Separation of metric in Wick's theorem
1National Research Center "Kurchatov Institute," Kurchatov Sq. 1, Moscow 123182, Russia.
The Journal of Chemical Physics
|November 20, 2023
Summary
This study introduces a new tensorial formulation of Wick's theorem in quantum chemistry. This approach separates metric and density matrices, simplifying calculations for complex quantum systems.
Area of Science:
- Quantum Chemistry
- Theoretical Chemistry
- Computational Quantum Mechanics
Background:
- Wick's theorem is crucial for simplifying operator products in quantum chemistry, particularly with reference states.
- Existing generalizations struggle with intertwined metric and density matrices, especially for multiconfigurational wave functions or nonorthogonal orbitals.
Purpose of the Study:
- To propose a general tensorial formulation of Wick's theorem that separates metric and density matrices.
- To provide a more robust theoretical framework for quantum chemical calculations involving complex reference states and nonorthogonality.
Main Methods:
- Developed a general tensorial formulation of Wick's theorem.
- Separated the metric matrix from density matrices by expressing coefficients as products of density matrix elements and Pfaffians of orbital overlap matrices.
Main Results:
- The proposed formalism naturally separates metric and density matrices, simplifying calculations.
- Demonstrated the utility of the approach for density cumulants, particle-hole symmetry, and transition density matrices with different bra and ket states.
Conclusions:
- The metric-separated Wick's theorem offers a powerful platform for deriving advanced quantum chemical methods.
- This formulation effectively addresses challenges posed by non-trivial reference states and orbital nonorthogonality.
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