1
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Menczer A, van Damme M, Rask A, Huntington L, Hammond J, Xantheas SS, Ganahl M, Legeza Ö. Parallel Implementation of the Density Matrix Renormalization Group Method Achieving a Quarter petaFLOPS Performance on a Single DGX-H100 GPU Node. J Chem Theory Comput 2024; 20:8397-8404. [PMID: 39297788 PMCID: PMC11465466 DOI: 10.1021/acs.jctc.4c00903] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/11/2024] [Revised: 09/04/2024] [Accepted: 09/05/2024] [Indexed: 10/09/2024]
Abstract
We report cutting edge performance results on a single node hybrid CPU-multi-GPU implementation of the spin adapted ab initio Density Matrix Renormalization Group (DMRG) method on current state-of-the-art NVIDIA DGX-H100 architectures. We evaluate the performance of the DMRG electronic structure calculations for the active compounds of the FeMoco, the primary cofactor of nitrogenase, and cytochrome P450 (CYP) enzymes with complete active space (CAS) sizes of up to 113 electrons in 76 orbitals [CAS(113, 76)] and 63 electrons in 58 orbitals [CAS(63, 58)], respectively. We achieve 246 teraFLOPS of sustained performance, an improvement of more than 2.5× compared to the performance achieved on the DGX-A100 architectures and an 80× acceleration compared to an OpenMP parallelized implementation on a 128-core CPU architecture. Our work highlights the ability of tensor network algorithms to efficiently utilize high-performance multi-GPU hardware and shows that the combination of tensor networks with modern large-scale GPU accelerators can pave the way toward solving some of the most challenging problems in quantum chemistry and beyond.
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Affiliation(s)
- Andor Menczer
- Strongly
Correlated Systems Lendület Research Group, Wigner Research Centre for Physics, H-1525 Budapest, Hungary
- Eötvös
Loránd University, Pázmány Péter Sétány 1/C, 1117 Budapest, Hungary
| | - Maarten van Damme
- SandboxAQ, 780 High Street, Palo Alto, California 94301, United States
| | - Alan Rask
- SandboxAQ, 780 High Street, Palo Alto, California 94301, United States
| | - Lee Huntington
- SandboxAQ, 780 High Street, Palo Alto, California 94301, United States
| | - Jeff Hammond
- NVIDIA
Helsinki Oy, Porkkalankatu 1, 00180 Helsinki, Finland
| | - Sotiris S. Xantheas
- Advanced
Computing, Mathematics, and Data Division, Pacific Northwest National Laboratory, Richland, Washington 99354, United States
- Department
of Chemistry, University of Washington, Seattle, Washington 98195, United States
| | - Martin Ganahl
- SandboxAQ, 780 High Street, Palo Alto, California 94301, United States
| | - Örs Legeza
- Strongly
Correlated Systems Lendület Research Group, Wigner Research Centre for Physics, H-1525 Budapest, Hungary
- Dynaflex
Ltd., Zrínyi u
7, 1028 Budapest, Hungary
- Institute
for Advanced Study,Technical University
of Munich, Germany, Lichtenbergstrasse
2a, 85748 Garching, Germany
- Parmenides
Stiftung, Hindenburgstr.
15, 82343 Pöcking, Germany
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2
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Zhang N, Liu W. Unified Implementation of Relativistic Wave Function Methods: 4C-iCIPT2 as a Showcase. J Chem Theory Comput 2024. [PMID: 39356987 DOI: 10.1021/acs.jctc.4c00967] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/04/2024]
Abstract
In parallel to the unified construction of relativistic Hamiltonians based solely on physical arguments (J. Chem. Phys. 2024, 160, 084111), a unified implementation of relativistic wave function methods is achieved here via programming techniques (e.g., template metaprogramming and polymorphism in C++). That is, once the code for constructing the Hamiltonian matrix is made ready, all the rest can be generated automatically from existing templates used for the nonrelativistic counterparts. This is facilitated by decomposing a second-quantized relativistic Hamiltonian into diagrams that are topologically the same as those required for computing the basic coupling coefficients between spin-free configuration state functions (CSF). Moreover, both time reversal and binary double point group symmetries can readily be incorporated into molecular integrals and Hamiltonian matrix elements. The latter can first be evaluated in the space of (randomly selected) spin-dependent determinants and then transformed to that of spin-dependent CSFs, thanks to simple relations in between. As a showcase, we consider here the no-pair four-component relativistic iterative configuration interaction with selection and perturbation correction (4C-iCIPT2), which is a natural extension of the spin-free iCIPT2 (J. Chem. Theory Comput. 2021, 17, 949), and can provide near-exact numerical results within the manifold of positive energy states (PES), as demonstrated by numerical examples.
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Affiliation(s)
- Ning Zhang
- Qingdao Institute for Theoretical and Computational Sciences, School of Chemistry and Chemical Engineering, Shandong University, Qingdao, Shandong 266237, China
| | - Wenjian Liu
- Qingdao Institute for Theoretical and Computational Sciences, School of Chemistry and Chemical Engineering, Shandong University, Qingdao, Shandong 266237, China
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3
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Song M, Alavi A, Li Manni G. Permutation symmetry in spin-adapted many-body wave functions. Faraday Discuss 2024. [PMID: 39158096 DOI: 10.1039/d4fd00061g] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 08/20/2024]
Abstract
In the domain of exchange-coupled polynuclear transition-metal (PNTM) clusters, local emergent symmetries exist which can be exploited to greatly increase the sparsity of the configuration interaction (CI) eigensolutions of such systems. Sparsity of the CI secular problem is revealed by exploring the site permutation space within spin-adapted many-body bases, and highly compressed wave functions may arise by finding optimal site orderings. However, the factorial cost of searching through the permutation space remains a bottleneck for clusters with a large number of metal centers. In this work, we explore ways to reduce the factorial scaling, by combining permutation and point group symmetry arguments, and using commutation relations between cumulative partial spin and the Hamiltonian operators, . Certain site orderings lead to commuting operators, from which more sparse wave functions arise. Two graphical strategies will be discussed, one to rapidly evaluate the commutators of interest, and one in the form of a tree search algorithm to predict how many and which distinct site permutations are to be analyzed, eliminating redundancies in the permutation space. Particularly interesting is the case of the singlet spin states for which an additional reversal symmetry can be utilized to further reduce the number of distinct site permutations.
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Affiliation(s)
- Maru Song
- Electronic Structure Theory Department, Max Planck Institute for Solid State Research, Heisenbergstraße 1, 70569 Stuttgart, Germany.
| | - Ali Alavi
- Electronic Structure Theory Department, Max Planck Institute for Solid State Research, Heisenbergstraße 1, 70569 Stuttgart, Germany.
- Yusuf Hamied Department of Chemistry, University of Cambridge, Lensfield Road, Cambridge CB2 1EW, UK
| | - Giovanni Li Manni
- Electronic Structure Theory Department, Max Planck Institute for Solid State Research, Heisenbergstraße 1, 70569 Stuttgart, Germany.
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4
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Damour Y, Scemama A, Kossoski F, Loos PF. Selected Configuration Interaction for Resonances. J Phys Chem Lett 2024; 15:8296-8305. [PMID: 39107252 DOI: 10.1021/acs.jpclett.4c02060] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 08/09/2024]
Abstract
Electronic resonances are metastable states that can decay by electron loss. They are ubiquitous across various fields of science, such as chemistry, physics, and biology. However, current theoretical and computational models for resonances cannot yet rival the level of accuracy achieved by bound-state methodologies. Here, we generalize selected configuration interaction (SCI) to treat resonances by using the complex absorbing potential (CAP) technique. By modifying the selection procedure and the extrapolation protocol of standard SCI, the resulting CAP-SCI method yields resonance positions and widths of full configuration interaction quality. Initial results for the shape resonances of N2- and CO- reveal the important effect of high-order correlation, which shifts the values obtained with CAP-augmented equation-of-motion coupled-cluster with singles and doubles by more than 0.1 eV. The present CAP-SCI approach represents a cornerstone in the development of highly accurate methodologies for resonances.
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Affiliation(s)
- Yann Damour
- Laboratoire de Chimie et Physique Quantiques (UMR 5626), Université de Toulouse, CNRS, UPS, 31062 Toulouse, France
| | - Anthony Scemama
- Laboratoire de Chimie et Physique Quantiques (UMR 5626), Université de Toulouse, CNRS, UPS, 31062 Toulouse, France
| | - Fábris Kossoski
- Laboratoire de Chimie et Physique Quantiques (UMR 5626), Université de Toulouse, CNRS, UPS, 31062 Toulouse, France
| | - Pierre-François Loos
- Laboratoire de Chimie et Physique Quantiques (UMR 5626), Université de Toulouse, CNRS, UPS, 31062 Toulouse, France
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5
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Xu Y, Liu C, Ma H. Kylin-V: An open-source package calculating the dynamic and spectroscopic properties of large systems. J Chem Phys 2024; 161:052501. [PMID: 39087896 DOI: 10.1063/5.0220712] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/28/2024] [Accepted: 07/14/2024] [Indexed: 08/02/2024] Open
Abstract
Quantum dynamics simulation and computational spectroscopy serve as indispensable tools for the theoretical understanding of various fundamental physical and chemical processes, ranging from charge transfer to photochemical reactions. When simulating realistic systems, the primary challenge stems from the overwhelming number of degrees of freedom and the pronounced many-body correlations. Here, we present Kylin-V, an innovative quantum dynamics package designed for accurate and efficient simulations of dynamics and spectroscopic properties of vibronic Hamiltonians for molecular systems and their aggregates. Kylin-V supports various quantum dynamics and computational spectroscopy methods, such as time-dependent density matrix renormalization group and our recently proposed single-site and hierarchical mapping approaches, as well as vibrational heat-bath configuration interaction. In this paper, we introduce the methodologies implemented in Kylin-V and illustrate their performances through a diverse collection of numerical examples.
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Affiliation(s)
- Yihe Xu
- School of Chemistry and Chemical Engineering, Nanjing University, Nanjing 210023, China
| | - Chungen Liu
- School of Chemistry and Chemical Engineering, Nanjing University, Nanjing 210023, China
| | - Haibo Ma
- Qingdao Institute for Theoretical and Computational Sciences, School of Chemistry and Chemical Engineering, Shandong University, Qingdao 266237, China
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6
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Zhao Z, Evangelista FA. Toward Accurate Spin-Orbit Splittings from Relativistic Multireference Electronic Structure Theory. J Phys Chem Lett 2024; 15:7103-7110. [PMID: 38954768 PMCID: PMC11261625 DOI: 10.1021/acs.jpclett.4c01372] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/10/2024] [Revised: 06/25/2024] [Accepted: 06/27/2024] [Indexed: 07/04/2024]
Abstract
Most nonrelativistic electron correlation methods can be adapted to account for relativistic effects, as long as the relativistic molecular spinor integrals are available, from either a four-, two-, or one-component mean-field calculation. However, relativistic multireference correlation methods remain a relatively unexplored area, with mixed evidence regarding the improvements brought by perturbative treatments. We report, for the first time, the implementation of state-averaged four-component relativistic multireference perturbation theories to second and third order based on the driven similarity renormalization group (DSRG). With our methods, named 4c-SA-DSRG-MRPT2 and 3, we find that the dynamical correlation included on top of 4c-CASSCF references can significantly improve the spin-orbit splittings in p-block elements and potential energy surfaces when compared to 4c-CASSCF and 4c-CASPT2 results. We further show that 4c-DSRG-MRPT2 and 3 are applicable to these systems over a wide range of the flow parameter, with systematic improvement from second to third order in terms of both improved error statistics and reduced sensitivity with respect to the flow parameter.
