spectrum is the existence of a low energy π* orbital which could play a role in low lying excited states, the polymerization process, and polymer conductivity. CI studies of the ground and excited states of S2N2 show several low lying singlet and triplet states of the type π→σ*, π→π*, and σ→π*, and possible identifications with experiment are discussed. A possibility of relating the observed paramagnetism ...

The properties of solvated electrons are analyzed in terms of a self- consistent modified continuum model based on the techniques of ab initio molecular quantum mechanics. The model is semiclassical in spirit, employing the quantum mechanical density for the excess charge and the first solvation shell in conjunction with classical electrostatics, and is developed in a general form which can be straightforwardly applied to special cases of interest, such as the solvated mono- and dielectron complexes. The advantages and disadvantages of the technique are discussed in relation to other more empirical approaches. Computational results are presented for excess electrons (mono- and dielectrons) in water and ammonia, and the role of long-range polarization of the medium in localizing the excess charge is analyzed. The variationally determined ground states are characterized in terms of equilibrium solvation shell geometry (appreciable cavities are implied for both water and ammonia), solvation energy, photoionization energy, and charge distribution. The finding of negative spin densities at the first solvent shell protons underscores the importance of a many electron theoretical treatment. Preliminary results for excited states are also reported. The calculated results are compared with experimental and other theoretical data, and the sensitivity of the results to variousmore » features of the model is discussed. Particular attention is paid to the number of solvent molecules required to trap the excess electron. (auth)« less

Ab initio effective core potentials have been obtained for the cadmium and mercury atoms by the methods of Kahn et al. (1976). Both two and twelve valence electron representations of Cd and Hg were tested for various atom state-configurations by comparison with all-electron calculations. The generated potentials were used to obtain the equilibrium bond distances and molecular binding energies for the dichloride and dimethyl compounds of both atoms from single and optimum-double configuration self-consistent field calculations.

Ab initio configuration interaction calculations have been carried out for important regions on the potential energy surfaces of the C + H2 system. The implications of the results for the reactivity of both thermal and energetic 3P, 1D, and 1S carbon atoms are discussed. Preliminary study does not reveal any low-energy pathways for the C(3P) + H2 reaction.

The conformational energetics of three ..cap alpha..-hydroxycarbonyl systems (glycolic acid, the glycolate anion, and glycolaldehyde) have been investigated using ab initio molecular orbital theory at the 4-31G level. The major aim of the study was to ascertain the role of intramolecular factors in the planarity or near-planarity of the carbon-oxygen framework observed in the ..cap alpha..-hydroxycarboxyl moiety of a large number of crystalline ..cap alpha..-hydroxy acids and carboxylates, irrespective of the conformation of the ..cap alpha..-hydroxy group. The calculations for the isolated species show that the equilibrium conformations correspond to internally hydrogen-bonded structures. Departures from equilibrium obtained by rotating the ..cap alpha..-hydroxyl group are calculated to cost appreciably less energy than distortions which destroy the planarity of the carbon oxygen framework, a result consistent with the data for the molecules in the crystalline state, where stronger intermolecular hydrogen bonding takes precedence over internal hydrogen bonding. The conformational energetics of the isolated species are discussed in detail, and the nature of the internal hydrogen bonding is analyzed in terms of energy and charge density criteria and by comparison with related intermolecular hydrogen-bonded systems.

The nature of the interoxygen bonding in O2, HO2, H2O2, O3, HO3, and H2O3 has been investigated on the basis of ab initio (LCAO‐MO) and experimental force constants, bond lengths, and energies. The fact that small basis sets appear to give the OO force constants for H2O2 and HO2 in the order opposite to that observed prompted an analysis of the sensitivity of the above properties with respect to various types of contracted Gaussian‐type orbitals (CGTOs). A large basis set of s and p CTGOs, [43/2] is found to give proper qualitative account of OO bond lengths and force constants. However, polarization functions (3d functions on oxygen) are necessary for accurate calculation of relative bond energies in H2O2 and HO2. The species HO3 is estimated to be [inverted lazy s] 15 kcal/mole unstable with respect to O2 + OH, in agreement with empirical estimates, thus making unlikely its potential role as a reaction intermediate. Hydrogen trioxide (H2O3) is calculated to have OO bonds slightly shorter ([inverted lazy s] 1.44 A) than in H2O2 (1.48 A), but with OO force constants similar in magnitude to H2O2, and a large OO stretching interaction force constant. The latter fact, in conjunction with spectral data from analogous systems, would be expected to make the symmetric stretch frequency in H2O3 larger than that for the antisymmetric mode, and this conclusion is discussed in the context of recent experimental data of Giguere et al., which is attributed to H2O3 and H2O4. The preferred anti conformation (C2 symmetry) of the OH bonds in H2O3 is noted as being potentially relevant to the conformation of intermediates in the ozonolysis of olefins. HO2 is calculated to have a very low lying (< 1 eV) excited state (2A′), as suggested by other workers, for which we estimate an OO bond length of 1.48 A. Variations in OO bonding strength are analyzed in terms of Pauling bond orders and π‐electron density matrix elements. Force constants are not always found to vary monotonically with bond length, and the distinction between symmetrized and unsymmetrized force constants is emphasized in this connection.

