1
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Ünal A, Bozkaya U. Equation-of-motion orbital-optimized coupled-cluster doubles method with the density-fitting approximation: An efficient implementation. J Comput Chem 2024. [PMID: 39235313 DOI: 10.1002/jcc.27495] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/06/2024] [Revised: 06/13/2024] [Accepted: 08/18/2024] [Indexed: 09/06/2024]
Abstract
Orbital-optimized coupled-cluster methods are very helpful for theoretical predictions of the molecular properties of challenging chemical systems, such as excited states. In this research, an efficient implementation of the equation-of-motion orbital-optimized coupled-cluster doubles method with the density-fitting (DF) approach, denoted by DF-EOM-OCCD, is presented. The computational cost of the DF-EOM-OCCD method for excitation energies is compared with that of the conventional EOM-OCCD method. Our results demonstrate that DF-EOM-OCCD excitation energies are dramatically accelerated compared to EOM-OCCD. There are almost 17-fold reductions for theC 5 H 12 $$ {\mathrm{C}}_5{\mathrm{H}}_{12} $$ molecule in an aug-cc-pVTZ basis set with the RHF reference. This dramatic performance improvement comes from the reduced cost of integral transformation with the DF approach and the efficient evaluation of the particle-particle ladder (PPL) term, which is the most expensive term to evaluate. Further, our results show that the DF-EOM-OCCD approach is very helpful for the computation of excitation energies in open-shell molecular systems. Overall, we conclude that our new DF-EOM-OCCD implementation is very promising for the study of excited states in large-sized challenging chemical systems.
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Affiliation(s)
- Aslı Ünal
- Department of Chemistry, Hacettepe University, Ankara, Turkey
| | - Uğur Bozkaya
- Department of Chemistry, Hacettepe University, Ankara, Turkey
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2
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Chen T, Zhang C, Cheng L, Ng KB, Malbrunot-Ettenauer S, Flambaum VV, Lasner Z, Doyle JM, Yu P, Conn CJ, Zhang C, Hutzler NR, Jayich AM, Augenbraun B, DeMille D. Relativistic Exact Two-Component Coupled-Cluster Study of Molecular Sensitivity Factors for Nuclear Schiff Moments. J Phys Chem A 2024. [PMID: 39047199 DOI: 10.1021/acs.jpca.4c02640] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 07/27/2024]
Abstract
Relativistic exact two-component coupled-cluster calculations of molecular sensitivity factors for nuclear Schiff moments (NSMs) are reported. We focus on molecules containing heavy nuclei, especially octupole-deformed nuclei. Analytic relativistic coupled-cluster gradient techniques are used and serve as useful tools for identifying candidate molecules that sensitively probe for physics beyond the Standard Model in the hadronic sector. Notably, these tools enable straightforward "black-box" calculations. Two competing chemical mechanisms that contribute to the NSM are analyzed, illuminating the physics of ligand effects on NSM sensitivity factors.
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Affiliation(s)
- Tianxiang Chen
- Department of Chemistry, The Johns Hopkins University, Baltimore, Maryland 21218, United States
| | - Chaoqun Zhang
- Department of Chemistry, The Johns Hopkins University, Baltimore, Maryland 21218, United States
| | - Lan Cheng
- Department of Chemistry, The Johns Hopkins University, Baltimore, Maryland 21218, United States
| | - Kia Boon Ng
- TRIUMF, 4004 Wesbrook Mall, Vancouver, BC V6T 2A3, Canada
| | - Stephan Malbrunot-Ettenauer
- TRIUMF, 4004 Wesbrook Mall, Vancouver, BC V6T 2A3, Canada
- Department of Physics, University of Toronto, Toronto M5S 1A7, Canada
| | - Victor V Flambaum
- School of Physics, University of New South Wales, Sydney 2052, Australia
| | - Zack Lasner
- Department of Physics, Harvard University, Cambridge, Massachusetts 02138, United States
- Harvard-MIT Center for Ultracold Atoms, Cambridge, Massachusetts 02138, United States
| | - John M Doyle
- Department of Physics, Harvard University, Cambridge, Massachusetts 02138, United States
- Harvard-MIT Center for Ultracold Atoms, Cambridge, Massachusetts 02138, United States
| | - Phelan Yu
- Division of Physics, Mathematics, and Astronomy, California Institute of Technology, Pasadena, California 91125, United States
| | - Chandler J Conn
- Division of Physics, Mathematics, and Astronomy, California Institute of Technology, Pasadena, California 91125, United States
| | - Chi Zhang
- Division of Physics, Mathematics, and Astronomy, California Institute of Technology, Pasadena, California 91125, United States
| | - Nicholas R Hutzler
- Division of Physics, Mathematics, and Astronomy, California Institute of Technology, Pasadena, California 91125, United States
| | - Andrew M Jayich
- Department of Physics, University of California, Santa Barbara, California 93106, United States
| | - Benjamin Augenbraun
- Department of Chemistry, Williams College, 47 Lab Campus Drive, Williamstown, Massachusetts 01267, United States
| | - David DeMille
- Department of Physics, University of Chicago, Chicago, Illinois 60637, United States
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3
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Bartlett RJ. Perspective on Coupled-cluster Theory. The evolution toward simplicity in quantum chemistry. Phys Chem Chem Phys 2024; 26:8013-8037. [PMID: 38390989 DOI: 10.1039/d3cp03853j] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 02/24/2024]
Abstract
Coupled-cluster theory has revolutionized quantum chemistry. It has provided the framework to effectively solve the problem of electron correlation, the main focus of the field for over 60 years. This has enabled ab initio quantum chemistry to provide predictive quality results for most quantities of interest that are obtainable from first-principle calculations. The best that one can do in a basis is the 'full CI,' the exact solution of the non-relativistic Schrödinger equation or, if need be, the relativistic Dirac equation. With due regard to converging the basis set and adequate consideration of higher clusters and relativity in a calculation, virtually predictive results can be obtained. But in addition to its numerical performance, coupled-cluster theory also offers a conceptually new, many-body foundation for the theory that should be appreciated by all practitioners. The latter is emphasized in this perspective, leading to the 'evolution toward simplicity' in the title. The ultimate theory will benefit from the several features that are uniquely exact in coupled-cluster theory and its equation-of-motion (EOM-CC) extensions.
