Advances in relativistic molecular quantum mechanics |
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Authors: | Wenjian Liu |
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Affiliation: | Beijing National Laboratory for Molecular Sciences, Institute of Theoretical and Computational Chemistry, State Key Laboratory of Rare Earth Materials Chemistry and Applications, College of Chemistry and Molecular Engineering, and Center for Computational Science and Engineering, Peking University, Beijing 100871, People’s Republic of China |
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Abstract: | A quantum mechanical equation HΨ=EΨ is composed of three components, viz., Hamiltonian H, wave function Ψ, and property E(λ), each of which is confronted with fundamental issues in the relativistic regime, e.g., (1) What is the most appropriate relativistic many-body Hamiltonian? How to solve the resulting equation? (2) How does the relativistic wave function behave at the coalescence of two electrons? How to do relativistic explicit correlation? (3) How to formulate relativistic properties properly?, to name just a few. It is shown here that the charge-conjugated contraction of Fermion operators, dictated by the charge conjugation symmetry, allows for a bottom-up construction of a relativistic Hamiltonian that is in line with the principles of quantum electrodynamics (QED). Various approximate but accurate forms of the Hamiltonian can be obtained based entirely on physical arguments. In particular, the exact two-component Hamiltonians can be formulated in a general way to cast electric and magnetic fields, as well as electron self-energy and vacuum polarization, into a unified framework. While such algebraic two-component Hamiltonians are incompatible with explicit correlation, four-component relativistic explicitly correlated approaches can indeed be made fully parallel to the nonrelativistic counterparts by virtue of the ‘extended no-pair projection’ and the coalescence conditions. These findings open up new avenues for future developments of relativistic molecular quantum mechanics. In particular, ‘molecular QED’ will soon become an active and exciting field. |
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Keywords: | Quantum electrodynamics Virtual pair effects Electron self-energy Electron vacuum polarization Charge conjugation symmetry Charge-conjugated contraction No-pair approximation Relativistic Hamiltonians Quasi-four-component Exact two-component Relativistic wave functions Relativistic coalescence conditions Relativistic explicit correlations Relativistic theory of nuclear magnetic resonance Relativistic theory of nuclear spin-rotation |
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