Relativistic radial electron density functions and natural orbitals from GRASP2018
Sacha Schiffmann, Jiguang Li, J. Ekman, Gediminas Gaigalas, Michel Godefroid, Per Jönsson, Jacek Bieroń
Abstract
A new module, RDENSITY, of the GRASP2018 package [1] is presented for evaluating the radial electron density function of an atomic state described by a multiconfiguration Dirac-Hartree-Fock or configuration interaction wave function in the fully relativistic scheme. The present module is the relativistic version of DENSITY [2] that was developed for the ATSP2K package [3]. The calculation of the spin-angular factors entering in the expression of the expectation value of the density operator is performed using the angular momentum theory in orbital, spin, and quasispin spaces, adopting a generalized graphical technique [4]. The natural orbitals (NOs) are evaluated from the diagonalization of the density matrix, taking advantage of its κ-block structure. The features of the code are discussed in detail, focusing on the advantages and properties of the NOs and on the electron radial density picture as a mean for investigating electron correlation and relativistic effects. Program title: RDENSITY CPC Library link to program files: https://doi.org/10.17632/4sdrf5kfzd.1 Licensing provisions: MIT license Programming language: FORTRAN 95 Nature of problem: This program determines the atomic electron radial density in the MCDHF approximation. It also evaluates the natural orbitals by diagonalizing the density matrix. Solution method: Building the density operator using second quantization - Spherical symmetry averaging - Evaluating the matrix elements of the one-body excitation operators in the configuration state function (CSF) space using the angular momentum theory in orbital, spin, and quasispin spaces. Additional comments including restrictions and unusual features: We evaluated the electron radial density and natural orbitals of the lowest states in Mg II. The MCDHF wave functions consisted of four non-interacting blocks and a total of 79 000 CSFs. The calculation took around 2 minutes using a computer with an Intel(R) Xeon(R) Gold 6148 processor @ 2.4 GHz. GRASP2018 - A Fortran 95 version of the General Relativistic Atomic Structure Package, C. Froese Fischer, G. Gaigalas, P. Jönsson and J. Bieroń, Comput. Phys. Commun. 237 (2019) 184-187. Multiconfiguration electron density function for the ATSP2K-package, A. Borgoo, O. Scharf, G. Gaigalas and M. Godefroid, Comput. Phys. Commun. 181 (2010) 426-439 An MCHF atomic-structure package for large-scale calculations, C. Froese Fischer, G. Tachiev, G. Gaigalas, and M. Godefroid, Comput. Phys. Commun. 176 (2007) 559-579 An efficient approach for spin-angular integrations in atomic structure calculations, G. Gaigalas, Z. Rudzikas, and C. Froese Fischer, J. Phys. B: At. Mol. Phys., 30 (1997) 3747-3771