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

为了构造适用于复坐标方法（CCM）的基组，并利用能量梯度法对标度角θ进行优化，使CCM能够应用于一般的分子问题，我们首先构造了一个具有最小θ依赖性的导数基组。在此基础上，所有的功能有一个共同的轨道指数。然而，由于导数基仍然包含小的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。该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计算共振能量。我们采用遗传算法和Newton-Raphson方法进行优化，从频变极化率的虚部中提取光电离截面，并将虚部作为泛函的稳态表达式导出。我们将这一变分原理应用于H原子光电离截面的计算。与以前的L^2方法不同，我们只需要几个复杂的基函数就可以得到非常精确的结果，包括STO和GTO，这表明了该方法的普遍适用性。

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.