1
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Uhlířová T, Cianchino D, Nottoli T, Lipparini F, Gauss J. Cholesky Decomposition in Spin-Free Dirac-Coulomb Coupled-Cluster Calculations. J Phys Chem A 2024; 128:8292-8303. [PMID: 39268870 DOI: 10.1021/acs.jpca.4c04353] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 09/15/2024]
Abstract
We present an implementation for the use of Cholesky decomposition (CD) of two-electron integrals within the spin-free Dirac-Coulomb (SFDC) scheme that enables to perform high-accuracy coupled-cluster (CC) calculations at costs almost comparable to those of their nonrelativistic counterparts. While for nonrelativistic CC calculations, atomic-orbital (AO)-based algorithms, due to their significantly reduced disk-space requirements, are the key to efficient large-scale computations, such algorithms are less advantageous in the SFDC case due to their increased computational cost in that case. Here, molecular-orbital (MO)-based algorithms exploiting the CD of the two-electron integrals allow us to reduce disk-space requirements and lead to computational cost in the CC step that is more or less the same as in the nonrelativistic case. The only remaining overhead in a CD-SFDC-CC calculation is due to the need to compute additional two-electron integrals, the somewhat higher cost of the Hartree-Fock calculation in the SFDC case, and additional cost in the transformation of the Cholesky vectors from the AO to the MO representation. However, these additional costs typically amount to less than 5-15% of the total wall time and are thus acceptable. We illustrate the efficiency of our CD scheme for SFDC-CC calculations on a series of illustrative calculations for the X(CO)4 molecules with X = Ni, Pd, Pt.
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Affiliation(s)
- Tereza Uhlířová
- Department Chemie, Johannes Gutenberg-Universität Mainz, Duesbergweg 10-14, Mainz D-55128, Germany
| | - Davide Cianchino
- Dipartimento di Chimica e Chimica Industriale, Universitá di Pisa, Via G. Moruzzi 13, Pisa I-56124, Italy
| | - Tommaso Nottoli
- Dipartimento di Chimica e Chimica Industriale, Universitá di Pisa, Via G. Moruzzi 13, Pisa I-56124, Italy
| | - Filippo Lipparini
- Dipartimento di Chimica e Chimica Industriale, Universitá di Pisa, Via G. Moruzzi 13, Pisa I-56124, Italy
| | - Jürgen Gauss
- Department Chemie, Johannes Gutenberg-Universität Mainz, Duesbergweg 10-14, Mainz D-55128, Germany
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2
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Zhang C, Peterson KA, Dyall KG, Cheng L. A new computational framework for spinor-based relativistic exact two-component calculations using contracted basis functions. J Chem Phys 2024; 161:054105. [PMID: 39087536 DOI: 10.1063/5.0217762] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/07/2024] [Accepted: 07/14/2024] [Indexed: 08/02/2024] Open
Abstract
A new computational framework for spinor-based relativistic exact two-component (X2C) calculations is developed using contracted basis sets with a spin-orbit contraction scheme. Generally contracted, j-adapted basis sets of p-block elements using primitive functions in the correlation-consistent basis sets are constructed for the X2C Hamiltonian with atomic mean-field spin-orbit integrals (the X2CAMF scheme). The contraction coefficients are taken from atomic X2CAMF Hartree-Fock spinors, thereby following the simple concept of a linear combination of atomic orbitals. Benchmark calculations of spin-orbit splittings, equilibrium bond lengths, and harmonic vibrational frequencies demonstrate the accuracy and efficacy of the j-adapted spin-orbit contraction scheme.
