Calculation of photoionization differential cross sections using complex Gauss‐type orbitals

Abstract

Accurate theoretical calculation of photoelectron angular distributions for general molecules is becoming an important tool to image various chemical reactions in real time. We show in this article that not only photoionization total cross sections but also photoelectron angular distributions can be accurately calculated using complex Gauss-type orbital (cGTO) basis functions. Our method can be easily combined with existing quantum chemistry techniques including electron correlation effects, and applied to various molecules. The so-called two-potential formula is applied to represent the transition dipole moment from an initial bound state to a final continuum state in the molecular coordinate frame. The two required continuum functions, the zeroth-order final continuum state and the first-order wave function induced by the photon field, have been variationally obtained using the complex basis function method with a mixture of appropriate cGTOs and conventional real Gauss-type orbitals (GTOs) to represent the continuum orbitals as well as the remaining bound orbitals. The complex orbital exponents of the cGTOs are optimized by fitting to the outgoing Coulomb functions. The efficiency of the current method is demonstrated through the calculations of the asymmetry parameters and molecular-frame photoelectron angular distributions of H2+ and H2 . In the calculations of H2 , the static exchange and random phase approximations are employed, and the dependence of the results on the basis functions is discussed. © 2017 Wiley Periodicals, Inc.

Multi-electron excitation contributions towards primary and satellite states in the photoelectron spectrum

“…In order to describe continuum orbitals, conventional L 2 Gaussian type or Slater type orbitals are not very accurate, despite efforts to adapt them. [47][48][49] Instead, we use a highly flexible linear combination of primitive B-spline functions (ζ ),…”

Fitting continuum wavefunctions with complex Gaussians: Computation of ionization cross sections

“…[8] The main drawback of this method is that it cannot cover all the necessary radial ranges because the radial grid must satisfy a specific square root distribution. This is why in [32] a clear difference is visible between the exact continuum function and its complex fitting in the range 0 < r < 5 a.u. Matsuzaki et al also optimized complex Gaussian sets to fit complex Slater functions.…”

A complex Gaussian approach to molecular photoionization

“…cGTOs were first introduced in the context of resonance stabilization calculations. [27][28][29][30] More recently cGTOs were used in atomic photoionization calculations 31,32 with an optimization method based on the Prony's algorithm used earlier by Huzinaga. 33 In ref.…”