Geminal theory within the seniority formalism and bi-variational principle

• URL: http://arxiv.org/abs/2408.06842v1
• Date: Tue, 13 Aug 2024 12:04:04 GMT
• Title: Geminal theory within the seniority formalism and bi-variational principle
• Authors: Stijn De Baerdemacker, Dimitri Van Neck,
• Abstract summary: We present an overview of the mathematical structure of geminal theory within the seniority formalism and bi-variational principle. Named after the constellation, geminal wavefunctions provide the mean-field like representation of paired-electron wavefunctions in quantum chemistry.
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• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: We present an overview of the mathematical structure of geminal theory within the seniority formalism and bi-variational principle. Named after the constellation, geminal wavefunctions provide the mean-field like representation of paired-electron wavefunctions in quantum chemistry, tying in with the Lewis picture of chemical bonding via electron pairs. Unfortunately, despite its mean-field product wave function description, the computational cost of computing geminal wavefunctions is dominated by the permanent overlaps with Slater determinant reference states. We review recent approaches to reduce the factorial scaling of the permanent, and present the bi-variational principle as a consistent framework for the projected Schr\"odinger Equation and the computation of reduced density matrices.

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