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Affiliation(s)
- Zijun Zhao
- Department of Chemistry and
Cherry Emerson Center for Scientific Computation, Emory University, Atlanta, Georgia 30322, United States
| | - Francesco A. Evangelista
- Department of Chemistry and
Cherry Emerson Center for Scientific Computation, Emory University, Atlanta, Georgia 30322, United States
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7
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Kossoski F, Boggio-Pasqua M, Loos PF, Jacquemin D. Reference Energies for Double Excitations: Improvement and Extension. J Chem Theory Comput 2024; 20:5655-5678. [PMID: 38885174 DOI: 10.1021/acs.jctc.4c00410] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 06/20/2024]
Abstract
In the realm of photochemistry, the significance of double excitations (also known as doubly excited states), where two electrons are concurrently elevated to higher energy levels, lies in their involvement in key electronic transitions essential in light-induced chemical reactions as well as their challenging nature from the computational theoretical chemistry point of view. Based on state-of-the-art electronic structure methods (such as high-order coupled-cluster, selected configuration interaction, and multiconfigurational methods), we improve and expand our prior set of accurate reference excitation energies for electronic states exhibiting a substantial amount of double excitations [Loos et al. J. Chem. Theory Comput. 2019, 15, 1939]. This extended collection encompasses 47 electronic transitions across 26 molecular systems that we separate into two distinct subsets: (i) 28 "genuine" doubly excited states where the transitions almost exclusively involve doubly excited configurations and (ii) 19 "partial" doubly excited states which exhibit a more balanced character between singly and doubly excited configurations. For each subset, we assess the performance of high-order coupled-cluster (CC3, CCSDT, CC4, and CCSDTQ) and multiconfigurational methods (CASPT2, CASPT3, PC-NEVPT2, and SC-NEVPT2). Using as a probe the percentage of single excitations involved in a given transition (%T1) computed at the CC3 level, we also propose a simple correction that reduces the errors of CC3 by a factor of 3, for both sets of excitations. We hope that this more complete and diverse compilation of double excitations will help future developments of electronic excited-state methodologies.
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Affiliation(s)
- Fábris Kossoski
- Laboratoire de Chimie et Physique Quantiques (UMR 5626), Université de Toulouse, CNRS, UPS, 31062 Toulouse, France
| | - Martial Boggio-Pasqua
- Laboratoire de Chimie et Physique Quantiques (UMR 5626), Université de Toulouse, CNRS, UPS, 31062 Toulouse, France
| | - Pierre-François Loos
- Laboratoire de Chimie et Physique Quantiques (UMR 5626), Université de Toulouse, CNRS, UPS, 31062 Toulouse, France
| | - Denis Jacquemin
- Nantes Université, CNRS, CEISAM UMR 6230, F-44000 Nantes, France
- Institut Universitaire de France (IUF), F-75005 Paris, France
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8
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Li X, Huang JC, Zhang GZ, Li HE, Shen ZP, Zhao C, Li J, Hu HS. Improved optimization for the neural-network quantum states and tests on the chromium dimer. J Chem Phys 2024; 160:234102. [PMID: 38884396 DOI: 10.1063/5.0214150] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/16/2024] [Accepted: 05/30/2024] [Indexed: 06/18/2024] Open
Abstract
The advent of Neural-network Quantum States (NQS) has significantly advanced wave function ansatz research, sparking a resurgence in orbital space variational Monte Carlo (VMC) exploration. This work introduces three algorithmic enhancements to reduce computational demands of VMC optimization using NQS: an adaptive learning rate algorithm, constrained optimization, and block optimization. We evaluate the refined algorithm on complex multireference bond stretches of H2O and N2 within the cc-pVDZ basis set and calculate the ground-state energy of the strongly correlated chromium dimer (Cr2) in the Ahlrichs SV basis set. Our results achieve superior accuracy compared to coupled cluster theory at a relatively modest CPU cost. This work demonstrates how to enhance optimization efficiency and robustness using these strategies, opening a new path to optimize large-scale restricted Boltzmann machine-based NQS more effectively and marking a substantial advancement in NQS's practical quantum chemistry applications.
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Affiliation(s)
- Xiang Li
- Department of Chemistry and Engineering Research Center of Advanced Rare-Earth Materials of Ministry of Education, Tsinghua University, Beijing 100084, China
| | - Jia-Cheng Huang
- Department of Chemistry and Engineering Research Center of Advanced Rare-Earth Materials of Ministry of Education, Tsinghua University, Beijing 100084, China
| | - Guang-Ze Zhang
- Department of Chemistry and Engineering Research Center of Advanced Rare-Earth Materials of Ministry of Education, Tsinghua University, Beijing 100084, China
| | - Hao-En Li
- Department of Chemistry and Engineering Research Center of Advanced Rare-Earth Materials of Ministry of Education, Tsinghua University, Beijing 100084, China
| | - Zhu-Ping Shen
- Department of Chemistry and Engineering Research Center of Advanced Rare-Earth Materials of Ministry of Education, Tsinghua University, Beijing 100084, China
| | - Chen Zhao
- Department of Chemistry and Engineering Research Center of Advanced Rare-Earth Materials of Ministry of Education, Tsinghua University, Beijing 100084, China
| | - Jun Li
- Department of Chemistry and Engineering Research Center of Advanced Rare-Earth Materials of Ministry of Education, Tsinghua University, Beijing 100084, China
- Department of Chemistry and Guangdong Provincial Key Laboratory of Catalytic Chemistry, Southern University of Science and Technology, Shenzhen 518055, China
- Fundamental Science Center of Rare Earths, Ganjiang Innovation Academy, Chinese Academy of Sciences, Ganzhou 341000, China
| | - Han-Shi Hu
- Department of Chemistry and Engineering Research Center of Advanced Rare-Earth Materials of Ministry of Education, Tsinghua University, Beijing 100084, China
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9
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Sukurma Z, Schlipf M, Humer M, Taheridehkordi A, Kresse G. Toward Large-Scale AFQMC Calculations: Large Time Step Auxiliary-Field Quantum Monte Carlo. J Chem Theory Comput 2024; 20:4205-4217. [PMID: 38750634 PMCID: PMC11137827 DOI: 10.1021/acs.jctc.4c00304] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/08/2024] [Revised: 04/29/2024] [Accepted: 05/06/2024] [Indexed: 05/29/2024]
Abstract
We report modifications of the ph-AFQMC algorithm that allow the use of large time steps and reliable time step extrapolation. Our modified algorithm eliminates size-consistency errors present in the standard algorithm when large time steps are employed. We investigate various methods to approximate the exponential of the one-body operator within the AFQMC framework, distinctly demonstrating the superiority of Krylov methods over the conventional Taylor expansion. We assess various propagators within AFQMC and demonstrate that the Split-2 propagator is the optimal method, exhibiting the smallest time-step errors. For the HEAT set molecules, the time-step extrapolated energies deviate on average by only 0.19 kcal/mol from the accurate small time-step energies. For small water clusters, we obtain accurate complete basis-set binding energies using time-step extrapolation with a mean absolute error of 0.07 kcal/mol compared to CCSD(T). Using large time-step ph-AFQMC for the N2 dimer, we show that accurate bond lengths can be obtained while reducing CPU time by an order of magnitude.
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Affiliation(s)
- Zoran Sukurma
- University
of Vienna, Faculty of Physics and Center for Computational Materials
Science, Kolingasse 14-16, A-1090 Vienna, Austria
- University
of Vienna, Faculty of Physics
& Vienna Doctoral School in Physics, Boltzmanngasse 5, A-1090 Vienna, Austria
| | - Martin Schlipf
- VASP
Software GmbH, Berggasse
21/14, 1090 Vienna, Austria
| | - Moritz Humer
- University
of Vienna, Faculty of Physics and Center for Computational Materials
Science, Kolingasse 14-16, A-1090 Vienna, Austria
- University
of Vienna, Faculty of Physics
& Vienna Doctoral School in Physics, Boltzmanngasse 5, A-1090 Vienna, Austria
| | - Amir Taheridehkordi
- University
of Vienna, Faculty of Physics and Center for Computational Materials
Science, Kolingasse 14-16, A-1090 Vienna, Austria
| | - Georg Kresse
- University
of Vienna, Faculty of Physics and Center for Computational Materials
Science, Kolingasse 14-16, A-1090 Vienna, Austria
- VASP
Software GmbH, Sensengasse
8, 1090 Vienna, Austria
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10
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Damour Y, Scemama A, Jacquemin D, Kossoski F, Loos PF. State-Specific Coupled-Cluster Methods for Excited States. J Chem Theory Comput 2024; 20:4129-4145. [PMID: 38749498 PMCID: PMC11137840 DOI: 10.1021/acs.jctc.4c00034] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/10/2024] [Revised: 03/06/2024] [Accepted: 03/06/2024] [Indexed: 05/29/2024]
Abstract
We reexamine ΔCCSD, a state-specific coupled-cluster (CC) with single and double excitations (CCSD) approach that targets excited states through the utilization of non-Aufbau determinants. This methodology is particularly efficient when dealing with doubly excited states, a domain in which the standard equation-of-motion CCSD (EOM-CCSD) formalism falls short. Our goal here to evaluate the effectiveness of ΔCCSD when applied to other types of excited states, comparing its consistency and accuracy with EOM-CCSD. To this end, we report a benchmark on excitation energies computed with the ΔCCSD and EOM-CCSD methods for a set of molecular excited-state energies that encompasses not only doubly excited states but also doublet-doublet transitions and (singlet and triplet) singly excited states of closed-shell systems. In the latter case, we rely on a minimalist version of multireference CC known as the two-determinant CCSD method to compute the excited states. Our data set, consisting of 276 excited states stemming from the quest database [Véril et al., WIREs Comput. Mol. Sci. 2021, 11, e1517], provides a significant base to draw general conclusions concerning the accuracy of ΔCCSD. Except for the doubly excited states, we found that ΔCCSD underperforms EOM-CCSD. For doublet-doublet transitions, the difference between the mean absolute errors (MAEs) of the two methodologies (of 0.10 and 0.07 eV) is less pronounced than that obtained for singly excited states of closed-shell systems (MAEs of 0.15 and 0.08 eV). This discrepancy is largely attributed to a greater number of excited states in the latter set exhibiting multiconfigurational characters, which are more challenging for ΔCCSD. We also found typically small improvements by employing state-specific optimized orbitals.
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Affiliation(s)
- Yann Damour
- Laboratoire
de Chimie et Physique Quantiques (UMR 5626), Université de Toulouse, CNRS, UPS, 31000 Toulouse, France
| | - Anthony Scemama
- Laboratoire
de Chimie et Physique Quantiques (UMR 5626), Université de Toulouse, CNRS, UPS, 31000 Toulouse, France
| | - Denis Jacquemin
- Nantes
Université, CNRS, CEISAM UMR 6230, F-44000 Nantes, France
- Institut
Universitaire de France (IUF), F-75005 Paris, France
| | - Fábris Kossoski
- Laboratoire
de Chimie et Physique Quantiques (UMR 5626), Université de Toulouse, CNRS, UPS, 31000 Toulouse, France
| | - Pierre-François Loos
- Laboratoire
de Chimie et Physique Quantiques (UMR 5626), Université de Toulouse, CNRS, UPS, 31000 Toulouse, France
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11
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Maniar R, Withanage KPK, Shahi C, Kaplan AD, Perdew JP, Pederson MR. Symmetry breaking and self-interaction correction in the chromium atom and dimer. J Chem Phys 2024; 160:144301. [PMID: 38587222 DOI: 10.1063/5.0180863] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/12/2023] [Accepted: 03/21/2024] [Indexed: 04/09/2024] Open
Abstract
Density functional approximations to the exchange-correlation energy can often identify strongly correlated systems and estimate their energetics through energy-minimizing symmetry-breaking. In particular, the binding energy curve of the strongly correlated chromium dimer is described qualitatively by the local spin density approximation (LSDA) and almost quantitatively by the Perdew-Burke-Ernzerhof generalized gradient approximation (PBE-GGA), where the symmetry breaking is antiferromagnetic for both. Here, we show that a full Perdew-Zunger self-interaction-correction (SIC) to LSDA seems to go too far by creating an unphysical symmetry-broken state, with effectively zero magnetic moment but non-zero spin density on each atom, which lies ∼4 eV below the antiferromagnetic solution. A similar symmetry-breaking, observed in the atom, better corresponds to the 3d↑↑4s↑3d↓↓4s↓ configuration than to the standard 3d↑↑↑↑↑4s↑. For this new solution, the total energy of the dimer at its observed bond length is higher than that of the separated atoms. These results can be regarded as qualitative evidence that the SIC needs to be scaled down in many-electron regions.
