Marshall D. Newton

Generalization of the Mulliken-Hush treatment for the calculation of electron transfer matrix elements

Abstract 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.

Calculation of electronic coupling matrix elements for ground and excited state electron transfer reactions: Comparison of the generalized Mulliken-Hush and block diagonalization methods

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 Zn2O...

Metal—lingad and metal—metal coupling elements

Abstract 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.

Stability of buckminsterfullerene and related carbon clusters.

Under appropriate collisional conditions the mass spectrum of carbon fragments produced by laser vaporization of graphite is dominated by C/sub 60/ and (to a lesser extent) C/sub 70/ clusters. The discoverers of this phenomenon have noted that the carbon valence requirements can be satisfied in closed, hollow structures. For C/sub 60/ they suggest an icosahedral soccer ball network, which they call buckminsterfullerene and we abbreviate as BF. Experimental support has come from studies with lanthanum-impregnated graphite. The resulting mass spectra show intense C/sub 60/La peaks, but no C/sub n/La/sub 2/ or C/sub n/La/sub 3/ peaks. Subsequent experiments have demonstrated the inertness of C/sub 60/ and, indeed, other large C/sub 2n/ clusters under NO attack. We report here the results of quantum calculations which were prompted by the experiments cited above and other earlier work. Our purpose has been to test the intrinsic stability of BF and related polyhedral species and to compare their stability with that of planar graphite fragments. The latter have the advantage of being strain free, but suffer from dangling valences on their perimeters. We also make comparisons with linear carbon chains.

Abinitio studies of the hydrated H3O+ ion. II. The energetics of proton motion in higher hydrates (n=3–5)

Ab initio molecular orbital calculations on the higher hydrates of H3O+, using a split valence level basis set (4–31G), have led to the following results. (1) Energies for successive hydration are in good accord with gas‐phase thermochemical data. (2) Hydrogen‐bonded OH and O⋅⋅⋅O distances in H9O4+ are in excellent agreement with condensed phase diffraction data. (3) Large variations in OH (≲0.08 A) and O⋅⋅⋅O (∼0.25 A) distances caused by strong hydrogen bonding are monotonically correlated with OH stretching force constants and frequencies, which cover a range of 1500 cm−1. (4) Excellent quantitative correlation is obtained between calculated and observed infrared gas‐phase frequencies for six intense OH stretching bands, as represented by the least‐squares fit, νexp=−704+1440 (FSGS)1/2±15 cm−1. This least squares relationship is used to assign some of the other experimental absorption bands from the gas phase. The only major uncertainty is in the case of the symmetric H3O+ mode in H3O+(H2O)3. (5) The re...

The electronic structure of small nickel atom clusters

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...

The theory of the Fe2+–Fe3+ electron exchange in 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 g...

Ab initio study of electronic coupling in the aqueous Fe2+–Fe3+ electron exchange process

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 ...

Green function theory of charge transfer processes in solution

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 structur...

The water dimer: Theory versus experiment

Abstract 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.