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Greiner J, Gianni I, Nottoli T, Lipparini F, Eriksen JJ, Gauss J. MBE-CASSCF Approach for the Accurate Treatment of Large Active Spaces. J Chem Theory Comput 2024; 20:4663-4675. [PMID: 38809011 DOI: 10.1021/acs.jctc.4c00388] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 05/30/2024]
Abstract
We present a novel implementation of the complete active space self-consistent field (CASSCF) method that makes use of the many-body expanded full configuration interaction (MBE-FCI) method to incrementally approximate electronic structures within large active spaces. On the basis of a hybrid first-order algorithm employing both Super-CI and quasi-Newton strategies for the optimization of molecular orbitals, we demonstrate both computational efficacy and high accuracy of the resulting MBE-CASSCF method. We assess the performance of our implementation on a set of established numerical tests before applying MBE-CASSCF in the investigation of the triplet-quintet spin gap of iron(II) porphyrin with active spaces as large as 50 electrons in 50 orbitals.
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Affiliation(s)
- Jonas Greiner
- Department Chemie, Johannes Gutenberg-Universität Mainz, Duesbergweg 10-14, Mainz 55128, Germany
| | - Ivan Gianni
- Dipartimento di Chimica e Chimica Industriale, Università di Pisa, Via G. Moruzzi 13, Pisa 56124, Italy
| | - Tommaso Nottoli
- Dipartimento di Chimica e Chimica Industriale, Università di Pisa, Via G. Moruzzi 13, Pisa 56124, Italy
| | - Filippo Lipparini
- Dipartimento di Chimica e Chimica Industriale, Università di Pisa, Via G. Moruzzi 13, Pisa 56124, Italy
| | - Janus J Eriksen
- DTU Chemistry, Technical University of Denmark, Kemitorvet Bldg. 206, Kgs. Lyngby 2800, Denmark
| | - Jürgen Gauss
- Department Chemie, Johannes Gutenberg-Universität Mainz, Duesbergweg 10-14, Mainz 55128, Germany
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Agarawal V, King DS, Hermes MR, Gagliardi L. Automatic State Interaction with Large Localized Active Spaces for Multimetallic Systems. J Chem Theory Comput 2024; 20:4654-4662. [PMID: 38787596 DOI: 10.1021/acs.jctc.4c00376] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 05/25/2024]
Abstract
The localized active space self-consistent field method factorizes a complete active space wave function into an antisymmetrized product of localized active space wave function fragments. Correlation between fragments is then reintroduced through localized active space state interaction (LASSI), in which the Hamiltonian is diagonalized in a model space of LAS states. However, the optimal procedure for defining the LAS fragments and LASSI model space is unknown. We here present an automated framework to explore systematically convergent sets of model spaces, which we call LASSI[r, q]. This method requires the user to select only r, the number of electron hops from one fragment to another, and q, the number of fragment basis functions per Hilbert space, which converges to CASCI in the limit of r, q → ∞. Numerical tests of this method on the trimetal oxo-centered complexes [Fe(III)Al(III)Fe(II)(μ3-O)(HCOO)6] and [Fe(III)2Fe(II)(μ3-O)(HCOO)6] show efficient convergence to the CASCI limit with 4-10 orders of magnitude fewer states than CASCI.
