Generalized relativistic small-core pseudopotentials accounting for quantum electrodynamic effects: construction and pilot applications

TL;DR

This paper introduces a method to incorporate quantum electrodynamic effects into relativistic pseudopotentials, improving accuracy for atomic and molecular calculations involving heavy elements.

Contribution

The authors develop a new approach to include QED corrections into generalized relativistic pseudopotentials, enhancing their precision for heavy-element atomic and molecular computations.

Findings

QED contributions exceed pseudopotential errors by an order of magnitude.

The new pseudopotentials accurately reproduce atomic excitation energies.

Application to two-valence-electron systems demonstrates improved excitation energy calculations.

Abstract

A simple procedure to incorporate one-loop quantum electrodynamic (QED) corrections into the generalized (Gatchina) nonlocal shape-consistent relativistic pseudopotential model is described. The pseudopotentials for Lu, Tl, and Ra replacing only inner core shells (with principal quantum numbers $n\le 3$ for the two former elements and $n\le 4$ for the latter one) are derived from the solutions of reference atomic SCF problems with the Dirac-Coulomb-Breit Hamiltonian to which the model Lamb shift operator added. QED contributions to atomic valence excitation energies evaluated at the SCF level are demonstrated to exceed the errors introduced by the pseudopotential approximation itself by an order of magnitude. Pilot applications of the new model to calculations of excitation energies of two-valence-electron atomic systems using the intermediate-Hamiltonian relativistic Fock space coupled cluster method reformulated here for incomplete main model spaces are reported. Implications for high-accuracy molecular excited state calculations are discussed.