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Affiliation(s)
- Rodney J Bartlett
- Quantum Theory Project, Department of Chemistry, University of Florida, P. O. Box 117200, Gainesville, Florida, USA.
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4
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Rutskoy B, Ozerov G, Bezrukov D. The Role of Bond Functions in Describing Intermolecular Electron Correlation for Van der Waals Dimers: A Study of (CH 4) 2 and Ne 2. Int J Mol Sci 2024; 25:1472. [PMID: 38338750 PMCID: PMC10855067 DOI: 10.3390/ijms25031472] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/16/2023] [Revised: 01/19/2024] [Accepted: 01/22/2024] [Indexed: 02/12/2024] Open
Abstract
We present a study of the intermolecular interactions in van der Waals complexes of methane and neon dimers within the framework of the CCSD method. This approach was implemented and applied to calculate and examine the behavior of the contracted two-particle reduced density matrix (2-RDM). It was demonstrated that the region near the minimum of the two-particle density matrix correlation part, corresponding to the primary bulk of the Coulomb hole contribution, exerts a significant influence on the dispersion interaction energetics of the studied systems. As a result, the bond functions approach was applied to improve the convergence performance for the intermolecular correlation energy results with respect to the size of the atomic basis. For this, substantial acceleration was achieved by introducing an auxiliary basis of bond functions centered on the minima of the 2-RDM. For both methane and neon dimers, this general conclusion was confirmed with a series of CCSD calculations for the 2-RDM and the correlation energies.
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Affiliation(s)
- Bogdan Rutskoy
- National Research Centre “Kurchatov Institute”, Moscow 123182, Russia;
- Institute of Nuclear Physics and Technology, National Research Nuclear University “MEPhI” (Moscow Engineering Physics Institute), Moscow 115409, Russia
- Chemistry Department, M.V. Lomonosov Moscow State University, Moscow 119991, Russia;
| | - Georgiy Ozerov
- Chemistry Department, M.V. Lomonosov Moscow State University, Moscow 119991, Russia;
| | - Dmitry Bezrukov
- Chemistry Department, M.V. Lomonosov Moscow State University, Moscow 119991, Russia;
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5
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Zheng X, Zhang C, Liu J, Cheng L. Geometry Optimizations with Spinor-Based Relativistic Coupled-Cluster Theory. J Chem Phys 2022; 156:151101. [DOI: 10.1063/5.0086281] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
Development of analytic gradients for relativistic coupled-cluster singles and doubles augmented with a non-iterative triples [CCSD(T)] method using an all-electron exact two-component Hamiltonian with atomic mean-field spin-orbit integrals (X2CAMF) is reported. This enables efficient CC geometry optimizations with spin-orbit coupling included in orbitals. The applicability of the implementation is demonstrated using benchmark X2CAMF-CCSD(T) calculations of equilibrium structures and harmonic vibrational frequencies for methyl halides, CH3X, X=Br, I, At, as well as calculations of rotational constants and infrared spectrum for RaSH+, a radioactive molecular ion of interest to spectroscopic study.
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Affiliation(s)
- Xuechen Zheng
- Johns Hopkins University Department of Chemistry, United States of America
| | - Chaoqun Zhang
- Johns Hopkins University Department of Chemistry, United States of America
| | - Junzi Liu
- Chemistry, Johns Hopkins University Department of Chemistry, United States of America
| | - Lan Cheng
- Chemistry, Johns Hopkins University Department of Chemistry, United States of America
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6
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Alagöz Y, Ünal A, Bozkaya U. Efficient implementations of the symmetric and asymmetric triple excitation corrections for the orbital-optimized coupled-cluster doubles method with the density-fitting approximation. J Chem Phys 2021; 155:114104. [PMID: 34551547 DOI: 10.1063/5.0061351] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
Efficient implementations of the symmetric and asymmetric triple excitation corrections for the orbital-optimized coupled-cluster doubles (OCCD) method with the density-fitting approach, denoted by DF-OCCD(T) and DF-OCCD(T)Λ, are presented. The computational cost of the DF-OCCD(T) method is compared with that of the conventional OCCD(T). In the conventional OCCD(T) and OCCD(T)Λ methods, one needs to perform four-index integral transformations at each coupled-cluster doubles iterations, which limits its applications to large chemical systems. Our results demonstrate that DF-OCCD(T) provides dramatically lower computational costs compared to OCCD(T), and there are more than 68-fold reductions in the computational time for the C5H12 molecule with the cc-pVTZ basis set. Our results show that the DF-OCCD(T) and DF-OCCD(T)Λ methods are very helpful for the study of single bond-breaking problems. Performances of the DF-OCCD(T) and DF-OCCD(T)Λ methods are noticeably better than that of the coupled-cluster singles and doubles with perturbative triples [CCSD(T)] method for the potential energy surfaces of the molecules considered. Specifically, the DF-OCCD(T)Λ method provides dramatic improvements upon CCSD(T), and there are 8-14-fold reductions in nonparallelity errors. Overall, we conclude that the DF-OCCD(T)Λ method is very promising for the study of challenging chemical systems, where the CCSD(T) fails.
