1
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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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2
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Li C, Mao S, Huang R, Evangelista FA. Frozen Natural Orbitals for the State-Averaged Driven Similarity Renormalization Group. J Chem Theory Comput 2024; 20:4170-4181. [PMID: 38747709 DOI: 10.1021/acs.jctc.4c00152] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 05/29/2024]
Abstract
We present a reduced-cost implementation of the state-averaged driven similarity renormalization group (SA-DSRG) based on the frozen natural orbital (FNO) approach. The natural orbitals (NOs) are obtained by diagonalizing the one-body reduced density matrix from SA-DSRG second-order perturbation theory (SA-DSRG-PT2). We consider three criteria to truncate the virtual NOs for the subsequent electron correlation treatment beyond SA-DSRG-PT2. An additive second-order correction is applied to the SA-DSRG Hamiltonian to reintroduce correlation effects from the discarded orbitals. The FNO SA-DSRG method is benchmarked on 35 small organic molecules in the QUEST database. When keeping 98-99% of the cumulative occupation numbers, the mean absolute error in the vertical transition energies due to FNO is less than 0.01 eV. Using the same FNO threshold, we observe a speedup of 9 times compared to the conventional SA-DSRG implementation for nickel carbonyl with a quadruple-ζ basis set. The FNO approach enables nonperturbative SA-DSRG computations on chloroiron corrole [FeCl(C19H11N4)] with more than 1000 basis functions, surpassing the current limit of a conventional implementation.
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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
| | - Shuxian Mao
- Key Laboratory of Theoretical and Computational Photochemistry, Ministry of Education, College of Chemistry, Beijing Normal University, Beijing 100875, China
| | - Renke Huang
- 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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3
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Tuckman H, Neuscamman E. Aufbau Suppressed Coupled Cluster Theory for Electronically Excited States. J Chem Theory Comput 2024; 20:2761-2773. [PMID: 38502102 DOI: 10.1021/acs.jctc.3c01285] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 03/20/2024]
Abstract
We introduce an approach to improve single-reference coupled cluster theory in settings where the Aufbau determinant is absent from or plays only a small role in the true wave function. Using a de-excitation operator that can be efficiently hidden within a similarity transform, we create a coupled cluster wave function in which de-excitations work to suppress the Aufbau determinant and produce wave functions dominated by other determinants. Thanks to an invertible and fully exponential form, the approach is systematically improvable, size consistent, size extensive, and, interestingly, size intensive in a granular way that should make the adoption of some ground state techniques, such as local correlation, relatively straightforward. In this initial study, we apply the general formalism to create a state-specific method for orbital-relaxed, singly excited states. We find that this approach matches the accuracy of similar-cost equation-of-motion methods in valence excitations while offering improved accuracy for charge transfer states. We also find the approach to be more accurate than excited-state-specific perturbation theory in both types of states.
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Affiliation(s)
- Harrison Tuckman
- Department of Chemistry, University of California, Berkeley, California 94720, United States
| | - Eric Neuscamman
- Department of Chemistry, University of California, Berkeley, California 94720, United States
- Chemical Sciences Division, Lawrence Berkeley National Laboratory, Berkeley, California 94720, United States
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4
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Schraivogel T, Kats D. Two determinant distinguishable cluster. J Chem Phys 2024; 160:124109. [PMID: 38526108 DOI: 10.1063/5.0199274] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/22/2024] [Accepted: 03/06/2024] [Indexed: 03/26/2024] Open
Abstract
A two reference determinant version of the distinguishable cluster with singles and doubles (DCSD) has been developed. We have implemented the two determinant distinguishable cluster (2D-DCSD) and the corresponding traditional 2D-CCSD method in a new open-source package written in Julia called ElemCo.jl. The methods were benchmarked on singlet and triplet excited states of valence and Rydberg character, as well as for singlet-triplet gaps of diradicals. It is demonstrated that the distinguishable cluster approximation improves the accuracy of 2D-CCSD.
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Affiliation(s)
- Thomas Schraivogel
- Max Planck Institute for Solid State Research, Heisenbergstraße 1, 70569 Stuttgart, Germany
| | - Daniel Kats
- Max Planck Institute for Solid State Research, Heisenbergstraße 1, 70569 Stuttgart, Germany
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5
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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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6
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Zielinski P, Black JA, Köhn A. Performance Tests of the Second-Order Approximate Internally Contracted Multireference Coupled-Cluster Singles and Doubles Method icMRCC2. J Chem Theory Comput 2023; 19:8671-8688. [PMID: 37991987 PMCID: PMC10720349 DOI: 10.1021/acs.jctc.3c00969] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/05/2023] [Revised: 11/03/2023] [Accepted: 11/06/2023] [Indexed: 11/24/2023]
Abstract
Benchmark results are presented for the second-order approximation of the internally contracted multireference coupled-cluster method with single and double excitations, icMRCC2 [Köhn, Bargholz, J. Chem. Phys. 2019, 151, 041106], which was designed as a multireference analogue of the single-reference second-order approximate coupled-cluster method CC2 [Christiansen, Koch, Jørgensen, Chem. Phys. Lett. 1995, 243, 409-418]. Vertical excitation energies of various small to medium-sized organic molecules are investigated based on established test sets from the literature. Additionally, the spectroscopic constants of ground and excited states of diatomics and the geometric parameters of excited triatomic molecules were determined and compared to the experimental data. The results show that the method clearly extends the applicability of single-reference CC2, including doubly excited states, and also artifacts of CC2 like too low Rydberg excitations and too weak multiple bonds are eliminated. The method is computationally more demanding than standard multireference second-order perturbation theories but improves significantly in accuracy, as shown by the benchmark results. In addition, it is demonstrated that small active spaces are often sufficient to obtain accurate energies with icMRCC2. Example applications like the automerization of cyclobutadiene, the deactivation pathway of ethylene, and the excited states of an iron complex with a noninnocent nitrosyl ligand demonstrate the potential of icMRCC2 in cases with strong multireference character.
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Affiliation(s)
- Patrik Zielinski
- Institute for Theoretical
Chemistry, University of Stuttgart, Paffenwaldring 55, Stuttgart D-70569, Germany
| | | | - Andreas Köhn
- Institute for Theoretical
Chemistry, University of Stuttgart, Paffenwaldring 55, Stuttgart D-70569, Germany
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7
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de Moraes MMF, Aoto YA. Multi- d-Occupancy as an Alternative Definition for the Double d-Shell Effect. J Phys Chem A 2023; 127:10075-10090. [PMID: 37983730 DOI: 10.1021/acs.jpca.3c04709] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/22/2023]
Abstract
Despite the prevalence of first-row transition metal-containing compounds in virtually all areas of chemistry, the accurate modeling of these systems is a known challenge for the theoretical chemistry community. Such a challenge is shown in a myriad of facets; among them are difficulties in defining ground-state multiplicities, disagreement in the results from methods considered highly accurate, and convergence problems in calculations for excited states. These problems cause a scarcity of reliable theoretical data for transition metal-containing systems. In this work, we explore the double d-shell effect that plagues and makes the application of multireference methods to this type of system difficult. We propose an alternative definition for this effect based on the mixing among d-occupancy configurations or the multi-d-occupancy character of the wave function. Moreover, we present a protocol able to include this effect in multireference calculations using an active space smaller than that usually used in the literature. A molybdenum-copper model system and its copper subsystem are used as example study cases, in particular, the molybdenum-copper charge transfer of the former and the electron affinity of the latter. We have shown that our alternative definition can be used to analyze their reference wave functions qualitatively. Based on this qualitative description, it is possible to optimize an active space without a second d-shell able to obtain relative energies accurately. Seeing the double d-shell effect through the lens of a multi-d-occupancy character, it is possible to correctly describe the wave function, improve the accuracy of the relative energies, and reduce the computational cost of multireference calculations. That way, we believe that this alternative definition has the potential to improve the modeling of first-row transition metal-containing compounds both for their ground and excited electronic structures.
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Affiliation(s)
- Matheus Morato F de Moraes
- Center of Mathematics Computing and Cognition, Federal University of ABC (UFABC), Santo André, SP 09280-560, Brazil
| | - Yuri Alexandre Aoto
- Center of Mathematics Computing and Cognition, Federal University of ABC (UFABC), Santo André, SP 09280-560, Brazil
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8
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Tuckman H, Neuscamman E. Excited-State-Specific Pseudoprojected Coupled-Cluster Theory. J Chem Theory Comput 2023; 19:6160-6171. [PMID: 37676752 DOI: 10.1021/acs.jctc.3c00194] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 09/09/2023]
Abstract
We present an excited-state-specific coupled-cluster approach in which both the molecular orbitals and cluster amplitudes are optimized for an individual excited state. The theory is formulated via a pseudoprojection of the traditional coupled-cluster wavefunction that allows correlation effects to be introduced atop an excited-state mean field starting point. The approach shares much in common with ground-state CCSD, including size extensivity and an N6 cost scaling. Preliminary numerical tests show that, when augmented with N5 cost perturbative corrections for key terms, the method can improve over excited-state-specific second-order perturbation theory in valence, charge transfer, and Rydberg states.
