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Bandshape analysis of charge-transfer optical bands in room-temperature ionic liquids (ILs) was performed to extract the reorganization energy of electron transfer. Remarkably, the reorganization energies in ILs are close to those in cyclohexane. This result runs against common wisdom in the field since conducting ILs, which are characterized by an infinite static dielectric constant, and nonpolar cyclohexane fall to the opposite ends of the polarity scale based on their dielectric constants. Theoretical calculations employing structure factors of ILs from molecular dynamics simulations support the low values of the reorganization energy. Standard dielectric arguments do not apply to solvation in ILs, and nonergodic reorganization energies are required for a quantitative analysis.

The pathway of activationless proton transfer induced by an electron-transfer reaction is studied theoretically. Long-range electron transfer produces highly nonequilibrium medium polarization that can drive proton transfer through an activationless transition during the process of thermalization, dynamically altering the screening of the electron-proton Coulomb interaction by the medium. The cross electron-proton reorganization energy is the main energy parameter of the theory, which exceeds in magnitude the proton-transfer reorganization energy roughly by the ratio of the electron-transfer to proton-transfer distance. This parameter, which can be either positive or negative, is related to the difference in pKa values in two electron-transfer states. The relaxation time of the medium is on the (sub)picosecond time scale, which establishes the characteristic time for activationless proton transfer. Microscopic calculations predict substantial retardation of the collective relaxation dynamics compared to the continuum estimates due to the phenomenology analogous to de Gennes narrowing. Nonequilibrium medium configuration promoting proton transfer can be induced by either thermal or photoinduced charge transfer.

An analytical formalism is developed for the calculation of absorption of radiation by charge-transfer molecules with electronic density delocalized between the donor and acceptor parts. The theory consistently incorporates both the vibronic coupling to quantum intramolecular vibrations and electrostatic interactions with a classical polarizable medium. The formulation operates in terms of basis-invariant parameters and can be used for calculations based on both the localized diabatic states and delocalized adiabatic wave function produced by standard quantum-chemistry algorithms. The basis-invariant reorganization energy is particularly important, since it determines observable spectroscopic parameters, in contrast to the adiabatic reorganization energy based on the molecular charge distributions in the adiabatic vacuum states. Analytical formulas are derived for the charge-transfer absorption band and first two spectral moments connecting spectroscopy to properties of charge-transfer molecules. Electronic delocalization requires a new definition of the Huang-Rhys factor traditionally used to construct vibronic band shapes. Theory's performance is illustrated by application to experimental data for self-exchange charge-transfer optical absorption and for metal-to-ligand emission transitions.

We present a thermodynamic analysis of the activation barrier for reactions which can be monitored through the difference in the energies of reactants and products defined as the reaction coordinate (electron and atom transfer, enzyme catalysis, etc.). The free-energy surfaces along the reaction coordinate are separated into the enthalpy and entropy surfaces. For the Gaussian statistics of the reaction coordinate, the free-energy surfaces are parabolas, and the entropy surface is an inverted parabola. Its maximum coincides with the transition state for reactions with zero value of the reaction free energy. Maximum entropic depression of the activation barrier, anticipated by the concept of transition-state ensembles, can be achieved for such reactions. From Onsager's reversibility, the entropy of equilibrium fluctuations encodes the entropic component of the activation barrier. The reorganization entropy thus becomes the critical parameter of the theory reducing the problem of activation entropy to the problem of reorganization entropy. Standard solvation theories do not allow reorganization entropy sufficient for the barrier depression. Complex media, characterized by many relaxation processes, need to be involved. Proteins provide several routes for achieving large entropic effects through incomplete (nonergodic) sampling of the complex energy landscape and by facilitating an active role of water in the reaction mechanism.

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.

