New expression for the effective transfer matrix element in long-range electron transfer reactions

Abstract

A new expression for the effective transfer matrix element, TDA, in long-range electron transfer is derived. This expression corrects the second-order perturbation theory estimate by accounting for an infinite number of terms in the perturbation expansion. The correction factors measure the extent of delocalization of the diabatic donor and acceptor states. A simple procedure is devised to adjust the molecule to its transition state, which is the point of avoided crossing of the energies of the adiabatic states. The new expression is used to compute the half-splitting in these eigenenergies, which equals TDA, without recourse to diagonalization. When checked against direct diagonalization for a truncated model of a ruthenium-modified azurin protein, this method located the point of avoided crossing and produced an estimate of the energy half-splitting which agreed with the result of diagonalization with exceptional accuracy.

Solvent Effects in Nonadiabatic Electron‐Transfer Reactions: Theoretical Aspects

“…This procedure is nonperturbative and turns out to be much more efficient than direct diagonalization of the same size of a problem. The strategy of the matrix element calculation due to Stuchebrukhov et al involves initial use of the perturbation theory [272,273] (or its extended version [274], which accounts for possible resonances with the bridge states but still avoids diagonalization of the full Hamiltonian matrix) to find relevant atom sequences on which the tunneling pathways are localized (protein pruning [275]). Further atomic details are examined on the pruned molecules, which are much smaller in size, with the method of interatomic tunneling currents.…”

DNA Repair Mechanism by Photolyase: Electron Transfer Path from the Photolyase Catalytic Cofactor FADH−to DNA Thymine Dimer

“…In particular, states "D2 and "A2 are moved and eventually brought into resonance. Fluctuations of the solvent can be modeled similarly by application of a homogeneous electric "eld in a direction from the donor to the acceptor site (Katz & Stuchebrukhov, 1998).…”

Reduced Electronic Spaces for Modeling Donor/Acceptor Interactions

“…The relevant D and A manifold also must take adequate account of the role of any intervening bridge states (B). 13,14,16,22,32,34,35 Quantitative means of assessing the degree to which this criterion is satisfied are considered below over a range of n values for a given ET system. The spaces adopted here are based on in vacuo adiabatic states, but may also be defined as in situ spaces (e.g., in the presence of a variable solvent reaction field).…”

“…We first employ a se model 13,14,32,35 to construct a PT estimate of ψ D d (2) and ψ A d (2) coupling for comparison with the actual 2-st (h DA d (2) ) result:…”