Method for making 2-electron response reduced density matrices approximately N-representable
| Autor: | Klaas Gunst, Patrick Bultinck, Paul W. Ayers, Dimitri Van Neck, Stijn De Baerdemacker, Caitlin Lanssens |
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| Rok vydání: | 2018 |
| Předmět: |
Normalization (statistics)
Matrix norm General Physics and Astronomy FOS: Physical sciences Positive-definite matrix 01 natural sciences Schrödinger equation RENORMALIZATION-GROUP ATOMS symbols.namesake MOLECULES CONFIGURATION-INTERACTION Physics - Chemical Physics 0103 physical sciences WAVE-FUNCTIONS Applied mathematics NONORTHOGONAL GEMINALS Physical and Theoretical Chemistry 010306 general physics OPTIMIZATION Eigenvalues and eigenvectors Chemical Physics (physics.chem-ph) Quantum Physics 010304 chemical physics Geminal QUANTUM-CHEMISTRY ELECTRONS Chemistry Coupled cluster Physics and Astronomy Norm (mathematics) symbols Quantum Physics (quant-ph) STRONGLY CORRELATED SYSTEMS |
| Zdroj: | JOURNAL OF CHEMICAL PHYSICS |
| ISSN: | 1089-7690 0021-9606 |
| Popis: | 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. Comment: 13 pages, 8 figures |
| Databáze: | OpenAIRE |
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