Generalized nonorthogonal matrix elements: Unifying Wick’s theorem and the Slater–Condon rules
| Autor: | Hugh G. A. Burton |
|---|---|
| Rok vydání: | 2021 |
| Předmět: |
010304 chemical physics
Zero (complex analysis) General Physics and Astronomy 010402 general chemistry 01 natural sciences 0104 chemical sciences Matrix (mathematics) Wick's theorem Computer Science::Sound Simple (abstract algebra) Biorthogonal system 0103 physical sciences Slater–Condon rules Physics::Atomic and Molecular Clusters Slater determinant Applied mathematics Physical and Theoretical Chemistry Scaling Mathematics |
| Zdroj: | The Journal of Chemical Physics. 154:144109 |
| ISSN: | 1089-7690 0021-9606 |
| DOI: | 10.1063/5.0045442 |
| Popis: | Matrix elements between nonorthogonal Slater determinants represent an essential component of many emerging electronic structure methods. However, evaluating nonorthogonal matrix elements is conceptually and computationally harder than their orthogonal counterparts. While several different approaches have been developed, these are predominantly derived from the first-quantized generalized Slater-Condon rules and usually require biorthogonal occupied orbitals to be computed for each matrix element. For coupling terms between nonorthogonal excited configurations, a second-quantized approach such as the nonorthogonal Wick's theorem is more desirable, but this fails when the two reference determinants have a zero many-body overlap. In this contribution, we derive an entirely generalized extension to the nonorthogonal Wick's theorem that is applicable to all pairs of determinants with nonorthogonal orbitals. Our approach creates a universal methodology for evaluating any nonorthogonal matrix element and allows Wick's theorem and the generalized Slater-Condon rules to be unified for the first time. Furthermore, we present a simple well-defined protocol for deriving arbitrary coupling terms between nonorthogonal excited configurations. In the case of overlap and one-body operators, this protocol recovers efficient formulas with reduced scaling, promising significant computational acceleration for methods that rely on such terms. |
| Databáze: | OpenAIRE |
| Externí odkaz: |
|