Wu Yinghua, Herman Michael F
Department of Chemistry, Tulane University, 6400 Freret Street, New Orleans, Louisiana 70118, USA.
J Chem Phys. 2006 Oct 21;125(15):154116. doi: 10.1063/1.2358352.
A justification is given for the validity of a nonadiabatic surface hopping Herman-Kluk (HK) semiclassical initial value representation (SC-IVR) method. The method is based on a propagator that combines the single surface HK SC-IVR method [J. Chem. Phys. 84, 326 (1986)] and Herman's nonadiabatic semiclassical surface hopping theory [J. Chem. Phys. 103, 8081 (1995)], which was originally developed using the primitive semiclassical Van Vleck propagator. We show that the nonadiabatic HK SC-IVR propagator satisfies the time-dependent Schrodinger equation to the first order of variant Planck's over 2pi and the error is O(variant Planck's over 2pi(2)). As a required lemma, we show that the stationary phase approximation, under current assumptions, has an error term variant Planck's over 2pi(1) order higher than the leading term. Our derivation suggests some changes to the previous development, and it is shown that the numerical accuracy in applications to Tully's three model systems in low energies is improved.
给出了一种非绝热表面跳跃Herman-Kluk（HK）半经典初值表示（SC-IVR）方法有效性的论证。该方法基于一种传播子，它结合了单表面HK SC-IVR方法[《化学物理杂志》84, 326 (1986)]和Herman的非绝热半经典表面跳跃理论[《化学物理杂志》103, 8081 (1995)]，后者最初是使用原始半经典Van Vleck传播子发展而来的。我们表明，非绝热HK SC-IVR传播子在普朗克常数除以2π的一阶近似下满足含时薛定谔方程，误差为O(普朗克常数除以2π的平方)。作为一个必要的引理，我们表明在当前假设下，驻相近似的误差项比主导项高普朗克常数除以2π的一阶。我们的推导对之前的发展提出了一些修改，并且表明在低能量下应用于Tully的三个模型系统时，数值精度得到了提高。