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Affiliation(s)
- Yavuz Alagöz
- Department of Chemistry, Hacettepe University, Ankara 06800, Turkey
| | - Aslı Ünal
- Department of Chemistry, Hacettepe University, Ankara 06800, Turkey
| | - Uğur Bozkaya
- Department of Chemistry, Hacettepe University, Ankara 06800, Turkey
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7
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Rice JE, Gujarati TP, Motta M, Takeshita TY, Lee E, Latone JA, Garcia JM. Quantum computation of dominant products in lithium-sulfur batteries. J Chem Phys 2021; 154:134115. [PMID: 33832277 DOI: 10.1063/5.0044068] [Citation(s) in RCA: 10] [Impact Index Per Article: 3.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022] Open
Abstract
Quantum chemistry simulations of some industrially relevant molecules are reported, employing variational quantum algorithms for near-term quantum devices. The energies and dipole moments are calculated along the dissociation curves for lithium hydride (LiH), hydrogen sulfide, lithium hydrogen sulfide, and lithium sulfide. In all cases, we focus on the breaking of a single bond to obtain information about the stability of the molecular species being investigated. We calculate energies and a variety of electrostatic properties of these molecules using classical simulators of quantum devices, with up to 21 qubits for lithium sulfide. Moreover, we calculate the ground-state energy and dipole moment along the dissociation pathway of LiH using IBM quantum devices. This is the first example, to the best of our knowledge, of dipole moment calculations being performed on quantum hardware.
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Affiliation(s)
- Julia E Rice
- IBM Quantum, Almaden Research Center, San Jose, California 95120, USA
| | - Tanvi P Gujarati
- IBM Quantum, Almaden Research Center, San Jose, California 95120, USA
| | - Mario Motta
- IBM Quantum, Almaden Research Center, San Jose, California 95120, USA
| | - Tyler Y Takeshita
- Mercedes Benz Research and Development North America, Sunnyvale, California 94085, USA
| | - Eunseok Lee
- Mercedes Benz Research and Development North America, Sunnyvale, California 94085, USA
| | - Joseph A Latone
- IBM Quantum, Almaden Research Center, San Jose, California 95120, USA
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8
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Liu J, Zheng X, Asthana A, Zhang C, Cheng L. Analytic evaluation of energy first derivatives for spin-orbit coupled-cluster singles and doubles augmented with noniterative triples method: General formulation and an implementation for first-order properties. J Chem Phys 2021; 154:064110. [PMID: 33588557 DOI: 10.1063/5.0038779] [Citation(s) in RCA: 8] [Impact Index Per Article: 2.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
A formulation of analytic energy first derivatives for the coupled-cluster singles and doubles augmented with noniterative triples [CCSD(T)] method with spin-orbit coupling included at the orbital level and an implementation for evaluation of first-order properties are reported. The standard density-matrix formulation for analytic CC gradient theory adapted to complex algebra has been used. The orbital-relaxation contributions from frozen core, occupied, virtual, and frozen virtual orbitals to analytic spin-orbit CCSD(T) gradients are fully taken into account and treated efficiently, which is of importance to calculations of heavy elements. Benchmark calculations of first-order properties including dipole moments and electric-field gradients using the corresponding exact two-component property integrals are presented for heavy-element containing molecules to demonstrate the applicability and usefulness of the present analytic scheme.