Localization and delocalization of electrons is a key concept in chemistry, and is one of the important factors determining the efficiency of electron transport through organic conjugated molecules, which have potential to act as "molecular wires". This, in turn, substantially influences the efficiencies of organic solar cells and other molecular electronic devices. It is also necessary to understand the electronic energy landscape and the dynamics that govern electron transport capabilities in one-dimensional conjugated chains so that we can better define the design principles for conjugated molecules for their applications. We show that nitrile ν(C≡N) vibrations respond to the degree of electron localization in nitrile-substituted organic anions by utilizing time-resolved infrared detection combined with pulse radiolysis. Measurements of a series of aryl nitrile anions allow us to construct a semiempirical calibration curve between the changes in the ν(C≡N) infrared (IR) shifts and the changes in the electronic charges from the neutral to the anion states in the nitriles; more electron localization in the nitrile anion results in larger IR shifts. Furthermore, the IR line width in anions can report a structural change accompanying changes in the electronic density distribution. Probing the shift of the nitrile ν(C≡N) IR vibrational bands enables us to determine how the electron is localized in anions of nitrile-functionalized oligofluorenes, considered as organic mixed-valence compounds. We estimate the diabatic electron transfer distance, electronic coupling strengths, and energy barriers in these mixed-valence compounds. The analysis reveals a dynamic picture, showing that the electron is moving back and forth within the oligomers with a small activation energy of ≤kBT, likely controlled by the movement of dihedral angles between monomer units. Implications for the electron transport capability in molecular wires are discussed.

A common strategy to calculate electronic coupling matrix elements for charge or energy transfer is to take the adiabatic states generated by electronic structure computations and rotate them to form localized diabatic states. In this paper, we show that, for intermolecular transfer of singlet electronic excitation, usually we cannot fully localize the electronic excitations in this way. Instead, we calculate putative initial and final states with small excitation tails caused by weak interactions with high energy excited states in the electronic manifold. These tails do not lead to substantial changes in the total diabatic coupling between states, but they do lead to a different partitioning of the total coupling between Coulomb (Forster), exchange (Dexter), and one-electron components. The tails may be reduced by using a multistate diabatic model or eliminated entirely by truncation (denoted as “chopping”). Without more information, we are unable to conclude with certainty whether the observed diabatic tails are a physical reality or a computational artifact. This research suggests that decomposition of the diabatic coupling between chromophores into Coulomb, exchange, and one-electron components may depend strongly on the number of states considered, and such results should be treated with caution.

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.

Design of visible-light-driven photocatalytic materials has attracted intense interest in recent years in an attempt to enhance photonic efficiencies of hydrogen production via water splitting. Recent studies have shown that a solid solution of GaN and ZnO, (Ga1-xZnx)(N1-xOx), can oxidize water under visible light in the presence of a sacrificial electron acceptor. Here we present a systematic study of the structural and electronic properties of this (Ga1-xZnx)(N1-xOx) solid solution as a function of zinc (oxygen) concentration, x, using density-functional theory (DFT). The DFT+U approach has been adopted, and two different periodic supercells, the 16-atom (Ga8-nZnn)(N8-nOn) and 32-atom (Ga16-nZnn)(N16-nOn), have been used to model this solid solution. Results obtained from both supercells are in qualitative agreement with available experimental findings (in the lower concentration range x < 0.25), although overall the larger 32-atom supercell provides a better description of the (Ga1-xZnx)(N1-xOx) solid ...

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 main structural and electronic factors playing a role in intramolecular dissociative electron transfer of a simple donor-peptide-acceptor (D-peptide-A) model have been investigated by an integrated computational protocol based on the density functional theory, its time-dependent extension, and the polarizable continuum model. Our results allow us to elucidate the electronic states involved in the process and how they are perturbed by the orientation of the donor and the acceptor with respect to the peptide chain and by the presence of the solvent. We also report a semiquantitative estimation of the rate constant governing electron transfer obtained by a direct quantum mechanical evaluation of all the terms entering the kinetic expressions based on the Marcus theory and its extensions.

Definitive X-ray structures of "separated" versus "contact" ion pairs, together with their spectral (UV-NIR, ESR) characterizations, provide the quantitative basis for evaluating the complex equilibria and intrinsic (self-exchange) electron-transfer rates for the potassium salts of p-dinitrobenzene radical anion (DNB(-)). Three principal types of ion pairs, K(L)(+)DNB(-), are designated as Classes S, M, and C via the specific ligation of K(+) with different macrocyclic polyether ligands (L). For Class S, the self-exchange rate constant for the separated ion pair (SIP) is essentially the same as that of the "free" anion, and we conclude that dinitrobenzenide reactivity is unaffected when the interionic distance in the separated ion pair is r(SIP)or =6 Angstroms. For Class M, the dynamic equilibrium between the contact ion pair (with r(CIP) = 2.7 Angstroms) and its separated ion pair is quantitatively evaluated, and the rather minor fraction of SIP is nonetheless the principal contributor to the overall electron-transfer kinetics. For Class C, the SIP rate is limited by the slow rate of CIP right arrow over left arrow SIP interconversion, and the self-exchange proceeds via the contact ion pair by default. Theoretically, the electron-transfer rate constant for the separated ion pair is well-accommodated by the Marcus/Sutin two-state formulation when the precursor in Scheme 2 is identified as the "separated" inner-sphere complex (IS(SIP)) of cofacial DNB(-)/DNB dyads. By contrast, the significantly slower rate of self-exchange via the contact ion pair requires an associative mechanism (Scheme 3) in which the electron-transfer rate is strongly governed by cationic mobility of K(L)(+) within the "contact" precursor complex (IS(CIP)) according to the kinetics in Scheme 4.

