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

本研究的目的是构建适用于复坐标法的基集，并利用能量梯度法提出标度角θ的优化方案，使复坐标法能够应用于一般分子问题。我们首先构造了一个所谓的导数基集，具有最小θ依赖。在这个基础上，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，我们进一步应用变分原理来获得完全最优的标度角θ，或者等效的复轨道指数。该方法大大提高了基集的灵活性，与导数基集相比，可以用更少的基函数来计算共振能量。我们采用遗传算法和牛顿-拉夫森方法进行优化。光电离截面可以从频率相关极化率的虚部提取，这反过来又导出为一个泛函的平稳表达式。我们将这一变分原理应用于氢原子光离截面的计算。与以往的L^2方法不同，我们只需要几个复杂的基函数，包括sto和gto，就可以得到非常精确的结果，表明了它的普遍适用性。

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.