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Affiliation(s)
- Junzi Liu
- Department of Chemistry, The Johns Hopkins University, Baltimore, Maryland 21218, USA
| | - Xuechen Zheng
- Department of Chemistry, The Johns Hopkins University, Baltimore, Maryland 21218, USA
| | - Ayush Asthana
- Department of Chemistry, The Johns Hopkins University, Baltimore, Maryland 21218, USA
| | - Chaoqun Zhang
- Department of Chemistry, The Johns Hopkins University, Baltimore, Maryland 21218, USA
| | - Lan Cheng
- Department of Chemistry, The Johns Hopkins University, Baltimore, Maryland 21218, USA
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9
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Bozkaya U, Ünal A, Alagöz Y. Energy and analytic gradients for the orbital-optimized coupled-cluster doubles method with the density-fitting approximation: An efficient implementation. J Chem Phys 2020; 153:244115. [PMID: 33380091 DOI: 10.1063/5.0035811] [Citation(s) in RCA: 8] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
Efficient implementations of the orbital-optimized coupled-cluster doubles (or simply "optimized CCD," OCCD, for short) method and its analytic energy gradients with the density-fitting (DF) approach, denoted by DF-OCCD, are presented. In addition to the DF approach, the Cholesky-decomposed variant (CD-OCCD) is also implemented for energy computations. The computational cost of the DF-OCCD method (available in a plugin version of the DFOCC module of PSI4) is compared with that of the conventional OCCD (from the Q-CHEM package). The OCCD computations were performed with the Q-CHEM package in which OCCD are denoted by OD. In the conventional OCCD method, one needs to perform four-index integral transformations at each of the CCD iterations, which limits its applications to large chemical systems. Our results demonstrate that DF-OCCD provides dramatically lower computational costs compared to OCCD, and there are almost eightfold reductions in the computational time for the C6H14 molecule with the cc-pVTZ basis set. For open-shell geometries, interaction energies, and hydrogen transfer reactions, DF-OCCD provides significant improvements upon DF-CCD. Furthermore, the performance of the DF-OCCD method is substantially better for harmonic vibrational frequencies in the case of symmetry-breaking problems. Moreover, several factors make DF-OCCD more attractive compared to CCSD: (1) for DF-OCCD, there is no need for orbital relaxation contributions in analytic gradient computations; (2) active spaces can readily be incorporated into DF-OCCD; (3) DF-OCCD provides accurate vibrational frequencies when symmetry-breaking problems are observed; (4) in its response function, DF-OCCD avoids artificial poles; hence, excited-state molecular properties can be computed via linear response theory; and (5) symmetric and asymmetric triples corrections based on DF-OCCD [DF-OCCD(T)] have a significantly better performance in near degeneracy regions.
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Affiliation(s)
- Uğur Bozkaya
- Department of Chemistry, Hacettepe University, Ankara 06800, Turkey
| | - Aslı Ünal
- Department of Chemistry, Hacettepe University, Ankara 06800, Turkey
| | - Yavuz Alagöz
- Department of Chemistry, Hacettepe University, Ankara 06800, Turkey
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10
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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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11
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Perera A, Bartlett RJ, Sanders BA, Lotrich VF, Byrd JN. Advanced concepts in electronic structure (ACES) software programs. J Chem Phys 2020; 152:184105. [DOI: 10.1063/5.0002581] [Citation(s) in RCA: 17] [Impact Index Per Article: 4.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/09/2023] Open
Affiliation(s)
- Ajith Perera
- Quantum Theory Project, Department of Chemistry, University of Florida, Gainesville, Florida 32605, USA
| | - Rodney J. Bartlett
- Quantum Theory Project, Department of Chemistry, University of Florida, Gainesville, Florida 32605, USA
| | - Beverly A. Sanders
- Department of Computer and Information Science and Engineering, University of Florida, Gainesville, Florida 32605, USA
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12
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Zhou X, Cao Z, Wang F. Analytical energy gradients for ionized states using equation-of-motion coupled-cluster theory with spin-orbit coupling. J Chem Phys 2019; 150:154114. [PMID: 31005096 DOI: 10.1063/1.5088639] [Citation(s) in RCA: 6] [Impact Index Per Article: 1.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022] Open
Abstract
Spin-orbit coupling (SOC) may have a significant effect on the structure and harmonic frequencies of particularly heavy p-block element compounds. However, reports on analytical energy gradients with SOC are scarce, especially for excited states. In this work, we implemented analytical energy gradients for ionized states using the equation-of-motion coupled-cluster (CC) theory at the CC singles and doubles level (EOM-IP-CCSD) with SOC. Effects of SOC on structure and harmonic frequencies as well as properties for both the ground and some excited states of open-shell compounds with one unpaired electron can be investigated efficiently with the present implementation. A closed-shell reference is required in the calculations, and SOC is included in post-Hartree-Fock treatment. Relativistic effective core potentials are employed in dealing with both scalar relativistic effects and SOC, and we treat perturbations that are even under time reversal in this work. Both time-reversal symmetry and double point group symmetry for D2h * and its subgroups are exploited in the implementation. The method is applicable to states which can be reached by removing one electron from a closed-shell reference state. The results of some open-shell cations indicate the importance of SOC on structures and harmonic frequencies of heavy element compounds.