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Affiliation(s)
- Chaoqun Zhang
- Department of Chemistry, The Johns Hopkins University, Baltimore, Maryland 21218, USA
| | - Kirk A Peterson
- Department of Chemistry, Washington State University, Pullman, Washington 99164, USA
| | | | - Lan Cheng
- Department of Chemistry, The Johns Hopkins University, Baltimore, Maryland 21218, USA
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3
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Yuwono SH, Li RR, Zhang T, Surjuse KA, Valeev EF, Li X, Eugene DePrince A. Relativistic Coupled Cluster with Completely Renormalized and Perturbative Triples Corrections. J Phys Chem A 2024. [PMID: 39074123 DOI: 10.1021/acs.jpca.4c02583] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 07/31/2024]
Abstract
We have implemented noniterative triples corrections to the energy from coupled-cluster with single and double excitations (CCSD) within the 1-electron exact two-component (1eX2C) relativistic framework. The effectiveness of both the CCSD(T) and the completely renormalized (CR) CC(2,3) approaches are demonstrated by performing all-electron computations of the potential energy curves and spectroscopic constants of copper, silver, and gold dimers in their ground electronic states. Spin-orbit coupling effects captured via the 1eX2C framework are shown to be crucial for recovering the correct shape of the potential energy curves, and the correlation effects due to triples in these systems change the dissociation energies by about 0.1-0.2 eV or about 4-7%. We also demonstrate that relativistic effects and basis set size and contraction scheme are significantly more important in Au2 than in Ag2 or Cu2.
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Affiliation(s)
- Stephen H Yuwono
- Department of Chemistry and Biochemistry, Florida State University, Tallahassee, Florida 32306-4390, United States
| | - Run R Li
- Department of Chemistry and Biochemistry, Florida State University, Tallahassee, Florida 32306-4390, United States
| | - Tianyuan Zhang
- Department of Chemistry, University of Washington, Seattle, Washington 98195, United States
| | | | - Edward F Valeev
- Department of Chemistry, Virginia Tech, Blacksburg, Virginia 24061, United States
| | - Xiaosong Li
- Department of Chemistry, University of Washington, Seattle, Washington 98195, United States
| | - A Eugene DePrince
- Department of Chemistry and Biochemistry, Florida State University, Tallahassee, Florida 32306-4390, United States
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4
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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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5
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Majee K, Chakraborty S, Mukhopadhyay T, Nayak MK, Dutta AK. A reduced cost four-component relativistic unitary coupled cluster method for atoms and molecules. J Chem Phys 2024; 161:034101. [PMID: 39007370 DOI: 10.1063/5.0207091] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/06/2024] [Accepted: 06/12/2024] [Indexed: 07/16/2024] Open
Abstract
We present a four-component relativistic unitary coupled cluster method for atoms and molecules. We have used commutator-based non-perturbative approximation using the "Bernoulli expansion" to derive an approximation to the relativistic unitary coupled cluster method. The performance of the full quadratic unitary coupled-cluster singles and doubles method (qUCCSD), as well as a perturbative approximation variant (UCC3), has been reported for both energies and properties. It can be seen that both methods give results comparable to those of the standard relativistic coupled cluster method. The qUCCSD method shows better agreement with experimental results due to the better inclusion of relaxation effects. The relativistic UCC3 and qUCCSD methods can simulate the spin-forbidden transition with easy access to transition properties. A natural spinor-based scheme to reduce the computational cost of relativistic UCC3 and qUCCSD methods has been discussed.
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Affiliation(s)
- Kamal Majee
- Department of Chemistry, Indian Institute of Technology Bombay, Powai, Mumbai 400076, India
| | - Sudipta Chakraborty
- Department of Chemistry, Indian Institute of Technology Bombay, Powai, Mumbai 400076, India
| | - Tamoghna Mukhopadhyay
- Department of Chemistry, Indian Institute of Technology Bombay, Powai, Mumbai 400076, India
| | - Malaya K Nayak
- Theoretical Chemistry Section, Bhabha Atomic Research Centre, Trombay, Mumbai 400085, India
- Homi Bhabha National Institute, BARC Training School Complex, Anushakti Nagar, Mumbai 400094, India
| | - Achintya Kumar Dutta
- Department of Chemistry, Indian Institute of Technology Bombay, Powai, Mumbai 400076, India
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6
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Zhang T, Banerjee S, Koulias LN, Valeev EF, DePrince AE, Li X. Dirac-Coulomb-Breit Molecular Mean-Field Exact-Two-Component Relativistic Equation-of-Motion Coupled-Cluster Theory. J Phys Chem A 2024; 128:3408-3418. [PMID: 38651293 DOI: 10.1021/acs.jpca.3c08167] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 04/25/2024]
Abstract
We present a relativistic equation-of-motion coupled-cluster with single and double excitation formalism within the exact two-component framework (X2C-EOM-CCSD), where both scalar relativistic effects and spin-orbit coupling are variationally included at the reference level. Three different molecular mean-field treatments of relativistic corrections, including the one-electron, Dirac-Coulomb, and Dirac-Coulomb-Breit Hamiltonian, are considered in this work. Benchmark calculations include atomic excitations and fine-structure splittings arising from spin-orbit coupling. Comparison with experimental values and relativistic time-dependent density functional theory is also carried out. The computation of the oscillator strength using the relativistic X2C-EOM-CCSD approach allows for studies of spin-orbit-driven processes, such as the spontaneous phosphorescence lifetime.
