Yangyang Song, Yang Guo, Yibo Lei, Ning Zhang, Wenjian Liu
{"title":"The Static–Dynamic–Static Family of Methods for Strongly Correlated Electrons: Methodology and Benchmarking","authors":"Yangyang Song, Yang Guo, Yibo Lei, Ning Zhang, Wenjian Liu","doi":"10.1007/s41061-021-00351-9","DOIUrl":null,"url":null,"abstract":"<div><p>A series of methods (SDSCI, SDSPT2, iCI, iCIPT2, iCISCF(2), iVI, and iCAS) is introduced to accurately describe strongly correlated systems of electrons. Born from the (restricted) static–dynamic–static (SDS) framework for designing many-electron wave functions, SDSCI is a minimal multireference (MR) configuration interaction (CI) approach that constructs and diagonalizes a <span>\\(3N_{\\text {P}}\\times 3N_{\\text {P}}\\)</span> matrix for <span>\\(N_{\\text {P}}\\)</span> states, regardless of the numbers of orbitals and electrons to be correlated. If the full molecular Hamiltonian <i>H</i> in the <i>QHQ</i> block (which describes couplings between functions of the first-order interaction space <i>Q</i>) of the SDSCI CI matrix is replaced with a zeroth-order Hamiltonian <span>\\(H_0\\)</span> before the diagonalization is taken, we obtain SDSPT2, a CI-like second-order perturbation theory (PT2). Unlike most variants of MRPT2, SDSPT2 treats single and multiple states in the same way and is particularly advantageous in the presence of near degeneracy. On the other hand, if the SDSCI procedure is repeated until convergence, we will have iterative CI (iCI), which can converge quickly from the above to the exact solutions (full CI) even when starting with a poor guess. When further combined with the selection of important configurations followed by a PT2 treatment of dynamic correlation, iCI becomes iCIPT2, which is a near-exact theory for medium-sized systems. The microiterations of iCI for relaxing the coefficients of contracted many-electron functions can be generalized to an iterative vector interaction (iVI) approach for finding exterior or interior roots of a given matrix, in which the dimension of the search subspace is fixed by either the number of target roots or the user-specified energy window. Naturally, iCIPT2 can be employed as the active space solver of the complete active space (CAS) self-consistent field, leading to iCISCF(2), which can further be combined with iCAS for automated selection of active orbitals and assurance of the same CAS for all states and all geometries. The methods are calibrated by taking the Thiel set of benchmark systems as examples. Results for the corresponding cations, a new set of benchmark systems, are also reported.</p></div>","PeriodicalId":802,"journal":{"name":"Topics in Current Chemistry","volume":"379 6","pages":""},"PeriodicalIF":8.6000,"publicationDate":"2021-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s41061-021-00351-9.pdf","citationCount":"9","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Topics in Current Chemistry","FirstCategoryId":"92","ListUrlMain":"https://link.springer.com/article/10.1007/s41061-021-00351-9","RegionNum":2,"RegionCategory":"化学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"Chemistry","Score":null,"Total":0}
引用次数: 9
Abstract
A series of methods (SDSCI, SDSPT2, iCI, iCIPT2, iCISCF(2), iVI, and iCAS) is introduced to accurately describe strongly correlated systems of electrons. Born from the (restricted) static–dynamic–static (SDS) framework for designing many-electron wave functions, SDSCI is a minimal multireference (MR) configuration interaction (CI) approach that constructs and diagonalizes a \(3N_{\text {P}}\times 3N_{\text {P}}\) matrix for \(N_{\text {P}}\) states, regardless of the numbers of orbitals and electrons to be correlated. If the full molecular Hamiltonian H in the QHQ block (which describes couplings between functions of the first-order interaction space Q) of the SDSCI CI matrix is replaced with a zeroth-order Hamiltonian \(H_0\) before the diagonalization is taken, we obtain SDSPT2, a CI-like second-order perturbation theory (PT2). Unlike most variants of MRPT2, SDSPT2 treats single and multiple states in the same way and is particularly advantageous in the presence of near degeneracy. On the other hand, if the SDSCI procedure is repeated until convergence, we will have iterative CI (iCI), which can converge quickly from the above to the exact solutions (full CI) even when starting with a poor guess. When further combined with the selection of important configurations followed by a PT2 treatment of dynamic correlation, iCI becomes iCIPT2, which is a near-exact theory for medium-sized systems. The microiterations of iCI for relaxing the coefficients of contracted many-electron functions can be generalized to an iterative vector interaction (iVI) approach for finding exterior or interior roots of a given matrix, in which the dimension of the search subspace is fixed by either the number of target roots or the user-specified energy window. Naturally, iCIPT2 can be employed as the active space solver of the complete active space (CAS) self-consistent field, leading to iCISCF(2), which can further be combined with iCAS for automated selection of active orbitals and assurance of the same CAS for all states and all geometries. The methods are calibrated by taking the Thiel set of benchmark systems as examples. Results for the corresponding cations, a new set of benchmark systems, are also reported.
期刊介绍:
Topics in Current Chemistry provides in-depth analyses and forward-thinking perspectives on the latest advancements in chemical research. This renowned journal encompasses various domains within chemical science and their intersections with biology, medicine, physics, and materials science.
Each collection within the journal aims to offer a comprehensive understanding, accessible to both academic and industrial readers, of emerging research in an area that captivates a broader scientific community.
In essence, Topics in Current Chemistry illuminates cutting-edge chemical research, fosters interdisciplinary collaboration, and facilitates knowledge-sharing among diverse scientific audiences.