The standard heterogeneous electron-transfer rate constants (k(n)0) between substrate gold electrodes and the ferrocene redox couple attached to the electrode surface by variable lengths of substituted or unsubstituted oligophenyleneethynylene (OPE) bridges as constituents of mixed self-assembled monolayers were measured as a function of temperature. The distance dependences of the unsubstituted OPE standard rate constants and of the preexponential factors (An) obtained from an Arrhenius analysis of the unsubstituted OPE k(n)0 versus temperature data are not monotonic. This surprising result, together with the distance dependence of the substituted OPE preexponential factors, may be assessed in terms of the likely conformational variability of the OPE bridges (as a result of the low intrinsic barrier to rotation of the phenylene rings in these bridges) and the associated sensitivity of the rate of electron transfer (and, hence, the single-molecule conductance which may be estimated using An) through these bridges to the conformation of the bridge. Additionally, the measured standard rate constants were independent of the identity of the diluent component of the mixed monolayer, and using an unsaturated OPE diluent has no effect on the rate of electron transfer through a long-chain alkanethiol bridge. These observations indicate that the diluent does not participate in the electron-transfer event.

This is the report of a DOE-sponsored workshop organized to discuss the status of our understanding of charge-transfer processes on the nanoscale and to identify research and other needs for progress in nanoscience and nanotechnology. The current status of basic electron-transfer research, both theoretical and experimental, is addressed, with emphasis on the distance-dependent measurements, and we have attempted to integrate terminology and notation of solution electron-transfer kinetics with that of conductance analysis. The interface between molecules or nanoparticles and bulk metals is examined, and new research tools that advance description and understanding of the interface are presented. The present state-of-the-art in molecular electronics efforts is summarized along with future research needs. Finally, novel strategies that exploit nanoscale architectures are presented for enhancing the efficiences of energy conversion based on photochemistry, catalysis, and electrocatalysis principles.

The charge-transfer transition energies and the electronic-coupling matrix element, |H(DA)|, for electron transfer from aminopyridine (ap) to the 4-carbonyl-2,2'-bipyridine (cbpy) in cbpy-(gly)(n)-ap (gly = glycine, n = 0-6) molecules were calculated using the Zerner's INDO/S, together with the Cave and Newton methods. The oligopeptide linkages used were those of the idealized protein secondary structures, the alpha-helix, 3(10)-helix, beta-strand, and polyproline I- and II-helices. The charge-transfer transition energies are influenced by the magnitude and direction of the dipole generated by the peptide secondary structure. The electronic coupling |H(DA)| between (cbpy) and (ap) is also dependent on the nature of the secondary structure of the peptide. A plot of 2.ln|H(DA)| versus the charge-transfer distance (assumed to be the dipole moment change between the ground state and the charge-transfer states) showed that the polyproline II structure is a more efficient bridge for long-distance electron-transfer reactions (beta = 0.7 A(-1)) than the other secondary structures (beta approximately 1.3 A(-1)). Similar calculations on charged dipeptide derivatives, [CH(3)CONHCH(2)CONHCH(3)](+/)(-), showed that peptide-peptide interaction is more dependent on conformation in the cationic than in the anionic dipeptides. The alpha-helix and polyproline II-helix both have large peptide-peptide interactions (|H(DA)|800 cm(-1)) which arise from the angular dependence of their pi-orbitals. Such an interaction is much weaker than in the beta-strand peptides. These combined results were found to be consistent with electron-transfer rates experimentally observed across short peptide bridges in polyproline II (n = 1-3). These results can also account for directional electron transfer observed in an alpha-helical structure (different ET rates versus the direction of the molecular dipole).

