Theoretical study on resonance states and photoionization processes with the combination of complex coordinate method and analytical derivative method

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The complex coordinate method is a theoretical method to evaluate directly both the energy level and lifetime of resonance states. This study develops an efficient theoretical method to evaluate atomic and molecular photoionization cross sections. To solve a long-standing problem in the previous calculation scheme, which is the difficulty in selecting appropriate basis functions, we propose to variationally optimize the frequency-dependent polarizability with respect to complex orbital exponents, with using analytically evaluated first and second derivatives of the polarizability.