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Affiliation(s)
- Rohan Maniar
- Department of Physics and Engineering Physics, Tulane University, 6400 Freret St., New Orleans, Louisiana 70118, USA
| | - Kushantha P K Withanage
- Department of Physics, The University of Texas at El Paso, 500 West University Ave., El Paso, Texas 79968, USA
| | - Chandra Shahi
- Department of Physics and Engineering Physics, Tulane University, 6400 Freret St., New Orleans, Louisiana 70118, USA
| | - Aaron D Kaplan
- Materials Project, Lawrence Berkeley National Laboratory, 1 Cyclotron Rd., B33-141B, Berkeley, California 94720, USA
| | - John P Perdew
- Department of Physics and Engineering Physics, Tulane University, 6400 Freret St., New Orleans, Louisiana 70118, USA
| | - Mark R Pederson
- Department of Physics, The University of Texas at El Paso, 500 West University Ave., El Paso, Texas 79968, USA
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12
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Burton HGA, Loos PF. Rationale for the extrapolation procedure in selected configuration interaction. J Chem Phys 2024; 160:104102. [PMID: 38456526 DOI: 10.1063/5.0192458] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/19/2023] [Accepted: 02/18/2024] [Indexed: 03/09/2024] Open
Abstract
Selected configuration interaction (SCI) methods have emerged as state-of-the-art methodologies for achieving high accuracy and generating benchmark reference data for ground and excited states in small molecular systems. However, their precision relies heavily on extrapolation procedures to produce a final estimate of the exact result. Using the structure of the exact electronic energy landscape, we provide a rationale for the common linear extrapolation of the variational energy as a function of the second-order perturbative correction. In particular, we demonstrate that the energy gap and the coupling between the so-called internal and external spaces are the key factors determining the rate at which the linear regime is reached. Starting from the first principles, we also derive a new non-linear extrapolation formula that improves the post-processing of data generated from SCI methods and can be applied to both ground- and excited-state energies.
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Affiliation(s)
- Hugh G A Burton
- Yusuf Hamied Department of Chemistry, University of Cambridge, Lensfield Road, Cambridge CB2 1EW, United Kingdom
| | - Pierre-François Loos
- Laboratoire de Chimie et Physique Quantiques (UMR 5626), Université de Toulouse, CNRS, UPS, Toulouse, France
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13
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Cheng Y, Ma H. Renormalized-Residue-Based Multireference Configuration Interaction Method for Strongly Correlated Systems. J Chem Theory Comput 2024; 20:1988-2009. [PMID: 38380619 DOI: 10.1021/acs.jctc.3c01247] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 02/22/2024]
Abstract
The implementation of multireference configuration interaction (MRCI) methods in quantum systems with large active spaces is hindered by the expansion of configuration bases or the intricate handling of reduced density matrices (RDMs). In this work, we present a spin-adapted renormalized-residue-based MRCI (RR-MRCI) approach that leverages renormalized residues to effectively capture the entanglement between active and inactive orbitals. This approach is reinforced by a novel efficient algorithm, which also facilitates an efficient deployment of spin-adapted matrix product state MRCI (MPS-MRCI). The RR-MRCI framework possesses several advantages: (1) It considers the orbital entanglement and utilizes highly compressed MPS structure, improving computational accuracy and efficiency compared with internally contracted (ic) MRCI. (2) Utilizing small-sized buffer environments of a few external orbitals as probes based on quantum information theory, it enhances computational efficiency over MPS-MRCI and offers potential application to large molecular systems. (3) The RR framework can be implemented in conjunction with ic-MRCI, eliminating the need for high-rank RDMs, by using distinct renormalized residues. We evaluated this method across nine diverse molecular systems, including Cu2O22+ with an active space of (24e,24o) and two complexes of lanthanide and actinide with active space (38e,36o), demonstrating the method's versatility and efficacy.
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Affiliation(s)
- Yifan Cheng
- School of Chemistry and Chemical Engineering, Nanjing University, Nanjing, Jiangsu 210023, China
| | - Haibo Ma
- Qingdao Institute for Theoretical and Computational Sciences, School of Chemistry and Chemical Engineering, Shandong University, Qingdao, Shandong 266237, China
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14
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Gao H, Imamura S, Kasagi A, Yoshida E. Distributed Implementation of Full Configuration Interaction for One Trillion Determinants. J Chem Theory Comput 2024; 20:1185-1192. [PMID: 38314701 PMCID: PMC10867839 DOI: 10.1021/acs.jctc.3c01190] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/27/2023] [Revised: 12/24/2023] [Accepted: 01/12/2024] [Indexed: 02/07/2024]
Abstract
Full configuration interaction (FCI) can provide an exact molecular ground-state energy within a given basis set and serve as a benchmark for approximate methods in quantum chemical calculations, including the emerging variational quantum eigensolver. However, its exponential computational and memory requirements easily exceed the capability of a single server and limit its applicability to large molecules. In this paper, we present a distributed FCI implementation employing a hybrid parallelization scheme with multithreading and multiprocessing to expand FCI's applicability. We optimize this scheme to minimize the bottlenecks arising from interprocess communications and interthread data management. Our implementation achieves higher scalability than the naive combination of prior works and successfully calculates the exact energy of C3H8/STO-3G with 1.31 trillion determinants, which is the largest FCI calculation to the best of our knowledge. Furthermore, we provide a comprehensive list of FCI results with 136 combinations of molecules and basis sets for future evaluation and development of approximate methods.
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Affiliation(s)
- Hong Gao
- Computing Laboratory, Fujitsu Laboratories, Fujitsu Limited, Kawasaki City, Kanagawa, 211-0053, Japan
| | - Satoshi Imamura
- Computing Laboratory, Fujitsu Laboratories, Fujitsu Limited, Kawasaki City, Kanagawa, 211-0053, Japan
| | - Akihiko Kasagi
- Computing Laboratory, Fujitsu Laboratories, Fujitsu Limited, Kawasaki City, Kanagawa, 211-0053, Japan
| | - Eiji Yoshida
- Computing Laboratory, Fujitsu Laboratories, Fujitsu Limited, Kawasaki City, Kanagawa, 211-0053, Japan
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15
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Song Y, Huang W, Liu C, Lei Y, Suo B, Ma H. Spin-Adapted Externally Contracted Multireference Configuration Interaction Method Based on Selected Reference Configurations. J Phys Chem A 2024; 128:958-971. [PMID: 38272019 DOI: 10.1021/acs.jpca.3c07526] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/27/2024]
Abstract
As one kind of approximation of the full configuration interaction solution, the selected configuration interaction (sCI) methods have been shown to be valuable for large active spaces. However, the inclusion of dynamic correlation beyond large active spaces is necessary for more quantitative results. Since the sCI wave function can provide a compact reference for multireference methods, previously, we proposed an externally contracted multireference configuration interaction method using the sCI reference reconstructed from the density matrix renormalization group wave function [J. Chem. Theory Comput. 2018, 14, 4747-4755]. The DMRG2sCI-EC-MRCI method is promising for dealing with more than 30 active orbitals and large basis sets. However, it suffers from two drawbacks: spin contamination and low efficiency when using Slater determinant bases. To solve these problems, in this work, we adopt configuration state function bases and introduce a new algorithm based on the hybrid of tree structure for convenient configuration space management and the graphical unitary group approach for efficient matrix element calculation. The test calculation of naphthalene shows that the spin-adapted version could achieve a speed-up of 6.0 compared with the previous version based on the Slater determinant. Examples of dinuclear copper(II) compound as well as Ln(III) and An(III) complexes show that the sCI-EC-MRCI can give quantitatively accurate results by including dynamic correlation over sCI for systems with large active spaces and basis sets.
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Affiliation(s)
- Yinxuan Song
- School of Chemistry and Chemical Engineering, Nanjing University, Nanjing 210023, People's Republic of China
| | - Wei Huang
- School of Chemistry and Chemical Engineering, Nanjing University, Nanjing 210023, People's Republic of China
| | - Chungen Liu
- School of Chemistry and Chemical Engineering, Nanjing University, Nanjing 210023, People's Republic of China
| | - 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, People's Republic of China
| | - Bingbing Suo
- Shaanxi Key Laboratory for Theoretical Physics Frontiers, Institute of Modern Physics, Northwest University, Xi'an 710127, People's Republic of China
| | - Haibo Ma
- Qingdao Institute for Theoretical and Computational Sciences, Qingdao Institute of Frontier and Interdisciplinary Science, Shandong University, Qingdao 266237, China
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16
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Ren X, Zou J, Zhang H, Li W, Li S. Block-Correlated Coupled Cluster Theory with up to Four-Pair Correlation for Accurate Static Correlation of Strongly Correlated Systems. J Phys Chem Lett 2024; 15:693-700. [PMID: 38207241 DOI: 10.1021/acs.jpclett.3c03373] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/13/2024]
Abstract
A block-correlated coupled cluster method with up to four-pair correlation based on the generalized valence bond wave function (GVB-BCCC4) is first implemented, which offers an alternative method for electronic structure calculations of strongly correlated systems. We developed some techniques to derive a set of compact and cost-effective equations for GVB-BCCC4, which include the definition of n-block (n = 1-4) Hamiltonian matrices, the combination of excitation operators, and the definition of independent amplitudes. We then applied the GVB-BCCC4 method to investigate several potential energy surfaces of strongly correlated systems with singlet ground states. Our calculations demonstrate that the GVB-BCCC4 method can provide nearly exact static correlation energies as the density matrix renormalization group method (on the basis of the same GVB orbitals). This work highlights the significance of four-pair correlation in quantitative descriptions of static correlation energy for strongly correlated systems.
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Affiliation(s)
- Xiaochuan Ren
- Key Laboratory of Mesoscopic Chemistry of Ministry of Education, New Cornerstone Science Laboratory, School of Chemistry and Chemical Engineering, Nanjing University, Nanjing, Jiangsu 210023, People's Republic of China
| | - Jingxiang Zou
- Key Laboratory of Mesoscopic Chemistry of Ministry of Education, New Cornerstone Science Laboratory, School of Chemistry and Chemical Engineering, Nanjing University, Nanjing, Jiangsu 210023, People's Republic of China
| | - Haodong Zhang
- Key Laboratory of Mesoscopic Chemistry of Ministry of Education, New Cornerstone Science Laboratory, School of Chemistry and Chemical Engineering, Nanjing University, Nanjing, Jiangsu 210023, People's Republic of China
| | - Wei Li
- Key Laboratory of Mesoscopic Chemistry of Ministry of Education, New Cornerstone Science Laboratory, School of Chemistry and Chemical Engineering, Nanjing University, Nanjing, Jiangsu 210023, People's Republic of China
| | - Shuhua Li
- Key Laboratory of Mesoscopic Chemistry of Ministry of Education, New Cornerstone Science Laboratory, School of Chemistry and Chemical Engineering, Nanjing University, Nanjing, Jiangsu 210023, People's Republic of China
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17
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Prentice AW, Coe JP, Paterson MJ. Modular Approach to Selected Configuration Interaction in an Arbitrary Spin Basis: Implementation and Comparison of Approaches. J Chem Theory Comput 2023; 19:9161-9176. [PMID: 38061390 PMCID: PMC10753805 DOI: 10.1021/acs.jctc.3c00897] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/15/2023] [Revised: 11/24/2023] [Accepted: 11/27/2023] [Indexed: 12/27/2023]
Abstract
A modular selected configuration interaction (SCI) code has been developed that is based on the existing Monte-Carlo configuration interaction code (MCCI). The modularity allows various selection protocols to be implemented with ease and allows for fair comparison between wave functions built via different criteria. We have initially implemented adaptations of existing SCI theories, which are based on either energy- or coefficient-driven selection schemes. These codes have been implemented not only in the basis of Slater determinants (SDs) but also in the basis of configuration state functions (CSFs) and extended to state-averaged regimes. This allows one to take advantage of the reduced dimensionality of the wave function in the CSF basis and also the guarantee of pure spin states. All SCI methods were found to be able to predict potential energy surfaces to high accuracy, producing compact wave functions, when compared to full configuration interaction (FCI) for a variety of bond-breaking potential energy surfaces. The compactness of the error-controlled adaptive configuration interaction approach, particularly in the CSF basis, was apparent with nonparallelity errors within chemical accuracy while containing as little as 0.02% of the FCI CSF space. The size-to-accuracy was also extended to FCI spaces approaching one billion configurations.
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Affiliation(s)
- Andrew W. Prentice
- Institute of Chemical Sciences, School
of Engineering and Physical Sciences, Heriot-Watt
University, Edinburgh EH14 4AS, U.K.
| | - Jeremy P. Coe
- Institute of Chemical Sciences, School
of Engineering and Physical Sciences, Heriot-Watt
University, Edinburgh EH14 4AS, U.K.
| | - Martin J. Paterson
- Institute of Chemical Sciences, School
of Engineering and Physical Sciences, Heriot-Watt
University, Edinburgh EH14 4AS, U.K.
