4.7 Article

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

期刊

JOURNAL OF CHEMICAL PHYSICS
卷 157, 期 9, 页码 -

出版社

AIP Publishing
DOI: 10.1063/5.0105355

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资金

  1. European Research Council [851421]
  2. UNKP-21-3 New National Excellence Program of the Ministry for Innovation and Technology from the source of the National Research, Development and Innovation Fund [UNKP-21-3-II-ELTE-41]
  3. European Research Council (ERC) [851421] Funding Source: European Research Council (ERC)

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Variational and perturbative relativistic energies are calculated and compared for two-electron atoms and molecules with low nuclear charge numbers. It is found that the two approaches show good agreement, and the deviations can be attributed to higher-order relativistic corrections. The analysis reveals the importance of resummation provided by the variational procedure, particularly for intermediate nuclear charge numbers.
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 alpha fine-structure constant. The analysis of the polynomial alpha 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 alpha dependence of the no-pair DCB energy shows that the higher-order (alpha E-4(h)) non-radiative QED correction is 5% of the leading-order (alpha E-3(h)) 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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