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Affiliation(s)
- Harrison Tuckman
- Department of Chemistry, University of California, Berkeley, Berkeley, California 94720, United States
| | - Eric Neuscamman
- Department of Chemistry, University of California, Berkeley, Berkeley, California 94720, United States
- Chemical Sciences Division, Lawrence Berkeley National Laboratory, Berkeley, California 94720, United States
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9
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Nishimoto Y. Analytic first-order derivatives of CASPT2 with IPEA shift. J Chem Phys 2023; 158:2888841. [PMID: 37144712 DOI: 10.1063/5.0147611] [Citation(s) in RCA: 2] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/24/2023] [Accepted: 04/18/2023] [Indexed: 05/06/2023] Open
Abstract
Complete active space second-order perturbation theory (CASPT2) is useful for accurately predicting properties of complex electronic structures, but it is well known that it systematically underestimates excitation energies. The underestimation can be corrected using the ionization potential-electron affinity (IPEA) shift. In this study, analytic first-order derivatives of CASPT2 with the IPEA shift are developed. CASPT2-IPEA is not invariant with respect to rotations among active molecular orbitals, and two additional constraint conditions are necessary in the CASPT2 Lagrangian to formulate analytic derivatives. The method developed here is applied to methylpyrimidine derivatives and cytosine, and minimum energy structures and conical intersections are located. By comparing energies relative to the closed-shell ground state, we find that the agreement with experiments and high-level calculations is indeed improved by the inclusion of the IPEA shift. The agreement of geometrical parameters with high-level calculations may also be improved in some cases.
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Affiliation(s)
- Yoshio Nishimoto
- Graduate School of Science, Kyoto University, Kyoto 606-8502, Japan
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10
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Evangelista FA. Automatic derivation of many-body theories based on general Fermi vacua. J Chem Phys 2022; 157:064111. [PMID: 35963725 DOI: 10.1063/5.0097858] [Citation(s) in RCA: 2] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
This paper describes Wick&d, an implementation of the algebra of second-quantized operators normal ordered with respect to general correlated references and the corresponding Wick theorem [D. Mukherjee, Chem. Phys. Lett. 274, 561 (1997) and W. Kutzelnigg and D. Mukherjee, J. Chem. Phys. 107, 432 (1997)]. Wick&d employs a compact representation of operators and a backtracking algorithm to efficiently evaluate Wick contractions. Since Wick&d can handle both fully and partially contracted terms, it can be applied to both projective and Fock-space many-body formalisms. To demonstrate the usefulness of Wick&d, we use it to evaluate the single-reference coupled cluster equations up to octuple excitations and report an automated derivation and implementation of the second-order driven similarity renormalization group multireference perturbation theory.
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Affiliation(s)
- Francesco A Evangelista
- Department of Chemistry and Cherry Emerson Center for Scientific Computation, Emory University, Atlanta, Georgia 30322, USA
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11
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Monino E, Boggio-Pasqua M, Scemama A, Jacquemin D, Loos PF. Reference Energies for Cyclobutadiene: Automerization and Excited States. J Phys Chem A 2022; 126:4664-4679. [PMID: 35820169 DOI: 10.1021/acs.jpca.2c02480] [Citation(s) in RCA: 8] [Impact Index Per Article: 4.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Abstract
Cyclobutadiene is a well-known playground for theoretical chemists and is particularly suitable to test ground- and excited-state methods. Indeed, due to its high spatial symmetry, especially at the D4h square geometry but also in the D2h rectangular arrangement, the ground and excited states of cyclobutadiene exhibit multiconfigurational characters and single-reference methods, such as standard adiabatic time-dependent density-functional theory (TD-DFT) or standard equation-of-motion coupled cluster (EOM-CC), are notoriously known to struggle in such situations. In this work, using a large panel of methods and basis sets, we provide an extensive computational study of the automerization barrier (defined as the difference between the square and rectangular ground-state energies) and the vertical excitation energies at D2h and D4h equilibrium structures. In particular, selected configuration interaction (SCI), multireference perturbation theory (CASSCF, CASPT2, and NEVPT2), and coupled-cluster (CCSD, CC3, CCSDT, CC4, and CCSDTQ) calculations are performed. The spin-flip formalism, which is known to provide a qualitatively correct description of these diradical states, is also tested within TD-DFT (combined with numerous exchange-correlation functionals) and the algebraic diagrammatic construction [ADC(2)-s, ADC(2)-x, and ADC(3)]. A theoretical best estimate is defined for the automerization barrier and for each vertical transition energy.
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Affiliation(s)
- Enzo Monino
- 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
| | - Anthony Scemama
- 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
| | - Pierre-François Loos
- Laboratoire de Chimie et Physique Quantiques (UMR 5626), Université de Toulouse, CNRS, UPS, 31062 Toulouse, France
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12
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Nishimoto Y, Battaglia S, Lindh R. Analytic First-Order Derivatives of (X)MS, XDW, and RMS Variants of the CASPT2 and RASPT2 Methods. J Chem Theory Comput 2022; 18:4269-4281. [PMID: 35699280 DOI: 10.1021/acs.jctc.2c00301] [Citation(s) in RCA: 19] [Impact Index Per Article: 9.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Abstract
Crossings between states involve complex electronic structures, making the accurate characterization of the crossing point difficult. In this study, the analytic derivatives of three complete active space second-order perturbation theory (CASPT2) variants as well as an extension of the restricted active space (RASPT2) are developed. These variants are applied to locating minimum energy conical intersections. Our results demonstrate that the three CASPT2 variants predict qualitatively similar results, but a recently developed variant, the rotated multistate CASPT2 (RMS-CASPT2), is least sensitive to the number of states considered in the calculation. We demonstrate that CASPT2 and the reference self-consistent field calculations predict qualitatively different energetics and bond lengths.
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Affiliation(s)
- Yoshio Nishimoto
- Graduate School of Science, Kyoto University, Kyoto 606-8502, Japan
| | - Stefano Battaglia
- Department of Chemistry - BMC, Uppsala University, P.O. Box 576, SE-75123 Uppsala, Sweden
| | - Roland Lindh
- Department of Chemistry - BMC, Uppsala University, P.O. Box 576, SE-75123 Uppsala, Sweden
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13
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Elayan IA, Gupta R, Hollett JW. ΔNO and the complexities of electron correlation in simple hydrogen clusters. J Chem Phys 2022; 156:094102. [DOI: 10.1063/5.0073227] [Citation(s) in RCA: 3] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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14
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Huang M, Li C, Evangelista FA. Theoretical Calculation of Core-Excited States along Dissociative Pathways beyond Second-Order Perturbation Theory. J Chem Theory Comput 2021; 18:219-233. [PMID: 34964628 DOI: 10.1021/acs.jctc.1c00884] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/19/2022]
Abstract
We extend the multireference driven similarity renormalization (MR-DSRG) method to compute core-excited states by combining it with a GASSCF treatment of orbital relaxation and static electron correlation effects. We consider MR-DSRG treatments of dynamical correlation truncated at the level of perturbation theory (DSRG-MRPT2/3) and iterative linearized approximations with one- and two-body operators [MR-LDSRG(2)] in combination with a spin-free exact-two-component (X2C) one-electron treatment of scalar relativistic effects. This approach is calibrated and tested on a series of 16 core-excited states of five closed- and open-shell diatomic molecules containing first-row elements (C, N, and O). All GASSCF-MR-DSRG theories show excellent agreement with experimental adiabatic transitions energies, with mean absolute errors ranging between 0.17 and 0.35 eV, even for the challenging partially doubly excited states of the N2+ molecule. The vibrational structure of all these transitions, obtained from using a full potential energy scan, shows a mean absolute error as low as 25 meV for DSRG-MRPT2 and 12/13 meV for DSRG-MRPT3 and MR-LDSRG(2). We generally find that a treatment of dynamical correlation that goes beyond the second-order level in perturbation theory improves the accuracy of the potential energy surface, especially in the bond-dissociation region.
