Department of Chemistry and Chemical Biology, Baker Laboratory, Cornell University, Ithaca, New York 14853, USA.
J Chem Phys. 2009 Nov 28;131(20):204504. doi: 10.1063/1.3266566.
Observables in linear and nonlinear infrared spectroscopy may be computed from vibrational response functions describing nuclear dynamics on a single electronic surface. We demonstrate that the Herman-Kluk (HK) semiclassical approximation to the quantum propagator yields an accurate representation of quantum coherence effects in linear and nonlinear response functions for coupled anharmonic oscillators. A considerable numerical price is paid for this accuracy; the calculation requires a multidimensional integral over a highly oscillatory integrand that also grows without bound as a function of evolution times. The interference among classical trajectories in the HK approximation produces quantization of good action variables. By treating this interference analytically, we develop a mean-trajectory (MT) approximation that requires only the propagation of classical trajectories linked by transitions in action. The MT approximation accurately reproduces coherence effects in response functions of coupled anharmonic oscillators in a regime in which the observables are strongly influenced by these interactions among vibrations.
在单电子表面上，描述原子核动力学的振动响应函数可以计算线性和非线性红外光谱中的可观测量。我们证明，量子传播子的赫尔曼-克鲁克（HK）半经典近似可以准确地表示耦合非谐振荡器中线性和非线性响应函数中的量子相干效应。这种准确性需要付出相当大的数值代价；该计算需要对高度振荡的积分进行多维积分，并且随着演化时间的增加而无限增长。在 HK 近似中，经典轨迹之间的干涉产生了良好作用变量的量子化。通过对这种干涉进行分析处理，我们开发了一种平均轨迹（MT）近似，该近似仅需要传播通过作用跃迁连接的经典轨迹。在观测值受到振动之间相互作用强烈影响的情况下，MT 近似可以准确地再现耦合非谐振荡器的响应函数中的相干效应。