Ab initio calculation of equilibrium geometries and quadratic force constants for a large group of first‐row polyatomic molecules has been carried out, using the previously described [J. Chem. Phys. 51, 2657 (1969)] STO–3G approximation for STO basis functions. The average deviation of calculated and experimental bond lengths and angles is 0.035 A and 1.7°, respectively. Nearly all important experimental trends are reproduced. For a few cases involving bonds between electronegative atoms, significant discrepancies are found. Quadratic force constants are evaluated for symmetric stretching and bending modes and are found to be overestimated, typically by 20%–30%. Nearly all experimental trends are satisfactorily accounted for. It is concluded that a minimal STO basis with properly chosen orbital exponents offers a useful and computationally efficient model for potential surface studies.

Ab initio molecular‐orbital wavefunctions for ethylene, butadiene, and benzene have been analyzed in terms of the localized orbitals (LMO's) defined by minimizing molecular exchange energy. The effect of conjugation on the LMO's is studied in terms of the delocalization of LMO's and the curvature of the energy surface which determines the LMO's. The degree of preference for bent double‐bond LMO's over σ–π double‐bond LMO's is also examined. In all cases, the former LMO's represent the correct solutions, while the latter LMO's, obtained by imposing the constraint of σ–π separation, correspond to saddle‐point solutions. The double‐bond LMO's for ethylene and butadiene are quite similar, whereas in the case of benzene, appreciably greater delocalization is found, and the preference for bent bonds over σ–π bonds is greatly reduced.

Energies and optimal geometries have been computed in the UHF LCAO MO GTO framework for reactant, product and likely intermediate structures in the exchange and abstraction reactions of H + CH4. The effects of addition of polarization functions to both the hydrogen and carbon basis sets have been evaluated.

Gaussian 76 is a general-purpose computer program for ab initio Hartree-Fock molecular orbital calculations. It can handle basis sets involving s, p and d-type gaussian functions. Certain standard sets (STO-3G, 4-31G, 6-31G*, etc.) are stored internally for easy use. Closed shell (RHF) or unrestricted open shell (UHF) wave functions can be obtained. Facilities are provided for geometry optimization to potential minima and for limited potential surface scans.

Electron transfer matrix elements are calculated and analyzed for several pairs of transition metal complexes of the type ML6 2+-ML6 3+, chosen so as to allow a comparison of t2g(π) vs eg (σ) transfer (M = Fe, Co, and Ru), and NH3 vs H2O ligands, based on an apex-to-apex orientation of the reactant complexes. The magnitude of the calculated matrix elements, which span the range from non-adiabatic to strongly adiabatic coupling, are found to exhibit a pronounced dependence on transfer type (eg > t2g) and ligand type (NH3 > H2O), an effect which is correlated with the degree of mixing of the metal and ligand orbitals, using a simple LCAO-type analysis of the ab initio molecular orbitals.

In its spectacular evolution through the past decades, the orbital theory of molecular structure has steadily progressed from simple semiempirical models of limited application (e.g., π-electron theories for planar systems) to elaborate ab initio models which include all electrons and are applicable to general molecular geometries.(1–6) Furthermore, the power of present generation computers means that these ab initio techniques can now be feasibly applied to rather large molecular systems (i.e., -50–75 electrons). As a result, the past few years have seen major progress in our understanding of a fundamentally important aspect of organic chemistry—the nature of strained organic molecules.(7,8) Although current semiempirical techniques provide much important information about strained molecules(2,9,10) ab initio studies have been imperative because the strained molecules transcend our usual concepts about the nature of bonding and thus, among other things, play a vital role in helping extend and recalibrate semiempirical methods. Ab initio capability for treating large molecules is very important in this connection, since many of the most intriguing aspects of strained systems only appear in rather large systems (i.e., 223c5-10 heavy atoms), especially the polycyclic variety.

Model calculations have been employed in elucidating the mechanism of electron transfer reactions in aqueous solution. The contribution of inner shell OH bonds to activation barriers has been estimated from calculation for metal ion hydrates. Calculated electron transfer matrix elements (Haf) for redox processes of the type, ML6 2+ + ML6 3+ = ML6 3+ + ML6 2+, M = Fe, Co, or Ru, L = H2O or NH3, have been analyzed in terms of various orbital concepts. The matrix elements are based on ab initio wavefunctions for model supermolecule clusters of the type, (MLn •••LnM)5+ with n = 1 or 3. The analysis shows that the many-electron Hif quantities can in fact be expressed to good approximation as effective 1-electron expressions of the type, Hif ∝ (λ↑)2 NchLlLr, where λ ’is the metal-ligand covalency parameter, hLlLr is a local 1-electron matrix element for ligand orbitals in contact in the transition state, and Nc is the number of such contacts. A least-squares fit of the data implies a value of ~ 5000 cm-1 for hLlLr showing that significant coupling can occur in the absence of formal bonding between reactants.