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Affiliation(s)
- Meng Huang
- Department of Chemistry and Cherry Emerson Center for Scientific Computation, Emory University, Atlanta, Georgia 30322, United States
| | - Chenyang Li
- Department of Chemistry and Cherry Emerson Center for Scientific Computation, Emory University, Atlanta, Georgia 30322, United States.,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, United States
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15
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Wang S, Li C, Evangelista FA. Analytic Energy Gradients for the Driven Similarity Renormalization Group Multireference Second-Order Perturbation Theory. J Chem Theory Comput 2021; 17:7666-7681. [PMID: 34839660 DOI: 10.1021/acs.jctc.1c00980] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Abstract
We derive analytic energy gradients of the driven similarity renormalization group (DSRG) multireference second-order perturbation theory (MRPT2) using the method of Lagrange multipliers. In the Lagrangian, we impose constraints for a complete-active-space self-consistent-field reference wave function and the semicanonical orthonormal molecular orbitals. Solving for the associated Lagrange multipliers is found to share the same asymptotic scaling of a single DSRG-MRPT2 energy computation. A pilot implementation of the DSRG-MRPT2 analytic gradients is used to optimize the geometry of the singlet and triplet states of p-benzyne. The equilibrium bond lengths and angles are similar to those computed via other MRPT2s and Mukherjee's multireference coupled cluster theory. An approximate DSRG-MRPT2 method that neglects the contributions of the three-body density cumulant is found to introduce negligible errors in the geometry of p-benzyne, lending itself to a promising low-cost approach for molecular geometry optimizations using large active spaces.
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Affiliation(s)
- Shuhe Wang
- Department of Chemistry and Cherry Emerson Center for Scientific Computation, Emory University, Atlanta, Georgia 30322, United States
| | - 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, United States
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16
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Nottoli T, Gauss J, Lipparini F. Second-Order CASSCF Algorithm with the Cholesky Decomposition of the Two-Electron Integrals. J Chem Theory Comput 2021; 17:6819-6831. [PMID: 34719925 PMCID: PMC8582256 DOI: 10.1021/acs.jctc.1c00327] [Citation(s) in RCA: 7] [Impact Index Per Article: 2.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Abstract
![]()
In this contribution,
we present the implementation of a second-order
complete active space–self-consistent field (CASSCF) algorithm
in conjunction with the Cholesky decomposition of the two-electron
repulsion integrals. The algorithm, called norm-extended optimization,
guarantees convergence of the optimization, but it involves the full
Hessian and is therefore computationally expensive. Coupling the second-order
procedure with the Cholesky decomposition leads to a significant reduction
in the computational cost, reduced memory requirements, and an improved
parallel performance. As a result, CASSCF calculations of larger molecular
systems become possible as a routine task. The performance of the
new implementation is illustrated by means of benchmark calculations
on molecules of increasing size, with up to about 3000 basis functions
and 14 active orbitals.
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Affiliation(s)
- Tommaso Nottoli
- Dipartimento di Chimica e Chimica Industriale, Università di Pisa. Via G. Moruzzi 13, I-56124 Pisa, Italy
| | - Jürgen Gauss
- Department Chemie, Johannes Gutenberg-Universität Mainz, Duesbergweg 10-14, D-55128 Mainz, Germany
| | - Filippo Lipparini
- Dipartimento di Chimica e Chimica Industriale, Università di Pisa. Via G. Moruzzi 13, I-56124 Pisa, Italy
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17
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Margócsy Á, Szabados Á. Dressing of Vertices by Cumulants in Multi-Reference Coupled Cluster. J Chem Theory Comput 2021; 17:6947-6964. [PMID: 34643380 DOI: 10.1021/acs.jctc.1c00730] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Abstract
A new scheme is introduced in Multi-Reference (MR) Coupled Cluster (CC) based on the MR Generalized Normal Ordering (MRGNO) and the corresponding MR Generalized Wick Theorem (MRGWT) of Kutzelnigg and Mukherjee. The key element is the identification of a structure in MRGWT generated terms, facilitated by Goldstone diagram techniques. This allows for bundling the many terms of the MRGWT expansion and introduces a hierarchy in the equations that can be harnessed in devising approximations. One- and two-particle interaction vertices are found to be uniformly substituted for their counterpart dressed by density cumulants. This allows for a straightforward rewriting of the ordinary energy expression of CC with interaction dressed (id) one- and two-particle terms and reveals the presence of three- and higher-rank dressed interaction vertices too. Cumulants appearing out of dressed interaction vertices contribute to the amplitude equations and can be interpreted to have an amplitude dressing role. Dressing of one- and two-particle interaction vertices is the most straightforward to implement and does not hinder computational feasibility, provided that the reference function involves strictly limited active space sizes. The Generalized Valence Bond wave function, underlying pilot numerical tests, fulfills this criterion. Results on multiple bond breaking scenarios point to the need of stepping beyond one- and two-particle id. An extremely simple version of incorporating amplitude dressing in addition to one- and two-particle id is seen to cure the potential energy curves remarkably, stimulating further investigations along this line.
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Affiliation(s)
- Ádám Margócsy
- ELTE Eötvös Loránd University, Faculty of Science, Institute of Chemistry Laboratory of Theoretical Chemistry Hevesy György PhD School of Chemistry, P.O. Box 32, Budapest 1518, Hungary
| | - Ágnes Szabados
- ELTE Eötvös Loránd University, Faculty of Science, Institute of Chemistry Laboratory of Theoretical Chemistry, P.O. Box 32, Budapest 1518, Hungary
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18
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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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19
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Marie A, Kossoski F, Loos PF. Variational coupled cluster for ground and excited states. J Chem Phys 2021; 155:104105. [PMID: 34525834 DOI: 10.1063/5.0060698] [Citation(s) in RCA: 13] [Impact Index Per Article: 4.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
In single-reference coupled-cluster (CC) methods, one has to solve a set of non-linear polynomial equations in order to determine the so-called amplitudes that are then used to compute the energy and other properties. Although it is of common practice to converge to the (lowest-energy) ground-state solution, it is also possible, thanks to tailored algorithms, to access higher-energy roots of these equations that may or may not correspond to genuine excited states. Here, we explore the structure of the energy landscape of variational CC and we compare it with its (projected) traditional version in the case where the excitation operator is restricted to paired double excitations (pCCD). By investigating two model systems (the symmetric stretching of the linear H4 molecule and the continuous deformation of the square H4 molecule into a rectangular arrangement) in the presence of weak and strong correlations, the performance of variational pCCD (VpCCD) and traditional pCCD is gauged against their configuration interaction (CI) equivalent, known as doubly occupied CI, for reference Slater determinants made of ground- or excited-state Hartree-Fock orbitals or state-specific orbitals optimized directly at the VpCCD level. The influence of spatial symmetry breaking is also investigated.
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Affiliation(s)
- Antoine Marie
- 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
| | - Pierre-François Loos
- Laboratoire de Chimie et Physique Quantiques (UMR 5626), Université de Toulouse, CNRS, UPS, Toulouse, France
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20
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Khedkar A, Roemelt M. Modern multireference methods and their application in transition metal chemistry. Phys Chem Chem Phys 2021; 23:17097-17112. [PMID: 34355719 DOI: 10.1039/d1cp02640b] [Citation(s) in RCA: 13] [Impact Index Per Article: 4.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/12/2022]
Abstract
Transition metal chemistry is a challenging playground for quantum chemical methods owing to the simultaneous presence of static and dynamic electron correlation effects in many systems. Wavefunction based multireference (MR) methods constitute a physically sound and systematically improvable Ansatz to deal with this complexity but suffer from some conceptual difficulties and high computational costs. The latter problem partially arises from the unfavorable scaling of the Full Configuration Interaction (Full-CI) problem which in the majority of MR methods is solved for a subset of the molecular orbital space, the so-called active space. In the last years multiple methods such as modern variants of selected CI, Full-CI Quantum Monte Carlo (FCIQMC) and the density matrix renormalization group (DMRG) have been developed that solve the Full-CI problem approximately for a fraction of the computational cost required by conventional techniques thereby significantly extending the range of applicability of modern MR methods. This perspective review outlines recent advancements in the field of MR electronic structure methods together with the resulting chances and challenges for theoretical studies in the field of transition metal chemistry. In light of its emerging importance a special focus is put on the selection of adequate active spaces and the concomitant development of numerous selection aides in recent years.
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Affiliation(s)
- Abhishek Khedkar
- Lehrstuhl für theoretische Chemie, Ruhr-Universität Bochum, D-44780 Bochum, Germany.
