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Extension of the Förster analogue for the ET rate constant (based on virtual intermediate electron detachment or attachment states) with inclusion of site-site correlation due to coulomb terms associated with solvent reorganization energy and the driving force, has been developed and illustrated for a simple three-state, two-mode model. The model is applicable to charge separation (CS), recombination (CR), and shift (CSh) ET processes, with or without an intervening bridge. The model provides a unified perspective on the role of virtual intermediate states in accounting for the thermal Franck-Condon weighted density of states (FCWD), the gaps controlling superexchange coupling, and mean absolute redox potentials, with full accommodation of site-site coulomb interactions. Two types of correlation have been analyzed: aside from the site-site correlation due to coulomb interactions, we have emphasized the intrinsic "nonorthogonality" which generally pertains to reaction coordinates (RCs) for different ET processes involving multiple electronic states, as may be expressed by suitably defined direction cosines (cos(θ)). A pair of RCs may be nonorthogonal even when the site-site coulomb correlations are absent. While different RCs are linearly independent in the mathematical sense for all θ ≠ 0°, they are independent in the sense of being "uncorrelated" only in the limit of orthogonality (θ = 90°). Application to more than two coordinates is straightforward and may include both discrete and continuum contributions.

Diabatic states for donor (D) and acceptor (A) interactions in electron transfer (ET) processes are formulated and evaluated, along with coupling elements (H(DA)) and effective D/A separation distances (r(DA)), for reduced electronic spaces of variable size, using the generalized Mulliken Hush model (GMH), applicable to an arbitrary state space and nuclear configuration, and encompassing Robin-Day class III and as well as class II situations. Once the electronic state space is selected (a set of n ≥ 2 adiabatic states approximated by an orbital space based on an effective 1-electron (1-e) Hamiltonian), the charge-localized GMH diabatic states are obtained as the eigenstates of the dipole moment operator, with rotations to yield locally adiabatic states for sites with multiple states. The 1-e states and energies are expressed in terms of Kohn-Sham orbitals and orbital energies. Addressing questions as to whether the estimate of H(DA) "improves" as one increases n, and in what sense the GMH approach "converges" with n, we carry out calculations for three mixed-valence binuclear Ru complexes, from which we conclude that the 2-state (2-st) model gives the most appropriate estimate of the effective coupling, similar (to within a rms deviation of ≤15%) to coupling elements obtained by superexchange correction of H(DA) values based on larger spaces (n = 3-6), and thus yielding a quasi-invariant value for H(DA) over the range explored in the calculations (n = 2-6). An analysis of the coupling and associated D and A states shows that the 2-st coupling involves crucial mixing with intervening bridge states (D and A "tails"), while increasingly larger state spaces for the same system yield increasingly more localized D and A states (and weaker coupling), with H(DA) tending to approach the limit of "bare" or "through space" coupling. These results help to reconcile seemingly contradictory assertions in the recent literature regarding the proper role of multistate frameworks in the formulation of coupling for both intra- and intermolecular ET systems.The present results are compared in detail with other reported results.

Intermolecular potential energy curves are presented and analyzed for three different water dimer structures: the normal hydrogen-bonded structure (C/sub s/); a weakly hydrogen-bonded structure (C/sub 1/) thought to be important in encounters of hydrated ions in aqueous solution; and a repulsive configuration (C/sub 2h/) characterized by a head-on approach of hydrogen atoms (OH...HO). Results are based on ab initio calculations (SCF and CI (at the MP2 level), with and without counterpoise (CP) correction for basis set superposition error (BSSE)) and also a recent semiempirical effective pair potential (RWK2). The CP corrections have a significant effect on the location and depth of the potential wells for the hydrogen-bonded structures, even when CI and extended basis sets are employed.

A method for approximating hybrid and exchange integrals over atomic orbitals is discussed and examined in detail for the case of Slater-type orbitals (STO'S). The crux of the approximation is the least-squares projection of 2-center charge distributions onto suitably chosen 1-center charge distributions. The approximate integrals are thus linear combinations of Coulomb-type integrals, and are generated at a rate of ∼150/sec on a CDC 1604A computer. The method is employed in an SCF MO study of benzene and several of its ions.