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18
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Ugandi M, Roemelt M. A configuration-based heatbath-CI for spin-adapted multireference electronic structure calculations with large active spaces. J Comput Chem 2023; 44:2374-2390. [PMID: 37589287 DOI: 10.1002/jcc.27203] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/16/2023] [Revised: 07/24/2023] [Accepted: 07/27/2023] [Indexed: 08/18/2023]
Abstract
This work reports on a spin-pure configuration-based implementation of the heatbath configuration interaction (HCI) algorithm for selective configuration interaction. Besides the obvious advantage of being spin-pure, the presented method combines the compactness of the configurational ansatz with the known efficiency of the HCI algorithm and a variety of algorithmic and conceptual ideas to achieve a high level of performance. In particular, through pruning of the selected configurational space after HCI selection by means of a more strict criterion, a more compact wavefunction representation is obtained. Moreover, the underlying logic of the method allows us to minimize the number of redundant matrix-matrix multiplications while making use of just-in-time compilation to achieve fast diagonalization of the Hamiltonian. The critical search for 2-electron connections within the configurational space is facilitated by a tree-based representation thereof as suggested previously by Gopal et al. Usage of a prefix-based parallelization and batching during the calculation of the PT2-correction leads to a good load balancing and significantly reduced memory requirements for these critical steps of the calculation. In this way, the need for a semistochastic approach to the PT2 correction is avoided even for large configurational spaces. Finally, several test-cases are discussed to demonstrate the strengths and weaknesses of the presented method.
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Affiliation(s)
- Mihkel Ugandi
- Institut für Chemie, Humboldt-Universität zu Berlin, Berlin, Germany
| | - Michael Roemelt
- Institut für Chemie, Humboldt-Universität zu Berlin, Berlin, Germany
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19
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Li X, Huang JC, Zhang GZ, Li HE, Cao CS, Lv D, Hu HS. A Nonstochastic Optimization Algorithm for Neural-Network Quantum States. J Chem Theory Comput 2023; 19:8156-8165. [PMID: 37962975 DOI: 10.1021/acs.jctc.3c00831] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/16/2023]
Abstract
Neural-network quantum states (NQS) employ artificial neural networks to encode many-body wave functions in a second quantization through variational Monte Carlo (VMC). They have recently been applied to accurately describe electronic wave functions of molecules and have shown the challenges in efficiency compared with traditional quantum chemistry methods. Here, we introduce a general nonstochastic optimization algorithm for NQS in chemical systems, which deterministically generates a selected set of important configurations simultaneously with energy evaluation of NQS. This method bypasses the need for Markov-chain Monte Carlo within the VMC framework, thereby accelerating the entire optimization process. Furthermore, this newly developed nonstochastic optimization algorithm for NQS offers comparable or superior accuracy compared to its stochastic counterpart and ensures more stable convergence. The application of this model to test molecules exhibiting strong electron correlations provides further insight into the performance of NQS in chemical systems and opens avenues for future enhancements.
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Affiliation(s)
- Xiang Li
- Department of Chemistry and Engineering Research Center of Advanced Rare-Earth Materials of Ministry of Education, Tsinghua University, Beijing 100084, China
| | - Jia-Cheng Huang
- Department of Chemistry and Engineering Research Center of Advanced Rare-Earth Materials of Ministry of Education, Tsinghua University, Beijing 100084, China
| | - Guang-Ze Zhang
- Department of Chemistry and Engineering Research Center of Advanced Rare-Earth Materials of Ministry of Education, Tsinghua University, Beijing 100084, China
| | - Hao-En Li
- Department of Chemistry and Engineering Research Center of Advanced Rare-Earth Materials of Ministry of Education, Tsinghua University, Beijing 100084, China
| | - Chang-Su Cao
- Department of Chemistry and Engineering Research Center of Advanced Rare-Earth Materials of Ministry of Education, Tsinghua University, Beijing 100084, China
- ByteDance Research, Zhonghang Plaza, No. 43, North Third Ring West Road, Haidian District, Beijing 100089, China
| | - Dingshun Lv
- ByteDance Research, Zhonghang Plaza, No. 43, North Third Ring West Road, Haidian District, Beijing 100089, China
| | - Han-Shi Hu
- Department of Chemistry and Engineering Research Center of Advanced Rare-Earth Materials of Ministry of Education, Tsinghua University, Beijing 100084, China
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20
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Coe JP. Analytic Non-adiabatic Couplings for Selected Configuration Interaction via Approximate Degenerate Coupled Perturbed Hartree-Fock. J Chem Theory Comput 2023; 19:8053-8065. [PMID: 37939698 PMCID: PMC10687870 DOI: 10.1021/acs.jctc.3c00601] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/05/2023] [Revised: 10/24/2023] [Accepted: 10/25/2023] [Indexed: 11/10/2023]
Abstract
We use degenerate perturbation theory and assume that for degenerate pairs of orbitals, the coupled perturbed Hartree-Fock coefficients are symmetric in the degenerate basis to show [Formula: see text] is the only modification needed in the original molecular orbital basis. This enables us to develop efficient and accurate analytic nonadiabatic couplings between electronic states for selected configuration interactions (CIs). Even when the states belong to different irreducible representations, degenerate orbital pairs cannot be excluded by symmetry. For various excited states of carbon monoxide and trigonal planar ammonia, we benchmark the method against the full CI and find it to be accurate. We create a semi-numerical approach and use it to show that the analytic approach is correct even when a high-symmetry structure is distorted to break symmetry so that near degeneracies in orbitals occur. For a range of geometries of trigonal planar ammonia, we find that the analytic non-adiabatic couplings for selected CI can achieve sufficient accuracy using a small fraction of the full CI space.
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Affiliation(s)
- Jeremy P. Coe
- Institute of Chemical Sciences, School
of Engineering and Physical Sciences, Heriot-Watt
University, Edinburgh EH14 4AS, U.K.
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21
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Jacquemin D, Kossoski F, Gam F, Boggio-Pasqua M, Loos PF. Reference Vertical Excitation Energies for Transition Metal Compounds. J Chem Theory Comput 2023. [PMID: 37965941 DOI: 10.1021/acs.jctc.3c01080] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/16/2023]
Abstract
To enrich and enhance the diversity of the quest database of highly accurate excitation energies [Véril, M.; et al. Wiley Interdiscip. Rev.: Comput. Mol. Sci. 2021, 11, e1517], we report vertical transition energies in transition metal compounds. Eleven diatomic molecules with a singlet or doublet ground state containing a fourth-row transition metal (CuCl, CuF, CuH, ScF, ScH, ScO, ScS, TiN, ZnH, ZnO, and ZnS) are considered, and the corresponding excitation energies are computed using high-level coupled-cluster (CC) methods, namely, CC3, CCSDT, CC4, and CCSDTQ, as well as multiconfigurational methods such as CASPT2 and NEVPT2. In many cases, to provide more comprehensive benchmark data, we also provide full configuration interaction estimates computed with the configuration interaction using a perturbative selection made iteratively (CIPSI) method. Based on these calculations, theoretical best estimates of the transition energies are established in both the aug-cc-pVDZ and aug-cc-pVTZ basis sets. This allows us to accurately assess the performance of the CC and multiconfigurational methods for this specific set of challenging transitions. Furthermore, comparisons with experimental data and previous theoretical results are also reported.
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Affiliation(s)
- Denis Jacquemin
- Nantes Université, CNRS, CEISAM UMR 6230, F-44000 Nantes, France
- Institut Universitaire de France (IUF), F-75005 Paris, France
| | - Fábris Kossoski
- Laboratoire de Chimie et Physique Quantiques (UMR 5626), Université de Toulouse, CNRS, UPS, F-31062 Toulouse, France
| | - Franck Gam
- Nantes Université, CNRS, CEISAM UMR 6230, F-44000 Nantes, France
| | - Martial Boggio-Pasqua
- Laboratoire de Chimie et Physique Quantiques (UMR 5626), Université de Toulouse, CNRS, UPS, F-31062 Toulouse, France
| | - Pierre-François Loos
- Laboratoire de Chimie et Physique Quantiques (UMR 5626), Université de Toulouse, CNRS, UPS, F-31062 Toulouse, France
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22
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Guo Y, Zhang N, Liu W. SOiCISCF: Combining SOiCI and iCISCF for Variational Treatment of Spin-Orbit Coupling. J Chem Theory Comput 2023; 19:6668-6685. [PMID: 37728243 DOI: 10.1021/acs.jctc.3c00789] [Citation(s) in RCA: 4] [Impact Index Per Article: 4.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 09/21/2023]
Abstract
It has recently been shown that the SOiCI approach [Zhang, N.; J. Phys.: Condens. Matter 2022, 34, 224007], in conjunction with the spin-separated exact two-component relativistic Hamiltonian, can provide very accurate fine structures of systems containing heavy elements by treating electron correlation and spin-orbit coupling (SOC) on an equal footing. Nonetheless, orbital relaxations/polarizations induced by SOC are not yet fully accounted for due to the use of scalar relativistic orbitals. This issue can be resolved by further optimizing the still real-valued orbitals self-consistently in the presence of SOC, as done in the spin-orbit coupled CASSCF approach [Ganyushin, D.; et al. J. Chem. Phys. 2013, 138, 104113] but with the iCISCF algorithm [Guo, Y.; J. Chem. Theory Comput. 2021, 17, 7545-7561] for large active spaces. The resulting SOiCISCF employs both double group and time reversal symmetries for computational efficiency and the assignment of target states. The fine structures of p-block elements are taken as showcases to reveal the efficacy of SOiCISCF.
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Affiliation(s)
- Yang Guo
- Qingdao Institute for Theoretical and Computational Sciences, Institute of Frontier and Interdisciplinary Science, Shandong University, Qingdao, Shandong 266237, China
| | - Ning Zhang
- Beijing National Laboratory for Molecular Sciences, Institute of Theoretical and Computational Chemistry, College of Chemistry and Molecular Engineering, Peking University, Beijing 100871, China
| | - Wenjian Liu
- Qingdao Institute for Theoretical and Computational Sciences, Institute of Frontier and Interdisciplinary Science, Shandong University, Qingdao, Shandong 266237, China
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23
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Braunscheidel NM, Abraham V, Mayhall NJ. Generalization of the Tensor Product Selected CI Method for Molecular Excited States. J Phys Chem A 2023; 127:8179-8193. [PMID: 37733948 DOI: 10.1021/acs.jpca.3c03161] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 09/23/2023]
Abstract
In a recent paper [JCTC, 2020, 16, 6098], we introduced a new approach for accurately approximating full CI ground states in large electronic active-spaces called Tensor Product Selected CI (TPSCI). In TPSCI, a large orbital active space is first partitioned into disjoint sets (clusters) for which the exact, local many-body eigenstates are obtained. Tensor products of these locally correlated many-body states are taken as the basis for the full, global Hilbert space. By folding correlation into the basis states themselves, the low-energy eigenstates become increasingly sparse, creating a more compact selected CI expansion. While we demonstrated that this approach can improve accuracy for a variety of systems, there is even greater potential for applications to excited states, particularly those which have some excited-state character. In this paper, we report on the accuracy of TPSCI for excited states, including a far more efficient implementation in the Julia programming language. In traditional SCI methods that use a Slater determinant basis, accurate excitation energies are obtained only after a linear extrapolation and at a large computational cost. We find that TPSCI with perturbative corrections provides accurate excitation energies for several excited states of various polycyclic aromatic hydrocarbons with respect to the extrapolated result (i.e., near exact result). Further, we use TPSCI to report highly accurate estimates of the lowest 31 eigenstates for a tetracene tetramer system with an active space of 40 electrons in 40 orbitals, giving direct access to the initial bright states and the resulting 18 doubly excited (biexcitonic) states.
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Affiliation(s)
| | - Vibin Abraham
- Department of Chemistry, University of Michigan, Ann Arbor, Michigan 48109, United States
| | - Nicholas J Mayhall
- Department of Chemistry, Virginia Tech, Blacksburg, Virginia 24060, United States
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24
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Park JW. Dynamic Correlation on the Adaptive Sampling Configuration Interaction (ASCI) Reference Function: ASCI-DSRG-MRPT2. J Chem Theory Comput 2023; 19:6263-6272. [PMID: 37611192 DOI: 10.1021/acs.jctc.3c00688] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 08/25/2023]
Abstract
A balanced description of static and dynamic electron correlations is at the heart of quantum chemical methods. To obtain accurate results in strongly correlated systems using wave-function-based methods, a large active space is necessary to ensure correct descriptions of static correlations. Correcting the results for dynamic correlations is also necessary. In this work, we present implementations of second-order perturbation theory for dynamic correlations based on the adaptive sampling configuration interaction self-consistent field (ASCI-SCF) method. In particular, we implemented spin-free driven similarity renormalization group second-order multireference perturbation theory (DSRG-MRPT2). The extrapolation of the ASCI + PT2 energy based on the relaxed Hamiltonian in DSRG-MRPT2 gives a reasonable approximation of DSRG-MRPT2 based on CASSCF. We demonstrate the application of the ASCI-DSRG-MRPT2 method in evaluations of the spin-state energy gaps in iron porphyrins, polyacenes, and periacenes along with the reaction energies of methane oxidation by FeO+ and electrocyclic ring formation in cethrene.