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21
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Nishimoto Y. Analytic gradients for restricted active space second-order perturbation theory (RASPT2). J Chem Phys 2021; 154:194103. [PMID: 34240887 DOI: 10.1063/5.0050074] [Citation(s) in RCA: 8] [Impact Index Per Article: 2.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/08/2023] Open
Abstract
The computational cost of analytic derivatives in multireference perturbation theory is strongly affected by the size of the active space employed in the reference self-consistent field calculation. To overcome previous limits on the active space size, the analytic gradients of single-state restricted active space second-order perturbation theory (RASPT2) and its complete active space second-order perturbation theory (CASPT2) have been developed and implemented in a local version of OpenMolcas. Similar to previous implementations of CASPT2, the RASPT2 implementation employs the Lagrangian or Z-vector method. The numerical results show that restricted active spaces with up to 20 electrons in 20 orbitals can now be employed for geometry optimizations.
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Affiliation(s)
- Yoshio Nishimoto
- Graduate School of Science, Kyoto University, Kyoto 606-8502, Japan
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22
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Kessler J, Calcavecchia F, Kühne TD. Artificial Neural Networks as Trial Wave Functions for Quantum Monte Carlo. ADVANCED THEORY AND SIMULATIONS 2021. [DOI: 10.1002/adts.202000269] [Citation(s) in RCA: 7] [Impact Index Per Article: 2.3] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 11/06/2022]
Affiliation(s)
- Jan Kessler
- Dynamics of Condensed Matter and Center for Sustainable Systems Design Chair of Theoretical Chemistry University of Paderborn Warburger Str. 100 D‐33098 Paderborn Germany
| | - Francesco Calcavecchia
- Dynamics of Condensed Matter and Center for Sustainable Systems Design Chair of Theoretical Chemistry University of Paderborn Warburger Str. 100 D‐33098 Paderborn Germany
| | - Thomas D. Kühne
- Dynamics of Condensed Matter and Center for Sustainable Systems Design Chair of Theoretical Chemistry University of Paderborn Warburger Str. 100 D‐33098 Paderborn Germany
- Paderborn Center for Parallel Computing and Institute for Lightweight Design University of Paderborn Warburger Str. 100 D‐33098 Paderborn Germany
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23
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Bartlett RJ, Park YC, Bauman NP, Melnichuk A, Ranasinghe D, Ravi M, Perera A. Index of multi-determinantal and multi-reference character in coupled-cluster theory. J Chem Phys 2020; 153:234103. [PMID: 33353328 DOI: 10.1063/5.0029339] [Citation(s) in RCA: 13] [Impact Index Per Article: 3.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/17/2022] Open
Abstract
A full configuration interaction calculation (FCI) ultimately defines the innate molecular orbital description of a molecule. Its density matrix and the natural orbitals obtained from it quantify the difference between having N-dominantly occupied orbitals in a reference determinant for a wavefunction to describe N-correlated electrons and how many of those N-electrons are left to the remaining virtual orbitals. The latter provides a measure of the multi-determinantal character (MDC) required to be in a wavefunction. MDC is further split into a weak correlation part and a part that indicates stronger correlation often called multi-reference character (MRC). If several virtual orbitals have high occupation numbers, then one might argue that these additional orbitals should be allowed to have a larger role in the calculation, as in MR methods, such as MCSCF, MR-CI, or MR-coupled-cluster (MR-CC), to provide adequate approximations toward the FCI. However, there are problems with any of these MR methods that complicate the calculations compared to the uniformity and ease of application of single-reference CC calculations (SR-CC) and their operationally single-reference equation-of-motion (EOM-CC) extensions. As SR-CC theory is used in most of today's "predictive" calculations, an assessment of the accuracy of SR-CC at some truncation of the cluster operator would help to quantify how large an issue MRC actually is in a calculation, and how it might be alleviated while retaining the convenient SR computational character of CC/EOM-CC. This paper defines indices that identify MRC situations and help assess how reliable a given calculation is.
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Affiliation(s)
- Rodney J Bartlett
- Quantum Theory Project, University of Florida, Gainesville, Florida 32611-8435, USA
| | - Young Choon Park
- Quantum Theory Project, University of Florida, Gainesville, Florida 32611-8435, USA
| | - Nicholas P Bauman
- Quantum Theory Project, University of Florida, Gainesville, Florida 32611-8435, USA
| | - Ann Melnichuk
- Quantum Theory Project, University of Florida, Gainesville, Florida 32611-8435, USA
| | - Duminda Ranasinghe
- Department of Chemical Engineering, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA
| | - Moneesha Ravi
- Quantum Theory Project, University of Florida, Gainesville, Florida 32611-8435, USA
| | - Ajith Perera
- Quantum Theory Project, University of Florida, Gainesville, Florida 32611-8435, USA
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24
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Xu E, Uejima M, Ten-No SL. Towards Near-Exact Solutions of Molecular Electronic Structure: Full Coupled-Cluster Reduction with a Second-Order Perturbative Correction. J Phys Chem Lett 2020; 11:9775-9780. [PMID: 33146534 DOI: 10.1021/acs.jpclett.0c03084] [Citation(s) in RCA: 4] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 06/11/2023]
Abstract
We introduce a new augmented adaptation of the recently developed full coupled-cluster reduction (FCCR) with a second-order perturbative correction, abbreviated as FCCR(2). FCCR is a selected coupled-cluster expansion aimed at optimally reducing the excitation manifold and commutator expansions for high-rank excitations for obtaining accurate solutions of the electronic Schödinger equation in a size-extensive manner. The present FCCR(2) enables estimating the residual correlation of FCCR by the second-order perturbative correction E(2) from the complementary space of the FCCR projection manifold. The linear relationship between E(2) and the energy of FCCR(2) allows accurate estimates of near-exact energies for a wide variety of molecules with strong electron correlation. The potential of the method is demonstrated using challenging cases, the ground-state electronic energy of the benzene molecule in equilibrium and stretched geometries, and the isomerization energy of the transition metal complex [Cu(NH3)]2O22+.
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Affiliation(s)
- Enhua Xu
- Graduate School of Science, Technology, and Innovation, Kobe University, Kobe 657-8501, Japan
| | - Motoyuki Uejima
- Graduate School of Science, Technology, and Innovation, Kobe University, Kobe 657-8501, Japan
| | - Seiichiro L Ten-No
- Graduate School of Science, Technology, and Innovation, Kobe University, Kobe 657-8501, Japan
- Graduate School of System Informatics, Kobe University, Kobe 657-8501, Japan
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25
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Eriksen JJ, Stopkowicz S, Jagau TC, Helgaker T. Foreword: Prof. Gauss Festschrift. Mol Phys 2020. [DOI: 10.1080/00268976.2020.1817247] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/23/2022]
Affiliation(s)
| | - Stella Stopkowicz
- Department Chemie, Johannes Gutenberg-Universität Mainz, Mainz, Germany
| | - Thomas-C. Jagau
- Departement Chemie, Katholieke Universiteit Leuven, Leuven, Belgium
| | - Trygve Helgaker
- Hylleraas Centre for Quantum Molecular Sciences, Department of Chemistry, University of Oslo, Oslo, Norway
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26
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Ghosh S, Kumar Dutta A, de Souza B, Berraud-Pache R, Izsák R. A new density for transition properties within the similarity transformed equation of motion approach. Mol Phys 2020. [DOI: 10.1080/00268976.2020.1818858] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/23/2022]
Affiliation(s)
- Soumen Ghosh
- Max-Planck-Institut für Kohlenforschung, Mülheim an der Ruhr, Germany
| | | | | | | | - Róbert Izsák
- Max-Planck-Institut für Kohlenforschung, Mülheim an der Ruhr, Germany
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27
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Vitale E, Alavi A, Kats D. FCIQMC-Tailored Distinguishable Cluster Approach. J Chem Theory Comput 2020; 16:5621-5634. [PMID: 32786911 PMCID: PMC7482318 DOI: 10.1021/acs.jctc.0c00470] [Citation(s) in RCA: 18] [Impact Index Per Article: 4.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/08/2020] [Indexed: 11/28/2022]
Abstract
The tailored approach is applied to the distinguishable cluster method together with a stochastic FCI solver (FCIQMC). It is demonstrated that the new method is more accurate than the corresponding tailored coupled cluster and the pure distinguishable cluster methods. An F12 correction for tailored methods and FCIQMC is introduced, which drastically improves the basis set convergence. A new black-box approach to define the active space using the natural orbitals from the distinguishable cluster is evaluated and found to be a convenient alternative to the usual CASSCF approach.
