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Coalescence Conditions of Relativistic Wave Functions

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Handbook of Relativistic Quantum Chemistry

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Abstract

The electron-electron coalescence conditions for the wave functions of the Dirac-Coulomb (DC), Dirac-Coulomb-Gaunt (DCG), and Dirac-Coulomb-Breit (DCB) Hamiltonians are analyzed by making use of the internal symmetries of the reduced two-electron systems. The results show that, at the coalescence point of two electrons, the wave functions of the DCG Hamiltonian are regular, while those of the DC and DCB Hamiltonians have r 12 ν-type weak singularities, with ν being negative and of \(\mathcal{O}(\alpha ^{2})\). Yet, such asymptotic expansions of the relativistic wave functions are only valid within an extremely small convergence radius R c of \(\mathcal{O}(\alpha ^{2})\). Beyond this radius, the behaviors of the relativistic wave functions are still dominated by the nonrelativistic limit.

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Acknowledgements

The research of this work was supported by grants from the National Natural Science Foundation of China (Project Nos. 21033001, 21273011, 21290192, and 11471025).

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Authors and Affiliations

  1. LMAM and School of Mathematical Sciences, Peking University, Beijing, People’s Republic of China

    Sihong Shao

  2. Beijing National Laboratory for Molecular Sciences, State Key Laboratory of Rare Earth Materials Chemistry and Applications, Institute of Theoretical and Computational Chemistry, College of Chemistry and Molecular Engineering, and Center for Computational Science and Engineering, Peking University, Beijing, People’s Republic of China

    Zhendong Li

  3. Beijing National Laboratory for Molecular Sciences, State Key Laboratory of Rare Earth Materials Chemistry and Applications, Institute of Theoretical and Computational Chemistry, College of Chemistry and Molecular Engineering, and Center for Computational Science and Engineering, Peking University, Beijing, People’s Republic of China

    Wenjian Liu

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  1. Sihong Shao
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  2. Zhendong Li
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Correspondence to Sihong Shao .

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Editors and Affiliations

  1. College of Chemistry and Molecular Engin, Peking University, Beijing, China

    Wenjian Liu

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Shao, S., Li, Z., Liu, W. (2015). Coalescence Conditions of Relativistic Wave Functions. In: Liu, W. (eds) Handbook of Relativistic Quantum Chemistry. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-41611-8_8-1

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  • DOI: https://doi.org/10.1007/978-3-642-41611-8_8-1

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