The linearized MD technique is developed in order to treat systematically free energies of simple charged and dipolar solutes in water. The solvent electrostatic response field in the solute region is modeled by averaging instantaneous fields found in a MD computation for solvent configurations confined within a cavity that conforms to the real shape of the solute particle. At this stage, all electrostatic interactions are explicitly treated inside the cavity. The solvent in the external region (outside the cavity) is modeled in terms of a standard continuum theory. For nonspherical cavities, the present approach is more accurate than the field computation employed at the preceding MD stage, where spherically truncated Coulomb potentials are modified by the reaction field corrections. We considered two different linearization schemes based on a computation of either the average response field or of its fluctuations. Only the first algorithm proved to be successful. For a series of single-charged monatomic...

We have developed a band-shape analysis of optical transitions in polarizable chromophores characterized by large magnitudes of the transition dipole (intense transitions). The model is tested on steady-state spectra of the coumarin-153 optical dye, employing an explicit solvent description accounting for dipole moment, quadrupole moment, and polarizability of the solvent molecules. The calculations are performed for solvents ranging from nondipolar to strongly dipolar. The solvent dependence of both the experimental Stokes shift and the spectral width is satisfactorily reproduced over the whole polarity range. The optical width is shown to demonstrate a qualitatively different solvent dependence for absorption and emission. The solvent-induced absorption width increases with solvent polarity, whereas the solvent-induced emission width passes through a maximum. This is a result of non-Gaussian statistics of the energy gap fluctuations in polarizable/electronically delocalized chromophores. The total (i.e....

We examine a simple approximate method for calculating the electron transfer (ET) distance suitable for extracting the off-diagonal electronic coupling element (Hab) of Marcus−Hush theory from the ...

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 spectral parameters for the optically induced intervalence charge transfer and the rates of thermal electron transfer as a function of temperature have been measured for a rigid, triply linked mixed-valence dinuclear tris(2,2‘-bipyridine)iron complex. The total reorganizational energy associated with the intramolecular electron exchange in this complex is almost exclusively outer-sphere in nature and comes from thermal fluctuations of the solvent. Thus, the system can be treated rigorously at the classical level, where in this context classical refers to treatments of the nuclear modes. The theories developed to describe the optical electron transfer and the thermal electron transfer are evaluated by analysis of the spectral and rate data, respectively. The quantities common to both theories are the donor−acceptor coupling matrix element, H12, and the total reorganizational energy. Applying the respective theories to the appropriate corresponding sets of data yields reorganizational energies that are ...

Coupling between donor and acceptor orbitals for optically-induced intervalence electron transfer processes has been considered for a series of rigid mixed-valent dinuclear tris(2,2‘-bipyridine)iron complexes. Each of the four complexes considered contains three saturated bridges which link the two tris(2,2‘-bipyridine)iron moieties. The bridging linkages are −CH2CH2−, −CH2CH2CH2−, −CH2OCH2−, and −CH2SCH2−. Despite differences in the composition of the bridges X-ray diffraction and/or molecular dynamics calculations show that the metal−metal separation and relative bipyridine orientations among all four complexes are nearly identical. Consequently, the only factor which differs significantly among these complexes and which might affect the donor−acceptor coupling in the mixed-valent forms is their connectivity. These complexes thus provide a unique opportunity to focus on potential superexchange coupling in the absence of ambiguities introduced by other structural and energetic considerations. Theories de...

Both metal-to-ligand charge transfer (MLCT) and oxidation (ionization) processes have been investigated for (NH3)5RuL2+ complexes with L = pyridine, pyrazine, and protonated pyrazine. Calculations ...

The recently developed generalized Mulliken-Hush approach for the calculation of the electronic coupling matrix element for electron-transfer processes is applied to two rigidly linked donor-bridge-acceptor systems having dimethoxyanthracene as the donor and a dicarbomethoxycyclobutene unit as the acceptor. The dependence of the electronic coupling matrix element as a function of bridge type is examined with and without solvent molecules present. For clamp-shaped bridge structures solvent can have a dramatic effect on the electronic coupling matrix element. The behavior with variation of solvent is in good agreement with that observed experimentally for these systems. 23 refs., 2 tabs.