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Affiliation(s)
- Tianyuan Zhang
- Department of Chemistry, University of Washington, Seattle, Washington 98195, United States
| | - Samragni Banerjee
- Department of Chemistry, University of Washington, Seattle, Washington 98195, United States
| | - Lauren N Koulias
- Department of Chemistry, University of Washington, Seattle, Washington 98195, United States
| | - Edward F Valeev
- Department of Chemistry, Virginia Tech, Blacksburg, Virginia 24061, United States
| | - A Eugene DePrince
- Department of Chemistry and Biochemistry, Florida State University, Tallahassee, Florida 32306-4390, United States
| | - Xiaosong Li
- Department of Chemistry, University of Washington, Seattle, Washington 98195, United States
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7
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Zhang C, Lipparini F, Stopkowicz S, Gauss J, Cheng L. Cholesky Decomposition-Based Implementation of Relativistic Two-Component Coupled-Cluster Methods for Medium-Sized Molecules. J Chem Theory Comput 2024; 20:787-798. [PMID: 38198515 DOI: 10.1021/acs.jctc.3c01236] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/12/2024]
Abstract
A Cholesky decomposition (CD)-based implementation of relativistic two-component coupled-cluster (CC) and equation-of-motion CC (EOM-CC) methods using an exact two-component Hamiltonian augmented with atomic-mean-field spin-orbit integrals (the X2CAMF scheme) is reported. The present CD-based implementation of X2CAMF-CC and EOM-CC methods employs atomic-orbital-based algorithms to avoid the construction of two-electron integrals and intermediates involving three and four virtual indices. Our CD-based implementation extends the applicability of X2CAMF-CC and EOM-CC methods to medium-sized molecules with the possibility to correlate around 1000 spinors. Benchmark calculations for uranium-containing small molecules were performed to assess the dependence of the CC results on the Cholesky threshold. A Cholesky threshold of 10-4 is shown to be sufficient to maintain chemical accuracy. Example calculations to illustrate the capability of the CD-based relativistic CC methods are reported for the bond-dissociation energy of the uranium hexafluoride molecule, UF6, with up to quadruple-ζ basis sets, and the lowest excitation energy in the solvated uranyl ion [UO22+(H2O)12].
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Affiliation(s)
- Chaoqun Zhang
- Department of Chemistry, the Johns Hopkins University, Baltimore, Maryland 21218, United States
| | - Filippo Lipparini
- Dipartimento di Chimica e Chimica Industriale, Università di Pisa, Via G. Moruzzi 13, Pisa I-56124, Italy
| | - Stella Stopkowicz
- Fachrichtung Chemie, Universität des Saarlandes, Saarbrücken D-66123, Germany
- Hylleraas Centre for Quantum Molecular Sciences, Department of Chemistry, University of Oslo, P.O. Box 1033, Blindern, Oslo N-0315, Norway
| | - Jürgen Gauss
- Department Chemie, Johannes Gutenberg-Universität Mainz, Duesbergweg 10-14, Mainz D-55128, Germany
| | - Lan Cheng
- Department of Chemistry, the Johns Hopkins University, Baltimore, Maryland 21218, United States
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8
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Wang X, Sharma S. Relativistic Semistochastic Heat-Bath Configuration Interaction. J Chem Theory Comput 2023; 19:848-855. [PMID: 36700783 DOI: 10.1021/acs.jctc.2c01025] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/27/2023]
Abstract
In this work we present the extension of semistochastic heat-bath configuration interaction (SHCI) to work with any two-component and four-component Hamiltonian. The vertical detachment energy (VDE) of AuH2- and zero-field splitting (ZFS) of NpO22+ is calculated by correlating more than 100 spinors in both cases. This work demonstrates the capability of SHCI to treat problems where both relativistic effect and electron correlation are important.
