Density matrices of seniority-zero geminal wavefunctions.

Area of Science:

• Quantum Chemistry
• Computational Physics
• Theoretical Chemistry

Background:

• Evaluating scalar products and density matrix elements of geminal wavefunctions is computationally intensive.
• Existing methods for fermionic and bosonic systems, like Wick's theorem, require adaptation for specific wavefunction types.

Purpose of the Study:

• To develop a tractable method for calculating properties of closed-shell pair geminal wavefunctions.
• To assess the feasibility of this method for specific quantum chemical states.
• To compute and analyze dissociation curves for hydrogen chains.

Main Methods:

• Direct evaluation of scalar products and density matrix elements in terms of pair amplitudes.
• Application of the derived method to Richardson-Gaudin (RG) states, antisymmetrized geminal power (AGP), and antisymmetrized product of strongly orthogonal geminals (APSWOG).
• Computation of hydrogen chain dissociation curves using off-shell RG states and antisymmetrized product of interacting geminals (APIG).

Main Results:

• An analog of Wick's theorem for fermions and bosons was derived for geminal wavefunctions.
• The method was shown to be feasible for RG states, AGP, and APSWOG.
• Dissociation curves for hydrogen chains computed with off-shell RG states and APIG were found to be near exact.

Conclusions:

• The developed method provides an efficient way to handle complex wavefunction calculations.
• Off-shell RG states and APIG show promise for accurate molecular dissociation modeling.
• Further investigation into different RG states may resolve discrepancies observed with ground-state RG calculations.