Projected quasiparticle theory for molecular electronic structure.

Area of Science:

• Quantum Chemistry
• Computational Physics
• Theoretical Chemistry

Background:

• Hartree-Fock-Bogoliubov (HFB) theory is a fundamental method in quantum chemistry.
• Accurately describing static correlations in molecular electronic structure is computationally challenging.
• Existing methods often struggle with the complexity of multireference systems.

Purpose of the Study:

• To derive and implement symmetry-projected Hartree-Fock-Bogoliubov (HFB) equations.
• To apply these equations to the molecular electronic structure problem.
• To provide a comprehensive treatment of static correlations with efficient computational cost.

Main Methods:

• A variation-after-projection approach was used to break and restore all relevant symmetries (particle number, spin, spatial, complex conjugation).
• The method was applied to molecular electronic structure calculations.
• Energy expressions were derived as functionals of an independent quasiparticle density matrix.

Main Results:

• The symmetry-projected HFB method provides a black-box treatment of static correlations.
• The computational cost is comparable to effective one-electron (mean-field) methods.
• The resulting wave function exhibits multireference character and spans the entire Hilbert space.
• Reduced density matrices are efficiently calculated via integration over a gauge grid.

Conclusions:

• Projected quasiparticle theory offers a compelling and powerful approach for quantum chemistry.
• This method effectively addresses static correlations in molecular systems.
• The developed technique demonstrates significant potential for advancing computational chemistry.