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Richardson-Gaudin states of non-zero seniority: Matrix elements.
1Département de Chimie, Université Laval, Québec, Québec G1V 0A6, Canada.
The Journal of Chemical Physics
|April 3, 2025
Summary
Seniority-zero wave functions offer qualitative insights into bond-breaking. This study extends Richardson-Gaudin states to higher seniorities, enabling efficient and accurate computational chemistry for complex molecular systems.
Area of Science:
- Quantum Chemistry
- Computational Physics
- Theoretical Chemistry
Background:
- Seniority-zero wave functions provide a qualitative description of bond-breaking.
- Richardson-Gaudin states, as eigenvectors of a model Hamiltonian, offer a clear physical picture and systematic improvement pathways.
- Previous treatments were limited to the seniority-zero sector.
Purpose of the Study:
- To identify and compute couplings for higher seniority Richardson-Gaudin states.
- To investigate the role of the Coulomb Hamiltonian in coupling these states.
- To demonstrate the efficiency of seniority-based configuration interaction methods.
Main Methods:
- Identification of higher seniority states.
- Computation of couplings using cofactors of the effective overlap matrix.
- Proof-of-principle single-reference configuration interaction calculations.
Main Results:
- Higher seniority states were successfully identified and their couplings computed.
- Couplings were accurately determined from the cofactors of the effective overlap matrix.
- Single-reference configuration interaction demonstrated comparable accuracy to seniority-based methods at reduced computational cost.
Conclusions:
- The extension of Richardson-Gaudin states to higher seniorities is feasible and computationally advantageous.
- Seniority-based configuration interaction offers a cost-effective approach for complex molecular systems.
- Future work will focus on Slater-Condon rules for enhanced computational feasibility.
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