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Affiliation(s)
- Xubo Wang
- Department of Chemistry, University of Colorado Boulder, Boulder, Colorado80309, United States
| | - Sandeep Sharma
- Department of Chemistry, University of Colorado Boulder, Boulder, Colorado80309, United States
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9
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Liu W. Perspective: Simultaneous treatment of relativity, correlation, and
QED. WIRES COMPUTATIONAL MOLECULAR SCIENCE 2022. [DOI: 10.1002/wcms.1652] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 12/24/2022]
Affiliation(s)
- Wenjian Liu
- Qingdao Institute for Theoretical and Computational Sciences, Institute of Frontier and Interdisciplinary Science Shandong University Qingdao Shandong China
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10
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Cheng L. Relativistic exact two-component coupled-cluster calculations of electronic g-factors for heavy-atom-containing molecules pertinent to search of new physics. Mol Phys 2022. [DOI: 10.1080/00268976.2022.2113567] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/15/2022]
Affiliation(s)
- Lan Cheng
- Department of Chemistry, The Johns Hopkins University, Baltimore, MD, USA
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11
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Chamoli S, Surjuse K, Jangid B, Nayak MK, Dutta AK. A reduced cost four-component relativistic coupled cluster method based on natural spinors. J Chem Phys 2022; 156:204120. [PMID: 35649878 DOI: 10.1063/5.0085932] [Citation(s) in RCA: 2] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 02/02/2023] Open
Abstract
We present the theory, implementation, and benchmark results for a frozen natural spinors based reduced cost four-component relativistic coupled cluster method. The natural spinors are obtained by diagonalizing the one-body reduced density matrix from a relativistic second-order Møller-Plesset calculation based on a four-component Dirac-Coulomb Hamiltonian. The correlation energy in the coupled cluster method converges more rapidly with respect to the size of the virtual space in the frozen natural spinor basis than that observed in the standard canonical spinors obtained from the Dirac-Hartree-Fock calculation. The convergence of properties is not smooth in the frozen natural spinor basis. However, the inclusion of the perturbative correction smoothens the convergence of the properties with respect to the size of the virtual space in the frozen natural spinor basis and greatly reduces the truncation errors in both energy and property calculations. The accuracy of the frozen natural spinor based coupled cluster methods can be controlled by a single threshold and is a black box to use.
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Affiliation(s)
- Somesh Chamoli
- Department of Chemistry, Indian Institute of Technology Bombay, Powai, Mumbai 400076, India
| | - Kshitijkumar Surjuse
- Department of Chemistry, Indian Institute of Technology Bombay, Powai, Mumbai 400076, India
| | - Bhavnesh Jangid
- Department of Chemistry, Indian Institute of Technology Bombay, Powai, Mumbai 400076, India
| | - Malaya K Nayak
- Theoretical Chemistry Section, Bhabha Atomic Research Centre, Trombay, Mumbai 400085, India
| | - Achintya Kumar Dutta
- Department of Chemistry, Indian Institute of Technology Bombay, Powai, Mumbai 400076, India
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12
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Zhang N, Xiao Y, Liu W. SOiCI and iCISO: combining iterative configuration interaction with spin-orbit coupling in two ways. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2022; 34:224007. [PMID: 35287124 DOI: 10.1088/1361-648x/ac5db4] [Citation(s) in RCA: 9] [Impact Index Per Article: 4.5] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/26/2022] [Accepted: 03/14/2022] [Indexed: 06/14/2023]
Abstract
The near-exact iCIPT2 approach for strongly correlated systems of electrons, which stems from the combination of iterative configuration interaction (iCI, an exact solver of full CI) with configuration selection for static correlation and second-order perturbation theory (PT2) for dynamic correlation, is extended to the relativistic domain. In the spirit of spin separation, relativistic effects are treated in two steps: scalar relativity is treated by the infinite-order, spin-free part of the exact two-component (X2C) relativistic Hamiltonian, whereas spin-orbit coupling (SOC) is treated by the first-order, Douglas-Kroll-Hess-like SOC operator derived from the same X2C Hamiltonian. Two possible combinations of iCIPT2 with SOC are considered, i.e., SOiCI and iCISO. The former treats SOC and electron correlation on an equal footing, whereas the latter treats SOC in the spirit of state interaction, by constructing and diagonalizing an effective spin-orbit Hamiltonian matrix in a small number of correlated scalar states. Both double group and time reversal symmetries are incorporated to simplify the computation. Pilot applications reveal that SOiCI is very accurate for the spin-orbit splitting (SOS) of heavy atoms, whereas the computationally very cheap iCISO can safely be applied to the SOS of light atoms and even of systems containing heavy atoms when SOC is largely quenched by ligand fields.
