Optimization of complex slater-type functions with analytic derivative methods for describing photoionization...

Area of Science:

• Quantum Chemistry
• Atomic and Molecular Physics
• Computational Chemistry

Background:

• The complex basis function (CBF) method is an L2 approach for solving the driven-type Schrödinger equation in photoionization.
• Previous studies using CBF were limited to total cross sections due to challenges in basis function representation and unclear connections to standard Schrödinger solutions.

Purpose of the Study:

• To investigate the applicability of the CBF method for calculating differential cross sections and asymmetry parameters.
• To explore efficient basis functions for representing solutions to the driven-type Schrödinger equation.
• To clarify the relationship between CBF solutions and those of the ordinary Schrödinger equation.

Main Methods:

• Variational optimization of complex trial functions for frequency-dependent polarizability to obtain complex-valued solutions.
• Application of the analytic derivative method for optimizing complex Slater-type orbitals (cSTOs) and their expansion coefficients.
• Extrapolation of CBF solutions to the asymptotic region using the WKB method for phase shifts and asymmetry parameters.

Main Results:

• Accurate determination of both real and imaginary parts of the photoionization solution across typical molecular regions.
• Successful calculation of phase shifts and asymmetry parameters for hydrogen photoionization.
• Analysis of optimized orbital exponent distributions in the complex plane, revealing connections to the driven-type equation.

Conclusions:

• The CBF method, when optimized, can accurately compute differential cross sections and asymmetry parameters.
• The study provides insights into constructing effective basis sets for future molecular photoionization calculations.
• The findings enhance the understanding and applicability of the CBF method in quantum chemistry.