The hybrid anti-symmetrized coupled channels method (haCC) for the tRecX code

Abstract

We present a new implementation of the hybrid antisymmetrized Coupled Channels (haCC) method in the framework of the tRecX (Scrinzi, 2022 [6]). The method represents atomic and molecular multi-electron functions by combining CI functions, Gaussian molecular orbitals, and a numerical single-electron basis. It is suitable for describing high harmonic generation and the strong-field dynamics of ionization. Fully differential photoemission spectra are computed by the tSurff method. The theoretical background of haCC is outlined and key improvements compared to its original formulation are highlighted. We discuss control of over-completeness resulting from the joint use of the numerical basis and Gaussian molecular orbitals by pseudo-inverses based on the Woodbury formula. Further new features of this tRecX release are the iSurff method, new input features, and the AMOS gateway interface. The mapping of haCC into the tRecX framework for solving the time-dependent Schrödinger equation is shown. Use, performance, and accuracy of haCC are discussed on the examples of high-harmonic generation and strong-field photo-emission by short laser pulses impinging on the Helium atom and on the linear molecules $N_2$ and CO.

Program summary

Program title: tRecX — time-dependent Recursive indeXing (tRecX=tSurff+irECS)

CPC Library link to program files: https://doi.org/10.17632/m9g2jc82sw.1

Developer's repository link: https://gitlab.physik.uni-muenchen.de/AG-Scrinzi/tRecX

Licensing provisions: GNU General Public License 2

Programming language: C++

External libraries: Eigen, arpack, lapack, blas, boost, FFTW (optional)

Journal Reference of previous version: A. Scrinzi, Comp. Phys. Comm., 270:108146, 2022.

Does the new version supersede the previous version: Yes

Reasons for the new version: Major new functionality: haCC — hybrid antisymmetrized coupled channels method

Summary of revisions: Main additions are haCC and iSurff. Code usage and compilation were improved.

Nature of problem: tRecX is a general solver for time-dependent Schrödinger-like problems, with applications mostly in strong field and attosecond physics. There are no technical restrictions on the spatial dimension of the problem with up to 6 spatial dimensions realized in the strong-field double ionization of Helium. Gaussian-based quantum chemical multi-electron atomic and molecular structure can be combined with the numerical basis. A selection of coordinate systems is available and any Hamiltonian involving up to second derivatives and arbitrary up to three dimensional potentials can be defined on input by simple scripts.

Solution method: The method of lines is used with spatial discretization by a flexible combination of one dimensional basis sets, DVR representations, discrete vectors, expansions into higher-dimensional eigenfunctions of user-defined operators, and Gaussian based molecular orbitals. Multi-electron Gaussian-based CI (configuration interaction) functions for neutrals and ions are combined with the numerical basis. Photo-emission spectra are calculated using the time-dependent surface flux method (tSurff) in combination with infinite range exterior complex scaling (irECS) for absorption. The code is object oriented and makes extensive use of tree-structures and recursive algorithms. Parallelization is by MPI. Code design and performance allow use in production as well as for graduate level training.