We report microscopic calculations of free energies and entropies for intramolecular electron transfer reactions. The calculation algorithm combines the atomistic geometry and charge distribution of a molecular solute obtained from quantum calculations with the microscopic polarization response of a polar solvent expressed in terms of its polarization structure factors. The procedure is tested on a donor-acceptor complex in which ruthenium donor and cobalt acceptor sites are linked by a four-proline polypeptide. The reorganization energies and reaction energy gaps are calculated as a function of temperature by using structure factors obtained from our analytical procedure and from computer simulations. Good agreement between two procedures and with direct computer simulations of the reorganization energy is achieved. The microscopic algorithm is compared to the dielectric continuum calculations. We found that the strong dependence of the reorganization energy on the solvent refractive index predicted by continuum models is not supported by the microscopic theory. Also, the reorganization and overall solvation entropies are substantially larger in the microscopic theory compared to continuum models., Comment: 21 pages, 15 figures, typos corrected

In the case of superexchange tunneling, sensitivity of the tunneling gap (A) to progress along the thermal et reaction coordinate (including molecular as well as solvent contributions) has been formulated in terms of a general linear response framework, which is used to express the correlation between linearly independent reaction coordinates for distinct et steps. When the tunneling gap is relatively small (i.e., of the order of magnitude of reorganization energies), the corresponding sensitivity of the donor (D)/acceptor (A) coupling (H D A ) and its distance dependence (decay coefficient β) may be significant. The magnitude of Δ at the thermal et transition state has been compared with other reference values obtainable from optical or thermodynamic data. The initial state at equilibrium yields an upper bound for Δ, and so also does the equilibrium free energy change for charge injection onto the bridge in cases of et processes which are only moderately exothermic. The in vacuo value of A may constitute either an upper or lower bound, depending on the nature of the et process ( charge separation or charge shift) and the details of the relevant reorganization energies.

Contemporary continuum-based models of solvation in polar media are surveyed and assessed, with special focus on non-equilibrium solvation. A new hybrid approach combining molecular-level treatment of inertial solvent response, and inclusion of inertialess solvent response at the continuum level, is presented and illustrated in terms of calculated equilibrium solvation free energies for small molecular ions and reorganization free energies for model dumbbell systems.

Long-range electronic coupling of local donor and acceptor sites is formulated in the context of thermal and optical electron transfer and then illustrated with examples based on electronic structure calculations. The relationship of the calculated results to available experimental kinetic and optical data is discussed in detail. The influence of nuclear modes on the magnitude of the coupling (i.e., departures from the Condon approximation) is investigated in terms of both discrete molecular modes and solvent modes, and a general expression is presented for the modulation of the superexchange tunneling gap by motion along the electron transfer reaction coordinate.

Current theories of electron transfer (ET) kinetics in conjunction with techniques of computational quantum chemistry are reviewed and applied to the analysis of thermal and optical ET processes involving transition metal complexes (TMCs). The roles of geometrical and electronic structure in controlling the relevant energetics and electronic coupling are discussed, and a number of limiting cases of kinetic behavior are displayed. Particular attention is paid to the formulation of the initial and final states involved in the ET, including the consequences of near-degeneracy and spin–orbit coupling. The roles of metal/ligand mixing and other types of ‘mediation’ of donor/acceptor coupling by molecular spacers are noted and illustrated with calculated results. An example of a detailed computation of activation parameters is also presented, including entropic effects and nuclear tunnelling.

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...

Quantum rate theory, molecular dynamics simulations, and semiempirical electronic structure calculations are used to fully investigate electron transfer mediated by a solvated polypeptide for the first time. Using a stationary-phase approximation, the nonadiabatic electron-transfer rate constant is calculated from the nuclear free energies and the electronic coupling between the initial and final states. The former are obtained from quantum path integral and classical molecular dynamics simulations; the latter are calculated using semiempirical electronic structure calculations and the generalized Mulliken−Hush method. Importantly, no parameters are fit to kinetic data. The simulated system consists of a solvated four-proline polypeptide with a tris(bipyridine)ruthenium donor group and an oxypentamminecobalt acceptor group. From the simulation data entropy and energy contributions to the free energies are distinguished. Quantum suppression of the barrier, including important solvent contributions, is demo...