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Affiliation(s)
- Jae Woo Park
- Department of Chemistry, Chungbuk National University (CBNU), Cheongju 28644, Korea
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25
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Gururangan K, Piecuch P. Converging high-level coupled-cluster energetics via adaptive selection of excitation manifolds driven by moment expansions. J Chem Phys 2023; 159:084108. [PMID: 37610021 DOI: 10.1063/5.0162873] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/16/2023] [Accepted: 08/03/2023] [Indexed: 08/24/2023] Open
Abstract
A novel approach to rapidly converging high-level coupled-cluster (CC) energetics in an automated fashion is proposed. The key idea is an adaptive selection of excitation manifolds defining higher--than--two-body components of the cluster operator inspired by CC(P;Q) moment expansions. The usefulness of the resulting methodology is illustrated by molecular examples where the goal is to recover the electronic energies obtained using the CC method with a full treatment of singly, doubly, and triply excited clusters (CCSDT) when the noniterative triples corrections to CCSD fail.
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Affiliation(s)
- Karthik Gururangan
- Department of Chemistry, Michigan State University, East Lansing, Michigan 48824, USA
| | - Piotr Piecuch
- Department of Chemistry, Michigan State University, East Lansing, Michigan 48824, USA
- Department of Physics and Astronomy, Michigan State University, East Lansing, Michigan 48824, USA
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26
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Nyvang A, Olsen J. A relativistic configuration interaction method with general expansions and initial applications to electronic g-factors. J Chem Phys 2023; 159:044102. [PMID: 37486047 DOI: 10.1063/5.0152655] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/31/2023] [Accepted: 06/28/2023] [Indexed: 07/25/2023] Open
Abstract
A new implementation of the orbital-based two-component relativistic configuration interaction approach is reported and applied to calculations of the electronic g-shifts of three diatomic radicals: AlO, HgF, and PdH. The new implementation augments efficient routines for the calculation of nonrelativistic Hamiltonians with new vectorized routines for the calculation of the action of the one-electron spin-orbit operator and allows efficient calculations for the expansion of generalized active space type. The program makes full use of double group as well as time-reversal symmetry. Particle-hole reorganization of the operators is used to improve the efficiency for expansions with nearly fully occupied orbital spaces. The flexibility of the algorithm and program is used to investigate the convergence of electronic g-shifts for the three diatomic radicals as functions of the active space, states included in the orbital optimization, and excitation levels. It was possible to converge to the valence limits within a few percent using expansions containing up to quadruple excitations. However, when excitations from the core orbitals were added, it was not possible to demonstrate convergence to within a few percent with expansions containing at most 10 × 109 determinants.
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Affiliation(s)
- Andreas Nyvang
- Department of Chemistry, Aarhus University, Langelandsgade 140, DK 8000 Aarhus C, Denmark
| | - Jeppe Olsen
- Department of Chemistry, Aarhus University, Langelandsgade 140, DK 8000 Aarhus C, Denmark
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27
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Xu Y, Cheng Y, Song Y, Ma H. New Density Matrix Renormalization Group Approaches for Strongly Correlated Systems Coupled with Large Environments. J Chem Theory Comput 2023. [PMID: 37471519 DOI: 10.1021/acs.jctc.2c01316] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 07/22/2023]
Abstract
Thanks to the high compression of the matrix product state (MPS) form of the wave function and the efficient site-by-site iterative sweeping optimization algorithm, the density matrix normalization group (DMRG) and its time-dependent variant (TD-DMRG) have been established as powerful computational tools in accurately simulating the electronic structure and quantum dynamics of strongly correlated molecules with a large number (101-2) of quantum degrees of freedom (active orbitals or vibrational modes). However, the quantitative characterization of the quantum many-body behaviors of realistic strongly correlated systems requires a further consideration of the interaction between the embedded active subsystem and the remaining correlated environment, e.g., a larger number (102-3) of external orbitals in electronic structure or infinite condensed-phase phononic modes in nucleus dynamics. To this end, we introduced three new post-DMRG and TD-DMRG approaches, namely (1) DMRG2sCI-MRCI and DMRG2sCI-ENPT by the reconstruction of selected configuration interaction (sCI) type of compact reference function from DMRG coefficients and the use of externally contracted MRCI (multireference configuration interaction) and Epstein-Nesbet perturbation theory (ENPT), without recourse to the expensive high order n-electron reduced density matrices (n-RDMs). (2) DMRG combined with RR-MRCI (renormalized residue-based MRCI), which improves the computational accuracy and efficiency of internally contracted (ic) MRCI by renormalizing the contracted bases with small-sized buffer environment(s) of a few external orbitals as probes based on quantum information theory. (3) HM (hierarchical mapping)-TD-DMRG in which a large environment is reduced to a small number of renormalized environmental modes (which accounts for the most vital system-environment interactions) through stepwise mapping transformation. These advances extend the efficacy of highly accurate DMRG/TD-DMRG computations to the quantitative characterization of the electronic structure and quantum dynamics in realistic strongly correlated systems coupled with large environments and are reviewed in this paper.
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Affiliation(s)
- Yihe Xu
- School of Chemistry and Chemical Engineering, Nanjing University, Nanjing 210023, China
| | - Yifan Cheng
- School of Chemistry and Chemical Engineering, Nanjing University, Nanjing 210023, China
| | - Yinxuan Song
- School of Chemistry and Chemical Engineering, Nanjing University, Nanjing 210023, China
| | - Haibo Ma
- Qingdao Institute for Theoretical and Computational Sciences, Qingdao Institute of Frontier and Interdisciplinary Science, Shandong University, Qingdao 266237, China
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28
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Abstract
We develop analytic gradients for selected configuration interaction wave functions. Despite all pairs of molecular orbitals now potentially having to be considered for the coupled perturbed Hartree-Fock equations, we show that degenerate orbital pairs belonging to different irreducible representations in the largest abelian subgroup do not need to be included and instabilities due to degeneracies are avoided. We introduce seminumerical gradients and use them to validate the analytic approach even when near degeneracies are present due to high-symmetry geometries being slightly distorted to break symmetry. The method is applied to carbon monoxide, ammonia, square planar H4, hexagonal planar H6, and methane for a range of bond lengths where we demonstrate that analytic gradients for selected configuration interaction can approach the quality of full configuration interaction yet only use a very small fraction of its determinants.
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29
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Damour Y, Quintero-Monsebaiz R, Caffarel M, Jacquemin D, Kossoski F, Scemama A, Loos PF. Ground- and Excited-State Dipole Moments and Oscillator Strengths of Full Configuration Interaction Quality. J Chem Theory Comput 2023; 19:221-234. [PMID: 36548519 DOI: 10.1021/acs.jctc.2c01111] [Citation(s) in RCA: 6] [Impact Index Per Article: 6.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/24/2022]
Abstract
We report ground- and excited-state dipole moments and oscillator strengths (computed in different "gauges" or representations) of full configuration interaction (FCI) quality using the selected configuration interaction method known as Configuration Interaction using a Perturbative Selection made Iteratively (CIPSI). Thanks to a set encompassing 35 ground- and excited-state properties computed in 11 small molecules, the present near-FCI estimates allow us to assess the accuracy of high-order coupled-cluster (CC) calculations including up to quadruple excitations. In particular, we show that incrementing the excitation degree of the CC expansion (from CC with singles and doubles (CCSD) to CC with singles, doubles, and triples (CCSDT) or from CCSDT to CC with singles, doubles, triples, and quadruples (CCSDTQ)) reduces the average error with respect to the near-FCI reference values by approximately 1 order of magnitude.
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Affiliation(s)
- Yann Damour
- Laboratoire de Chimie et Physique Quantiques (UMR 5626), Université de Toulouse, CNRS, UPS, 31062 Toulouse, France
| | - Raúl Quintero-Monsebaiz
- Laboratoire de Chimie et Physique Quantiques (UMR 5626), Université de Toulouse, CNRS, UPS, 31062 Toulouse, France
| | - Michel Caffarel
- Laboratoire de Chimie et Physique Quantiques (UMR 5626), Université de Toulouse, CNRS, UPS, 31062 Toulouse, France
| | - Denis Jacquemin
- Nantes Université, CNRS, CEISAM UMR 6230, F-44000 Nantes, France.,Institut Universitaire de France (IUF), F-75005 Paris, France
| | - Fábris Kossoski
- Laboratoire de Chimie et Physique Quantiques (UMR 5626), Université de Toulouse, CNRS, UPS, 31062 Toulouse, France
| | - Anthony Scemama
- Laboratoire de Chimie et Physique Quantiques (UMR 5626), Université de Toulouse, CNRS, UPS, 31062 Toulouse, France
| | - Pierre-François Loos
- Laboratoire de Chimie et Physique Quantiques (UMR 5626), Université de Toulouse, CNRS, UPS, 31062 Toulouse, France
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30
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Liu W. Perspective: Simultaneous treatment of relativity, correlation, and
QED. WIRES COMPUTATIONAL MOLECULAR SCIENCE 2022. [DOI: 10.1002/wcms.1652] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 12/24/2022]
Affiliation(s)
- Wenjian Liu
- Qingdao Institute for Theoretical and Computational Sciences, Institute of Frontier and Interdisciplinary Science Shandong University Qingdao Shandong China
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31
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Cotton SJ. A truncated Davidson method for the efficient “chemically accurate” calculation of full configuration interaction wavefunctions without any large matrix diagonalization. J Chem Phys 2022; 157:224105. [DOI: 10.1063/5.0115796] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/13/2022] Open
Abstract
This work develops and illustrates a new method of calculating “chemically accurate” electronic wavefunctions (and energies) via a truncated full configuration interaction (CI) procedure, which arguably circumvents the large matrix diagonalization that is the core problem of full CI and is also central to modern selective CI approaches. This is accomplished simply by following the standard/ubiquitous Davidson method in its “direct” form—wherein, in each iteration, the electronic Hamiltonian operator is applied directly in second quantization to the Ritz vector/wavefunction from the prior iteration—except that (in this work) only a small portion of the resultant expansion vector is actually even computed (through the application of only a similarly small portion of the Hamiltonian). Specifically, at each iteration of this truncated Davidson approach, the new expansion vector is taken to be twice as large as that from the prior iteration. In this manner, a small set of highly truncated expansion vectors (say 10–30) of increasing precision is incrementally constructed, forming a small subspace within which diagonalization of the Hamiltonian yields clear, consistent, and monotonically variational convergence to the approximate full CI limit. The good efficiency in which convergence to the level of chemical accuracy (1.6 mhartree) is achieved suggests, at least for the demonstrated problem sizes—Hilbert spaces of 1018 and wavefunctions of 108 determinants—that this truncated Davidson methodology can serve as a replacement of standard CI and complete-active space approaches in circumstances where only a few chemically significant digits of accuracy are required and/or meaningful in view of ever-present basis set limitations.
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Affiliation(s)
- Stephen J. Cotton
- Quantum Artificial Intelligence Laboratory (QuAIL), NASA Ames Research Center, Moffett Field, California 94035, USA and Employed By KBR, 601 Jefferson St., Houston, Texas 77002, USA
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32
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Li J, Yang J. Downfolded Configuration Interaction for Chemically Accurate Electron Correlation. J Phys Chem Lett 2022; 13:10042-10047. [PMID: 36264261 DOI: 10.1021/acs.jpclett.2c02868] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 06/16/2023]
Abstract
A model subspace configuration interaction method is developed to obtain chemically accurate electron correlations by diagonalizing a very compact effective Hamiltonian of a realistic molecule. The construction of the effective Hamiltonian is deterministic and implemented by iteratively building a sufficiently small model subspace comprising local clusters of a small number of Slater determinants. Through the low-rank reciprocal of interaction Hamiltonian, important determinants can be incrementally identified to couple with selected local pairwise clusters and then downfolded into the model subspace. This method avoids direct ordering and selection of the configurations in the entire space. We demonstrate the efficiency and accuracy of this theory for obtaining the near-FCI ground- and excited-state potential energies by benchmarking the C2 molecule and illustrate its application potential in computing accurate excitation energies of organometallic [Cu(NHC)2(pyridine)2]x+ complexes and other organic molecules of various excitation character.
