Department of Chemistry and Biochemistry, Queens College of the City University of New York, 65-30 Kissena Boulevard, Flushing, New York 11367-1597, USA.
J Chem Phys. 2012 Dec 14;137(22):22A536. doi: 10.1063/1.4748142.
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.
本文提出了一种在绝热电子态和核坐标态基底下的非绝热分子哈密顿量紧凑形式。哈密顿量包含一阶和二阶导数耦合项，是厄米的，因此为密度算符的量子刘维尔方程提供了一个标准表达式。应用投影算符技术，推导出了密度算符对角分量的量子主方程。在假设核态比电子态的范围小得多且没有奇点的情况下，引入了半绝热近似，得到了非绝热分子哈密顿量和量子刘维尔方程的表达式，这些表达式更适合高级量子动力学计算。半绝热近似也被应用于一个由供体和受体组成的共振能量转移系统，它们通过库仑项相互作用，推导出了包含所有非绝热项的激子-溶剂哈密顿量的显式详细表达式。