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Affiliation(s)
- Ning Zhang
- Beijing National Laboratory for Molecular Sciences, Institute of Theoretical and Computational Chemistry, College of Chemistry and Molecular Engineering, Peking University, Beijing 100871, People's Republic of China
| | - Yunlong Xiao
- Beijing National Laboratory for Molecular Sciences, Institute of Theoretical and Computational Chemistry, College of Chemistry and Molecular Engineering, Peking University, Beijing 100871, People's Republic of China
| | - Wenjian Liu
- Qingdao Institute for Theoretical and Computational Sciences, Institute of Frontier and Interdisciplinary Science, Shandong University, Qingdao, Shandong 266237, People's Republic of China
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13
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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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14
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Liu J, Matthews DA, Cheng L. Quadratic Unitary Coupled-Cluster Singles and Doubles Scheme: Efficient Implementation, Benchmark Study, and Formulation of an Extended Version. J Chem Theory Comput 2022; 18:2281-2291. [PMID: 35312299 DOI: 10.1021/acs.jctc.1c01210] [Citation(s) in RCA: 4] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/30/2022]
Abstract
An efficient implementation of the quadratic unitary coupled-cluster singles and doubles (qUCCSD) scheme for calculations of electronic ground and excited states using an unrestricted molecular spin-orbital formulation and an efficient tensor contraction library is reported. The accuracy of the qUCCSD scheme and the efficiency of the present implementation are demonstrated using extensive benchmark calculations of excitation energies and an application to S0 → S1 vertical excitation energies for cis- and trans-4a,4b-dihydrotriphenylene. The qUCCSD scheme has been shown to provide improved excitation energies compared with the UCC3 scheme formulated based on perturbation theory. A UCC truncation scheme that can provide excitation energies correct through the fourth order is also presented to further improve the accuracy of the qUCCSD scheme.
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Affiliation(s)
- Junzi Liu
- School of Chemistry and Biological Engineering, University of Science and Technology Beijing, Beijing, 100083, China
| | - Devin A Matthews
- Department of Chemistry, Southern Methodist University, Dallas, Texas 75275, United States
| | - Lan Cheng
- Department of Chemistry, The Johns Hopkins University, Baltimore, Maryland 21218, United States
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15
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Liu J, Cheng L. Relativistic coupled‐cluster and equation‐of‐motion coupled‐cluster methods. WIRES COMPUTATIONAL MOLECULAR SCIENCE 2021. [DOI: 10.1002/wcms.1536] [Citation(s) in RCA: 9] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 01/01/2023]
Affiliation(s)
- Junzi Liu
- Department of Chemistry The Johns Hopkins University Baltimore Maryland USA
| | - Lan Cheng
- Department of Chemistry The Johns Hopkins University Baltimore Maryland USA
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16
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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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17
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Saue T, Bast R, Gomes ASP, Jensen HJA, Visscher L, Aucar IA, Di Remigio R, Dyall KG, Eliav E, Fasshauer E, Fleig T, Halbert L, Hedegård ED, Helmich-Paris B, Iliaš M, Jacob CR, Knecht S, Laerdahl JK, Vidal ML, Nayak MK, Olejniczak M, Olsen JMH, Pernpointner M, Senjean B, Shee A, Sunaga A, van Stralen JNP. The DIRAC code for relativistic molecular calculations. J Chem Phys 2020; 152:204104. [PMID: 32486677 DOI: 10.1063/5.0004844] [Citation(s) in RCA: 118] [Impact Index Per Article: 29.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
DIRAC is a freely distributed general-purpose program system for one-, two-, and four-component relativistic molecular calculations at the level of Hartree-Fock, Kohn-Sham (including range-separated theory), multiconfigurational self-consistent-field, multireference configuration interaction, electron propagator, and various flavors of coupled cluster theory. At the self-consistent-field level, a highly original scheme, based on quaternion algebra, is implemented for the treatment of both spatial and time reversal symmetry. DIRAC features a very general module for the calculation of molecular properties that to a large extent may be defined by the user and further analyzed through a powerful visualization module. It allows for the inclusion of environmental effects through three different classes of increasingly sophisticated embedding approaches: the implicit solvation polarizable continuum model, the explicit polarizable embedding model, and the frozen density embedding model.