The frequency-resolved cavity model (FRCM), a generalized continuum reaction field model, which allows for distinct effective solute cavities pertaining to optical (op) and inertial (in) solvent response, has been implemented and applied to the evaluation of solvent reorganization energy ( E s ) for a number of intramolecular electron transfer (ET) processes in polar media. Specifically, effective radii are defined for the solute atoms: r ∞ = κ · r vdW (where κ is taken as a universal scale factor) and r in = r ∞ + δ (where δ is specific to a particular solvent). Optimal values of κ and δ are determined through the use of solvation free energy data for small atomic and molecular ions, together with the experimental estimates of solvation reorganization energy ( E s ) for intramolecular ET in the steroid-based radical ions studied by Closs, Miller and co-workers [G.L. Closs, L.T. Calcaterra, N.J. Green, K.W. Penfield, J.R. Miller, J. Phys. Chem. 90 (1986) 3673; M.D. Johnson, J.R. Miller, N.S. Green, G.L. Closs, J. Phys. Chem. 93 (1989) 1173; J.R. Miller, B.P. Paulson, R. Bal, G.L. Closs, J. Phys. Chem. 99 (1995) 6923]. With these optimal parameters, E s is then evaluated for a number of other intramolecular ET processes, yielding results which are in generally good agreement with experimentally based estimates, and which give support for some of the assumptions employed in the analysis of the experimental data. Calculations with conventional solute atom radii ( r ∞ = r in , with κ =1.2 and δ =0) fitted to equilibrium solvation data yield E s values exceeding the FRCM results by factors of ≥2.

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.

A new method for the calculation of the electronic coupling matrix element for electron transfer processes is introduced and results for several systems are presented. The method can be applied to ground and excited state systems and can be used in cases where several states interact strongly. Within the set of states chosen it is a non-perturbative treatment, and can be implemented using quantities obtained solely in terms of the adiabatic states. Several applications based on quantum chemical calculations are briefly presented. Finally, since quantities for adiabatic states are the only input to the method, it can also be used with purely experimental data to estimate electron transfer matrix elements.

The electronic matrix element coupling a ground and charge-transfer excited state can be calculated from the energy intensity of the appropriate charge-transfer transition. An expression for the electronic coupling element widely used for this purpose is based on equations derived by Mulliken and Hush for an effective two-state model and is frequently assumed to be valid only in the perturbation limit. This expression is shown to be exact within a two-state model. Provided that overlap can be neglected and that the spectroscopic transition is polarized along the donor—acceptor axis, it can be applied to system ranging from those which are very weakly coupled to those which are very strongly coupled. Application of the Mulliken—Hush expression to (NH3)5RuL2+ complexes, for which metal—lingand backbonding is important, yields metal—lingand coupling elements of 5000–6000 cm−1 with pyridyl lingands (donor—acceptor separation 3.5 A), in very good agreement with estimates obtained from a molecular orbital analysis of the band energies. With use of the superexchange formalism, the metal—lingand coupling elements were used to calculate metal—metal coupling elements for binuclear mixed-valence complexes. Comparison of these values with those obtained from the Mulliken—Hush expression applied directly to the metal-to-metal charge-transfer transition yields agreement within a factor of two or better.

For the prototypical dyad (TCNE2)-*, previous in vacuo calculations indicate that sizable distortion of the equilibrium gas-phase structure may be required to reduce the donor/acceptor electronic coupling element (HDA) to the solution-phase experimental estimates. We employ the polarizable continuum model (PCM) to simulate the solvation environment for several polar solvents, finding noticeable structure change associated with the promotion of charge localization due to solvation. We have extended the counterpoise (CP) correction procedure so as to include fragment relaxation energies within the PCM model, and it would be of interest to incorporate this approach into schemes for optimizing coordinates on CP-corrected energy surfaces. The calculations include face-to-face encounter geometries as well as several lateral and twist distortions of the face-to-face structures. In proceeding from vacuum to solution, the calculated stabilization energy is reduced from -18 to -3 kcal/mol, and the calculated energy surface becomes flatter, with a somewhat larger minimum-energy separation of the monomer units (rDA). The corresponding minimum-energy structures are, respectively, delocalized and charge-localized. Using TD-DFT, spin-projected MP2 (PUMP2), and state-averaged two-configuration SCF (SA-TCSCF) calculations to evaluate HDA for symmetric encounter complex geometries (models for transition-state structures) indicates that HDA has comparable magnitude in the gas phase and in solution for a given dimer structure. SA-TCSCF calculations comparing HDA based on symmetric charge-delocalized structures and their asymmetric (minimum-energy) charge-localized counterparts (at a given rDA) yield very similar values. Even with account taken of the energetically accessible configurations probed by the PCM calculations, the HDA values remain significantly higher than the experimental estimates inferred from solution spectra and assumption of rDA based on crystal data. Clearly, additional calculations based on molecular-level solvent models would be of value in helping to characterize the intermolecular structures accessible to the encounter complex in polar solution.