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Affiliation(s)
- Eugenio Vitale
- Max Planck Institute for
Solid State Research, Heisenbergstrasse 1, 70569 Stuttgart, Germany
| | - Ali Alavi
- Max Planck Institute for
Solid State Research, Heisenbergstrasse 1, 70569 Stuttgart, Germany
| | - Daniel Kats
- Max Planck Institute for
Solid State Research, Heisenbergstrasse 1, 70569 Stuttgart, Germany
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28
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Bodenstein T, Kvaal S. A state-specific multireference coupled-cluster method based on the bivariational principle. J Chem Phys 2020; 153:024106. [PMID: 32668937 DOI: 10.1063/5.0009429] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/13/2022] Open
Abstract
A state-specific multireference coupled-cluster (MRCC) method based on Arponen's bivariational principle is presented, the bivar-MRCC method. The method is based on single-reference theory and therefore has a relatively straightforward formulation and modest computational complexity. The main difference from established methods is the bivariational formulation, in which independent parameterizations of the wave function (ket) and its complex conjugate (bra) are made. Importantly, this allows manifest multiplicative separability of the state (exact in the extended bivar-MRECC version of the method and approximate otherwise), and additive separability of the energy, while preserving polynomial scaling of the working equations. A feature of the bivariational principle is that the formal bra and ket references can be included as bivariational parameters, which eliminates much of the bias toward the formal reference. A pilot implementation is described, and extensive benchmark calculations on several standard problems are performed. The results from the bivar-MRCC method are comparable to established state-specific multireference methods. Considering the relative affordability of the bivar-MRCC method, it may become a practical tool for non-experts.
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Affiliation(s)
- Tilmann Bodenstein
- Hylleraas Centre for Quantum Molecular Sciences, Department of Chemistry, University of Oslo, P.O. Box 1033 Blindern, N-0315 Oslo, Norway
| | - Simen Kvaal
- Hylleraas Centre for Quantum Molecular Sciences, Department of Chemistry, University of Oslo, P.O. Box 1033 Blindern, N-0315 Oslo, Norway
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29
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Madsen NK, Hansen MB, Worth GA, Christiansen O. MR-MCTDH[n]: Flexible Configuration Spaces and Nonadiabatic Dynamics within the MCTDH[n] Framework. J Chem Theory Comput 2020; 16:4087-4097. [DOI: 10.1021/acs.jctc.0c00379] [Citation(s) in RCA: 4] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/27/2022]
Affiliation(s)
- Niels Kristian Madsen
- Department of Chemistry, University of Aarhus, Langelandsgade 140, DK−8000 Aarhus C, Denmark
| | - Mads Bøttger Hansen
- Department of Chemistry, University of Aarhus, Langelandsgade 140, DK−8000 Aarhus C, Denmark
| | - Graham A. Worth
- Department of Chemistry, University College London, 20, Gordon St., WC1H 0AJ London, United Kingdom
| | - Ove Christiansen
- Department of Chemistry, University of Aarhus, Langelandsgade 140, DK−8000 Aarhus C, Denmark
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30
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Matthews DA, Cheng L, Harding ME, Lipparini F, Stopkowicz S, Jagau TC, Szalay PG, Gauss J, Stanton JF. Coupled-cluster techniques for computational chemistry: The CFOUR program package. J Chem Phys 2020; 152:214108. [DOI: 10.1063/5.0004837] [Citation(s) in RCA: 214] [Impact Index Per Article: 53.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/30/2022] Open
Affiliation(s)
- Devin A. Matthews
- Department of Chemistry, Southern Methodist University, Dallas, Texas 75275, USA
| | - Lan Cheng
- Department of Chemistry, Johns Hopkins University, Baltimore, Maryland 21218, USA
| | - Michael E. Harding
- Institut für Physikalische Chemie, Karlsruher Institut für Technologie (KIT), Kaiserstr. 12, D-76131 Karlsruhe, Germany
| | - Filippo Lipparini
- Dipartimento di Chimica e Chimica Industriale, Università di Pisa, Via G. Moruzzi 13, I-56124 Pisa, Italy
| | - Stella Stopkowicz
- Department Chemie, Johannes Gutenberg-Universität Mainz, Duesbergweg 10-14, D-55128 Mainz, Germany
| | - Thomas-C. Jagau
- Department of Chemistry, University of Munich (LMU), Butenandtstr. 5-13, D-81377 Munich, Germany
| | - Péter G. Szalay
- ELTE Eötvös Loránd University, Institute of Chemistry, Pázmány Péter sétány 1/A, H-1117 Budapest, Hungary
| | - Jürgen Gauss
- Department Chemie, Johannes Gutenberg-Universität Mainz, Duesbergweg 10-14, D-55128 Mainz, Germany
| | - John F. Stanton
- Quantum Theory Project, Departments of Chemistry and Physics, University of Florida, Gainesville, Florida 32611, USA
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31
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Margócsy Á, Szabados Á. Ring coupled cluster doubles at the multireference level. J Chem Phys 2020; 152:204114. [PMID: 32486660 DOI: 10.1063/5.0005075] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
A ring approximation within an internally contracted multireference (MR) Coupled Cluster (CC) framework is worked out and tested. Derivation of equations utilizes MR based, generalized normal ordering and the corresponding generalized Wick-theorem (MR-GWT). Contractions among cluster operators are avoided by adopting a normal ordered exponential ansatz. The original version of the MR ring CC doubles (MR-rCCD) equations [Á. Szabados and Á. Margócsy, Mol. Phys. 115, 2731 (2017)] is rectified in two aspects. On the one hand, over-completeness of double excitations is treated by relying on the concept of frames. On the other hand, restriction on the maximal cumulant rank is lifted from two to four. This is found essential for obtaining reliable correlation corrections to the energy. The MR function underlying the approach is provided by the Generalized Valence Bond (GVB) model. The pair structure of the reference ensures a fragment structure of GVB cumulants. This represents a benefit when evaluating cumulant contractions appearing as a consequence of MR-GWT. In particular, cumulant involving terms remain less expensive than their traditional, pair-contracted counterpart, facilitating an O(N6) eventual scaling of the proposed MR-rCCD method. Pilot applications are presented for covalent bond breaking, deprotonation energies, and torsional potentials.
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Affiliation(s)
- Á Margócsy
- Laboratory of Theoretical Chemistry, Institute of Chemistry, Faculty of Science, ELTE Eötvös Loránd University, Budapest, Hungary
| | - Á Szabados
- Laboratory of Theoretical Chemistry, Institute of Chemistry, Faculty of Science, ELTE Eötvös Loránd University, Budapest, Hungary
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32
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Werner HJ, Knowles PJ, Manby FR, Black JA, Doll K, Heßelmann A, Kats D, Köhn A, Korona T, Kreplin DA, Ma Q, Miller TF, Mitrushchenkov A, Peterson KA, Polyak I, Rauhut G, Sibaev M. The Molpro quantum chemistry package. J Chem Phys 2020; 152:144107. [PMID: 32295355 DOI: 10.1063/5.0005081] [Citation(s) in RCA: 431] [Impact Index Per Article: 107.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/13/2022] Open
Abstract
Molpro is a general purpose quantum chemistry software package with a long development history. It was originally focused on accurate wavefunction calculations for small molecules but now has many additional distinctive capabilities that include, inter alia, local correlation approximations combined with explicit correlation, highly efficient implementations of single-reference correlation methods, robust and efficient multireference methods for large molecules, projection embedding, and anharmonic vibrational spectra. In addition to conventional input-file specification of calculations, Molpro calculations can now be specified and analyzed via a new graphical user interface and through a Python framework.
