Nonadiabatic quantum Liouville and master equations in the adiabatic basis

Journal Article · Fri Dec 14 04:00:00 EST 2012 · Journal of Chemical Physics

DOI:https://doi.org/10.1063/1.4748142· OSTI ID:22099133

Jang, Seogjoo ^[1]

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1. Department of Chemistry and Biochemistry, Queens College of the City University of New York, 65-30 Kissena Boulevard, Flushing, New York 11367-1597 (United States)

A compact form of nonadiabatic molecular Hamiltonian in the basis of adiabatic electronic states and nuclear position states is presented. The Hamiltonian, which includes both the first and the second derivative couplings, is Hermitian and thus leads to a standard expression for the quantum Liouville equation for the density operator. With the application of a projection operator technique, a quantum master equation for the diagonal components of the density operator is derived. Under the assumption that nuclear states are much more short ranged compared to electronic states and assuming no singularity, a semi-adiabatic approximation is invoked, which results in expressions for the nonadiabatic molecular Hamiltonian and the quantum Liouville equation that are much more amenable to advanced quantum dynamics calculation. The semi-adiabatic approximation is also applied to a resonance energy transfer system consisting of a donor and an acceptor interacting via Coulomb terms, and explicit detailed expressions for exciton-bath Hamiltonian including all the non-adiabatic terms are derived.

• OSTI ID: 22099133
• Journal Information: Journal of Chemical Physics, Journal Name: Journal of Chemical Physics Journal Issue: 22 Vol. 137; ISSN JCPSA6; ISSN 0021-9606
• Country of Publication: United States
• Language: English

Related Subjects

71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
74 ATOMIC AND MOLECULAR PHYSICS
ADIABATIC APPROXIMATION
BOLTZMANN-VLASOV EQUATION
COUPLINGS
ENERGY TRANSFER
HAMILTONIANS
POTENTIAL ENERGY
PROJECTION OPERATORS
SINGULARITY
STANDARDS