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A theory of redox reactions involving electron transfer between a metal electrode and a molecule in solution is formulated in terms of two types of nuclear coordinates of the thermal bath: electrostatic polarization of the medium and local low-frequency vibrations. The polarization fluctuations follow Gaussian statistics. In contrast, the vibrational coordinate is allowed to change its force constant between two oxidation states of the reactant, which is projected onto non-Gaussian fluctuations of the reactant's electronic states. A closed-form analytical theory for the electrode redox reactions is formulated in terms of three reorganization energies: the reorganization energy for the electrostatic polarization of the medium and two internal (vibrational) reorganization energies for the reduced and oxidized states of the reactant. The theory predicts asymmetry between the cathodic and anodic branches of the electrode current driven by the corresponding difference in the vibrational force constants.

The separation of slow nuclear and fast electronic polarization in problems related to electron mobility in polarizable media was considered by Pekar 70 years ago. Within dielectric continuum models, this separation leads to the Pekar factor in the free energy of solvation by the nuclear degrees of freedom. The main qualitative prediction of Pekar's perspective is a significant, by about a factor of two, drop of the nuclear solvation free energy compared to the total (electronic plus nuclear) free energy of solvation. The Pekar factor enters the solvent reorganization energy of electron transfer reactions and is a significant mechanistic parameter accounting for the solvent effect on electron transfer. Here, we study the separation of the fast and slow polarization modes in polar molecular liquids (polarizable dipolar liquids and polarizable water force fields) without relying on the continuum approximation. We derive the nonlocal free energy functional and use atomistic numerical simulations to obtain nonlocal, reciprocal space electronic and nuclear susceptibilities. A consistent transition to the continuum limit is introduced by extrapolating the results of finite-size numerical simulation to zero wavevector. The continuum nuclear susceptibility extracted from the simulations is numerically close to the Pekar factor. However, we derive a new functionality involving the static and high-frequency dielectric constants. The main distinction of our approach from the traditional theories is found in the solvation free energy due to the nuclear polarization: the anticipated significant drop of its magnitude with increasing liquid polarizability does not occur. The reorganization energy of electron transfer is either nearly constant with increasing the solvent polarizability and the corresponding high-frequency dielectric constant (polarizable dipolar liquids) or actually noticeably increases (polarizable force fields of water).

Standard models of reaction kinetics in condensed materials rely on the Boltzmann-Gibbs distribution for the population of reactants at the top of the free energy barrier separating them from the products. While energy dissipation and quantum effects at the barrier top can potentially affect the transmission coefficient entering the rate pre-exponential factor, much stronger dynamical effects on the reaction barrier are caused by the breakdown of ergodicity for populating the reaction barrier (violation of the Boltzmann-Gibbs statistics). When the spectrum of medium modes coupled to the reaction coordinate includes fluctuations slower than the reaction rate, such nuclear motions dynamically freeze on the reaction time scale and do not contribute to the activation barrier. Here we consider the consequences of this scenario for electrode reactions in slowly relaxing media. Changing the electrode overpotential speeds the electrode electron transfer up, potentially cutting through the spectrum of nuclear modes coupled to the reaction coordinate. The reorganization energy of electrochemical electron transfer becomes a function of the electrode overpotential, switching between the thermodynamic value at low rates to the nonergodic limit at higher rates. The sharpness of this transition depends on the relaxation spectrum of the medium. The reorganization energy experiences a sudden drop with increasing overpotential for a medium with a Debye relaxation but becomes a much shallower function of the overpotential for media with stretched exponential dynamics. The latter scenario characterizes the electron transfer in ionic liquids. The analysis of electrode reactions in room-temperature ionic liquids shows that the magnitude of the free energy of nuclear solvation is significantly below its thermodynamic limit. This result applies to reaction times faster than microseconds and is currently limited by the available dielectric relaxation data.

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.

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

The hybrid molecular–continuum model for polar solvation considered in this paper combines the dielectric continuum approximation for treating fast electronic (inertialess) polarization effects and a molecular dynamics (MD) simulation for the slow (inertial) polarization component, including orientational and translational solvent modes. The inertial polarization is generated by average charge distributions of solvent particles, composed of permanent and induced (electronic) components. MD simulations are performed in a manner consistent with the choice of solvent and solute charges such that all electrostatic interactions are scaled by the factor 1/e∞, where e∞ is the optical dielectric permittivity. This approach yields an ensemble of equilibrium solvent configurations adjusted to the electric field created by a charged or strongly polar solute. The electrostatic solvent response field is found as the solution of the Poisson equation including both solute and explicit solvent charges, with accurate acco...

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...

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.

