Method For Making 2-Electron Response Reduced Density Matrices Approximately N-representable

In methods like geminal-based approaches or coupled cluster that are solved using the projected Schr\"odinger equation, direct computation of the 2-electron reduced density matrix (2-RDM) is impractical and one falls back to a 2-RDM based on response theory. However, the 2-RDMs from response th...

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Bibliographic Details
Published inarXiv.org
Main Authors Lanssens, Caitlin, Ayers, Paul W, Dimitri Van Neck, De Baerdemacker, Stijn, Gunst, Klaas, Bultinck, Patrick
Format Paper Journal Article
LanguageEnglish
Published Ithaca Cornell University Library, arXiv.org 08.01.2018
Subjects
Algorithms
Approximation
Density
Eigenvalues
Electrons
Mathematical analysis
Matrix methods
Optimization
Physics - Chemical Physics
Physics - Quantum Physics
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Summary:In methods like geminal-based approaches or coupled cluster that are solved using the projected Schr\"odinger equation, direct computation of the 2-electron reduced density matrix (2-RDM) is impractical and one falls back to a 2-RDM based on response theory. However, the 2-RDMs from response theory are not \(N\)-representable. That is, the response 2-RDM does not correspond to an actual physical \(N\)-electron wave function. We present a new algorithm for making these non-\(N\)-representable 2-RDMs approximately \(N\)-representable, i.e. it has the right symmetry and normalization and it fulfills the \(P\)-, \(Q\)- and \(G\)-conditions. Next to an algorithm which can be applied to any 2-RDM, we have also developed a 2-RDM optimization procedure specifically for seniority-zero 2-RDMs. We aim to find the 2-RDM with the right properties that is the closest (in the sense of the Frobenius norm) to the non-N-representable 2-RDM by minimizing the square norm of the difference between the initial 2-RDM and the targeted 2-RDM under the constraint that the trace is normalized and the 2-RDM, \(Q\)- and \(G\)-matrices are positive semidefinite, i.e. their eigenvalues are non-negative. Our method is suitable for fixing non-N-respresentable 2-RDMs which are close to being N-representable. Through the N-representability optimization algorithm we add a small correction to the initial 2-RDM such that it fulfills the most important N-representability conditions.
ISSN:2331-8422
DOI:10.48550/arxiv.1707.01022