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Affiliation(s)
- Valay Agarawal
- Department of Chemistry, University of Chicago, Chicago, Illinois 60637, United States
| | - Daniel S King
- Department of Chemistry, University of Chicago, Chicago, Illinois 60637, United States
| | - Matthew R Hermes
- Department of Chemistry, University of Chicago, Chicago, Illinois 60637, United States
| | - Laura Gagliardi
- Department of Chemistry, University of Chicago, Chicago, Illinois 60637, United States
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Han R, Luber S, Li Manni G. Magnetic Interactions in a [Co(II) 3Er(III)(OR) 4] Model Cubane through Forefront Multiconfigurational Methods. J Chem Theory Comput 2023; 19:2811-2826. [PMID: 37126736 DOI: 10.1021/acs.jctc.2c01318] [Citation(s) in RCA: 3] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 05/03/2023]
Abstract
Strong electron correlation effects are one of the major challenges in modern quantum chemistry. Polynuclear transition metal clusters are peculiar examples of systems featuring such forms of electron correlation. Multireference strategies, often based on but not limited to the concept of complete active space, are adopted to accurately account for strong electron correlation and to resolve their complex electronic structures. However, transition metal clusters already containing four magnetic centers with multiple unpaired electrons make conventional active space based strategies prohibitively expensive, due to their unfavorable scaling with the size of the active space. In this work, forefront techniques, such as density matrix renormalization group (DMRG), full configuration interaction quantum Monte Carlo (FCIQMC), and multiconfiguration pair-density functional theory (MCPDFT), are employed to overcome the computational limitation of conventional multireference approaches and to accurately investigate the magnetic interactions taking place in a [Co(II)3Er(III)(OR)4] (chemical formula [Co(II)3Er(III)(hmp)4(μ2-OAc)2(OH)3(H2O)], hmp = 2-(hydroxymethyl)-pyridine) model cubane water oxidation catalyst. Complete active spaces with up to 56 electrons in 56 orbitals have been constructed for the seven energetically lowest different spin states. Relative energies, local spin, and spin-spin correlation values are reported and provide crucial insights on the spin interactions for this model system, pivotal in the rationalization of the catalytic activity of this system in the water-splitting reaction. A ferromagnetic ground state is found with a very small, ∼50 cm-1, highest-to-lowest spin gap. Moreover, for the energetically lowest states, S = 3-6, the three Co(II) sites exhibit parallel aligned spins, and for the lower states, S = 0-2, two Co(II) sites retain strong parallel spin alignment.
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Affiliation(s)
- Ruocheng Han
- Department of Chemistry A, University of Zurich, Winterthurerstrasse 190, 8057 Zurich, Switzerland
| | - Sandra Luber
- Department of Chemistry A, University of Zurich, Winterthurerstrasse 190, 8057 Zurich, Switzerland
| | - Giovanni Li Manni
- Max Planck Institute for Solid State Research, Heisenbergstrasse 1, 70569 Stuttgart, Germany
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Weser O, Guther K, Ghanem K, Li Manni G. Stochastic Generalized Active Space Self-Consistent Field: Theory and Application. J Chem Theory Comput 2021; 18:251-272. [PMID: 34898215 PMCID: PMC8757470 DOI: 10.1021/acs.jctc.1c00936] [Citation(s) in RCA: 13] [Impact Index Per Article: 4.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Abstract
An algorithm to perform stochastic generalized active space calculations, Stochastic-GAS, is presented, that uses the Slater determinant based FCIQMC algorithm as configuration interaction eigensolver. Stochastic-GAS allows the construction and stochastic optimization of preselected truncated configuration interaction wave functions, either to reduce the computational costs of large active space wave function optimizations, or to probe the role of specific electron correlation pathways. As for the conventional GAS procedure, the preselection of the truncated wave function is based on the selection of multiple active subspaces while imposing restrictions on the interspace excitations. Both local and cumulative minimum and maximum occupation number constraints are supported by Stochastic-GAS. The occupation number constraints are efficiently encoded in precomputed probability distributions, using the precomputed heat bath algorithm, which removes nearly all runtime overhead of GAS. This strategy effectively allows the FCIQMC dynamics to a priori exclude electronic configurations that are not allowed by GAS restrictions. Stochastic-GAS reduced density matrices are stochastically sampled, allowing orbital relaxations via Stochastic-GASSCF, and direct evaluation of properties that can be extracted from density matrices, such as the spin expectation value. Three test case applications have been chosen to demonstrate the flexibility of Stochastic-GAS: (a) the Stochastic-GASSCF [5·(6, 6)] optimization of a stack of five benzene molecules, that shows the applicability of Stochastic-GAS toward fragment-based chemical systems; (b) an uncontracted stochastic MRCISD calculation that correlates 96 electrons and 159 molecular orbitals, and uses a large (32, 34) active space reference wave function for an Fe(II)-porphyrin model system, showing how GAS can be applied to systematically recover dynamic electron correlation, and how in the specific case of the Fe(II)-porphyrin dynamic correlation further differentially stabilizes the 3Eg over the 5A1g spin state; (c) the study of an Fe4S4 cluster's spin-ladder energetics via highly truncated stochastic-GAS [4·(5, 5)] wave functions, where we show how GAS can be applied to understand the competing spin-exchange and charge-transfer correlating mechanisms in stabilizing different spin-states.