We extend a recent molecular theory of solvation dynamics to accommodate static solvent effects on the energetics of charge transfer (CT) processes. Our theory is based on a simple renormalized linear response development which incorporates nonlinear aspects of equilibrium solvation. It can accommodate polarizable solvent molecules as well as the limiting case represented by electronically rigid interaction site model (ISM) solvent molecules. We focus on the diabatic free energy profiles governing CT processes in solute donor–acceptor systems of chemical interest. By studying CT in ISM solution models we naturally cover both the short range and long range solute‐solvent interactions, thereby enabling applications to CT in solvents of higher multipolar as well as dipolar character. We derive expressions for the key energetic parameters of a CT process; the solvent reorganization energy, the solvent contribution to the change in thermodynamic free energy, and the optical absorption and fluorescence frequencies.

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.

The continuum multi-configurational dynamical theory of electron transfer (ET) reactions in a chemical solute immersed in a polar solvent is developed. The solute wave function is represented as a CI expansion. The corresponding decomposition of the solute charge density generates a set of dynamical variables, the discrete medium coordinates. A new expression for the free energy surface in terms of these coordinates is derived. The stochastic equations of motion derived earlier are shown to be invariant under unitary transformations of orbitals used to build the CI expansion provided the latter is complete over the corresponding orbital subspace, and also under general linear transformations of the bases employed in expanding the charge density. The interrelation between the present general treatment and the reduced theory applied previously in terms of the two-level ET model is investigated. Finally, the explicit expression for the screening potential of medium electrons is derived in the electronic Born-Oppenheimer approximation (fast (slow) electronic timescale for solvent (solute)). The theory leads to a self-consistent scheme for practical calculations of rate constants for ET reactions involving complex solutes. Illustrative test calculations for two-level ET systems are presented, and the importance of proper boundary conditions for realistic molecular cavities is demonstrated.

Understanding the physical and chemical factors that control the kinetics of interfacial electron-transfer (ET) reactions is important for a large number of technological applications. The present article describes electrochemical kinetic studies of these factors, in which standard interfacial ET rate constants (k(0)(l)) have been measured for ET between substrate Au electrodes and various redox couples attached to the electrode surfaces by variable lengths (l) of oligomethylene (OM), oligophenylenevinylene (OPV) and oligophenyleneethynylene (OPE) bridges, which were constituents of mixed self-assembled monolayers (SAMs). The k(0)(l) measurements employed the indirect laser-induced temperature jump (ILIT) technique, which permits the measurement of interfacial ET rates that are orders of magnitude faster than those measurable by conventional techniques using the macroelectrodes that are the most convenient substrates for the mixed SAMs. The robustness of the measured rate constants (k(0)(l)), together with the Arrhenius activation energies (E(a)(l)) and preexponential factors (A(l)), is demonstrated by their invariance with respect to several experimental system parameters (including the chemical nature and length of the diluent component of the mixed SAM). Analysis of the kinetic results demonstrates that all of the observed interfacial ET processes proceed through a common type of transition state (predominantly associated with solvent reorganization around the redox moiety) and that the actual ET step involves direct electronic tunnelling between the Au electrode and the redox moiety. However, for the full range of l investigated, a global exponential decay of A(l) is not found for any of the three types of bridges. Possible reasons for this behavior, including the role of rate determining steps associated with adiabatic mechanisms within or beyond the transition state theory framework, are discussed, and comparisons with related conductance measurements are presented.

