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Theoretical studies on superexcited states and photoionization processes of molecules by analytical continuation of Hamiltonian.

利用哈密顿量的解析延拓对分子超激发态和光电离过程进行理论研究。

基本信息

批准号：
13640516
负责人：
YABUSHITA Satoshi
金额：
$ 2.37万
依托单位：
Keio University
依托单位国家：
日本
项目类别：
Grant-in-Aid for Scientific Research (C)
财政年份：
2001
资助国家：
日本
起止时间：
2001 至 2003
项目状态：
已结题

项目摘要

The purpose of this study is to construct basis sets that are suitable for the complex coordinate method(CCM) and to develop the optimization scheme for the scaling angle θ with the energy gradient method, so that the CCM can be applied to general molecular problems.We first constructed a so-called derivative basis set, with a minimum θ-dependence. In this basis, all the functions have a common orbital exponent. However, since the derivative basis still contains a small θ-dependence, we further applied the variational principle to have the completely optimal scaling angle θ, or equivalently, complex orbital exponents. By applying this method, the flexibility of the basis set is enhanced greatly, thus the resonance energy can be calculated with a smaller number of basis functions than the case of the derivative basis set. We applied both the Genetic Algorithm and the Newton-Raphson method for the optimization.The photoionization cross section can be extracted from the imaginary part of the frequency-dependent polarizability, which is in turn derived as a stationary expression of a functional. We applied this variational principle to the calculation of photoionization cross sections of H atom. Contrary to previous L^2 methods, we could obtain very accurate results with only a few complex basis functions, both STOs and GTOs, suggesting the general applicability.

本研究的目的是构造适用于复坐标法的基集，并利用能量梯度法开发标度角θ的优化方案，从而使复坐标法可以应用于一般的分子问题。我们首先构造了一个所谓的导数基集，它具有最小的θ依赖性。在此基础上，所有的函数都有一个共同的轨道指数。然而，由于导数基仍然包含一个小的θ依赖性，我们进一步应用变分原理来获得完全最优的标度角θ，或者等价地，复轨道指数。这种方法大大增强了基组的灵活性，从而可以用比导数基组更少的基函数来计算共振能。我们同时应用遗传算法和牛顿-拉夫森方法进行优化，可以从随频率变化的极化率的虚部中提取光致电离截面，然后将其导出为泛函的固定表达式。我们用这个变分原理计算了H原子的光致电离截面。与以前的L^2方法不同，我们只需要几个复基函数，无论是STO还是GTO，都能得到非常精确的结果，这表明它具有普遍的适用性。