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Affiliation(s)
- Oskar Weser
- Max-Planck-Institute for Solid State Research, Stuttgart, 70569, Germany
| | - Kai Guther
- Max-Planck-Institute for Solid State Research, Stuttgart, 70569, Germany.,RIKEN Center for Computational Science, 7-1-26 minatojima-minami, Chuo Kobe 650-0047, Japan
| | - Khaldoon Ghanem
- Max-Planck-Institute for Solid State Research, Stuttgart, 70569, Germany
| | - Giovanni Li Manni
- Max-Planck-Institute for Solid State Research, Stuttgart, 70569, Germany
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Lei Y, Suo B, Liu W. iCAS: Imposed Automatic Selection and Localization of Complete Active Spaces. J Chem Theory Comput 2021; 17:4846-4859. [PMID: 34314180 DOI: 10.1021/acs.jctc.1c00456] [Citation(s) in RCA: 17] [Impact Index Per Article: 5.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/18/2023]
Abstract
It is shown that in the spirit of "from fragments to molecule" for localizing molecular orbitals [J. Chem. Theory Comput. 2011, 7, 3643], a prechosen set of occupied/virtual valence/core atomic/fragmental orbitals can be transformed to an equivalent set of localized occupied/virtual pre-localized molecular orbitals (pre-LMO), which can then be taken as probes to select the same number of maximally matching localized occupied/virtual Hartree-Fock (HF) or restricted open-shell HF (ROHF) molecular orbitals as the initial local orbitals spanning the desired complete active space (CAS). In each cycle of the self-consistent field (SCF) calculation, the CASSCF orbitals can be localized by means of the noniterative "top-down least-change" algorithm for localizing ROHF orbitals [J. Chem. Phys. 2017, 146, 104104] such that the maximum matching between the orbitals of two adjacent iterations can readily be monitored, leading finally to converged localized CASSCF orbitals that overlap most the guess orbitals. Such an approach is to be dubbed as "imposed CASSCF" (iCASSCF or simply iCAS in short) for good reasons: (1) it has been assumed that only those electronic states that have largest projections onto the active space defined by the prechosen atomic/fragmental orbitals are to be targeted. This is certainly an imposed constraint but has wide applications in organic and transition metal chemistry where valence (or core) atomic/fragmental orbitals can readily be identified. (2) The selection of both initial and optimized local active orbitals is imposed from the very beginning by the pre-LMOs (which span the same space as the prechosen atomic/fragmental orbitals). Apart from the (imposed) automation and localization, iCAS has two additional merits: (a) the guess orbitals are guaranteed to be the same for all geometries, for the pre-LMOs do not change in character with geometry and (b) the use of localized orbitals facilitates the SCF convergence, particularly for large active spaces. Both organic molecules and transition-metal complexes are taken as showcases to reveal the efficacy of iCAS.