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Affiliation(s)
- Trond Saue
- Laboratoire de Chimie et Physique Quantique, UMR 5626 CNRS-Université Toulouse III-Paul Sabatier, 118 Route de Narbonne, F-31062 Toulouse, France
| | - Radovan Bast
- Department of Information Technology, UiT The Arctic University of Norway, N-9037 Tromsø, Norway
| | - André Severo Pereira Gomes
- Université de Lille, CNRS, UMR 8523-PhLAM-Physique des Lasers, Atomes et Molécules, F-59000 Lille, France
| | - Hans Jørgen Aa Jensen
- Department of Physics, Chemistry and Pharmacy, University of Southern Denmark, DK-5230 Odense M, Denmark
| | - Lucas Visscher
- Department of Chemistry and Pharmaceutical Sciences, Vrije Universiteit Amsterdam, NL-1081HV Amsterdam, The Netherlands
| | - Ignacio Agustín Aucar
- Instituto de Modelado e Innovación Tecnológica, CONICET, and Departamento de Física-Facultad de Ciencias Exactas y Naturales, UNNE, Avda. Libertad 5460, W3404AAS Corrientes, Argentina
| | - Roberto Di Remigio
- Hylleraas Centre for Quantum Molecular Sciences, Department of Chemistry, UiT The Arctic University of Norway, N-9037 Tromsø, Norway
| | - Kenneth G Dyall
- Dirac Solutions, 10527 NW Lost Park Drive, Portland, Oregon 97229, USA
| | - Ephraim Eliav
- School of Chemistry, Tel Aviv University, Ramat Aviv, Tel Aviv 69978, Israel
| | - Elke Fasshauer
- Department of Physics and Astronomy, Aarhus University, Ny Munkegade 120, 8000 Aarhus, Denmark
| | - Timo Fleig
- Laboratoire de Chimie et Physique Quantique, UMR 5626 CNRS-Université Toulouse III-Paul Sabatier, 118 Route de Narbonne, F-31062 Toulouse, France
| | - Loïc Halbert
- Université de Lille, CNRS, UMR 8523-PhLAM-Physique des Lasers, Atomes et Molécules, F-59000 Lille, France
| | - Erik Donovan Hedegård
- Division of Theoretical Chemistry, Lund University, Chemical Centre, P.O. Box 124, SE-221 00 Lund, Sweden
| | - Benjamin Helmich-Paris
- Max-Planck-Institut für Kohlenforschung, Kaiser-Wilhelm-Platz 1, 45470 Mülheim an der Ruhr, Germany
| | - Miroslav Iliaš
- Department of Chemistry, Faculty of Natural Sciences, Matej Bel University, Tajovského 40, 974 01 Banská Bystrica, Slovakia
| | - Christoph R Jacob
- Technische Universität Braunschweig, Institute of Physical and Theoretical Chemistry, Gaußstr. 17, 38106 Braunschweig, Germany
| | - Stefan Knecht
- ETH Zürich, Laboratorium für Physikalische Chemie, Vladimir-Prelog-Weg 2, 8093 Zürich, Switzerland
| | - Jon K Laerdahl
- Department of Microbiology, Oslo University Hospital, Oslo, Norway
| | - Marta L Vidal
- Department of Chemistry, Technical University of Denmark, 2800 Kgs. Lyngby, Denmark
| | - Malaya K Nayak
- Theoretical Chemistry Section, Bhabha Atomic Research Centre, Trombay, Mumbai 400085, India
| | - Małgorzata Olejniczak
- Centre of New Technologies, University of Warsaw, S. Banacha 2c, 02-097 Warsaw, Poland
| | - Jógvan Magnus Haugaard Olsen
- Hylleraas Centre for Quantum Molecular Sciences, Department of Chemistry, UiT The Arctic University of Norway, N-9037 Tromsø, Norway
| | | | - Bruno Senjean
- Department of Chemistry and Pharmaceutical Sciences, Vrije Universiteit Amsterdam, NL-1081HV Amsterdam, The Netherlands
| | - Avijit Shee
- Department of Chemistry, University of Michigan, Ann Arbor, Michigan 48109, USA
| | - Ayaki Sunaga
- Department of Chemistry, Tokyo Metropolitan University, 1-1 Minami-Osawa, Hachioji-city, Tokyo 192-0397, Japan
| | - Joost N P van Stralen
- Department of Chemistry and Pharmaceutical Sciences, Vrije Universiteit Amsterdam, NL-1081HV Amsterdam, The Netherlands
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18