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Affiliation(s)
- Xiaojun Zhou
- Institute of Atomic and Molecular Physics, Key Laboratory of High Energy Density Physics and Technology, Ministry of Education, Sichuan University, Chengdu, People's Republic of China
| | - Zhanli Cao
- School of Science, Xi'an University of Posts and Telecommunications, Xi'an 710121, People's Republic of China
| | - Fan Wang
- Institute of Atomic and Molecular Physics, Key Laboratory of High Energy Density Physics and Technology, Ministry of Education, Sichuan University, Chengdu, People's Republic of China
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13
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Datta D, Gauss J. Accurate Prediction of Hyperfine Coupling Tensors for Main Group Elements Using a Unitary Group Based Rigorously Spin-Adapted Coupled-Cluster Theory. J Chem Theory Comput 2019; 15:1572-1592. [PMID: 30698956 DOI: 10.1021/acs.jctc.8b01048] [Citation(s) in RCA: 10] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Abstract
We present the development of a perturbative triples correction scheme for the previously reported unitary group based spin-adapted combinatoric open-shell coupled-cluster (CC) singles and doubles (COS-CCSD) approach and report on the applications of the newly developed method, termed "COS-CCSD(T)", to the calculation of hyperfine coupling (HFC) tensors for radicals consisting of hydrogen, second- and third-row elements. The COS-CCSD(T) method involves a single noniterative step with [Formula: see text] scaling of the computational cost for the calculation of triples corrections to the energy. The key feature of this development is the use of spatial semicanonical orbitals generated from standard restricted open-shell Hartree-Fock (ROHF) orbitals, which allows the unperturbed Hamiltonian operator to be defined in terms of a diagonal spin-free Fock operator. The HFC tensors are computed as a first-order property via implementation of an analytic derivative scheme. The required one-particle spin density matrix is computed by using one- and two-particle spin-free density matrices that are obtained from the analytic derivative implementation, in this way avoiding the use of any spin-dependent operator and maintaining spin adaptation of the CC wavefunction. Benchmark calculations of HFC tensors for a set of 21 radicals indicate reasonably good agreement of the COS-CCSD(T) results with experiment and a consistent improvement over the COS-CCSD method. We demonstrate that the accuracies of the isotropic hyperfine coupling constants obtained in unrestricted HF (UHF) reference based spin-orbital CCSD(T) calculations deteriorate when spin contamination in the UHF wavefunction is large, and the results may even become qualitatively incorrect when spin polarization is the driving mechanism. Within a similar noniterative perturbative treatment of triple excitations, the spin-adapted COS-CCSD(T) approach produces accurate results, thus ensuring cost-effectiveness together with reliability.
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Affiliation(s)
- Dipayan Datta
- Institut für Physikalische Chemie , Johannes Gutenberg-Universität Mainz , Duesbergweg 10-14 , 55128 Mainz , Germany
| | - Jürgen Gauss
- Institut für Physikalische Chemie , Johannes Gutenberg-Universität Mainz , Duesbergweg 10-14 , 55128 Mainz , Germany
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14
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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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15
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Bozkaya U, Sherrill CD. Analytic energy gradients for the coupled-cluster singles and doubles with perturbative triples method with the density-fitting approximation. J Chem Phys 2018; 147:044104. [PMID: 28764345 DOI: 10.1063/1.4994918] [Citation(s) in RCA: 30] [Impact Index Per Article: 5.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022] Open
Abstract
An efficient implementation of analytic gradients for the coupled-cluster singles and doubles with perturbative triples [CCSD(T)] method with the density-fitting (DF) approximation, denoted as DF-CCSD(T), is reported. For the molecules considered, the DF approach substantially accelerates conventional CCSD(T) analytic gradients due to the reduced input/output time and the acceleration of the so-called "gradient terms": formation of particle density matrices (PDMs), computation of the generalized Fock-matrix (GFM), solution of the Z-vector equation, formation of the effective PDMs and GFM, back-transformation of the PDMs and GFM, from the molecular orbital to the atomic orbital (AO) basis, and computation of gradients in the AO basis. For the largest member of the molecular test set considered (C6H14), the computational times for analytic gradients (with the correlation-consistent polarized valence triple-ζ basis set in serial) are 106.2 [CCSD(T)] and 49.8 [DF-CCSD(T)] h, a speedup of more than 2-fold. In the evaluation of gradient terms, the DF approach completely avoids the use of four-index two-electron integrals. Similar to our previous studies on DF-second-order Møller-Plesset perturbation theory and DF-CCSD gradients, our formalism employs 2- and 3-index two-particle density matrices (TPDMs) instead of 4-index TPDMs. Errors introduced by the DF approximation are negligible for equilibrium geometries and harmonic vibrational frequencies.
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Affiliation(s)
- Uğur Bozkaya
- Department of Chemistry, Hacettepe University, Ankara 06800, Turkey
| | - C David Sherrill
- Center for Computational Molecular Science and Technology, School of Chemistry and Biochemistry, and School of Computational Science and Engineering, Georgia Institute of Technology, Atlanta, Georgia 30332, USA
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16
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Bazante AP, Perera A, Bartlett RJ. Towards core-excitation spectra in attosecond spectroscopy: A coupled-cluster study of ClF. Chem Phys Lett 2017. [DOI: 10.1016/j.cplett.2017.05.017] [Citation(s) in RCA: 10] [Impact Index Per Article: 1.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/06/2023]
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17
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Bozkaya U, Sherrill CD. Analytic energy gradients for the coupled-cluster singles and doubles method with the density-fitting approximation. J Chem Phys 2017; 144:174103. [PMID: 27155621 DOI: 10.1063/1.4948318] [Citation(s) in RCA: 30] [Impact Index Per Article: 4.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022] Open
Abstract
An efficient implementation is presented for analytic gradients of the coupled-cluster singles and doubles (CCSD) method with the density-fitting approximation, denoted DF-CCSD. Frozen core terms are also included. When applied to a set of alkanes, the DF-CCSD analytic gradients are significantly accelerated compared to conventional CCSD for larger molecules. The efficiency of our DF-CCSD algorithm arises from the acceleration of several different terms, which are designated as the "gradient terms": computation of particle density matrices (PDMs), generalized Fock-matrix (GFM), solution of the Z-vector equation, formation of the relaxed PDMs and GFM, back-transformation of PDMs and GFM to the atomic orbital (AO) basis, and evaluation of gradients in the AO basis. For the largest member of the alkane set (C10H22), the computational times for the gradient terms (with the cc-pVTZ basis set) are 2582.6 (CCSD) and 310.7 (DF-CCSD) min, respectively, a speed up of more than 8-folds. For gradient related terms, the DF approach avoids the usage of four-index electron repulsion integrals. Based on our previous study [U. Bozkaya, J. Chem. Phys. 141, 124108 (2014)], our formalism completely avoids construction or storage of the 4-index two-particle density matrix (TPDM), using instead 2- and 3-index TPDMs. The DF approach introduces negligible errors for equilibrium bond lengths and harmonic vibrational frequencies.