This work provides a detailed account of the application of our multichromophoric Förster resonance energy transfer (MC-FRET) theory (Phys. Rev. Lett. 2004, 92, 218301) for the calculation of the energy transfer rate from the B800 unit to the B850 unit in the light harvesting complex 2 (LH2) of purple bacteria. The model Hamiltonian consists of the B800 unit represented by a single bacteriochlorophyll (BChl), the B850 unit represented by its entire set of BChls, the electronic coupling between the two units, and the bath terms representing all environmental degrees of freedom. The model parameters are determined, independent of the rate calculation, from the literature data and by a fitting to an ensemble line shape. Comparing our theoretical rate and a low-temperature experimental rate, we estimate the magnitude of the BChl-Qy transition dipole to be in the range of 6.5-7.5 D, assuming that the optical dielectric constant of the medium is in the range of 1.5-2. We examine how the bias of the average excitation energy of the B800-BChl relative to that of the B850-BChl affects the energy transfer time by calculating the transfer rates based on both our MC-FRET theory and the original FRET theory, varying the value of the bias. Within our model, we find that the value of bias 260 cm-1, which we determine from the fitting to an ensemble line shape, is very close to the value at which the ratio between MC-FRET and FRET rates is a maximum. This provides evidence that the bacterial system utilizes the quantum mechanical coherence among the multiple chromophores within the B850 in a constructive way so as to achieve efficient energy transfer from B800 to B850.

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.

The theory of Förster resonance energy transfer is generalized for multichromophoric (MC) and nonequilibrium situations. For the first time, it is clarified that the far-field linear spectroscopic information is insufficient for the determination of the reaction rate and that distance dependence of the rate can vary with the disorder and temperature. Application to a light harvesting complex LH2 reveals the important consequences of a MC structure.

Some recent advances in dielectric continuum models for static and dynamic aspects of molecular solvation are discussed, and connections with molecular-level solvent models are noted. The traditional Born-Onsager-Kirkwood (BKO) model is compared to a more flexible model (the so-called frequency-resolved cavity model (FRCM)) which assigns distinct inner and outer solute cavities in accommodating, respectively, the inertialess (optical) and inertial solvent response. Sample calculations of solvent reorganization energy (λs) are presented for various thermal and optical electron transfer (ET) processes, based on self-consistent reaction field models using molecular orbital (MO) or configuration interaction (CI) solvent wave functions.

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.

The rate constant for the Fe2+–Fe3+ electron exchange is formulated as k23= ∫ 0∞g23(r) k23(r) 4πr2 dr, a form which also is used to analyze the data for the nuclear spin relaxation in Al3+ induced by collision with Ni2+. It is assumed that the equilibrium pair correlation function g23(r) is the same function of ionic composition and temperature in the two cases and that in the spin relaxation process the local rate constant k23(r) has the form that may be deduced from the Solomon–Bloembergen equations. In the case of the exchange reaction the theory of k23(r) is developed with respect to the contributions from slow inner shell or outer shell reorganization (activation) dynamics. It is concluded that in the present case these complications are not important and that the controlling dynamics is the crossing from the reactant to the product diabatic Born– Oppenheimer surface. Neither the exchange nor the spin relaxation data can be accounted for if the smallest metal–metal distance in collisions is that given by the closest approach of the envelopes of the M(H2O)6n+ complexes. However, allowing for overlap of the envelopes as one complex pokes into the interstices of the other reduces the distance of closest approach from 6.9 to 4.5 A. Then one can find Gurney type models for the ion–ion forces in solution such that the model calculations are in good agreement with the experimental exchange and relaxation rate constants and their dependence on temperature and ionic strength, as far as the limited data for the last allow.

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.

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.

The 4s and 3d ionization manifolds for Ni 2 and Ni 4 (D 4h clusters are compared, using symmetry-broken SCF wave-functions. The 4s ion states remain delocalized whereas each 3d ion hole is essentially localized on a single atom, thus causing appreciable 4s polarization. Significant overlap of 4s and 4d levels is predicted for clusters with as few as four Ni atoms.

