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Seniority-zero linear canonical transformation theory.

Daniel F Calero-Osorio¹, Paul W Ayers¹

¹Department of Chemistry, McMaster University, Hamilton, Ontario L8S 4M1, Canada.

The Journal of Chemical Physics

|March 10, 2026

Summary

This summary is machine-generated.

We developed a Seniority-zero Linear Canonical Transformation (SZ-LCT) method to efficiently solve the electronic Schrödinger equation for complex systems. This approach significantly reduces computational complexity while maintaining high accuracy, achieving sub-milliHartree errors.

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Area of Science:

Computational Quantum Chemistry
Strongly Correlated Electron Systems
Electronic Structure Theory

Background:

Solving the electronic Schrödinger equation for strongly correlated systems is computationally demanding.
Existing methods struggle with the complexity arising from strong electron correlations.
Seniority-zero wavefunctions offer a computationally tractable subspace that captures essential correlation effects.

Purpose of the Study:

To develop a novel method for solving the electronic Schrödinger equation in strongly correlated systems.
To reduce the computational complexity by transforming the Hamiltonian into a seniority-zero space.
To achieve highly accurate results with improved computational scaling.

Main Methods:

Application of a unitary transformation to the physical Hamiltonian.
Utilizing canonical transformation (CT) theory and the Baker-Campbell-Hausdorff expansion, truncated to two-body operators.
Minimizing non-seniority-zero elements in the transformed Hamiltonian by optimizing the generator.

Main Results:

The Seniority-zero Linear Canonical Transformation (SZ-LCT) method was successfully implemented.
Numerical tests demonstrate highly accurate results, with typical errors below the milliHartree level.
The method exhibits an effective computational scaling of O(N^8/nc), where nc is the number of computational cores.

Conclusions:

SZ-LCT provides a computationally efficient and accurate approach for strongly correlated electron systems.
The method effectively reduces Hamiltonian complexity by targeting the seniority-zero space.
This advancement offers a promising tool for tackling complex quantum chemistry problems.