The kinetics of electron transfer between a substrate gold electrode and a self-assembled monolayer formed from CH{sub 3}(CH{sub 2}){sub n-1}SH and ({eta}{sup 5} C{sub 5}H{sub 5})Fe ({eta}{sup 5}-C{sub 5}H{sub 4})CO{sub 2}(CH{sub 2}){sub n}SH were studied as a function of n, the number of methylenes in the alkyl chain tethering the ferrocene moiety to the electrode, using the indirect laser-induced temperature jump method (ILIT). For 5 {

Electron transfer between an electrode and a redox couple separated from the electrode by an organic film is analyzed using a local dielectric continuum model. The solvent reorganization energy (E[sub s]) is calculated as a function of the cavity radius of the redox group, the thickness of the organic film, and the static and optical dielectric constants of the solvent, the organic film, and the electrode. Comparison is made between results for E[sub s] based on alternative formulations in terms of electric field vectors, and significant differences are found, both quantitative and qualitative. 59 refs., 6 figs.

We have performed molecular dynamics simulations for two different models of a photosynthetic reaction center (Rps.viridis) to examine the diabatic surfaces governing the primary charge separation after photoexcitation. We include the electrostatic energy of the entire proteic complex and also account for the energies of the electronic states of chromophores as computed by semiempirical quantum theory. The statistics we have acquired from our dynamics trajectories is sufficient to contrast the behaviors of the two models, to deduce the effect of crystallization water, and to measure the size of nonlinear response on the pertinent diabetic surfaces. Further, with the perspective we develop, we are able to juxtapose the active and inactive branches of the reaction center. By renormalizing our computed diabetic surfaces with a physically reasonable value for the high-frequency dielectric response of the system, the simulation results can be brought into accord with experimental observations of the thermodynamic driving force for the primary electron transfer. With no further adjustment, we find that the diabatic surfaces for the excited special pair state, SP*, and the charge-separated state SP[sup +]-BPL intersect with essentially no activation barrier. Here, BPL refers to the bacteriopheophytin on the L branch. In contrast, the SP* and SP[supmore » +]-BPM-surfaces intersect in the normal region with an activation barrier and an endothermic thermodynamic driving force. A related observation is that we find fluctuations in the pertinent energy gaps to be significantly smaller on the active L branch than they are on the inactive M branch. We also examine the surfaces associated with moving charge to the accessory bacteriochlorophylls, BCL and BCM. We find that these surfaces lies at energies far above SP*. 41 refs., 11 figs., 3 tabs.« less

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.

Using a corresponding orbital approach implemented computational with the INDO method of Zerner et al, the authors have evaluated and analyzed the electron-transfer matrix elements (H{sub if}) for the ferrocene/ferrocenium and cobaltocene/cobaltocenium (Cp{sub 2}M/(Cp{sub 2}M){sup +}) electron exchange processes. Taking due account of the relative energies of different orientations of the reactants, they obtain good agreement with estimates of H{sub if} inferred from experimental kinetic data, as well as a detailed interpretation of the coupling based on a fully specified effective one-electron model. This model reveals distinct electronic mechanisms for the M = Fe and M = Co cases, corresponding, respectively, to superexchange of the 'electron' and 'hole' type. Variationally defined effective donor and acceptor orbitals are shown to be essentially equivalent to appropriately selected canonical molecular orbitals of the Cp{sub 2}M/(Cp{sub 2}M){sup +} transition-state complex. Departures from a simple one-electron model affect the calculated H{sub if} values by less than 10% (i.e., the many-electron core overlap integral is {approx gt} 0.9) even though the wave functions properly reflect the appreciable degree of electronic relaxation which is known to accompany the oxidation of the Cp{sub 2}M molecules. {sigma} as well as {pi}-type orbitals of the Cp rings are shown tomore » play a significant role in facilitating the electronic coupling between reactants.« less

Electron-transfer matrix elements are calculated for several pairs of transition-metal complexes of the type ML/sub 6//sup 2 +/-ML/sub 6//sup 3 +/, chosen so as to allow a comparison of t/sub 2g/(..pi..) vs. e/sub g/(sigma) transfer and NH/sub 3/ vs. H/sub 2/O ligands, primarily for the apex-to-apex orientation of reactants (M = Fe, Co, and Ru). The magnitude of the matrix element has a pronounced dependence on transfer type (e/sub g/ > t/sub 2g/) and ligand type (NH/sub 3/ > H/sub 2/O), an effect which is correlated with the degree of mixing of the metal and ligand orbitals, based on a corresponding orbital analysis. Use of the calculated matrix element for the Co(NH/sub 3/)/sub 6//sup 2+/3+/ electron exchange, in conjunction with a semiclassical kinetic formalism and a spin-orbit attenuation factor, yields a rate constant for the ground-state reaction path which is about 2 orders of magnitude less than the experimental rate constant. (Orientational averaging would lower the calculated rate constant even further.)

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.

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 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.