Quantum dynamics of electrons in a molecular segment with phonon interaction

Abstract

A Hamiltonian model for a molecular segment or molecular chain with phonon or vibrational coupling is introduced which admits analytic solutions. A time correlation function Q(t) for the average position of an electron inserted at the end of a chain with a thermal average of the phonons is defined. A prominent feature of the dynamics is that the phonons drive the electron density to decay to a steady-state distribution along the chain. We demonstrate that two imaging methods based on the time derivatives of Q(t) at zero time are capable of producing the average velocity of the electron along the chain using a reasonable number of the time derivatives. We further show that this average velocity increases as the coupling to the phonons is increased and as the temperature is increased; that is, the decay to a steady state is enhanced in both cases.

Condensed-Phase Relaxation of Multilevel Quantum Systems. I. An Exactly Solvable Model

“…In particular, we showed that the reduced system density matrix of an N -level condensed-phase system can be obtained as a linear combination of N 2 time-dependent functions, which can be calculated exactly for certain types of baths and system−bath couplings. This technique has been used recently by Cook, Evans, and Coalson to study non-Condon effects in condensed-phase electron transfer and constitutes a generalization of simpler Hamiltonians discussed by Creechly and Dahnovsky and Gayen et al in a different context.…”

Effectiveness of Perturbation Theory Approaches for Computing Non-Condon Electron Transfer Dynamics in Condensed Phases

“…This particular non-Condon electron transfer Hamiltonian , is a special case of a more general class of nontrivial N -level Hamiltonians coupled to a dissipative environment (or bath) for which the time evolution of the composite quantum many-body system can be calculated exactly. In fact, we − and others − have shown that for this general class of Hamiltonians, the exact time dependence of the reduced system dynamics of the N -level system can be determined. It should be noted that this general class of Hamiltonians includes a very specific form for the system−bath coupling term, which means that these exactly solvable Hamiltonians are limited to a special region of parameter space.…”

“…Chem exactly. In fact, we [32][33][34][35] and others [42][43][44] have shown that for this general class of Hamiltonians, the exact time dependence of the reduced system dynamics of the N-level system can be determined. It should be noted that this general class of Hamiltonians includes a very specific form for the system-bath coupling term, which means that these exactly solvable Hamiltonians are limited to a special region of parameter space.…”