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Affiliation(s)
- Jiasheng Li
- Department of Chemistry, The University of Hong Kong, Hong KongSAR, P.R. China
| | - Jun Yang
- Department of Chemistry, The University of Hong Kong, Hong KongSAR, P.R. China
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33
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Coe JP, Moreno Carrascosa A, Simmermacher M, Kirrander A, Paterson MJ. Efficient Computation of Two-Electron Reduced Density Matrices via Selected Configuration Interaction. J Chem Theory Comput 2022; 18:6690-6699. [PMID: 36198067 PMCID: PMC9648180 DOI: 10.1021/acs.jctc.2c00738] [Citation(s) in RCA: 6] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Abstract
![]()
We create an approach to efficiently calculate two-electron
reduced
density matrices (2-RDMs) using selected configuration interaction
wavefunctions. This is demonstrated using the specific example of
Monte Carlo configuration interaction (MCCI). The computation of the
2-RDMs is accelerated by using ideas from fast implementations of
full configuration interaction (FCI) and recent advances in implementing
the Slater–Condon rules using hardware bitwise operations.
This method enables a comparison of MCCI and truncated CI 2-RDMs with
FCI values for a range of molecules, which includes stretched bonds
and excited states. The accuracy in energies, wavefunctions, and 2-RDMs
is seen to exhibit a similar behavior. We find that MCCI can reach
sufficient accuracy of the 2-RDM using significantly fewer configurations
than truncated CI, particularly for systems with strong multireference
character.
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Affiliation(s)
- Jeremy P Coe
- Institute of Chemical Sciences, School of Engineering and Physical Sciences, Heriot-Watt University, EdinburghEH14 4AS, U.K
| | | | - Mats Simmermacher
- EaStCHEM, School of Chemistry, University of Edinburgh, EdinburghEH9 3FJ, U.K
| | - Adam Kirrander
- EaStCHEM, School of Chemistry, University of Edinburgh, EdinburghEH9 3FJ, U.K
| | - Martin J Paterson
- Institute of Chemical Sciences, School of Engineering and Physical Sciences, Heriot-Watt University, EdinburghEH14 4AS, U.K
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34
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Zou J, Wang Q, Ren X, Wang Y, Zhang H, Li S. Efficient Implementation of Block-Correlated Coupled Cluster Theory Based on the Generalized Valence Bond Reference for Strongly Correlated Systems. J Chem Theory Comput 2022; 18:5276-5285. [PMID: 35922401 DOI: 10.1021/acs.jctc.2c00445] [Citation(s) in RCA: 4] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Abstract
An optimized implementation of block-correlated coupled cluster theory based on the generalized valence bond wave function (GVB-BCCC) for the singlet ground state of strongly correlated systems is presented. The GVB-BCCC method with two-pair correlation (GVB-BCCC2b) or up to three-pair correlation (GVB-BCCC3b) will be the focus of this work. Three major techniques have been adopted to dramatically accelerate GVB-BCCC2b and GVB-BCCC3b calculations. First, the GVB-BCCC2b and GVB-BCCC3b codes are noticeably optimized by removing redundant calculations. Second, independent amplitudes are identified by constraining excited configurations to be pure singlet states and only independent amplitudes need to be solved. Third, an incremental updating scheme for the amplitudes in solving the GVB-BCCC equations is adopted. With these techniques, accurate GVB-BCCC3b calculations are now accessible for systems with relatively large active spaces (50 electrons in 50 orbitals) and GVB-BCCC2b calculations are affordable for systems with much larger active spaces. We have applied GVB-BCCC methods to investigate three typical kinds of systems: polyacenes, pentaprismane, and [Cu2O2]2+ isomers. For polyacenes, we demonstrate that GVB-BCCC3b can capture more than 94% of the total correlation energy even for 12-acene with 50 π electrons. For the potential energy curve of simultaneously stretching 15 C-C bonds in pentaprismane, our calculations show that the GVB-BCCC3b results are quite close to the results from the density matrix renormalization group (DMRG) over the whole range. For two dinuclear copper oxide isomers, their relative energy predicted by GVB-BCCC3b is also in good accord with the DMRG result. All calculations show that the inclusion of three-pair correlation in GVB-BCCC is critical for accurate descriptions of strongly correlated systems.
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Affiliation(s)
- Jingxiang Zou
- Institute of Theoretical and Computational Chemistry, Key Laboratory of Mesoscopic Chemistry of Ministry of Education, School of Chemistry and Chemical Engineering, Nanjing University, Nanjing 210023, People's Republic of China
| | - Qingchun Wang
- Key Laboratory of Quantum Information, Chinese Academy of Sciences, School of Physics, University of Science and Technology of China, Hefei, Anhui 230026, People's Republic of China
| | - Xiaochuan Ren
- Institute of Theoretical and Computational Chemistry, Key Laboratory of Mesoscopic Chemistry of Ministry of Education, School of Chemistry and Chemical Engineering, Nanjing University, Nanjing 210023, People's Republic of China
| | - Yuqi Wang
- Institute of Theoretical and Computational Chemistry, Key Laboratory of Mesoscopic Chemistry of Ministry of Education, School of Chemistry and Chemical Engineering, Nanjing University, Nanjing 210023, People's Republic of China
| | - Haodong Zhang
- Institute of Theoretical and Computational Chemistry, Key Laboratory of Mesoscopic Chemistry of Ministry of Education, School of Chemistry and Chemical Engineering, Nanjing University, Nanjing 210023, People's Republic of China
| | - Shuhua Li
- Institute of Theoretical and Computational Chemistry, Key Laboratory of Mesoscopic Chemistry of Ministry of Education, School of Chemistry and Chemical Engineering, Nanjing University, Nanjing 210023, People's Republic of China
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35
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Ren M, Liu X, Zhang L, Lin X, Wu W, Chen Z. Compact and accurate ab initio valence bond wave functions for electron transfer: the classic but challenging covalent-ionic interaction in LiF. J Chem Phys 2022; 157:084106. [DOI: 10.1063/5.0097614] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
The paper combines the valence bond block diabatization approach (VBBDA) with the idea of orbital breathing. With highly compact wave functions, the breathing orbital valence bond (BOVB) method is applied to investigate several atomic and molecular properties including the electron affinity of F, the adiabatic and diabatic potential energy curves and the dipole moment curves of the two lowest-lying 1Σ+ states, the electronic coupling curve and the crossing distance of the two diabatic states, and the spectroscopic constants of the ground states for LiF. The configuration selection scheme proposed in this work is quite general, requiring only the selection of several de-excitation and excitation orbitals in a sense like the restricted active space self-consistent field method. Practically, this is also the first time that BOVB results are extrapolated to complete basis set limit. Armed with the chemical intuition provided by VB theory, the classic but challenging covalent-ionic interaction in the title molecule is not only conceptually interpreted but is also accurately computed.
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Affiliation(s)
- Mingxing Ren
- College of Chemistry and Chemical Engineering, Xiamen University, China
| | | | - Lina Zhang
- College of Chemistry and Chemical Engineering, Xiamen University, China
| | | | - Wei Wu
- Chemistry, Xiamen University, China
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36
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Magoulas I, Shen J, Piecuch P. Addressing strong correlation by approximate coupled-pair methods with active-space and full treatments of three-body clusters. Mol Phys 2022. [DOI: 10.1080/00268976.2022.2057365] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/18/2022]
Affiliation(s)
- Ilias Magoulas
- Department of Chemistry, Michigan State University, East Lansing, MI, USA
| | - Jun Shen
- Department of Chemistry, Michigan State University, East Lansing, MI, USA
| | - Piotr Piecuch
- Department of Chemistry, Michigan State University, East Lansing, MI, USA
- Department of Physics and Astronomy, Michigan State University, East Lansing, MI, USA
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37
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Zhang N, Xiao Y, Liu W. SOiCI and iCISO: combining iterative configuration interaction with spin-orbit coupling in two ways. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2022; 34:224007. [PMID: 35287124 DOI: 10.1088/1361-648x/ac5db4] [Citation(s) in RCA: 10] [Impact Index Per Article: 5.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/26/2022] [Accepted: 03/14/2022] [Indexed: 06/14/2023]
Abstract
The near-exact iCIPT2 approach for strongly correlated systems of electrons, which stems from the combination of iterative configuration interaction (iCI, an exact solver of full CI) with configuration selection for static correlation and second-order perturbation theory (PT2) for dynamic correlation, is extended to the relativistic domain. In the spirit of spin separation, relativistic effects are treated in two steps: scalar relativity is treated by the infinite-order, spin-free part of the exact two-component (X2C) relativistic Hamiltonian, whereas spin-orbit coupling (SOC) is treated by the first-order, Douglas-Kroll-Hess-like SOC operator derived from the same X2C Hamiltonian. Two possible combinations of iCIPT2 with SOC are considered, i.e., SOiCI and iCISO. The former treats SOC and electron correlation on an equal footing, whereas the latter treats SOC in the spirit of state interaction, by constructing and diagonalizing an effective spin-orbit Hamiltonian matrix in a small number of correlated scalar states. Both double group and time reversal symmetries are incorporated to simplify the computation. Pilot applications reveal that SOiCI is very accurate for the spin-orbit splitting (SOS) of heavy atoms, whereas the computationally very cheap iCISO can safely be applied to the SOS of light atoms and even of systems containing heavy atoms when SOC is largely quenched by ligand fields.
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Affiliation(s)
- Ning Zhang
- Beijing National Laboratory for Molecular Sciences, Institute of Theoretical and Computational Chemistry, College of Chemistry and Molecular Engineering, Peking University, Beijing 100871, People's Republic of China
| | - Yunlong Xiao
- Beijing National Laboratory for Molecular Sciences, Institute of Theoretical and Computational Chemistry, College of Chemistry and Molecular Engineering, Peking University, Beijing 100871, People's Republic of China
| | - Wenjian Liu
- Qingdao Institute for Theoretical and Computational Sciences, Institute of Frontier and Interdisciplinary Science, Shandong University, Qingdao, Shandong 266237, People's Republic of China
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38
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Weser O, Liebermann N, Kats D, Alavi A, Li Manni G. Spin Purification in Full-CI Quantum Monte Carlo via a First-Order Penalty Approach. J Phys Chem A 2022; 126:2050-2060. [PMID: 35298155 PMCID: PMC8978180 DOI: 10.1021/acs.jpca.2c01338] [Citation(s) in RCA: 7] [Impact Index Per Article: 3.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/05/2022]
Abstract
![]()
In this article,
we demonstrate that a first-order spin penalty
scheme can be efficiently applied to the Slater determinant based
Full-CI Quantum Monte Carlo (FCIQMC) algorithm, as a practical route
toward spin purification. Two crucial applications are presented to
demonstrate the validity and robustness of this scheme: the 1Δg ← 3Σg vertical excitation in O2 and
key spin gaps in a [Mn3(IV)O4] cluster.
In the absence of a robust spin adaptation/purification technique,
both applications would be unattainable by Slater determinant based
ground state methods, with any starting wave function collapsing into
the higher-spin ground state during the optimization. This strategy
can be coupled to other algorithms that use the Slater determinant
based FCIQMC algorithm as configuration interaction eigensolver, including
the Stochastic Generalized Active Space, the similarity-transformed
FCIQMC, the tailored-CC, and second-order perturbation theory approaches.
Moreover, in contrast to the GUGA-FCIQMC technique, this strategy
features both spin projection and total spin adaptation, making it
appealing when solving anisotropic Hamiltonians. It also provides
spin-resolved reduced density matrices, important for the investigation
of spin-dependent properties in polynuclear transition metal clusters,
such as the hyperfine-coupling constants.
