Optimization of complex slater-type functions with analytic derivative methods for describing photoionization differential cross sections

Rei Matsuzaki, Satoshi Yabushita

Research output: Contribution to journalArticle

2 Citations (Scopus)

Abstract

The complex basis function (CBF) method applied to various atomic and molecular photoionization problems can be interpreted as an L2 method to solve the driven-type (inhomogeneous) Schrödinger equation, whose driven term being dipole operator times the initial state wave function. However, efficient basis functions for representing the solution have not fully been studied. Moreover, the relation between their solution and that of the ordinary Schrödinger equation has been unclear. For these reasons, most previous applications have been limited to total cross sections. To examine the applicability of the CBF method to differential cross sections and asymmetry parameters, we show that the complex valued solution to the driven-type Schrödinger equation can be variationally obtained by optimizing the complex trial functions for the frequency dependent polarizability. In the test calculations made for the hydrogen photoionization problem with five or six complex Slater-type orbitals (cSTOs), their complex valued expansion coefficients and the orbital exponents have been optimized with the analytic derivative method. Both the real and imaginary parts of the solution have been obtained accurately in a wide region covering typical molecular regions. Their phase shifts and asymmetry parameters are successfully obtained by extrapolating the CBF solution from the inner matching region to the asymptotic region using WKB method. The distribution of the optimized orbital exponents in the complex plane is explained based on the close connection between the CBF method and the driven-type equation method. The obtained information is essential to constructing the appropriate basis sets in future molecular applications.

Original languageEnglish
Pages (from-to)910-925
Number of pages16
JournalJournal of Computational Chemistry
Volume38
Issue number12
DOIs
Publication statusPublished - 2017 May 5

Fingerprint

Photoionization
Cross section
Complex Functions
Basis Functions
Derivatives
Derivative
Optimization
Asymmetry
Slater-type Orbitals
Exponent
WKB Method
Time Operator
Wave functions
Phase Shift
Phase shift
Wave Function
Argand diagram
Dipole
Hydrogen
Mathematical operators

Keywords

  • Asymmetry parameter
  • Complex basis function method
  • Photoionization cross section
  • Variational principle-orbital exponent optimization

ASJC Scopus subject areas

  • Chemistry(all)
  • Computational Mathematics

Cite this

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title = "Optimization of complex slater-type functions with analytic derivative methods for describing photoionization differential cross sections",
abstract = "The complex basis function (CBF) method applied to various atomic and molecular photoionization problems can be interpreted as an L2 method to solve the driven-type (inhomogeneous) Schr{\"o}dinger equation, whose driven term being dipole operator times the initial state wave function. However, efficient basis functions for representing the solution have not fully been studied. Moreover, the relation between their solution and that of the ordinary Schr{\"o}dinger equation has been unclear. For these reasons, most previous applications have been limited to total cross sections. To examine the applicability of the CBF method to differential cross sections and asymmetry parameters, we show that the complex valued solution to the driven-type Schr{\"o}dinger equation can be variationally obtained by optimizing the complex trial functions for the frequency dependent polarizability. In the test calculations made for the hydrogen photoionization problem with five or six complex Slater-type orbitals (cSTOs), their complex valued expansion coefficients and the orbital exponents have been optimized with the analytic derivative method. Both the real and imaginary parts of the solution have been obtained accurately in a wide region covering typical molecular regions. Their phase shifts and asymmetry parameters are successfully obtained by extrapolating the CBF solution from the inner matching region to the asymptotic region using WKB method. The distribution of the optimized orbital exponents in the complex plane is explained based on the close connection between the CBF method and the driven-type equation method. The obtained information is essential to constructing the appropriate basis sets in future molecular applications.",
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author = "Rei Matsuzaki and Satoshi Yabushita",
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AB - The complex basis function (CBF) method applied to various atomic and molecular photoionization problems can be interpreted as an L2 method to solve the driven-type (inhomogeneous) Schrödinger equation, whose driven term being dipole operator times the initial state wave function. However, efficient basis functions for representing the solution have not fully been studied. Moreover, the relation between their solution and that of the ordinary Schrödinger equation has been unclear. For these reasons, most previous applications have been limited to total cross sections. To examine the applicability of the CBF method to differential cross sections and asymmetry parameters, we show that the complex valued solution to the driven-type Schrödinger equation can be variationally obtained by optimizing the complex trial functions for the frequency dependent polarizability. In the test calculations made for the hydrogen photoionization problem with five or six complex Slater-type orbitals (cSTOs), their complex valued expansion coefficients and the orbital exponents have been optimized with the analytic derivative method. Both the real and imaginary parts of the solution have been obtained accurately in a wide region covering typical molecular regions. Their phase shifts and asymmetry parameters are successfully obtained by extrapolating the CBF solution from the inner matching region to the asymptotic region using WKB method. The distribution of the optimized orbital exponents in the complex plane is explained based on the close connection between the CBF method and the driven-type equation method. The obtained information is essential to constructing the appropriate basis sets in future molecular applications.

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