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Affiliation(s)
- Hans-Joachim Werner
- Institut für Theoretische Chemie, Universität Stuttgart, Pfaffenwaldring 55, 70569 Stuttgart, Germany
| | - Peter J Knowles
- School of Chemistry, Cardiff University, Main Building, Park Place, Cardiff CF10 3AT, United Kingdom
| | - Frederick R Manby
- School of Chemistry, University of Bristol, Cantock's Close, Bristol BS8 1TS, United Kingdom
| | - Joshua A Black
- Institut für Theoretische Chemie, Universität Stuttgart, Pfaffenwaldring 55, 70569 Stuttgart, Germany
| | - Klaus Doll
- Institut für Theoretische Chemie, Universität Stuttgart, Pfaffenwaldring 55, 70569 Stuttgart, Germany
| | - Andreas Heßelmann
- Institut für Theoretische Chemie, Universität Stuttgart, Pfaffenwaldring 55, 70569 Stuttgart, Germany
| | - Daniel Kats
- Max-Planck Institute for Solid State Research, Heisenbergstraße 1, 70569 Stuttgart, Germany
| | - Andreas Köhn
- Institut für Theoretische Chemie, Universität Stuttgart, Pfaffenwaldring 55, 70569 Stuttgart, Germany
| | - Tatiana Korona
- Faculty of Chemistry, University of Warsaw, L. Pasteura 1 St., 02-093 Warsaw, Poland
| | - David A Kreplin
- Institut für Theoretische Chemie, Universität Stuttgart, Pfaffenwaldring 55, 70569 Stuttgart, Germany
| | - Qianli Ma
- Institut für Theoretische Chemie, Universität Stuttgart, Pfaffenwaldring 55, 70569 Stuttgart, Germany
| | - Thomas F Miller
- Division of Chemistry and Chemical Engineering, California Institute of Technology, Pasadena, California 91125, USA
| | | | - Kirk A Peterson
- Department of Chemistry, Washington State University, Pullman, Washington 99164-4630, USA
| | - Iakov Polyak
- School of Chemistry, Cardiff University, Main Building, Park Place, Cardiff CF10 3AT, United Kingdom
| | - Guntram Rauhut
- Institut für Theoretische Chemie, Universität Stuttgart, Pfaffenwaldring 55, 70569 Stuttgart, Germany
| | - Marat Sibaev
- School of Chemistry, Cardiff University, Main Building, Park Place, Cardiff CF10 3AT, United Kingdom
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33
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Reference spaces for multireference coupled-cluster theory: the challenge of the CoH molecule. Theor Chem Acc 2020. [DOI: 10.1007/s00214-020-2584-1] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/24/2022]
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34
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Wu CH, Magers DB, Harding LB, Klippenstein SJ, Allen WD. Reaction Profiles and Kinetics for Radical-Radical Hydrogen Abstraction via Multireference Coupled Cluster Theory. J Chem Theory Comput 2020; 16:1511-1525. [PMID: 32073856 DOI: 10.1021/acs.jctc.9b00966] [Citation(s) in RCA: 4] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Abstract
Radical-radical abstractions in hydrocarbon oxidation chemistry are disproportionation reactions that are generally exothermic with little or no barrier yet are underappreciated and poorly studied. Such challenging multireference electronic structure problems are tackled here using the recently developed state-specific multireference coupled cluster methods Mk-MRCCSD and Mk-MRCCSD(T), as well as the companion perturbation theory Mk-MRPT2 and the established MRCISD, MRCISD+Q, and CASPT2 approaches. Reaction paths are investigated for five prototypes involving radical-radical hydrogen abstraction: H + BeH → H2+ Be, H + NH2 → H2 + NH, CH3 + C2H5 → CH4 + C2H4, H + C2H5 → H2 + C2H4, and H + HCO → H2 + CO. Full configuration interaction (FCI) benchmark computations for the H + BeH, H + NH2, and H + HCO reactions prove that Mk-MRCCSD(T) provides superior accuracy for the interaction energies in the entrance channel, with mean absolute errors less than 0.3 kcal mol-1 and percentage deviations less than 10% over the fragment separations of relevance to kinetics. To facilitate combustion studies, energetics for the CH3 + C2H5, H + C2H5, and H + HCO reactions were computed at each level of theory with correlation-consistent basis sets (cc-pVXZ, X = T, Q, 5) and extrapolated to the complete basis set (CBS) limit. These CBS energies were coupled with CASPT2 projected vibrational frequencies along a minimum energy path to obtain rate constants for these three reactions. The rigorous Mk-MRCCSD(T)/CBS results demonstrate unequivocally that these three reactions proceed with no barrier in the entrance channel, contrary to some earlier predictions. Mk-MRCCSD(T) also reveals that the economical CASPT2 method performs well for large interfragment separations but may deteriorate substantially at shorter distances.
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Affiliation(s)
- Chia-Hua Wu
- Center for Computational Quantum Chemistry and Department of Chemistry, University of Georgia, Athens, Georgia 30602, United States
| | - D Brandon Magers
- Center for Computational Quantum Chemistry and Department of Chemistry, University of Georgia, Athens, Georgia 30602, United States.,Department of Chemistry and Physics, Belhaven University, Jackson, Mississippi 39202, United States
| | - Lawrence B Harding
- Chemical Sciences and Engineering Division, Argonne National Laboratory, Lemont, Illinois 60439, United States
| | - Stephen J Klippenstein
- Chemical Sciences and Engineering Division, Argonne National Laboratory, Lemont, Illinois 60439, United States
| | - Wesley D Allen
- Center for Computational Quantum Chemistry and Department of Chemistry, University of Georgia, Athens, Georgia 30602, United States
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35
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He N, Evangelista FA. A zeroth-order active-space frozen-orbital embedding scheme for multireference calculations. J Chem Phys 2020; 152:094107. [PMID: 33480706 DOI: 10.1063/1.5142481] [Citation(s) in RCA: 10] [Impact Index Per Article: 2.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/11/2022] Open
Abstract
Multireference computations of large-scale chemical systems are typically limited by the computational cost of quantum chemistry methods. In this work, we develop a zeroth-order active space embedding theory [ASET(0)], a simple and automatic approach for embedding any multireference dynamical correlation method based on a frozen-orbital treatment of the environment. ASET(0) is combined with the second-order multireference driven similarity renormalization group and tested on several benchmark problems, including the excitation energy of 1-octene and bond-breaking in ethane and pentyldiazene. Finally, we apply ASET(0) to study the singlet-triplet gap of p-benzyne and 9,10-anthracyne diradicals adsorbed on a NaCl surface. Our results show that despite its simplicity, ASET(0) is a powerful and sufficiently accurate embedding scheme applicable when the coupling between the fragment and the environment is in the weak to medium regime.
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Affiliation(s)
- Nan He
- Department of Chemistry, Cherry Emerson Center for Scientific Computation, Emory University, Atlanta, Georgia 30322, USA
| | - Francesco A Evangelista
- Department of Chemistry, Cherry Emerson Center for Scientific Computation, Emory University, Atlanta, Georgia 30322, USA
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36
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Baiardi A, Reiher M. The density matrix renormalization group in chemistry and molecular physics: Recent developments and new challenges. J Chem Phys 2020; 152:040903. [DOI: 10.1063/1.5129672] [Citation(s) in RCA: 85] [Impact Index Per Article: 21.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 02/03/2023] Open
Affiliation(s)
- Alberto Baiardi
- ETH Zürich, Laboratorium für Physikalische Chemie, Vladimir-Prelog-Weg 2, 8093 Zürich, Switzerland
| | - Markus Reiher
- ETH Zürich, Laboratorium für Physikalische Chemie, Vladimir-Prelog-Weg 2, 8093 Zürich, Switzerland
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37
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Hollett JW, Loos PF. Capturing static and dynamic correlation with ΔNO-MP2 and ΔNO-CCSD. J Chem Phys 2020; 152:014101. [PMID: 31914756 DOI: 10.1063/1.5140669] [Citation(s) in RCA: 11] [Impact Index Per Article: 2.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
The ΔNO method for static correlation is combined with second-order Møller-Plesset perturbation theory (MP2) and coupled-cluster singles and doubles (CCSD) to account for dynamic correlation. The MP2 and CCSD expressions are adapted from finite-temperature CCSD, which includes orbital occupancies and vacancies, and expanded orbital summations. Correlation is partitioned with the aid of damping factors incorporated into the MP2 and CCSD residual equations. Potential energy curves for a selection of diatomics are in good agreement with extrapolated full configuration interaction results and on par with conventional multireference approaches.