We propose a new theoretical approach to study the kinetics of the electron transfer (ET) under the dynamical influence of the complex environments with the first passage times (FPT) of the reaction events. By measuring the mean and high order moments of FPT and their ratios, the full kinetics of ET, especially the dynamical transitions across different temperature zones, is revealed. The potential applications of the current results to single molecule electron transfer are discussed. Electron transfer is very important in governing many natural and biological processes, for instance, long range electron transfer in the photosynthetic reaction centers, the adenosine triphosphate (ATP) energy pump, etc. Environment has a great impact on the electron transfer dynamics. Marcus’s theory [1] of electron transfer (ET) describes the influence of environments in electron transfer reactions by a single collective reaction coordinate. The classical (nonquantum) model should be a reasonable approximation provided the high frequency modes do not contribute strongly to the reaction coordinate. The free energy profile on this one-dimensional coordinate appears to be smooth. In general, the environment can be best described by a multidimensional landscape with a large number of energy valleys and therefore is intrinsically complex. The treatment of the reaction coordinate in an explicit way often becomes very difficult due to the large number of conformational degrees of freedom involved, such as the positions and the orientations of each solvent molecules (solvent coordinates). It is thus important to ask when the single collective coordinate description of Marcus breaks down and a general multidimensional description of the landscape becomes necessary [2]. This question has first been addressed by Onuchic and Wolynes (OW) [3]. They considered environments as polar solvents or polar groups in proteins (the orientations of solvent molecules are mimicked by spins) interacting with a charged cavity, representing the donor or acceptor site for electron transfer. For every temperature, this model has two thermodynamic regions in polarization space: a glassy trappinglike region with multidimensional valleys of the underlying solvent landscape, and another one exhibiting normal smooth landscape where the one-dimensional effective coordinate picture of Marcus is recovered. Further realistic studies addressing the outer shells for different layers of solvents are given by Tanimura, Leite, and Onuchic [4] with trapping transitions found in each corresponding layer. Onuchic and Wolynes [3] studied the polarization-dependent thermodynamic phase transition. Leite and Onuchic [5,6] showed that the reactive region has a slow average dynamics below the transition temperatures; they argued that this phase transition should influence the dynamics of the system. Electron transfer process can be seen as motions on, and transitions between, a multidimensional potential energy landscape. The landscape represents the potential energy of the system (electronic donor and acceptor states) as a function of reaction coordinates, as shown in Fig. 1. For a smooth landscape, a single coordinate description is appropriate, and for a rugged landscape, the multidimensional description is necessary. In this Letter, we give a quantitative description of this environment. In particular, we study the single molecule electron transfer reaction kinetics under influence of such dynamic environments at different temperatures. We find that the kinetics experiences a transition from the high temperature self-averaging exponential behavior to low temperature non-self-averaging and nonexponential behavior. At even lower temperatures, we find the kinetics is single exponential again. The fluctuations of the kinetics reflect the complex structure of the underlying energy landscape. In the bulk, these fluctuations are suppressed by the large number of molecules and cannot be observed. In single molecules, in principle, one can explicitly measure these fluctuations and the corresponding statistics

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.

We use first principles density functional theory to calculate the electronic structure of the phenylthiolate (S-C$_6$H$_5$) self-assembled monolayer (SAM) on Cu(111) and Au(111) substrates. We find significant lateral dispersion of the SAM molecular states and discuss its implications for transport properties of the molecular wire array. We calculate the two photon photoemission spectra and the work function of the SAM on Cu(111) and compare them with the available experimental data. Our results are used to discuss assignments of the observed spectral data and yield predictions for new electronic states due to the monolayer not yet accessed experimentally., Comment: 7 pages, 7 figures

The paper develops a theory of electron transfer with torsionally induced non-Condon (NC) effects. The starting point of the theory is a generalized spin-boson Hamiltonian, where an additional torsional oscillator bilinearly coupled to other bath modes causes a sinusoidal NC modulation. We derive closed form time dependent nonadiabatic rate expressions for both sudden and relaxed initial conditions, which are applicable for general spectral densities and energetic condition. Under the assumption that the torsional motion is not correlated with the polaronic shift of the bath, simple stationary limit rate expression is obtained. Model calculations of this rate expression illustrate the effects of torsional quantization and gating on the driving force and temperature dependences of the electron transfer rate. The classical limit of the rate expression consists of three Marcus-type terms, and is shown to agree very well with the exact numerical result.

Equilibrium O…O separations ( r e ) and bond energies ( D e ) are calculated for the water dimer, with electron correlation included at the Moller—Plesset (MP2 or MP3) level. Inclusion of corrections for basis set superposition error allows the experimental data for r e and D e to be bracketed. The r e for the dimer is significantly larger than the mean O…O distance in liquid water.

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.

The distribution of eigenvalues of the overlap matrix is analyzed for large and, in the limit, infinite overcomplete multicenter basis sets. It is shown that in the limit the eigenvalues become infinitely degenerate. A numerical example is given and discussed in terms of a semiclassical distribution in phase space.

Calculations using effective potentials demonstrate sensitivity of the SiOSi bond angle to basis set. The important polarization functions for obtaining reasonable bond angles are oxygen d functions have greater population. No significant angular variation of the pπ-dπ bonding is obtained; rather, coulombic and steric repulsions open the SiOSi angle.

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.

