Buchholz Max, Grossmann Frank, Ceotto Michele
Institut für Theoretische Physik, Technische Universität Dresden, 01062 Dresden, Germany.
Dipartimento di Chimica, Università degli Studi di Milano, via C. Golgi 19, 20133 Milano, Italy.
J Chem Phys. 2016 Mar 7;144(9):094102. doi: 10.1063/1.4942536.
A mixed semiclassical initial value representation expression for spectroscopic calculations is derived. The formulation takes advantage of the time-averaging filtering and the hierarchical properties of different trajectory based propagation methods. A separable approximation is then introduced that greatly reduces (about an order of magnitude) the computational cost compared with a full Herman-Kluk time-averaging semiclassical calculation for the same systems. The expression is exact for the harmonic case and it is tested numerically for a Morse potential coupled to one or two additional harmonic degrees of freedom. Results are compared to full Herman-Kluk time-averaging calculations and exact quantum wavepacket propagations. We found the peak positions of the mixed semiclassical approximations to be always in very good agreement with full quantum calculations, while overtone peak intensities are lower with respect to the exact ones. Given the reduced computational effort required by this new mixed semiclassical approximation, we believe the present method to make spectroscopic calculations available for higher dimensional systems than accessible before.
推导了用于光谱计算的混合半经典初值表示表达式。该公式利用了时间平均滤波以及不同基于轨迹传播方法的层次特性。接着引入了一种可分离近似，与对相同系统进行的完整Herman-Kluk时间平均半经典计算相比，该近似极大地降低了（约一个数量级）计算成本。该表达式对于谐波情况是精确的，并针对耦合到一个或两个附加谐波自由度的莫尔斯势进行了数值测试。将结果与完整的Herman-Kluk时间平均计算和精确的量子波包传播进行了比较。我们发现混合半经典近似的峰值位置总是与全量子计算非常吻合，而泛音峰值强度相对于精确值较低。鉴于这种新的混合半经典近似所需的计算量减少，我们相信本方法能够对比以前可及的更高维系统进行光谱计算。