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Affiliation(s)
- Joshua W Hollett
- Department of Chemistry, University of Winnipeg, Winnipeg, Manitoba R3B 2G3, Canada
| | - Pierre-François Loos
- Laboratoire de Chimie et Physique Quantiques (UMR 5626), Université de Toulouse, CNRS, UPS, Toulouse, France
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38
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Bauman NP, Low GH, Kowalski K. Quantum simulations of excited states with active-space downfolded Hamiltonians. J Chem Phys 2019; 151:234114. [DOI: 10.1063/1.5128103] [Citation(s) in RCA: 19] [Impact Index Per Article: 3.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- Nicholas P. Bauman
- William R. Wiley Environmental Molecular Sciences Laboratory, Battelle, Pacific Northwest National Laboratory, K8-91, P.O. Box 999, Richland, Washington 99352, USA
| | | | - Karol Kowalski
- William R. Wiley Environmental Molecular Sciences Laboratory, Battelle, Pacific Northwest National Laboratory, K8-91, P.O. Box 999, Richland, Washington 99352, USA
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39
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Tsuchimochi T, Ten-no SL. Second-Order Perturbation Theory with Spin-Symmetry-Projected Hartree–Fock. J Chem Theory Comput 2019; 15:6688-6702. [DOI: 10.1021/acs.jctc.9b00897] [Citation(s) in RCA: 9] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/12/2023]
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40
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Hansen MB, Madsen NK, Zoccante A, Christiansen O. Time-dependent vibrational coupled cluster theory: Theory and implementation at the two-mode coupling level. J Chem Phys 2019; 151:154116. [DOI: 10.1063/1.5117207] [Citation(s) in RCA: 9] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022] Open
Affiliation(s)
- Mads Bøttger Hansen
- Department of Chemistry, Aarhus University, Langelandsgade 140, DK–8000 Aarhus C, Denmark
| | - Niels Kristian Madsen
- Department of Chemistry, Aarhus University, Langelandsgade 140, DK–8000 Aarhus C, Denmark
| | - Alberto Zoccante
- Department of Chemistry, Aarhus University, Langelandsgade 140, DK–8000 Aarhus C, Denmark
| | - Ove Christiansen
- Department of Chemistry, Aarhus University, Langelandsgade 140, DK–8000 Aarhus C, Denmark
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41
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Nishimoto Y. Analytic first-order derivatives of partially contracted n-electron valence state second-order perturbation theory (PC-NEVPT2). J Chem Phys 2019; 151:114103. [PMID: 31542000 DOI: 10.1063/1.5115819] [Citation(s) in RCA: 17] [Impact Index Per Article: 3.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 02/04/2023] Open
Abstract
A balanced treatment of dynamic and static electron correlation is important in computational chemistry, and multireference perturbation theory (MRPT) is able to do this at a reasonable computational cost. In this paper, analytic first-order derivatives, specifically gradients and dipole moments, are developed for a particular MRPT method, state-specific partially contracted n-electron valence state second-order perturbation theory (PC-NEVPT2). Only one linear equation needs to be solved for the derivative calculation if the Z-vector method is employed, which facilitates the practical application of this approach. A comparison of the calculated results with experimental geometrical parameters of O3 indicates excellent agreement although the calculated results for O3 - are slightly outside the experimental error bars. The 0-0 transition energies of various methylpyrimidines and trans-polyacetylene are calculated by performing geometry optimizations and seminumerical second-order geometrical derivative calculations. In particular, the deviations of 0-0 transition energies of trans-polyacetylene from experimental values are consistently less than 0.1 eV with PC-NEVPT2, indicating the reliability of the method. These results demonstrate the importance of adding dynamic electron correlation on top of methods dominated by static electron correlation and of developing analytic derivatives for highly accurate methods.
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Affiliation(s)
- Yoshio Nishimoto
- Fukui Institute for Fundamental Chemistry, Kyoto University, 34-4 Takano Nishihiraki-cho, Sakyo-ku, Kyoto 606-8103, Japan
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42
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Chatterjee K, Sokolov AY. Second-Order Multireference Algebraic Diagrammatic Construction Theory for Photoelectron Spectra of Strongly Correlated Systems. J Chem Theory Comput 2019; 15:5908-5924. [DOI: 10.1021/acs.jctc.9b00528] [Citation(s) in RCA: 9] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Affiliation(s)
- Koushik Chatterjee
- Department of Chemistry and Biochemistry, The Ohio State University, Columbus, Ohio 43210, United States
| | - Alexander Yu. Sokolov
- Department of Chemistry and Biochemistry, The Ohio State University, Columbus, Ohio 43210, United States
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43
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Zhang T, Li C, Evangelista FA. Improving the Efficiency of the Multireference Driven Similarity Renormalization Group via Sequential Transformation, Density Fitting, and the Noninteracting Virtual Orbital Approximation. J Chem Theory Comput 2019; 15:4399-4414. [PMID: 31268704 DOI: 10.1021/acs.jctc.9b00353] [Citation(s) in RCA: 12] [Impact Index Per Article: 2.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Abstract
This study examines several techniques to improve the efficiency of the linearized multireference driven similarity renormalization group truncated to one- and two-body operators [MR-LDSRG(2)]. We propose a sequential MR-LDSRG(2) [sq-MR-LDSRG(2)] scheme, in which one-body substitutions are folded exactly into the Hamiltonian. This new approach is combined with density fitting (DF) to reduce the storage cost of two-electron integrals. To further avoid storage of large four-index intermediates, we propose a noninteracting virtual orbital (NIVO) approximation of the Baker-Campbell-Hausdorff series that neglects commutators terms with three and four virtual indices. The NIVO approximation reduces the computational prefactor of the MR-LDSRG(2), bringing it closer to that of coupled cluster with singles and doubles (CCSD). We test the effect of the DF and NIVO approximations on the MR-LDSRG(2) and sq-MR-LDSRG(2) methods by computing properties of eight diatomic molecules. The diatomic constants obtained by DF-sq-MR-LDSRG(2)+NIVO are found to be as accurate as those from the original MR-LDSRG(2) and coupled cluster theory with singles, doubles, and perturbative triples. Finally, we demonstrate that the DF-sq-MR-LDSRG(2)+NIVO scheme can be applied to chemical systems with more than 550 basis functions by computing the automerization energy of cyclobutadiene with a quintuple-ζ basis set. The predicted automerization energy is found to be similar to the value computed with Mukherjee's state-specific multireference coupled cluster theory with singles and doubles.
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Affiliation(s)
- Tianyuan Zhang
- Department of Chemistry and Cherry L. Emerson Center for Scientific Computation , Emory University , Atlanta , Georgia 30322 , United States
| | - Chenyang Li
- Department of Chemistry and Cherry L. Emerson Center for Scientific Computation , Emory University , Atlanta , Georgia 30322 , United States
| | - Francesco A Evangelista
- Department of Chemistry and Cherry L. Emerson Center for Scientific Computation , Emory University , Atlanta , Georgia 30322 , United States
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44
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Li C, Evangelista FA. Multireference Theories of Electron Correlation Based on the Driven Similarity Renormalization Group. Annu Rev Phys Chem 2019; 70:245-273. [DOI: 10.1146/annurev-physchem-042018-052416] [Citation(s) in RCA: 16] [Impact Index Per Article: 3.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/09/2022]
Abstract
The driven similarity renormalization group (DSRG) provides an alternative way to address the intruder state problem in quantum chemistry. In this review, we discuss recent developments of multireference methods based on the DSRG. We provide a pedagogical introduction to the DSRG and its various extensions and discuss its formal properties in great detail. In addition, we report several illustrative applications of the DSRG to molecular systems.
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Affiliation(s)
- Chenyang Li
- Department of Chemistry and Cherry L. Emerson Center for Scientific Computation, Emory University, Atlanta, Georgia 30322, USA; emails: ,
| | - Francesco A. Evangelista
- Department of Chemistry and Cherry L. Emerson Center for Scientific Computation, Emory University, Atlanta, Georgia 30322, USA; emails: ,
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45
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Hodecker M, Dempwolff AL, Rehn DR, Dreuw A. Algebraic-diagrammatic construction scheme for the polarization propagator including ground-state coupled-cluster amplitudes. I. Excitation energies. J Chem Phys 2019; 150:174104. [DOI: 10.1063/1.5081663] [Citation(s) in RCA: 11] [Impact Index Per Article: 2.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- Manuel Hodecker
- Interdisciplinary Center for Scientific Computing, Heidelberg University, Im Neuenheimer Feld 205, D–69120 Heidelberg, Germany
| | - Adrian L. Dempwolff
- Interdisciplinary Center for Scientific Computing, Heidelberg University, Im Neuenheimer Feld 205, D–69120 Heidelberg, Germany
| | - Dirk R. Rehn
- Interdisciplinary Center for Scientific Computing, Heidelberg University, Im Neuenheimer Feld 205, D–69120 Heidelberg, Germany
| | - Andreas Dreuw
- Interdisciplinary Center for Scientific Computing, Heidelberg University, Im Neuenheimer Feld 205, D–69120 Heidelberg, Germany
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46
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Faulstich FM, Máté M, Laestadius A, Csirik MA, Veis L, Antalik A, Brabec J, Schneider R, Pittner J, Kvaal S, Legeza Ö. Numerical and Theoretical Aspects of the DMRG-TCC Method Exemplified by the Nitrogen Dimer. J Chem Theory Comput 2019; 15:2206-2220. [PMID: 30802406 PMCID: PMC7002028 DOI: 10.1021/acs.jctc.8b00960] [Citation(s) in RCA: 27] [Impact Index Per Article: 5.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/26/2022]
Abstract
![]()
In
this article, we investigate the numerical and theoretical aspects
of the coupled-cluster method tailored by matrix-product states. We
investigate formal properties of the used method, such as energy size
consistency and the equivalence of linked and unlinked formulation.