Molecular dynamics simulations of molecular models of Fe2+ and Fe3+ in water (L2O = H2O or D2O) are used to generate various correlation functions that characterize the respective hexaaquo hydration complexes. The static Fe2+-oxygen and Fe2+-hydrogen correlation functions are compared in detail with the first difference neutron diffraction results of Enderby et al. for Ni2+ . Velocity autocorrelation functions and corresponding power spectra are generated and analyzed for those modes of hydration shell water molecules whose reduced masses are most sensitive to the changes from H2O to D2O. Various approximations are applied to these data to calculate the solvent isotope effect on the difference in hydration free energies for Fe2+ and Fe3+ . These different approximations all lead to the qualitative conclusion that the net solvent isotope effect reflects a large degree of cancellation between the OL stretching modes and the librational modes. The simulation results generally agree with the results of earlier quantum chemical calculations applied to the same system, but in some respects the new results are not as realistic as the earlier ones. It is proposed that the agreement with experiment would be improved by changes in the model potential which are motivated by other, independent considerations.

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.

By using a Green function Q to characterize the linear response of a dielectric body to electric charges, we obtain a theory for the solvent dielectric contribution to relaxation along the reaction coordinate RC(t) in an electron transfer process. For an electron transfer reaction model, in which the ions are embedded in a dielectric continuum, the theory gives, at t=0, the reorganization free energy derived by Marcus in 1956. For the same model the characteristic time τQ associated with RC(t) is evaluated in terms of the dielectric function eω of the medium. How the rate constant ket for an electron transfer process depends on τQ is illustrated for both high‐barrier and low‐barrier cases by approximating RC(t) as a Smoluchowski process on a potential surface. Applying the theory to a molecular model (charged hard sphere ions in a dipolar hard sphere solvent), treated in the mean spherical approximation for the response at any frequency (Wolynes, 1987), indicates that the effects of the molecular structure of the solvent on τQ are large even if the ion is several times larger than a solvent molecule.

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.

The relatively large differences in D e and R e obtained at the STO-3G level for hydrogen bonded dimers of water, methanol and dimethyl ether, and which correlate monotonically with atomic charges, are strongly attenuated with extended basis sets, and relationships among D e , R e , and electron populations are reversed. Ratios of D e R e products for pairs of proton donors (acceptors) with a common acceptor (donor), however, are constant for a given basis set.

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...

A novel method for investigating solute–solvent H/D exchange equilibria in aqueous solution is described. The ‘‘first‐order difference’’ neutron diffraction method of Enderby and co‐workers is combined with a variation of the isotopic composition of the solvent, ideally from pure D2O to that D2O–H2O mixture in which the average neutron scattering length of the H and D species vanishes. The new technique can give the location of the exchange site with respect to a particular atom as well as the H/D exchange constant for the site with reference to the bulk solvent. The relevant solution thermodynamic data are reviewed to identify systems for which the proposed neutron diffraction experiment is feasible. The literature data are complemented by new calculations of the effect of an ion on the O–H stretch vibration and the libration of the neighboring water. For +3 ions the dominant isotope effect is associated with the O–H stretch of the water; the shift to lower frequencies is proportional to the square of th...

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 ...

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.

Lowdin's canonical orthonormalization procedure is non-unique if the overlap matrix has degenerate eigenvalues. A recent attempt by Roby to justify neglect of differential overlap is re-examined taking proper account of this lack of uniqueness. We conclude that his central result, eq. (6) in our paper, is formally correct in the limit of complete basis sets, but Roby's presentation lends a misleading interpretation to this equation. Consequently, some conclusions which are claimed to follow are, in fact, not valid. We briefly investigate the Roby approximation for finite basis sets and indicate the strengths and weaknesses when used for practical computations.

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 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.

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.

A method is developed for approximating 1‐ and 2‐electron integrals over Slater‐type orbitals (STO's) involving 2‐center charge distributions. The latter are projected by least‐squares, with overlap and dipole constraints, onto STO's with appropriate exponents, located only on the relevant atomic centers. The approach is applicable to any AO basis set, and is illustrated for first‐row atom minimal STO basis sets. Error analysis is given for the projection per se, and for the 1‐ and 2‐electron integrals obtained from the projected distributions. For integrals with magnitude > 10−2 a.u., the rms relative error is ∼1%. Integral errors are sytematic, and balance of errors in nuclear attraction and hybrid 2‐electron integrals is examined. Comparison is made with earlier results of Boys and Shavitt for 1s orbitals.

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.

Ab initio calculations at the SCF and Cl level have been carried out for the singlet ground state of ortho-benzyne (1,2,-dehydrobenzene) at a variety of C 2v molecular geometries. The principal features of the equilibrium geometry are: (1) an “acetylenic” C 1 C 2 bond (1.22 A): (2) a C 4 C 5 bond slightly elongated (1.42 A) with respect to benzene; (3) no elongation of the C 2 C 3 and C 1 C 6 bonds, due to the high s-character and angular deviation of the hybrid orbitals. Extended basis SCF calculations lead to an estimate of ≈ 120 kcal/mole for the Δ H 298° f of o -benzyne.