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Affiliation(s)
- Oskar Weser
- Max-Planck-Institute for Solid State Research, 70569 Stuttgart, Germany
| | - Niklas Liebermann
- Max-Planck-Institute for Solid State Research, 70569 Stuttgart, Germany
| | - Daniel Kats
- Max-Planck-Institute for Solid State Research, 70569 Stuttgart, Germany
| | - Ali Alavi
- Max-Planck-Institute for Solid State Research, 70569 Stuttgart, Germany.,Department of Chemistry, University of Cambridge, Lensfield Road, Cambridge CB2 1EW, U.K
| | - Giovanni Li Manni
- Max-Planck-Institute for Solid State Research, 70569 Stuttgart, Germany
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39
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Fan JQ, Zhang WY, Ren Q, Chen F. Calculations of atomisation energy and singlet–triplet gap with iterative multireference configuration interaction. Mol Phys 2022. [DOI: 10.1080/00268976.2022.2048109] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/18/2022]
Affiliation(s)
- Jia-Qi Fan
- Department of Chemistry and Chemical Engineering, School of Chemistry and Biological Engineering, University of Science and Technology Beijing, Beijing, People’s Republic of China
- Beijing Key Laboratory for Science and Application of Functional Molecular and Crystalline Materials, Beijing, People’s Republic of China
| | - Wen-Yan Zhang
- Department of Chemistry and Chemical Engineering, School of Chemistry and Biological Engineering, University of Science and Technology Beijing, Beijing, People’s Republic of China
- Beijing Key Laboratory for Science and Application of Functional Molecular and Crystalline Materials, Beijing, People’s Republic of China
| | - Qing Ren
- Department of Chemistry and Chemical Engineering, School of Chemistry and Biological Engineering, University of Science and Technology Beijing, Beijing, People’s Republic of China
- Beijing Key Laboratory for Science and Application of Functional Molecular and Crystalline Materials, Beijing, People’s Republic of China
| | - Feiwu Chen
- Department of Chemistry and Chemical Engineering, School of Chemistry and Biological Engineering, University of Science and Technology Beijing, Beijing, People’s Republic of China
- Beijing Key Laboratory for Science and Application of Functional Molecular and Crystalline Materials, Beijing, People’s Republic of China
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40
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Mejuto-Zaera C, Tzeli D, Williams-Young D, Tubman NM, Matoušek M, Brabec J, Veis L, Xantheas SS, de Jong WA. The Effect of Geometry, Spin, and Orbital Optimization in Achieving Accurate, Correlated Results for Iron-Sulfur Cubanes. J Chem Theory Comput 2022; 18:687-702. [PMID: 35034448 DOI: 10.1021/acs.jctc.1c00830] [Citation(s) in RCA: 3] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/18/2022]
Abstract
Iron-sulfur clusters comprise an important functional motif in the catalytic centers of biological systems, capable of enabling important chemical transformations at ambient conditions. This remarkable capability derives from a notoriously complex electronic structure that is characterized by a high density of states that is sensitive to geometric changes. The spectral sensitivity to subtle geometric changes has received little attention from correlated, large active space calculations, owing partly to the exceptional computational complexity for treating these large and correlated systems accurately. To provide insight into this aspect, we report the first Complete Active Space Self Consistent Field (CASSCF) calculations for different geometries of the [Fe(II/III)4S4(SMe)4]-2 clusters using two complementary, correlated solvers: spin-pure Adaptive Sampling Configuration Interaction (ASCI) and Density Matrix Renormalization Group (DMRG). We find that the previously established picture of a double-exchange driven magnetic structure, with minute energy gaps (<1 mHa) between consecutive spin states, has a weak dependence on the underlying geometry. However, the spin gap between the singlet and the spin state 2S + 1 = 19, corresponding to a maximal number of Fe-d electrons being unpaired and of parallel spin, is strongly geometry dependent, changing by a factor of 3 upon slight deformations that are still within biologically relevant parameters. The CASSCF orbital optimization procedure, using active spaces as large as 86 electrons in 52 orbitals, was found to reduce this gap compared to typical mean-field orbital approaches. Our results show the need for performing large active space calculations to unveil the challenging electronic structure of these complex catalytic centers and should serve as accurate starting points for fully correlated treatments upon inclusion of dynamical correlation outside the active space.
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Affiliation(s)
- Carlos Mejuto-Zaera
- University of California, Berkeley, California 94720, United States.,Computational Research Division, Lawrence Berkeley National Laboratory, Berkeley, California 94720, United States
| | - Demeter Tzeli
- Laboratory of Physical Chemistry, Department of Chemistry, National and Kapodistrian University of Athens, Panepistimiopolis Zografou, Athens 15784, Greece.,Theoretical and Physical Chemistry Institute, National Hellenic Research Foundation, Vas. Constantinou 48, Athens 11635, Greece
| | - David Williams-Young
- Computational Research Division, Lawrence Berkeley National Laboratory, Berkeley, California 94720, United States
| | - Norm M Tubman
- Quantum Artificial Intelligence Lab. (QuAIL), Exploration Technology Directorate, NASA Ames Research Center, Moffett Field, California 94035, United States
| | - Mikuláš Matoušek
- J. Heyrovský Institute of Physical Chemistry, Academy of Sciences of the Czech Republic, v.v.i., Dolejškova 3, 18223 Prague 8, Czech Republic
| | - Jiri Brabec
- J. Heyrovský Institute of Physical Chemistry, Academy of Sciences of the Czech Republic, v.v.i., Dolejškova 3, 18223 Prague 8, Czech Republic
| | - Libor Veis
- J. Heyrovský Institute of Physical Chemistry, Academy of Sciences of the Czech Republic, v.v.i., Dolejškova 3, 18223 Prague 8, Czech Republic
| | - Sotiris S Xantheas
- Advanced Computing, Mathematics and Data Division, Pacific Northwest National Laboratory, 902 Battelle Boulevard, P.O. Box 999, MS K1-83, Richland, Washington 99352, United States.,Department of Chemistry, University of Washington, Seattle, Washington 98185, United States
| | - Wibe A de Jong
- Computational Research Division, Lawrence Berkeley National Laboratory, Berkeley, California 94720, United States
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41
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Kollmar C, Sivalingam K, Guo Y, Neese F. An efficient implementation of the NEVPT2 and CASPT2 methods avoiding higher-order density matrices. J Chem Phys 2021; 155:234104. [PMID: 34937355 DOI: 10.1063/5.0072129] [Citation(s) in RCA: 14] [Impact Index Per Article: 4.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
A factorization of the matrix elements of the Dyall Hamiltonian in N-electron valence state perturbation theory allowing their evaluation with a computational effort comparable to the one needed for the construction of the third-order reduced density matrix at the most is presented. Thus, the computational bottleneck arising from explicit evaluation of the fourth-order density matrix is avoided. It is also shown that the residual terms arising in the case of an approximate complete active space configuration interaction solution and containing even the fifth-order density matrix for two excitation classes can be evaluated with little additional effort by choosing again a favorable factorization of the corresponding matrix elements. An analogous argument is also provided for avoiding the fourth-order density matrix in complete active space second-order perturbation theory. Practical calculations indicate that such an approach leads to a considerable gain in computational efficiency without any compromise in numerical accuracy or stability.
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Affiliation(s)
- Christian Kollmar
- Max-Planck-Institut für Kohlenforschung, Kaiser-Wilhelm-Platz 1, D-45470 Mülheim an der Ruhr, Germany
| | - Kantharuban Sivalingam
- Max-Planck-Institut für Kohlenforschung, Kaiser-Wilhelm-Platz 1, D-45470 Mülheim an der Ruhr, Germany
| | - Yang Guo
- Qingdao Institute for Theoretical and Computational Sciences, Shandong University, Qingdao, Shandong 266237, China
| | - Frank Neese
- Max-Planck-Institut für Kohlenforschung, Kaiser-Wilhelm-Platz 1, D-45470 Mülheim an der Ruhr, Germany
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42
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Guo Y, Zhang N, Lei Y, Liu W. iCISCF: An Iterative Configuration Interaction-Based Multiconfigurational Self-Consistent Field Theory for Large Active Spaces. J Chem Theory Comput 2021; 17:7545-7561. [PMID: 34757746 DOI: 10.1021/acs.jctc.1c00781] [Citation(s) in RCA: 16] [Impact Index Per Article: 5.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/28/2022]
Abstract
An iterative configuration interaction (iCI)-based multiconfigurational self-consistent field (SCF) theory, iCISCF, is proposed to handle systems that require large active spaces. The success of iCISCF stems from three ingredients: (1) efficient selection of individual configuration state functions spanning the active space while maintaining full spin symmetry; (2) the use of Jacobi rotation for optimization of the active orbitals in conjunction with a quasi-Newton algorithm for the core/active-virtual and core-active orbital rotations; (3) a second-order perturbative treatment of the residual space left over by the selection procedure (i.e., iCISCF(2)). Several examples that go beyond the capability of CASSCF are taken as showcases to reveal the efficacy of iCISCF and iCISCF(2), facilitated by iCAS for imposed automatic selection and localization of active orbitals.
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Affiliation(s)
- Yang Guo
- Qingdao Institute for Theoretical and Computational Sciences, Institute of Frontier and Interdisciplinary Science, Shandong University, Qingdao, Shandong 266237, China
| | - Ning Zhang
- Beijing National Laboratory for Molecular Sciences, Institute of Theoretical and Computational Chemistry, College of Chemistry and Molecular Engineering, Peking University, Beijing 100871, China
| | - Yibo Lei
- Key Laboratory of Synthetic and Natural Functional Molecule Chemistry of Ministry of Education, College of Chemistry and Materials Science, Shaanxi Key Laboratory of Physico-Inorganic Chemistry, Northwest University, Xi'an, Shaanxi 710127, China
| | - Wenjian Liu
- Qingdao Institute for Theoretical and Computational Sciences, Institute of Frontier and Interdisciplinary Science, Shandong University, Qingdao, Shandong 266237, China
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43
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Neville SP, Schuurman MS. Removing the Deadwood from DFT/MRCI Wave Functions: The p-DFT/MRCI Method. J Chem Theory Comput 2021; 17:7657-7665. [PMID: 34861111 DOI: 10.1021/acs.jctc.1c00959] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/30/2022]
Abstract
The combined density functional theory and multireference configuration interaction (DFT/MRCI) method is a powerful tool for the calculation of excited electronic states of large molecules. There exists, however, a large amount of superfluous configurations in a typical DFT/MRCI wave function. We show that this deadwood may be effectively removed using a simple configuration pruning algorithm based on second-order Epstein-Nesbet perturbation theory. The resulting method, which we denote p-DFT/MRCI, is shown to result in orders of magnitude saving in computational timings, while retaining the accuracy of the original DFT/MRCI method.
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Affiliation(s)
- Simon P Neville
- National Research Council of Canada, 100 Sussex Drive, Ottawa, Ontario K1A 0R6, Canada
| | - Michael S Schuurman
- National Research Council of Canada, 100 Sussex Drive, Ottawa, Ontario K1A 0R6, Canada.,Department of Chemistry and Biomolecular Sciences, University of Ottawa, 10 Marie Curie, Ottawa, Ontario K1N 6N5, Canada
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44
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Gururangan K, Deustua JE, Shen J, Piecuch P. High-level coupled-cluster energetics by merging moment expansions with selected configuration interaction. J Chem Phys 2021; 155:174114. [PMID: 34742204 DOI: 10.1063/5.0064400] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
Inspired by our earlier semi-stochastic work aimed at converging high-level coupled-cluster (CC) energetics [J. E. Deustua, J. Shen, and P. Piecuch, Phys. Rev. Lett. 119, 223003 (2017) and J. E. Deustua, J. Shen, and P. Piecuch, J. Chem. Phys. 154, 124103 (2021)], we propose a novel form of the CC(P; Q) theory in which the stochastic Quantum Monte Carlo propagations, used to identify dominant higher-than-doubly excited determinants, are replaced by the selected configuration interaction (CI) approach using the perturbative selection made iteratively (CIPSI) algorithm. The advantages of the resulting CIPSI-driven CC(P; Q) methodology are illustrated by a few molecular examples, including the dissociation of F2 and the automerization of cyclobutadiene, where we recover the electronic energies corresponding to the CC calculations with a full treatment of singles, doubles, and triples based on the information extracted from compact CI wave functions originating from relatively inexpensive Hamiltonian diagonalizations.
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Affiliation(s)
- Karthik Gururangan
- Department of Chemistry, Michigan State University, East Lansing, Michigan 48824, USA
| | - J Emiliano Deustua
- Department of Chemistry, Michigan State University, East Lansing, Michigan 48824, USA
| | - Jun Shen
- Department of Chemistry, Michigan State University, East Lansing, Michigan 48824, USA
| | - Piotr Piecuch
- Department of Chemistry, Michigan State University, East Lansing, Michigan 48824, USA
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Song Y, Guo Y, Lei Y, Zhang N, Liu W. The Static-Dynamic-Static Family of Methods for Strongly Correlated Electrons: Methodology and Benchmarking. Top Curr Chem (Cham) 2021; 379:43. [PMID: 34724123 DOI: 10.1007/s41061-021-00351-9] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.7] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/15/2021] [Accepted: 09/15/2021] [Indexed: 11/28/2022]
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 [Formula: see text] matrix for [Formula: see text] 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 [Formula: see text] 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.
