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

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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.