Relativistic radial electron density functions and natural orbitals from GRASP2018

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 summaryProgram title:RDENSITYCPC Library link to program files:https://doi.org/10.17632/4sdrf5kfzd.1Licensing provisions: MIT licenseProgramming language: FORTRAN 95Nature 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.