用一般瞬子路径研究振动激发态的调谐分裂
Tunneling splittings of vibrationally excited states using general instanton paths
摘要：
本文提出了一种用笛卡尔坐标计算分子振动激发态隧穿劈裂的多维半经典方法。它是Mil'nikov和Nakamura [ $\textit{ J. Chem. Phys.}$ $\textbf{122}$，$124311$ $(2005)$ ]的理论的扩展，适用于计算多井系统中隧道分裂模式所必需的非对称路径，如水团簇。此外，在半经典波函数的描述中引入了新的术语，大大提高了某些系统的分裂估计。该方法以瞬子理论为基础，从基态瞬子波函数出发，沿最小作用路径及其谐波邻域构造振动激发态的半经典波函数。因此，激发态的分裂得到在一个可以忽略不计的附加数值努力。由于基态分裂的代价集中在瞬子路径优化和沿路径的Hessian估计上，因此该方法可以不加修改地应用于许多全维中等分子，并与电子势的实时估计相结合。对几种模型电位和水二聚体进行了测试。
英文摘要：
A multidimensional semiclassical method for calculating tunneling splittings in vibrationally excited states of molecules using Cartesian coordinates is developed. It is an extension of the theory by Mil'nikov and Nakamura [$\textit{ J. Chem. Phys.}$ $\textbf{122}$, $124311$ $(2005)$] to asymmetric paths that are necessary for calculating tunneling splitting patterns in multi-well systems, such as water clusters. Additionally, new terms are introduced in the description of the semiclassical wavefunction that drastically improve the splitting estimates for certain systems. The method is based on the instanton theory and builds the semiclassical wavefunction of the vibrationally excited states from the ground-state instanton wavefunction along the minimum action path and its harmonic neighborhood. The splittings of excited states are thus obtained at a negligible added numerical effort. The cost is concentrated, as for the ground-state splittings, in the instanton path optimization and the hessian evaluation along the path. The method can thus be applied without modification to many mid-sized molecules in full dimensionality and in combination with on-the-fly evaluation of electronic potentials. The tests were performed on several model potentials and on the water dimer.
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