LIBGRPP: A Library for the Evaluation of Molecular Integrals of the Generalized Relativistic Pseudopotential Operator over Gaussian Functions

Alexander V. Oleynichenko, Andréi Zaitsevskii, Nikolai S. Mosyagin, Alexander N. Petrov, Ephraim Eliav*, Anatoly V. Titov

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review


Generalized relativistic pseudopotentials (GRPP) of atomic cores implying the use of different potentials for atomic electronic shells with different principal quantum numbers give rise to accurate and reliable relativistic electronic structure models of atoms, molecules, clusters, and solids. These models readily incorporate the effects of Breit electron–electron interactions and one-loop quantum electrodynamics effects. Here, we report the computational procedure for evaluating one-electron integrals of GRPP over contracted Gaussian functions. This procedure was implemented in a library of routines named LIBGRPP, which can be integrated into existing quantum chemistry software, thus enabling the application of various methods to solve the many-electron problem with GRPPs. Pilot applications to electronic transitions in the ThO and UO (Formula presented.) molecules using the new library and intermediate-Hamiltonian Fock space relativistic coupled cluster method are presented. Deviations of excitation energies obtained within the GRPP approach from their all-electron Dirac–Coulomb–Gaunt counterparts do not exceed 50 cm (Formula presented.) for the 31 lowest-energy states of ThO and 110 cm (Formula presented.) for the 79 states of UO (Formula presented.). The results clearly demonstrate that rather economical tiny-core GRPP models can exceed in accuracy relativistic all-electron models defined by Dirac–Coulomb and Dirac–Coulomb–Gaunt Hamiltonians.

Original languageEnglish
Article number197
Issue number1
StatePublished - Jan 2023


FundersFunder number
National Research Council Canada
Ministry of Education and Science of the Russian Federation075-10-2020-117
Russian Science Foundation20-13-00225


    • Gaussian basis functions
    • excited states
    • generalized relativistic pseudopotentials
    • heavy-element compounds
    • high-precision electronic structure modeling
    • molecular integrals
    • relativistic coupled cluster theory
    • thorium oxide
    • uranium dioxide


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