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Affiliation(s)
- Uğur Bozkaya
- Department of Chemistry, Hacettepe University, Ankara 06800, Turkey
| | - C David Sherrill
- Center for Computational Molecular Science and Technology, School of Chemistry and Biochemistry, and School of Computational Science and Engineering, Georgia Institute of Technology, Atlanta, Georgia 30332, USA
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Bozkaya U. A noniterative asymmetric triple excitation correction for the density-fitted coupled-cluster singles and doubles method: Preliminary applications. J Chem Phys 2016; 144:144108. [DOI: 10.1063/1.4945706] [Citation(s) in RCA: 13] [Impact Index Per Article: 1.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/15/2022] Open
Affiliation(s)
- Uğur Bozkaya
- Department of Chemistry, Hacettepe University, Ankara 06800, Turkey
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Cheng L. Benchmark calculations on the nuclear quadrupole-coupling parameters for open-shell molecules using non-relativistic and scalar-relativistic coupled-cluster methods. J Chem Phys 2015; 143:064301. [DOI: 10.1063/1.4928054] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- Lan Cheng
- Department of Chemistry, Institute for Theoretical Chemistry, The University of Texas at Austin, Austin, Texas 78712, USA
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Datta D, Gauss J. Communication: Spin densities within a unitary group based spin-adapted open-shell coupled-cluster theory: Analytic evaluation of isotropic hyperfine-coupling constants for the combinatoric open-shell coupled-cluster scheme. J Chem Phys 2015; 143:011101. [DOI: 10.1063/1.4923436] [Citation(s) in RCA: 11] [Impact Index Per Article: 1.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- Dipayan Datta
- Institut für Physikalische Chemie, Johannes Gutenberg-Universität Mainz, Duesbergweg 10-14, D-55128 Mainz, Germany
| | - Jürgen Gauss
- Institut für Physikalische Chemie, Johannes Gutenberg-Universität Mainz, Duesbergweg 10-14, D-55128 Mainz, Germany
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Morgan WJ, Fortenberry RC. Theoretical Rovibronic Treatment of the X̃ 2Σ+ and à 2Π States of C2H and the X̃ 1Σ+ State of C2H– from Quartic Force Fields. J Phys Chem A 2015; 119:7013-25. [DOI: 10.1021/acs.jpca.5b03489] [Citation(s) in RCA: 29] [Impact Index Per Article: 3.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/30/2022]
Affiliation(s)
- W. James Morgan
- Department of Chemistry, Georgia Southern University, Statesboro, Georgia 30460, United States
| | - Ryan C. Fortenberry
- Department of Chemistry, Georgia Southern University, Statesboro, Georgia 30460, United States
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Datta D, Gauss J. Analytic first derivatives for a spin-adapted open-shell coupled cluster theory: Evaluation of first-order electrical properties. J Chem Phys 2014; 141:104102. [DOI: 10.1063/1.4894773] [Citation(s) in RCA: 8] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/24/2022] Open
Affiliation(s)
- Dipayan Datta
- Institut für Physikalische Chemie, Johannes Gutenberg-Universität Mainz, Duesbergweg 10-14, D-55128 Mainz, Germany
| | - Jürgen Gauss
- Institut für Physikalische Chemie, Johannes Gutenberg-Universität Mainz, Duesbergweg 10-14, D-55128 Mainz, Germany
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Dutta AK, Dar M, Vaval N, Pal S. Structure, stability, and properties of the trans peroxo nitrate radical: the importance of nondynamic correlation. J Phys Chem A 2014; 118:1350-62. [PMID: 24502288 DOI: 10.1021/jp409218c] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Abstract
We report a comparative single-reference and multireference coupled-cluster investigation on the structure, potential energy surface, and IR spectroscopic properties of the trans peroxo nitrate radical, one of the key intermediates in stratospheric NOX chemistry. The previous single-reference ab initio studies predicted an unbound structure for the trans peroxo nitrate radical. However, our Fock space multireference coupled-cluster calculation confirms a bound structure for the trans peroxo nitrate radical, in accordance with the experimental results reported earlier. Further, the analysis of the potential energy surface in FSMRCC method indicates a well-behaved minima, contrary to the shallow minima predicted by the single-reference coupled-cluster method. The harmonic force field analysis, of various possible isomers of peroxo nitrate also reveals that only the trans structure leads to the experimentally observed IR peak at 1840 cm(-1). The present study highlights the critical importance of nondynamic correlation in predicting the structure and properties of high-energy stratospheric NOx radicals.
