A mixed quantum-classical Liouville study of the population dynamics in a model photo-induced condensed phase electron transfer reaction
- Department of Chemistry, University of Alberta, Edmonton, Alberta T6G 2G2 (Canada)
- Department of Chemistry, University of Toronto, Toronto, Ontario M5S 3H6 (Canada)
We apply two approximate solutions of the quantum-classical Liouville equation (QCLE) in the mapping representation to the simulation of the laser-induced response of a quantum subsystem coupled to a classical environment. These solutions, known as the Poisson Bracket Mapping Equation (PBME) and the Forward-Backward (FB) trajectory solutions, involve simple algorithms in which the dynamics of both the quantum and classical degrees of freedom are described in terms of continuous variables, as opposed to standard surface-hopping solutions in which the classical degrees of freedom hop between potential energy surfaces dictated by the discrete adiabatic state of the quantum subsystem. The validity of these QCLE-based solutions is tested on a non-trivial electron transfer model involving more than two quantum states, a time-dependent Hamiltonian, strong subsystem-bath coupling, and an initial energy shift between the donor and acceptor states that depends on the strength of the subsystem-bath coupling. In particular, we calculate the time-dependent population of the photoexcited donor state in response to an ultrafast, on-resonance pump pulse in a three-state model of an electron transfer complex that is coupled asymmetrically to a bath of harmonic oscillators through the optically dark acceptor state. Within this approach, the three-state electron transfer complex is treated quantum mechanically, while the bath oscillators are treated classically. When compared to the more accurate QCLE-based surface-hopping solution and to the numerically exact quantum results, we find that the PBME solution is not capable of qualitatively capturing the population dynamics, whereas the FB solution is. However, when the subsystem-bath coupling is decreased (which also decreases the initial energy shift between the donor and acceptor states) or the initial shift is removed altogether, both the PBME and FB results agree better with the QCLE-based surface-hopping results. These findings highlight the challenges posed by various conditions such as a time-dependent external field, the strength of the subsystem-bath coupling, and the degree of asymmetry on the accuracy of the PBME and FB algorithms.
- OSTI ID:
- 22105471
- Journal Information:
- Journal of Chemical Physics, Vol. 138, Issue 14; Other Information: (c) 2013 American Institute of Physics; Country of input: International Atomic Energy Agency (IAEA); ISSN 0021-9606
- Country of Publication:
- United States
- Language:
- English
Similar Records
On the proper derivation of the Floquet-based quantum classical Liouville equation and surface hopping describing a molecule or material subject to an external field
Can we derive Tully's surface-hopping algorithm from the semiclassical quantum Liouville equation? Almost, but only with decoherence
Related Subjects
ACCURACY
ALGORITHMS
APPROXIMATIONS
BOLTZMANN-VLASOV EQUATION
COUPLING
DEGREES OF FREEDOM
ELECTRON TRANSFER
HAMILTONIANS
HARMONIC OSCILLATORS
MATHEMATICAL SOLUTIONS
OSCILLATORS
PHOTON-ATOM COLLISIONS
PHOTON-MOLECULE COLLISIONS
POPULATION DYNAMICS
POTENTIAL ENERGY
QUANTUM STATES
SIMULATION
SURFACES
TIME DEPENDENCE