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Relativistic explicit correlation: coalescence conditions and practical suggestions.
Zhendong Li1, Sihong Shao, Wenjian Liu
1Beijing National Laboratory for Molecular Sciences, Institute of Theoretical and Computational Chemistry, College of Chemistry and Molecular Engineering, and Center for Computational Science and Engineering, Peking University, Beijing 100871, People's Republic of China.
The Journal of Chemical Physics
|April 17, 2012
Summary
This study derives electron-electron coalescence conditions for relativistic wave functions, revealing singularities in Dirac-Coulomb and Dirac-Coulomb-Breit Hamiltonians. Relativistic explicitly correlated methods are shown to parallel nonrelativistic ones under specific approximations.
Area of Science:
- Quantum Chemistry
- Relativistic Quantum Mechanics
- Computational Chemistry
Background:
- Relativistic effects are crucial for accurate electronic structure calculations of heavy elements.
- Explicitly correlated wave function methods incorporate inter-electron distances to improve convergence.
- Understanding wave function behavior at electron coalescence is key for developing accurate relativistic methods.
Purpose of the Study:
- To establish a general framework for relativistic explicitly correlated wave function methods.
- To derive and analyze electron-electron coalescence conditions for various relativistic Hamiltonians.
- To investigate the behavior of relativistic wave functions near the electron-electron coalescence point.
Main Methods:
- Derivation of electron-electron coalescence conditions for Dirac-Coulomb (DC), Dirac-Coulomb-Gaunt (DCG), Dirac-Coulomb-Breit (DCB), modified Dirac-Coulomb (MDC), and zeroth-order regularly approximated (ZORA) Hamiltonians.
- Analysis of wave function asymptotic behaviors using internal symmetries of reduced two-electron Hamiltonians.
- Comparison of relativistic wave function behaviors with nonrelativistic counterparts and direct perturbation theory (DPT).
Main Results:
- DCG Hamiltonian wave functions are regular at the coalescence point, while DC and DCB exhibit weak singularities.
- MDC wave function behaviors show a simple relation to original ones; ZORA behaviors depend on the kinetic energy operator's potential.
- Relativistic explicitly correlated wave function methods can be parallelized with nonrelativistic ones under the no-pair approximation using an extended projector.
Conclusions:
- The study provides fundamental insights into the behavior of relativistic wave functions at electron coalescence.
- Singularities in DC and DCB Hamiltonians suggest potential issues with bound electronic states.
- The findings enable the development of more accurate and efficient relativistic explicitly correlated computational methods.
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