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

Abstract

Two independent methods are presented for the nonperturbative calculation of the electronic coupling matrix element (H ab) for electron transfer reactions using ab initio electronic structure theory. The first is based on the generalized Mulliken-Hush ͑GMH͒ model, a multistate generalization of the Mulliken Hush formalism for the electronic coupling. The second is based on the block diagonalization ͑BD͒ approach of Cederbaum, Domcke, and co-workers. Detailed quantitative comparisons of the two methods are carried out based on results for ͑a͒ several states of the system Zn 2 OH 2 ϩ and ͑b͒ 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 Zn 2 OH 2 ϩ. Both methods also yield a natural definition of the effective distance (r DA) between donor (D) and acceptor (A) sites, in contrast to earlier approaches which required independent estimates of r DA , generally based on molecular structure data.

Solvent as Electron Donor: Donor/Acceptor Electronic Coupling Is a Dynamical Variable

“…To evaluate the electronic coupling element between donor and acceptor we used the Generalized Mulliken-Hush (GMH) approach. 54,55 The GMH method requires adiabatic energies and dipole moments (diagonal and off-diagonal, projected onto the two-state adiabatic dipole moment difference for the pair of adiabatic states that correlate with initial and final diabatic states of interest). 54,55 The ZINDO semiempirical electronic structure method of Zerner and co-workers 90 was used to obtain the energies and dipole matrix elements in the present study, with standard parameters (INDO/S; we chose the oxygen value to be the solution phase value of -34.0).…”

“…The very rapid rates of electron-transfer observed in a number of systems for which the solvent is the donor imply that the electron is transferred before solvent reorganization is complete and that the rate is faster than reorientational or translational diffusion. Combining methods of femtosecond optical spectroscopy, computer simulations, and the generalized Mulliken-Hush theory 54,55 for evaluating electron donor/acceptor electronic coupling, we have arrived at a substantially new picture for describing the earliest events in solution phase electron transfer.…”

A Theoretical Study of the Electronic Coupling Element for Electron Transfer in Water

“…23,30 Following discussion of the solvated Zn 2 + results several other donoracceptor pairs (Li 2 + , Be 2 + , Na 2 + , Mg 2 + , Cu 2 + ) are examined at the semiempirical and/or ab initio level in order to assess the donor-acceptor energy-dependence of the conclusions drawn from the Zn data.…”

Mixed valence: origins and developments

“…Such compounds, like the Pt(II,IV) ones extensively investigated by Clark Clark & Turtle 1978;Clark 1990) and further by Yamashita in this discussion ( Takaishi & Yamashita 2008), are manifestations of deeply trapped charge density waves, in essence of 'negative U' (Anderson 1958;Clark & Turtle 1978;Clark 1990). A modified method for estimating J due to Cave & Newton (1997), named the generalized Mulliken-Hush theory, has been proposed more recently and applied widely. A topic of continuing interest, since the earliest models for mixed valence were put forward, is the distinction between localized and delocalized mixed-valence systems on the vibrational time scale (classes 2 and 3 in the generalized kinetic sense).…”