Ivan Kondov

Perturbative treatment of intercenter coupling in the framework of Redfield theory

Abstract The quantum dynamics of coupled subsystems connected to a thermal bath is studied. In some of the earlier work the effect of intercenter coupling on the dissipative part was neglected. This is equivalent to a zeroth-order perturbative expansion of the damping term with respect to the intercenter coupling. It is shown numerically for two coupled harmonic oscillators that this treatment can lead to artifacts and a completely wrong description, for example, of a charge transfer processes even for very weak intercenter coupling. Here we perform a first-order treatment and show that these artifacts disappear. In addition, we demonstrate that the thermodynamic equilibrium population is almost reached even for strong intercenter coupling strength.

Efficiency of different numerical methods for solving Redfield equations

The numerical efficiency of different schemes for solving the Liouville–von Neumann equation within multilevel Redfield theory has been studied. Among the tested algorithms are the well-known Runge–Kutta scheme in two different implementations as well as methods especially developed for time propagation: the short iterative Arnoldi, Chebyshev, and Newtonian propagators. In addition, an implementation of a symplectic integrator has been studied. For a simple example of a two-center electron transfer system we discuss some aspects of the efficiency of these methods to integrate the equations of motion. Overall, for time-independent potentials the Newtonian method is recommended. For time-dependent potentials implementations of the Runge–Kutta algorithm are very efficient.

A density matrix approach to photoinduced electron injection

Abstract Electron injection from an adsorbed molecule to the substrate (heterogeneous electron transfer) is studied. One reaction coordinate is used to model this process. The surface phonons and/or the electron–hole pairs together with the internal degrees of freedom of the adsorbed molecule as well as a liquid possibly surrounding the molecule provide a dissipative environment, which may lead to dephasing, relaxation, and sometimes excitation of the relevant system. In the process studied, the adsorbed molecule is excited by a light pulse. This is followed by an electron transfer from the excited donor state to the quasi-continuum of the substrate. It is assumed that the substrate is a semiconductor. The effects of dissipation on electron injection are investigated.

Stochastic unraveling of Redfield master equations and its application to electron transfer problems

A method for stochastic unraveling of general time-local quantum master equations (QMEs) is proposed. The present kind of jump algorithm allows a numerically efficient treatment of QMEs which are not in Lindblad form, i.e., are not positive semidefinite by definition. The unraveling can be achieved by allowing for trajectories with negative weights. Such a property is necessary, e.g., to unravel the Redfield QME and to treat various related problems with high numerical efficiency. The method is successfully tested on the damped harmonic oscillator and on electron transfer models including one and two reaction coordinates. The obtained results are compared to those from a direct propagation of the reduced density matrix (RDM) as well as from the standard quantum jump method. Comparison of the numerical efficiency is performed considering both the population dynamics and the RDM in the Wigner phase space representation.

Stochastic unraveling of time-local quantum master equations beyond the Lindblad class

A method for stochastic unraveling of general time-local quantum master equations (QME) which involve the reduced density operator at time t only is proposed. The present kind of jump algorithm enables a numerically efficient treatment of QMEs that are not of Lindblad form. So it opens large fields of application for stochastic methods. The unraveling can be achieved by allowing for trajectories with negative weight. We present results for the quantum Brownian motion and the Redfield QMEs as test examples. The algorithm can also unravel non-Markovian QMEs when they are in a time-local form like in the time-convolutionless formalism.

Different direct integrators for Redfield equations applied to electron transfer dynamics

Abstract The numerical efficiency of different schemes for solving the Liouville-von Neumann equation within Redfield theory has been studied. Among the tested algorithms are the general Runge-Kutta and Bulirsch-Stoer methods as well as methods especially developed for time propagation like the Short Iterative Arnoldi and Newtonian propagators. Also two different time step control mechanisms have been applied. The calculations have been performed for a system consisting of two charge localization centers modeling electron transfer. Two different cases have been investigated, i.e., the coherent dissipationless and the dissipative case. The tested integrators perform quite differently for these cases.

Numerical Simulation of Electron Transfer Rates in Betaine-30

Within the density matrix theory we are calculating the photoinduced S 1 M S 0 reverse electron transfer rates in betaine-30 in two solvents, acetonitrile and acetone. The results are compared with experimental results and predictions of the Marcus and the Jortner-Bixon theory. An advantage of the density matrix theory is the possibility to predict the time-dependent behavior of the transfer system and not just transfer rates.

Femtosecond Dynamics in the Anisotropy of Emission in LH2 Units

Circular aggregates of 18 pigments are studied to model the B850 ring of bacteriochlorophylls within the LH2 complexes of the purple bacterium Rhodopseudomonas acidophila . Previously, the time evolution of the anisotropy of emission after an impulsive excitation has been calculated for varying degrees of static disorder but without dynamic disorder (interaction with a heat bath). In this case, modest degrees of static disorder are sufficient to cause the experimentally found initial drop of the anisotropy on a sub-100 v; fs time scale. We have taken into account the simultaneous influence of static and dynamic disorders and found that larger static disorder is needed to guarantee temperature independent initial drop of the anisotropy. In the present paper we extend our previous calculations and investigate non-Markovian effects in the description of the bath.