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J Chem Phys. 2009 Jul 21;131(3):031104. doi: 10.1063/1.3159445.

Exact two-component Hamiltonians revisited.

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  • 1Beijing National Laboratory for Molecular Sciences, Institute of Theoretical and Computational Chemistry, College of Chemistry and Molecular Engineering, Peking University, Beijing 100871, People's Republic of China. liuwj@pku.edu.cn

Abstract

Two routes for deriving the exact two-component Hamiltonians are compared. In the first case, as already known, we start directly from the matrix representation of the Dirac operator in a restricted kinetically balanced basis and make a single block diagonalization. In the second case, not considered before, we start instead from the Foldy-Wouthuysen operator and make proper use of resolutions of the identity. The expressions are surprisingly different. It turns out that a mistake was made in the former formulation when going from the Dirac to the Schrodinger picture. The two formulations become equivalent after the mistake is corrected.

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