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Affiliation(s)
- Yangyang Song
- Qingdao Institute for Theoretical and Computational Sciences, Institute of Frontier and Interdisciplinary Science, Shandong University, Qingdao, 266237, Shandong, China
| | - Yang Guo
- Qingdao Institute for Theoretical and Computational Sciences, Institute of Frontier and Interdisciplinary Science, Shandong University, Qingdao, 266237, Shandong, China
| | - Yibo Lei
- Key Laboratory of Synthetic and Natural Functional Molecule of the Ministry of Education, College of Chemistry and Materials Science, Shaanxi key Laboratory of Physico-Inorganic Chemistry, Northwest University, Xi'an, 710127, Shaanxi, China
| | - Ning Zhang
- Beijing National Laboratory for Molecular Sciences, Institute of Theoretical and Computational Chemistry, College of Chemistry and Molecular Engineering, Peking University, Beijing, 100871, China
| | - Wenjian Liu
- Qingdao Institute for Theoretical and Computational Sciences, Institute of Frontier and Interdisciplinary Science, Shandong University, Qingdao, 266237, Shandong, China.
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Damour Y, Véril M, Kossoski F, Caffarel M, Jacquemin D, Scemama A, Loos PF. Accurate full configuration interaction correlation energy estimates for five- and six-membered rings. J Chem Phys 2021; 155:134104. [PMID: 34624964 DOI: 10.1063/5.0065314] [Citation(s) in RCA: 4] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/11/2022] Open
Abstract
Following our recent work on the benzene molecule [P.-F. Loos, Y. Damour, and A. Scemama, J. Chem. Phys. 153, 176101 (2020)], motivated by the blind challenge of Eriksen et al. [J. Phys. Chem. Lett. 11, 8922 (2020)] on the same system, we report accurate full configuration interaction (FCI) frozen-core correlation energy estimates for 12 five- and six-membered ring molecules (cyclopentadiene, furan, imidazole, pyrrole, thiophene, benzene, pyrazine, pyridazine, pyridine, pyrimidine, s-tetrazine, and s-triazine) in the standard correlation-consistent double-ζ Dunning basis set (cc-pVDZ). Our FCI correlation energy estimates, with an estimated error smaller than 1 millihartree, are based on energetically optimized-orbital selected configuration interaction calculations performed with the configuration interaction using a perturbative selection made iteratively algorithm. Having at our disposal these accurate reference energies, the respective performance and convergence properties of several popular and widely used families of single-reference quantum chemistry methods are investigated. In particular, we study the convergence properties of (i) the Møller-Plesset perturbation series up to fifth-order (MP2, MP3, MP4, and MP5), (ii) the iterative approximate coupled-cluster series CC2, CC3, and CC4, and (iii) the coupled-cluster series CCSD, CCSDT, and CCSDTQ. The performance of the ground-state gold standard CCSD(T) as well as the completely renormalized CC model, CR-CC(2,3), is also investigated. We show that MP4 provides an interesting accuracy/cost ratio, while MP5 systematically worsens the correlation energy estimates. In addition, CC3 outperforms CCSD(T) and CR-CC(2,3), as well as its more expensive parent CCSDT. A similar trend is observed for the methods including quadruple excitations, where the CC4 model is shown to be slightly more accurate than CCSDTQ, both methods providing correlation energies within 2 millihartree of the FCI limit.
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Affiliation(s)
- Yann Damour
- Laboratoire de Chimie et Physique Quantiques (UMR 5626), Université de Toulouse, CNRS, UPS, Toulouse, France
| | - Mickaël Véril
- Laboratoire de Chimie et Physique Quantiques (UMR 5626), Université de Toulouse, CNRS, UPS, Toulouse, France
| | - Fábris Kossoski
- Laboratoire de Chimie et Physique Quantiques (UMR 5626), Université de Toulouse, CNRS, UPS, Toulouse, France
| | - Michel Caffarel
- Laboratoire de Chimie et Physique Quantiques (UMR 5626), Université de Toulouse, CNRS, UPS, Toulouse, France
| | - Denis Jacquemin
- Université de Nantes, CNRS, CEISAM UMR 6230, F-44000 Nantes, France
| | - Anthony Scemama
- Laboratoire de Chimie et Physique Quantiques (UMR 5626), Université de Toulouse, CNRS, UPS, Toulouse, France
| | - Pierre-François Loos
- Laboratoire de Chimie et Physique Quantiques (UMR 5626), Université de Toulouse, CNRS, UPS, Toulouse, France
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Li C, Evangelista FA. Spin-free formulation of the multireference driven similarity renormalization group: A benchmark study of first-row diatomic molecules and spin-crossover energetics. J Chem Phys 2021; 155:114111. [PMID: 34551530 DOI: 10.1063/5.0059362] [Citation(s) in RCA: 6] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022] Open
Abstract
We report a spin-free formulation of the multireference (MR) driven similarity renormalization group (DSRG) based on the ensemble normal ordering of Mukherjee and Kutzelnigg [J. Chem. Phys. 107, 432 (1997)]. This ensemble averages over all microstates of a given total spin quantum number, and therefore, it is invariant with respect to SU(2) transformations. As such, all equations may be reformulated in terms of spin-free quantities and they closely resemble those of spin-adapted closed-shell coupled cluster (CC) theory. The current implementation is used to assess the accuracy of various truncated MR-DSRG methods (perturbation theory up to third order and iterative methods with single and double excitations) in computing the constants of 33 first-row diatomic molecules. The accuracy trends for these first-row diatomics are consistent with our previous benchmark on a small subset of closed-shell diatomic molecules. We then present the first MR-DSRG application on transition-metal complexes by computing the spin splittings of the [Fe(H2O)6]2+ and [Fe(NH3)6]2+ molecules. A focal point analysis (FPA) shows that third-order perturbative corrections are essential to achieve reasonably converged energetics. The FPA based on the linearized MR-DSRG theory with one- and two-body operators and up to a quintuple-ζ basis set predicts the spin splittings of [Fe(H2O)6]2+ and [Fe(NH3)6]2+ to be -35.7 and -17.1 kcal mol-1, respectively, showing good agreement with the results of local CC theory with singles, doubles, and perturbative triples.
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Affiliation(s)
- Chenyang Li
- Key Laboratory of Theoretical and Computational Photochemistry, Ministry of Education, College of Chemistry, Beijing Normal University, Beijing 100875, China
| | - Francesco A Evangelista
- Department of Chemistry and Cherry Emerson Center for Scientific Computation, Emory University, Atlanta, Georgia 30322, USA
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Zhao R, Hettich CP, Chen X, Gao J. Minimal-active-space multistate density functional theory for excitation energy involving local and charge transfer states. NPJ COMPUTATIONAL MATERIALS 2021; 7:148. [PMID: 36713117 PMCID: PMC9881008 DOI: 10.1038/s41524-021-00624-3] [Citation(s) in RCA: 11] [Impact Index Per Article: 3.7] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/13/2021] [Accepted: 08/19/2021] [Indexed: 06/15/2023]
Abstract
Multistate density functional theory (MSDFT) employing a minimum active space (MAS) is presented to determine charge transfer (CT) and local excited states of bimolecular complexes. MSDFT is a hybrid wave function theory (WFT) and density functional theory, in which dynamic correlation is first incorporated in individual determinant configurations using a Kohn-Sham exchange-correlation functional. Then, nonorthogonal configuration-state interaction is performed to treat static correlation. Because molecular orbitals are optimized separately for each determinant by including Kohn-Sham dynamic correlation, a minimal number of configurations in the active space, essential to representing low-lying excited and CT states of interest, is sufficient to yield the adiabatic states. We found that the present MAS-MSDFT method provides a good description of covalent and CT excited states in comparison with experiments and high-level computational results. Because of the simplicity and interpretive capability through diabatic configuration weights, the method may be useful in dynamic simulations of CT and nonadiabatic processes.
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Affiliation(s)
- Ruoqi Zhao
- Institute of Systems and Physical Biology, Shenzhen Bay Laboratory, Shenzhen 518055, China
- Institute of Theoretical Chemistry, Jilin University, Changchun, Jilin Province 130023, China
| | - Christian P. Hettich
- Department of Chemistry and Supercomputing Institute, University of Minnesota, Minneapolis, Minnesota 55455, USA
| | - Xin Chen
- Institute of Systems and Physical Biology, Shenzhen Bay Laboratory, Shenzhen 518055, China
- Beijing University Shenzhen Graduate School, Shenzhen 518055, China
| | - Jiali Gao
- Institute of Systems and Physical Biology, Shenzhen Bay Laboratory, Shenzhen 518055, China
- Department of Chemistry and Supercomputing Institute, University of Minnesota, Minneapolis, Minnesota 55455, USA
- Beijing University Shenzhen Graduate School, Shenzhen 518055, China
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Dobrautz W, Weser O, Bogdanov NA, Alavi A, Li Manni G. Spin-Pure Stochastic-CASSCF via GUGA-FCIQMC Applied to Iron-Sulfur Clusters. J Chem Theory Comput 2021; 17:5684-5703. [PMID: 34469685 PMCID: PMC8444347 DOI: 10.1021/acs.jctc.1c00589] [Citation(s) in RCA: 24] [Impact Index Per Article: 8.0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/15/2021] [Indexed: 11/28/2022]
Abstract
In this work, we demonstrate how to efficiently compute the one- and two-body reduced density matrices within the spin-adapted full configuration interaction quantum Monte Carlo (FCIQMC) method, which is based on the graphical unitary group approach (GUGA). This allows us to use GUGA-FCIQMC as a spin-pure configuration interaction (CI) eigensolver within the complete active space self-consistent field (CASSCF) procedure and hence to stochastically treat active spaces far larger than conventional CI solvers while variationally relaxing orbitals for specific spin-pure states. We apply the method to investigate the spin ladder in iron-sulfur dimer and tetramer model systems. We demonstrate the importance of the orbital relaxation by comparing the Heisenberg model magnetic coupling parameters from the CASSCF procedure to those from a CI-only (CASCI) procedure based on restricted open-shell Hartree-Fock orbitals. We show that the orbital relaxation differentially stabilizes the lower-spin states, thus enlarging the coupling parameters with respect to the values predicted by ignoring orbital relaxation effects. Moreover, we find that, while CASCI results are well fit by a simple bilinear Heisenberg Hamiltonian, the CASSCF eigenvalues exhibit deviations that necessitate the inclusion of biquadratic terms in the model Hamiltonian.
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Affiliation(s)
- Werner Dobrautz
- Max
Planck Institute for Solid State Research, Heisenbergstr. 1, 70569 Stuttgart, Germany
| | - Oskar Weser
- Max
Planck Institute for Solid State Research, Heisenbergstr. 1, 70569 Stuttgart, Germany
| | - Nikolay A. Bogdanov
- Max
Planck Institute for Solid State Research, Heisenbergstr. 1, 70569 Stuttgart, Germany
| | - Ali Alavi
- Max
Planck Institute for Solid State Research, Heisenbergstr. 1, 70569 Stuttgart, Germany
- Yusuf
Hamied Department of Chemistry, University
of Cambridge, Lensfield
Road, Cambridge CB2 1EW, United Kingdom
| | - Giovanni Li Manni
- Max
Planck Institute for Solid State Research, Heisenbergstr. 1, 70569 Stuttgart, Germany
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Goings JJ, Hu H, Yang C, Li X. Reinforcement Learning Configuration Interaction. J Chem Theory Comput 2021; 17:5482-5491. [PMID: 34423637 DOI: 10.1021/acs.jctc.1c00010] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Abstract
Selected configuration interaction (sCI) methods exploit the sparsity of the full configuration interaction (FCI) wave function, yielding significant computational savings and wave function compression without sacrificing the accuracy. Despite recent advances in sCI methods, the selection of important determinants remains an open problem. We explore the possibility of utilizing reinforcement learning approaches to solve the sCI problem. By mapping the configuration interaction problem onto a sequential decision-making process, the agent learns on-the-fly which determinants to include and which to ignore, yielding a compressed wave function at near-FCI accuracy. This method, which we call reinforcement-learned configuration interaction, adds another weapon to the sCI arsenal and highlights how reinforcement learning approaches can potentially help solve challenging problems in electronic structure theory.
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Affiliation(s)
- Joshua J Goings
- Department of Chemistry, University of Washington, Seattle, Washington 98195, United States
| | - Hang Hu
- Department of Chemistry, University of Washington, Seattle, Washington 98195, United States
| | - Chao Yang
- Computational Research Division, Lawrence Berkeley National Laboratory, Berkeley, California 94720, United States
| | - Xiaosong Li
- Department of Chemistry, University of Washington, Seattle, Washington 98195, United States
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