Many-Body Expanded Full Configuration Interaction. II. Strongly Correlated Regime

Eriksen, Janus J.; Gauß, Jürgen

doi:10.1021/acs.jctc.9b00456

Cited by 55 publications

(72 citation statements)

References 80 publications

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“…The Hamiltonian matrix elements over configuration state functions (CSF) are then discussed in detail in Sec. 3. The storage and selection of orbital configurations (oCFG) and CSFs are presented in Sec.…”

Section: Introductionmentioning

confidence: 99%

Iterative Configuration Interaction with Selection

Zhang

Liu

Hoffmann

2020

J. Chem. Theory Comput.

105

160

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Even when starting with a very poor initial guess, the iterative configuration interaction (iCI) approach [J. Chem. Theory Comput. 12, 1169] for strongly correlated electrons can converge from above to full CI (FCI) very quickly by constructing and diagonalizing a very small Hamiltonian matrix at each macro/micro-iteration. However, as a direct solver of the FCI problem, iCI scales exponentially with respect to the numbers of electrons and orbitals. The problem can be mitigated by observing that a vast number of configurations have little weights in the wave function and hence do not contribute discernibly to the correlation energy. The real questions are then (a) how to identify those important configurations as early as possible in the calculation and (b) how to account for the residual contributions of those unimportant configurations. It 1 arXiv:1911.12506v2 [physics.chem-ph] 6 Jan 2020is generally true that if a high-quality yet compact variational space can be determined for describing the static correlation, a low-order treatment of the residual dynamic correlation would then be sufficient. While this is common to all selected CI schemes, the 'iCI with selection' scheme presented here has the following distinctive features:(1) Full spin symmetry is always maintained by taking configuration state functions (CSF) as the many-electron basis. (2) Although the selection is performed on individual CSFs, it is orbital configurations (oCFG) that are used as the organizing units. (3) Given a coefficient pruning-threshold C min (which determines the size of the variational space for static correlation), the selection of important oCFGs/CSFs is performed iteratively until convergence. (4) At each iteration for the growth of the wave function, the first-order interacting space is decomposed into disjoint subspaces, so as to reduce memory requirement on one hand and facilitate parallelization on the other. (5) Upper bounds (which involve only two-electron integrals) for the interactions between doubly connected oCFG pairs are used to screen each first-order interacting subspace before the first-order coefficients of individual CSFs are evaluated. (6) Upon convergence of the static correlation for a given C min , dynamic correlation is estimated by using the state-specific Epstein-Nesbet second-order perturbation theory (PT2). The efficacy of the iCIPT2 scheme is demonstrated numerically by benchmark examples, including C 2 , O 2 , Cr 2 and C 6 H 6 .

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Section: Introductionmentioning

confidence: 99%

Iterative Configuration Interaction with Selection

Zhang

Liu

Hoffmann

2020

J. Chem. Theory Comput.

105

160

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“…Furthermore, our π-pruning prescreening filter of Ref. 22 has been used in order to guarantee convergence onto the ground state of 1 Σ + g symmetry. In contrast to the Hubbard example in Figure 2, no exact reference energy is available for Cr 2 , even in the modest basis set used here, and we hence compare our results to a de facto standard from the literature, which is an elaborately extrapolated DMRG result obtained by Chan and co-workers with a conservative error bar of ±0.32 mE H .…”

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confidence: 99%

Generalized Many-Body Expanded Full Configuration Interaction Theory

Eriksen

Gauß

2019

J. Phys. Chem. Lett.

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Facilitated by a rigorous partitioning of a molecular system's orbital basis into two fundamental subspaces-a reference and an expansion space, both with orbitals of unspecified occupancy-we generalize our recently introduced many-body expanded full configuration interaction (MBE-FCI) method to allow for electron-rich model and molecular systems dominated by both weak and strong correlation to be addressed. By employing minimal or even empty reference spaces, we show through calculations on the 1-dimensional Hubbard model with up to 46 lattice sites, the chromium dimer, and the benzene molecule how near-exact results may be obtained in a entirely unbiased manner for chemical and physical problems of not only academic, but also applied chemical interest. Given the massive parallelism and overall accuracy of the resulting method, we argue that generalized MBE-FCI theory possesses an immense potential to yield near-exact correlation energies for molecular systems of unprecedented size, composition, and complexity in the years to come.

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“…125 and stateaveraged CASSCF energy and analytical gradient evaluation (these all use the PYSCF MCSCF module to optimize multi-reference wavefunctions), as well as for localized orbital construction via the PYWANNIER90 library. 120 The PYMBE package, 126 which implements the many-body expanded full CI method, [127][128][129][130] utilizes PYSCF to perform all the underlying electronic structure calculations. Green's functions methods such as the second-order Green's function theory (GF2) and the self-consistent GW approximation have been explored using PYSCF as the underlying ab initio infrastructure.…”

Section: B External Projects That Build On Pyscfmentioning

confidence: 99%

Recent developments in the PySCF program package

Sun

Zhang

Banerjee

et al. 2020

The Journal of Chemical Physics

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625

443

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PYSCF is a Python-based general-purpose electronic structure platform that both supports first-principles simulations of molecules and solids, as well as accelerates the development of new methodology and complex computational workflows. The present paper explains the design and philosophy behind PYSCF that enables it to meet these twin objectives. With several case studies, we show how users can easily implement their own methods using PYSCF as a development environment. We then summarize the capabilities of PYSCF for molecular and solid-state simulations. Finally, we describe the growing ecosystem of projects that use PYSCF across the domains of quantum chemistry, materials science, machine learning and quantum information science.

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Many-Body Expanded Full Configuration Interaction. II. Strongly Correlated Regime

Cited by 55 publications

References 80 publications

Iterative Configuration Interaction with Selection

Iterative Configuration Interaction with Selection

Generalized Many-Body Expanded Full Configuration Interaction Theory

Recent developments in the PySCF program package

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