Powerful approximate methods for propagating the density matrix of complex systems that are conveniently described in terms of electronic subsystem states and nuclear degrees of freedom have recently been developed that involve linearizing the density matrix propagator in the difference between the forward and backward paths of the nuclear degrees of freedom while keeping the interference effects between the different forward and backward paths of the electronic subsystem described in terms of the mapping Hamiltonian formalism and semi-classical mechanics. Here we demonstrate that different approaches to developing the linearized approximation to the density matrix propagator can yield a mean-field like approximate propagator in which the nuclear variables evolve classically subject to Ehrenfest-like forces that involve an average over quantum subsystem states, and by adopting an alternative approach to linearizing we obtain an algorithm that involves classical like nuclear dynamics influenced by a quantum subsystem state dependent force reminiscent of trajectory surface hopping methods. We show how these different short time approximations can be implemented iteratively to achieve accurate, stable long time propagation and explore their implementation in different representations. The merits of the different approximate quantum dynamics methods that are thus consistently derived from the density matrix propagator starting point and different partial linearization approximations are explored in various model system studies of multi-state scattering problems and dissipative non-adiabatic relaxation in condensed phase environments that demonstrate the capabilities of these different types of approximations for treating non-adiabatic electronic relaxation, bifurcation of nuclear distributions, and the passage from nonequilibrium coherent dynamics at short times to long time thermal equilibration in the presence of a model dissipative environment.
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14 December 2012
Research Article|
September 04 2012
Consistent schemes for non-adiabatic dynamics derived from partial linearized density matrix propagation
Pengfei Huo;
Pengfei Huo
a)
1Department of Chemistry,
Boston University
, 590 Commonwealth Avenue, Boston, Massachusetts 02215, USA
2Division of Chemistry and Chemical Engineering,
California Institute of Technology
, Pasadena, California 91125, USA
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David F. Coker
David F. Coker
a)
1Department of Chemistry,
Boston University
, 590 Commonwealth Avenue, Boston, Massachusetts 02215, USA
3Department of Physics, and Complex Adaptive Systems Laboratory,
University College Dublin
, Dublin 4, Ireland
Search for other works by this author on:
a)
Electronic addresses: [email protected] and [email protected].
J. Chem. Phys. 137, 22A535 (2012)
Article history
Received:
June 04 2012
Accepted:
August 14 2012
Citation
Pengfei Huo, David F. Coker; Consistent schemes for non-adiabatic dynamics derived from partial linearized density matrix propagation. J. Chem. Phys. 14 December 2012; 137 (22): 22A535. https://doi.org/10.1063/1.4748316
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