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Affiliation(s)
- Yibo Lei
- Key Laboratory of Synthetic and Natural Functional Molecule of the Ministry of Education, College of Chemistry & Materials Science, Shaanxi Key Laboratory of Physico-Inorganic Chemistry, Northwest University, Xi'an 710127, Shaanxi, P. R. China
| | - Bingbing Suo
- Institute of Modern Physics, Northwest University, and Shaanxi Key Laboratory for Theoretical Physics Frontiers, Xi'an 710127, Shaanxi, P. R. China
| | - Wenjian Liu
- Qingdao Institute for Theoretical and Computational Sciences, Institute of Frontier and Interdisciplinary Science, Shandong University, Qingdao 266237, Shandong, P. R. China
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Hermes MR, Pandharkar R, Gagliardi L. Variational Localized Active Space Self-Consistent Field Method. J Chem Theory Comput 2020; 16:4923-4937. [DOI: 10.1021/acs.jctc.0c00222] [Citation(s) in RCA: 14] [Impact Index Per Article: 3.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/08/2023]
Affiliation(s)
- Matthew R. Hermes
- Department of Chemistry, Chemical Theory Center, and The Minnesota Supercomputing Institute, University of Minnesota, Minneapolis, Minnesota 55455, United States
| | - Riddhish Pandharkar
- Department of Chemistry, Chemical Theory Center, and The Minnesota Supercomputing Institute, University of Minnesota, Minneapolis, Minnesota 55455, United States
| | - Laura Gagliardi
- Department of Chemistry, Chemical Theory Center, and The Minnesota Supercomputing Institute, University of Minnesota, Minneapolis, Minnesota 55455, United States
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Kathir RK, de Graaf C, Broer R, Havenith RWA. Reduced Common Molecular Orbital Basis for Nonorthogonal Configuration Interaction. J Chem Theory Comput 2020; 16:2941-2951. [PMID: 32279493 PMCID: PMC7222100 DOI: 10.1021/acs.jctc.9b01144] [Citation(s) in RCA: 19] [Impact Index Per Article: 4.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/10/2023]
Abstract
Electron and charge transfers are part of many vital processes in nature and technology. Ab initio descriptions of these processes provide useful insights that can be utilized for applications. A combination of the embedded cluster material model and nonorthogonal configuration interaction (NOCI), in which the cluster wave functions are expanded in many-electron basis functions (MEBFs) consisting of spin-adapted, antisymmetrized products of multiconfigurational wave functions of fragments (which are usually molecules) in the cluster, appears to provide a compromise between accuracy and calculation time. Additional advantages of this NOCI-Fragments approach are the chemically convenient interpretation of the wave function in terms of molecular states, and the direct accessibility of electronic coupling between diabatic states to describe energy and electron transfer processes. Bottlenecks in this method are the large number of two-electron integrals that have to be handled for the calculation of an electronic coupling matrix element and the enormous number of matrix elements over determinant pairs that have to be evaluated for the calculation of one matrix element between the MEBFs. We show here how we created a reduced common molecular orbital basis that is utilized to significantly reduce the number of two-electron integrals that need to be handled. The results obtained with this basis do not show any loss of accuracy in relevant quantities like electronic couplings and vertical excitation energies. We also show a significant reduction in computation time without loss in accuracy when matrix elements over determinant pairs with small weights are neglected in the NOCI. These improvements in the methodology render NOCI-Fragments to be also applicable to treat clusters of larger molecular systems with larger atomic basis sets and larger active spaces, as the computation time becomes dependent on the number of occupied orbitals and less dependent on the size of the active space.
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Affiliation(s)
- R K Kathir
- Theoretical Chemistry, Zernike Institute for Advanced Materials, University of Groningen, Nijenborgh 4, 9747 AG Groningen, The Netherlands
| | - Coen de Graaf
- Department of Physical and Inorganic Chemistry, Universitat Rovira i Virgili, C. Marcel·lı́ Domingo 1, 43007 Tarragona, Spain.,Theoretical Chemistry Group, Zernike Institute for Advanced Materials, University of Groningen, Nijenborgh 4, 9747 AG Groningen, The Netherlands.,ICREA, Passeig Lluı́s Companys 23, 08010 Barcelona, Spain
