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arXiv · 2311.15266

Unified construction of relativistic Hamiltonians

Wenjian Liu
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Abstract

It is shown that four-component (4C), quasi-four-component (Q4C), and exact two-component (X2C) relativistic Hartree-Fock (HF) equations can be implemented in an unified manner, by making use of the atomic nature of the small components of molecular 4-spinors. A model density matrix approximation can first be invoked for the small-component charge/current density functions, which gives rise to a static, pre-molecular mean field (pmf) to be combined with the one-electron term. As a result, only the nonrelativistic-like two-electron term of the 4C/Q4C/X2C Fock matrix needs to be updated during the iterations. A `one-center small-component' approximation can then be invoked in the evaluation of relativistic integrals. That is, all atom-centered small-component basis functions are regarded as extremely localized nearby the position of the atom to which they belong, such that they have vanishing overlaps with all small- or large-component functions centered at other nuclei. Under these approximations, the 4C, Q4C, and X2C mean-field and many-electron Hamiltonians share precisely the same structure and accuracy. Beyond these is the effective quantum electrodynamics Hamiltonian that can be constructed in the same way. Such approximations lead to errors that are orders of magnitude smaller than other sources of errors (e.g., truncation errors in the one- and many-particle bases as well as uncertainties of experimental measurements) and are hence safe to use for whatever purposes. The quaternion forms of the 4C, Q4C, and X2C equations are also presented in the most general way, based on which the corresponding Kramers-restricted open-shell (RKOHF) variants are formulated for `high-spin' open-shell systems.

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Wenjian Liu. 2023-11-26. Unified construction of relativistic Hamiltonians. https://arxiv.org/abs/2311.15266

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