Small nickel atom clusters exhibit an energetic preference for localized, open 3d-shells. This tendency is attributed to weak 3d-3d overlap and is analyzed in terms of the competition between resonance integrals and screening terms. Analogous competition between resonance and screening leads to (spatially) symmetry-broken charge-localized SCF solutions for 3d ion-hole states in nickel atom clusters. Charge-localized symmetry broken wavefunctions are also employed as initial and final diabatic (nonstationary) states in the electron transfer processes associated with transition metal complexes of the type MX, where M = Fe, Ru; X = H2O; NH3, n = 2, 3. Resonance integrals coupling the initial (reactants) and final (products) states have been calculated for several geometrical structures and electronic states of interest. An important contributor to the screening effects which promote charge localization in these systems is the charge-dependence of metal-ligand bond lengths. The decrease in oxidation-state dependence of metal-ligand bond length in the series Fe2+/3+ (H2O)6 Ru2+/3+ (H2O)6 Ru2+/3+ (NH3)6 is analyzed in terms of ligand-to-metal charge transfer (LMCT), and the trend is attributed to diminished participation of the metal atom in the redox process. The electronic rearrangement upon reduction is dominated by the eg (σ) manifold, even though the reducing electron is added to the t2g (π) manifold.

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

The MNDO approximation is employed to compute normal modes of vibration for the proposed C/sub 60/ isomer known as buckminsterullerene. Group theoretical invariance theorems are derived to aid in the interpretation of the normal modes. One particularly interesting mode (the sole A/sub u/ vibration) consists of a rotary oscillation of the pentagonal rings of C/sub 60/, with all rings rotating in the same direction.

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.

The ground state electronic structure of small nickel atom clusters (Nin, n=1–6) has been calculated using the ab initio effective core potential self‐consistent field (SCF) method in a Gaussian expansion basis. The electronic configuration of the nickel atoms in the clusters is found to be very close to 3d94s1. The ground state electronic configurations for Nin generally have n unpaired 3d electrons in molecular orbitals (MO’s) spanning the same irreducible representations as the 4s atomic orbitals while the n 4s electrons fill their MO’s in accord with a simple three‐dimensional Huckel model with overlap. Exceptions to this description are found in the cases of linear systems where the 3d holes prefer δ over σ symmetry and in octahedral Ni6 where a different preferred set of 3d holes is obtained. The SCF ground state wave functions correspond roughly to a model in which the 3d electrons can be viewed as weakly interacting localized 3d9 units. The clusters are bound together primarily by the 4s electrons with the 4p orbital contribution increasing in importance with cluster size and dimensionality. The binding energy per nickel atom generally increases as the size of the cluster increases, although at six atoms this quantity has not yet converged with cluster size. The density of states diagram for the occupied one electron energy levels in Ni6 is found to be very different from the corresponding types of diagrams obtained in the muffin tin (MT)–Xα method for small nickel atom clusters. This difference is examined in detail, with consideration given to the effects of relaxation energy and to the different orbital level filling criteria used in the two methods.

Localized molecular orbitals which minimize the exchange energy have been obtained for CH4, C2H6, C2H4, C2H2, CH3CCH, C3H6, HCN, and H2CO. These objectively determined orbitals correspond to the inner shells, lone pairs, and two‐center bonds of classical bonding theory. In each case where double or triple bonds occur, the local orbitals correspond to equivalent bent bonds. The hybrids in the C–C bonds of cyclopropane form angles of 28° with the internuclear direction. The local orbitals are analyzed in terms of hybridization, polarity, bond moments, bond directions, and delocalization. Calculation of the curvature of the self‐repulsion energy surface provides an indication of the uniqueness of the results. Sigma–pi separability and the sensitivity of the local orbitals to changes in basis set are also discussed.

Looyenga has recently pointed out at an apparent anomaly between the valence-bond and molecular-orbital descriptions of a single Kekule structure, whereby in the VB model there are repulsions between non-bonded electrons in adjacent double bonds, which do not appear in the MO model. It is shown that if proper account is taken of atomic overlap integrals, and if the wave function is put into determinantal form, this difference disappears. Thus the difference between localized and delocalized π-electron energies in the two models is closely similar. In the MO description of a Kekule structure, negative π-bond orders appear across the formally ‘single’ bonds. On delocalization these may or may not be converted to postive bond orders. Two different ways are described for easy calculation of these negative bond orders and numerical examples are provided. These negative bond orders are important for any proper study of hyperconjugation, as is shown by consideration of ethane and methylacetylene.

Molecular SCF orbitals of B2H6 have been computed from optimized minimum basis sets which employ isotropic or anisotropic atomic 2p orbitals. These SCF wavefunctions have been transformed to localized MO's which maximize the self‐energy, D = Σi(φiφi | φiφi). This objective procedure strongly supports the three‐center bond for each BHB bridge. The resulting hybrids are sp2.5, with ∠Ht–B–Ht=125° and ∠Hb–B–Hb=93° for terminal and bridge H's, respectively.

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.