| | - Ria Broer
- Theoretical Chemistry Group, Zernike Institute for Advanced Materials, University of Groningen, Nijenborgh 4, 9747 AG Groningen, The Netherlands
| | - Remco W A Havenith
- Theoretical Chemistry Group, Zernike Institute for Advanced Materials, University of Groningen, Nijenborgh 4, 9747 AG Groningen, The Netherlands.,Stratingh Institute for Chemistry, University of Groningen, Nijenborgh 4, 9747 AG Groningen, The Netherlands.,Ghent Quantum Chemistry Group, Department of Inorganic and Physical Chemistry, Ghent University, 9000 Gent, Belgium
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Baiardi A, Reiher M. The density matrix renormalization group in chemistry and molecular physics: Recent developments and new challenges. J Chem Phys 2020; 152:040903. [DOI: 10.1063/1.5129672] [Citation(s) in RCA: 85] [Impact Index Per Article: 21.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 02/03/2023] Open
Affiliation(s)
- Alberto Baiardi
- ETH Zürich, Laboratorium für Physikalische Chemie, Vladimir-Prelog-Weg 2, 8093 Zürich, Switzerland
| | - Markus Reiher
- ETH Zürich, Laboratorium für Physikalische Chemie, Vladimir-Prelog-Weg 2, 8093 Zürich, Switzerland
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Pham HQ, Hermes MR, Gagliardi L. Periodic Electronic Structure Calculations with the Density Matrix Embedding Theory. J Chem Theory Comput 2019; 16:130-140. [DOI: 10.1021/acs.jctc.9b00939] [Citation(s) in RCA: 18] [Impact Index Per Article: 3.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Affiliation(s)
- Hung Q. Pham
- Department of Chemistry, Chemical Theory Center, and Supercomputing Institute, University of Minnesota, 207 Pleasant Street SE, Minneapolis, Minnesota 55455, United States
| | - Matthew R. Hermes
- Department of Chemistry, Chemical Theory Center, and Supercomputing Institute, University of Minnesota, 207 Pleasant Street SE, Minneapolis, Minnesota 55455, United States
| | - Laura Gagliardi
- Department of Chemistry, Chemical Theory Center, and Supercomputing Institute, University of Minnesota, 207 Pleasant Street SE, Minneapolis, Minnesota 55455, United States
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Nishio S, Kurashige Y. Rank-one basis made from matrix-product states for a low-rank approximation of molecular aggregates. J Chem Phys 2019; 151:084110. [DOI: 10.1063/1.5093346] [Citation(s) in RCA: 11] [Impact Index Per Article: 2.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- Soichiro Nishio
- Department of Chemistry, Graduate School of Science, Kyoto University, Kitashirakawa Oiwake-cho, Sakyo-ku Kyoto 606-8502, Japan
| | - Yuki Kurashige
- Department of Chemistry, Graduate School of Science, Kyoto University, Kitashirakawa Oiwake-cho, Sakyo-ku Kyoto 606-8502, Japan
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Affiliation(s)
- Yuhong Liu
- Department of Chemistry, University of the Pacific, Stockton, California, USA
| | - Anthony D. Dutoi
- Department of Chemistry, University of the Pacific, Stockton, California, USA
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Affiliation(s)
- Anthony D. Dutoi
- Department of Chemistry, University of the Pacific, Stockton, CA, USA
| | - Yuhong Liu
- Department of Chemistry, University of the Pacific, Stockton, CA, USA
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Ito S, Nagami T, Nakano M. Molecular design for efficient singlet fission. JOURNAL OF PHOTOCHEMISTRY AND PHOTOBIOLOGY C-PHOTOCHEMISTRY REVIEWS 2018. [DOI: 10.1016/j.jphotochemrev.2018.01.002] [Citation(s) in RCA: 84] [Impact Index Per Article: 14.0] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 12/24/2022]
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14
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Sun Q, Yang J, Chan GKL. A general second order complete active space self-consistent-field solver for large-scale systems. Chem Phys Lett 2017. [DOI: 10.1016/j.cplett.2017.03.004] [Citation(s) in RCA: 56] [Impact Index Per Article: 8.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/20/2022]
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15
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Shiozaki T. BAGEL
: Brilliantly Advanced General Electronic‐structure Library. WILEY INTERDISCIPLINARY REVIEWS-COMPUTATIONAL MOLECULAR SCIENCE 2017. [DOI: 10.1002/wcms.1331] [Citation(s) in RCA: 98] [Impact Index Per Article: 14.0] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 12/25/2022]
Affiliation(s)
- Toru Shiozaki
- Department of ChemistryNorthwestern University Evanston IL USA
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