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Affiliation(s)
- Achintya Kumar Dutta
- Physical Chemistry Division, CSIR-National Chemical Laboratory , Pune 411008, India
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Lyakh DI, Bartlett RJ. Algebraic connectivity analysis in molecular electronic structure theory II: total exponential formulation of second-quantised correlated methods. Mol Phys 2013. [DOI: 10.1080/00268976.2013.807946] [Citation(s) in RCA: 7] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/26/2022]
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25
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Cheng L, Stopkowicz S, Stanton JF, Gauss J. The route to high accuracy inab initiocalculations of Cu quadrupole-coupling constants. J Chem Phys 2012; 137:224302. [DOI: 10.1063/1.4767767] [Citation(s) in RCA: 16] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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Tu Z, Wang F, Li X. Equation-of-motion coupled-cluster method for ionized states with spin-orbit coupling. J Chem Phys 2012; 136:174102. [DOI: 10.1063/1.4704894] [Citation(s) in RCA: 38] [Impact Index Per Article: 3.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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Lyakh DI, Bartlett RJ. A remark on the disconnected nature of Lagrange equations in the context of a linear-scaling implementation of the coupled-cluster energy gradients. Mol Phys 2012. [DOI: 10.1080/00268976.2012.679639] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/28/2022]
Affiliation(s)
- Dmitry I. Lyakh
- a Quantum Theory Project, University of Florida , Gainesville , FL, 32611 , USA
| | - Rodney J. Bartlett
- a Quantum Theory Project, University of Florida , Gainesville , FL, 32611 , USA
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Yang DD, Wang F, Guo J. Equation of motion coupled cluster method for electron attached states with spin–orbit coupling. Chem Phys Lett 2012. [DOI: 10.1016/j.cplett.2012.02.014] [Citation(s) in RCA: 36] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
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Tu Z, Yang DD, Wang F, Guo J. Symmetry exploitation in closed-shell coupled-cluster theory with spin-orbit coupling. J Chem Phys 2011; 135:034115. [DOI: 10.1063/1.3611052] [Citation(s) in RCA: 34] [Impact Index Per Article: 2.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/23/2022] Open
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Cheng L, Gauss J. Analytical evaluation of first-order electrical properties based on the spin-free Dirac-Coulomb Hamiltonian. J Chem Phys 2011; 134:244112. [DOI: 10.1063/1.3601056] [Citation(s) in RCA: 37] [Impact Index Per Article: 2.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/16/2023] Open
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MATSUOKA T, SOMENO S, HADA M. Electronic Excited States Calculated Using Generalized Spin-Orbital Functions Including Spin-Orbit Interactions. JOURNAL OF COMPUTER CHEMISTRY-JAPAN 2011. [DOI: 10.2477/jccj.h2219] [Citation(s) in RCA: 7] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/05/2022]
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Puzzarini C, Stanton JF, Gauss J. Quantum-chemical calculation of spectroscopic parameters for rotational spectroscopy. INT REV PHYS CHEM 2010. [DOI: 10.1080/01442351003643401] [Citation(s) in RCA: 188] [Impact Index Per Article: 13.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/19/2022]
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33
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Wang F, Gauss J. Analytic second derivatives in closed-shell coupled-cluster theory with spin-orbit coupling. J Chem Phys 2009; 131:164113. [DOI: 10.1063/1.3245954] [Citation(s) in RCA: 25] [Impact Index Per Article: 1.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/08/2023] Open
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34
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Prochnow E, Evangelista FA, Schaefer HF, Allen WD, Gauss J. Analytic gradients for the state-specific multireference coupled cluster singles and doubles model. J Chem Phys 2009; 131:064109. [DOI: 10.1063/1.3204017] [Citation(s) in RCA: 68] [Impact Index Per Article: 4.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/23/2023] Open
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35
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Wang F, Gauss J. Analytic energy gradients in closed-shell coupled-cluster theory with spin-orbit coupling. J Chem Phys 2008; 129:174110. [DOI: 10.1063/1.3000010] [Citation(s) in RCA: 36] [Impact Index Per Article: 2.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/30/2023] Open
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36
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Taube AG, Bartlett RJ. Frozen natural orbital coupled-cluster theory: Forces and application to decomposition of nitroethane. J Chem Phys 2008; 128:164101. [DOI: 10.1063/1.2902285] [Citation(s) in RCA: 86] [Impact Index Per Article: 5.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/17/2023] Open
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Pittner J, Smydke J. Analytic gradient for the multireference Brillouin-Wigner coupled cluster method and for the state-universal multireference coupled cluster method. J Chem Phys 2007; 127:114103. [PMID: 17887824 DOI: 10.1063/1.2770705] [Citation(s) in RCA: 42] [Impact Index Per Article: 2.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/22/2023] Open
Abstract
We present the analytic gradient theory and its pilot implementation for the multireference Brillouin-Wigner coupled cluster (BWCC) method and for the state-universal multireference coupled cluster method. The analytic gradient has been derived for three cases: (i) BWCC method without a size-extensivity correction, (ii) BWCC method with the iterative size-extensivity correction, and (iii) for the rigorously size-extensive state-universal method. The pilot implementation is based on full-configuration interaction expansions and is presently limited to single and double excitation levels; however, the resulting equations are general. For BWCC methods, they also do not contain terms explicitly mixing amplitudes of different reference configurations and can thus be implemented in an efficient way. The analytic gradients have been verified with respect to numerically computed ones on the example of CH2 molecule, and geometry optimizations of CH2 and SiH2 have been carried out.
