Variational versus perturbative relativistic energies for small and light atomic and molecular systems

Ferenc, Dávid and Jeszenszki, Péter and Mátyus, Edit (2022) Variational versus perturbative relativistic energies for small and light atomic and molecular systems. JOURNAL OF CHEMICAL PHYSICS, 157. ISSN 0021-9606

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Abstract

Variational and perturbative relativistic energies are computed and compared for two-electron atoms and molecules with low nuclear charge numbers. In general, good agreement of the two approaches is observed. Remaining deviations can be attributed to higher-order relativistic, also called non-radiative quantum electrodynamics (QED), corrections of the perturbative approach that are automatically included in the variational solution of the no-pair Dirac−Coulomb−Breit (DCB) equation to all orders of the α fine-structure constant. The analysis of the polynomial α dependence of the DCB energy makes it possible to determine the leading-order relativistic correction to the non-relativistic energy to high precision without regularization. Contributions from the Breit−Pauli Hamiltonian, for which expectation values converge slowly due the singular terms, are implicitly included in the variational procedure. The α dependence of the no-pair DCB energy shows that the higher-order (α4Eh) non-radiative QED correction is 5 % of the leading-order (α3Eh) non-radiative QED correction for Z=2 (He), but it is 40 % already for Z=4 (Be2+), which indicates that resummation provided by the variational procedure is important already for intermediate nuclear charge numbers.

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