The existing mathematical analysis is here elaborated in a quantum
chemical framework. In particular, we highlight the use of what we
have defined as a complete active space-external space gap describing
the basis splitting between the complete active space and the external
part generalizing the concept of a HOMO–LUMO gap. Furthermore,
the behavior of the energy error for an optimal basis splitting, i.e.,
an active space choice minimizing the density matrix renormalization
group-tailored coupled-cluster singles doubles error, is discussed.
We show numerical investigations on the robustness with respect to
the bond dimensions of the single orbital entropy and the mutual information,
which are quantities that are used to choose a complete active space.
Moreover, the dependence of the ground-state energy error on the complete
active space has been analyzed numerically in order to find an optimal
split between the complete active space and external space by minimizing
the density matrix renormalization group-tailored coupled-cluster
error.
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Affiliation(s)
- Fabian M Faulstich
- Hylleraas Centre for Quantum Molecular Sciences, Department of Chemistry , University of Oslo , P.O. Box 1033 Blindern, N-0315 Oslo , Norway
| | - Mihály Máté
- Strongly Correlated Systems "Lendület" Research Group , Wigner Research Center for Physics , H-1525 , P.O. Box 49, Budapest , Hungary.,Department of Physics of Complex Systems , Eötvös Loránd University , Pf. 32 , H-1518 Budapest , Hungary
| | - Andre Laestadius
- Hylleraas Centre for Quantum Molecular Sciences, Department of Chemistry , University of Oslo , P.O. Box 1033 Blindern, N-0315 Oslo , Norway
| | - Mihály András Csirik
- Strongly Correlated Systems "Lendület" Research Group , Wigner Research Center for Physics , H-1525 , P.O. Box 49, Budapest , Hungary
| | - 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
| | - Andrej Antalik
- J. Heyrovský Institute of Physical Chemistry , Academy of Sciences of the Czech Republic , v.v.i., Dolejškova 3 , 18223 Prague 8 , Czech Republic.,Faculty of Mathematics and Physics , Charles University , 11636 Prague , Czech Republic
| | - Jiří Brabec
- J. Heyrovský Institute of Physical Chemistry , Academy of Sciences of the Czech Republic , v.v.i., Dolejškova 3 , 18223 Prague 8 , Czech Republic
| | - Reinhold Schneider
- Modeling, Simulation and Optimization in Science, Department of Mathematics , Technische Universität Berlin , Sekretariat MA 5-3, Straße des 17. Juni 136 , 10623 Berlin , Germany
| | - Jiří Pittner
- J. Heyrovský Institute of Physical Chemistry , Academy of Sciences of the Czech Republic , v.v.i., Dolejškova 3 , 18223 Prague 8 , Czech Republic
| | - Simen Kvaal
- Hylleraas Centre for Quantum Molecular Sciences, Department of Chemistry , University of Oslo , P.O. Box 1033 Blindern, N-0315 Oslo , Norway
| | - Örs Legeza
- Strongly Correlated Systems "Lendület" Research Group , Wigner Research Center for Physics , H-1525 , P.O. Box 49, Budapest , Hungary
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47
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Aoto YA, Bargholz A, Kats D, Werner HJ, Köhn A. Perturbation Expansion of Internally Contracted Coupled-Cluster Theory up to Third Order. J Chem Theory Comput 2019; 15:2291-2305. [DOI: 10.1021/acs.jctc.8b01301] [Citation(s) in RCA: 11] [Impact Index Per Article: 2.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/30/2022]
Affiliation(s)
- Yuri Alexandre Aoto
- Institut für Theoretische Chemie, Universität Stuttgart, Pfaffenwaldring 55, D-70569 Stuttgart, Germany
- Center for Mathematics Computing and Cognition, Federal University of ABC (UFABC), Avenida dos Estados 5001, Santo André, Brazil
| | - Arne Bargholz
- Institut für Theoretische Chemie, Universität Stuttgart, Pfaffenwaldring 55, D-70569 Stuttgart, Germany
| | - Daniel Kats
- Institut für Theoretische Chemie, Universität Stuttgart, Pfaffenwaldring 55, D-70569 Stuttgart, Germany
- Max Planck Institute for Solid State Research, Heisenbergstraße 1, 70569 Stuttgart, Germany
| | - Hans-Joachim Werner
- Institut für Theoretische Chemie, Universität Stuttgart, Pfaffenwaldring 55, D-70569 Stuttgart, Germany
| | - Andreas Köhn
- Institut für Theoretische Chemie, Universität Stuttgart, Pfaffenwaldring 55, D-70569 Stuttgart, Germany
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48
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Tsuchimochi T, Ten-No SL. Extending spin-symmetry projected coupled-cluster to large model spaces using an iterative null-space projection technique. J Comput Chem 2018; 40:265-278. [PMID: 30520115 DOI: 10.1002/jcc.25587] [Citation(s) in RCA: 7] [Impact Index Per Article: 1.2] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/26/2018] [Revised: 07/31/2018] [Accepted: 08/01/2018] [Indexed: 11/06/2022]
Abstract
Recently, we introduced an orbital-invariant approximate coupled-cluster (CC) method in the spin-projection manifold. The multi-determinantal property of spin-projection means that the parametrization in the spin-extended CC (ECC) ansatz is nonorthogonal and overcomplete. Therefore, the linear dependencies must be removed by an orthogonalization procedure to obtain meaningful solutions. Multi-reference methods often achieve this by diagonalizing a metric of the equation system, but this is not feasible with ECC because of the enormous size of the metric, a consequence of the incomplete active space of the spin-projected Hartree-Fock reference. As a result, the applicability of ECC has been limited to small benchmark systems, for which the ansatz was shown to be superior to the configuration interaction and linearized approximations. In this article, we provide a solution to this problem that completely avoids the metric diagonalization by iteratively projecting out its null-space from the working equations. As the additional computational cost required for this iterative projection is only marginal, it greatly expands the application range of ECC. We demonstrate the potential of approximate ECC by studying the complete basis set limit of F2 and transition metal complexes such as NiO, Mn2 , and [Cu2 O2 ]2+ , which have all been hindered by the prohibitively large metric size. We also identify the potential inadequacy of the molecular orbitals given by spin-projected Hartree-Fock in some cases, and propose possible solutions. © 2018 Wiley Periodicals, Inc.
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Affiliation(s)
- Takashi Tsuchimochi
- Graduate School of Science, Technology, and Innovation, Kobe University, Kobe, Hyogo, 657-0025, Japan
| | - Seiichiro L Ten-No
- Graduate School of Science, Technology, and Innovation, Kobe University, Kobe, Hyogo, 657-0025, Japan
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49
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Sen A, de Souza B, Huntington LMJ, Krupička M, Neese F, Izsák R. An efficient pair natural orbital based configuration interaction scheme for the calculation of open-shell ionization potentials. J Chem Phys 2018; 149:114108. [DOI: 10.1063/1.5048688] [Citation(s) in RCA: 8] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- Avijit Sen
- Max-Planck-Institut für Kohlenforschung, Kaiser-Wilhelm-Platz 1, D-45470 Mülheim an der Ruhr, Germany
| | - Bernardo de Souza
- Max-Planck-Institute for Chemical Energy Conversion, Mülheim an der Ruhr, Germany
- Universidade Federal de Santa Catarina, Florianópolis, Brazil
| | - Lee M. J. Huntington
- Max-Planck-Institute for Chemical Energy Conversion, Mülheim an der Ruhr, Germany
| | - Martin Krupička
- Max-Planck-Institute for Chemical Energy Conversion, Mülheim an der Ruhr, Germany
- University of Chemistry and Technology, Prague, Czech Republic
| | - Frank Neese
- Max-Planck-Institut für Kohlenforschung, Kaiser-Wilhelm-Platz 1, D-45470 Mülheim an der Ruhr, Germany
| | - Róbert Izsák
- Max-Planck-Institut für Kohlenforschung, Kaiser-Wilhelm-Platz 1, D-45470 Mülheim an der Ruhr, Germany
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50
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Samanta PK, Köhn A. First-order properties from internally contracted multireference coupled-cluster theory with particular focus on hyperfine coupling tensors. J Chem Phys 2018; 149:064101. [DOI: 10.1063/1.5040587] [Citation(s) in RCA: 7] [Impact Index Per Article: 1.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022] Open
Affiliation(s)
| | - Andreas Köhn
- Institut für Theoretische Chemie, Universität Stuttgart, D-70569 Stuttgart, Germany
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