Department of Chemistry and Institute of Theoretical Science, University of Oregon, Eugene, Oregon 97403, USA.
J Chem Phys. 2012 Jan 14;136(2):024114. doi: 10.1063/1.3674994.
Recent works have shown that a generalization of the spectroscopic effective Hamiltonian can describe spectra in surprising regions, such as isomerization barriers. In this work, we seek to explain why the effective Hamiltonian is successful where there was reason to doubt that it would work at all. All spectroscopic Hamiltonians have an underlying abstract zero-order basis (ZOB) which is the "ideal" basis for a given form and parameterization of the Hamiltonian. Without a physical model there is no way to transform this abstract basis into a coordinate representation. To this end, we present a method of obtaining the coordinate space representation of the abstract ZOB of a spectroscopic effective Hamiltonian. This method works equally well for generalized effective Hamiltonians that encompass above-barrier multiwell behavior, and standard effective Hamiltonians for the vicinity of a single potential minimum. Our approach relies on a set of converged eigenfunctions obtained from a variational calculation on a potential surface. By making a one-to-one correspondence between the energy eigenstates of the effective Hamiltonian and those of the coordinate space Hamiltonian, a physical representation of the abstract ZOB is calculated. We find that the ZOB basis naturally adjusts its complexity depending on the underlying nature of phase space, which allows spectroscopic Hamiltonians to succeed for systems sampling multiple stationary points.
最近的研究表明，光谱有效哈密顿量的推广可以描述令人惊讶的区域的光谱，例如异构化势垒。在这项工作中，我们试图解释为什么有效哈密顿量在人们认为它根本不可能起作用的地方取得了成功。所有的光谱哈密顿量都有一个潜在的抽象零阶基（ZOB），这是给定哈密顿量形式和参数化的“理想”基。如果没有物理模型，就无法将这个抽象基转换为坐标表示。为此，我们提出了一种获取光谱有效哈密顿量抽象 ZOB 的坐标空间表示的方法。这种方法对于包含势垒上多阱行为的广义有效哈密顿量以及单个势能极小附近的标准有效哈密顿量同样有效。我们的方法依赖于从势能表面上的变分计算中获得的一组收敛的本征函数。通过在有效哈密顿量的能量本征态和坐标空间哈密顿量的能量本征态之间建立一一对应关系，计算出抽象 ZOB 的物理表示。我们发现，ZOB 基根据相空间的基本性质自然地调整其复杂性，这使得光谱哈密顿量能够成功地用于采样多个稳定点的系统。
