Generalized Relativistic Effective Core Potential Method: Theory and calculations

TL;DR

This paper introduces a generalized relativistic effective core potential (RECP) method that improves accuracy and enables detailed calculations of heavy-atom molecules by overcoming limitations of traditional RECP approaches.

Contribution

The authors develop and validate a new generalized RECP method that enhances accuracy and allows for precise calculations of properties near heavy nuclei, including P,T-odd effects.

Findings

Achieved up to 2000 cm^{-1} accuracy improvements in dissociation and transition energies.

Enabled calculation of electronic densities and matrix elements near heavy nuclei.

Validated the method on atoms and molecules like TlH, HgH, PbF, HgF, BaF, and YbF.

Abstract

In calculations of heavy-atom molecules with the shape-consistent Relativistic Effective Core Potential (RECP), only valence and some outer-core shells are treated explicitly, the shapes of spinors are smoothed in the atomic core regions and the small components of four-component spinors are excluded from calculations. Therefore, the computational efforts can be dramatically reduced. However, in the framework of the standard nodeless radially local RECP versions, any attempt to extend the space of explicitly treated electrons more than some limit does not improve the accuracy of the calculations. The errors caused by these (nodeless) RECPs can range up to 2000 $cm^{-1}$ and more for the dissociation and transition energies even for lowest-lying excitations that can be unsatisfactory for many applications. Moreover, the direct calculation of such properties as electronic densities near heavy nuclei, hyperfine structure, and matrix elements of other operators singular on heavy nuclei is impossible as a result of the smoothing of the orbitals in the core regions. In the present paper, ways to overcome these disadvantages of the RECP method are discussed. The developments of the RECP method suggested by the authors are studied in many precise calculations of atoms and of the TlH, HgH molecules. The technique of nonvariational restoration of electronic structure in cores of heavy atoms in molecules is applied to calculation of the P,T-odd spin-rotational Hamiltonian parameters including the weak interaction terms which break the symmetry over the space inversion (P) and time-reversal invariance (T) in the PbF, HgF, BaF, and YbF molecules.