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Affiliation(s)
- Jirí Pittner
- J. Heyrovský Institute of Physical Chemistry of the Academy of Sciences of the Czech Republic, v. v. i. Dolejskova 3, 18223 Prague 8, Czech Republic.
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Crawford TD, Schaefer HF. An Introduction to Coupled Cluster Theory for Computational Chemists. REVIEWS IN COMPUTATIONAL CHEMISTRY 2007. [DOI: 10.1002/9780470125915.ch2] [Citation(s) in RCA: 372] [Impact Index Per Article: 21.9] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 12/05/2022]
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39
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Bartlett RJ, Stanton JF. Applications of Post-Hartree-Fock Methods: A Tutorial. REVIEWS IN COMPUTATIONAL CHEMISTRY 2007. [DOI: 10.1002/9780470125823.ch2] [Citation(s) in RCA: 226] [Impact Index Per Article: 13.3] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 02/08/2023]
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40
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Fan PD, Kowalski K, Piecuch * P. Non-iterative corrections to extended coupled-cluster energies employing the generalized method of moments of coupled-cluster equations. Mol Phys 2005. [DOI: 10.1080/00268970500131595] [Citation(s) in RCA: 43] [Impact Index Per Article: 2.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/25/2022]
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41
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Fau S, Bartlett RJ. Gaussian Basis Sets for Highly Accurate Calculations of Isotropic Hyperfine Coupling Constants at Hydrogen. J Phys Chem A 2003. [DOI: 10.1021/jp0276294] [Citation(s) in RCA: 21] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Affiliation(s)
- Stefan Fau
- Quantum Theory Project, University of Florida, Gainesville, Florida 32611-8435
| | - Rodney J. Bartlett
- Quantum Theory Project, University of Florida, Gainesville, Florida 32611-8435
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42
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Hald K, Halkier A, Jørgensen P, Coriani S, Hättig C, Helgaker T. A Lagrangian, integral-density direct formulation and implementation of the analytic CCSD and CCSD(T) gradients. J Chem Phys 2003. [DOI: 10.1063/1.1531106] [Citation(s) in RCA: 55] [Impact Index Per Article: 2.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022] Open
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43
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Brinkmann NR, Wesolowski SS, Schaefer HF. Coupled-cluster characterization of the ground and excited states of the CH2N and CH2P radicals. J Chem Phys 2001. [DOI: 10.1063/1.1337062] [Citation(s) in RCA: 23] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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45
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Meissner H, Paldus J. Analytic Energy Derivatives for the Direct Iterative Approach to the Generalized Bloch Equation. ACTA ACUST UNITED AC 2001. [DOI: 10.1135/cccc20011164] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/05/2022]
Abstract
A general formalism for the analytic energy derivatives in the context of the recently developed state-selective version of the direct iterative approach to the generalized Bloch equation is presented. An explicit formalism is developed for both the gradients and the Hessian by exploiting the so-called Z-vector method. A procedure for the development of the corresponding algorithm for higher than the second-order properties is also briefly outlined.
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Kostov MK, Cole MW, Lewis JC, Diep P, Johnson J. Many-body interactions among adsorbed atoms and molecules within carbon nanotubes and in free space. Chem Phys Lett 2000. [DOI: 10.1016/s0009-2614(00)01245-8] [Citation(s) in RCA: 43] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022]
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47
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Petraco NDK, Wesolowski SS, Leininger ML, Schaefer HF. Coupled-cluster studies of the hyperfine splitting constants of the thioformyl radical. J Chem Phys 2000. [DOI: 10.1063/1.481599] [Citation(s) in RCA: 11] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/03/2023] Open
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48
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Affiliation(s)
- Victor G. Solomonik
- Institute for Theoretical Chemistry, Departments of Chemistry and Biochemistry, The University of Texas at Austin, Austin, Texas 78712
| | - James E. Boggs
- Institute for Theoretical Chemistry, Departments of Chemistry and Biochemistry, The University of Texas at Austin, Austin, Texas 78712
| | - John F. Stanton
- Institute for Theoretical Chemistry, Departments of Chemistry and Biochemistry, The University of Texas at Austin, Austin, Texas 78712
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Wetmore SD, Eriksson LA, Boyd RJ. The calculation of accurate 17O hyperfine coupling constants in the hydroxyl radical: A difficult problem for current quantum chemical methods. J Chem Phys 1998. [DOI: 10.1063/1.477607] [Citation(s) in RCA: 9] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022] Open
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50
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Sherrill CD, Krylov AI, Byrd EFC, Head-Gordon M. Energies and analytic gradients for a coupled-cluster doubles model using variational Brueckner orbitals: Application to symmetry breaking in O4+. J Chem Phys 1998. [DOI: 10.1063/1.477023] [Citation(s) in RCA: 219] [Impact Index Per Article: 8.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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