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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...

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.

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.

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.

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...

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.

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.

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.

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.