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Park JW, Al-Saadon R, MacLeod MK, Shiozaki T, Vlaisavljevich B. Multireference Electron Correlation Methods: Journeys along Potential Energy Surfaces. Chem Rev 2020; 120:5878-5909. [PMID: 32239929 DOI: 10.1021/acs.chemrev.9b00496] [Citation(s) in RCA: 77] [Impact Index Per Article: 19.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/16/2022]
Abstract
Multireference electron correlation methods describe static and dynamical electron correlation in a balanced way and, therefore, can yield accurate and predictive results even when single-reference methods or multiconfigurational self-consistent field theory fails. One of their most prominent applications in quantum chemistry is the exploration of potential energy surfaces. This includes the optimization of molecular geometries, such as equilibrium geometries and conical intersections and on-the-fly photodynamics simulations, both of which depend heavily on the ability of the method to properly explore the potential energy surface. Because such applications require nuclear gradients and derivative couplings, the availability of analytical nuclear gradients greatly enhances the scope of quantum chemical methods. This review focuses on the developments and advances made in the past two decades. A detailed account of the analytical nuclear gradient and derivative coupling theories is presented. Emphasis is given to the software infrastructure that allows one to make use of these methods. Notable applications of multireference electron correlation methods to chemistry, including geometry optimizations and on-the-fly dynamics, are summarized at the end followed by a discussion of future prospects.
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Affiliation(s)
- Jae Woo Park
- Department of Chemistry, Chungbuk National University, Chungdae-ro 1, Cheongju 28644, Korea
| | - Rachael Al-Saadon
- Department of Chemistry, Northwestern University, 2145 Sheridan Road, Evanston, Illinois 60208, United States
| | - Matthew K MacLeod
- Workday, 4900 Pearl Circle East, Suite 100, Boulder, Colorado 80301, United States
| | - Toru Shiozaki
- Department of Chemistry, Northwestern University, 2145 Sheridan Road, Evanston, Illinois 60208, United States.,Quantum Simulation Technologies, Inc., 625 Massachusetts Avenue, Cambridge, Massachusetts 02139, United States
| | - Bess Vlaisavljevich
- Department of Chemistry, University of South Dakota, 414 East Clark Street, Vermillion, South Dakota 57069, United States
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19
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Kállay M, Nagy PR, Mester D, Rolik Z, Samu G, Csontos J, Csóka J, Szabó PB, Gyevi-Nagy L, Hégely B, Ladjánszki I, Szegedy L, Ladóczki B, Petrov K, Farkas M, Mezei PD, Ganyecz Á. The MRCC program system: Accurate quantum chemistry from water to proteins. J Chem Phys 2020; 152:074107. [DOI: 10.1063/1.5142048] [Citation(s) in RCA: 152] [Impact Index Per Article: 38.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/09/2023] Open
Affiliation(s)
- Mihály Kállay
- Department of Physical Chemistry and Materials Science, Budapest University of Technology and Economics, P.O. Box 91, H-1521 Budapest, Hungary
| | - Péter R. Nagy
- Department of Physical Chemistry and Materials Science, Budapest University of Technology and Economics, P.O. Box 91, H-1521 Budapest, Hungary
| | - Dávid Mester
- Department of Physical Chemistry and Materials Science, Budapest University of Technology and Economics, P.O. Box 91, H-1521 Budapest, Hungary
| | - Zoltán Rolik
- Department of Physical Chemistry and Materials Science, Budapest University of Technology and Economics, P.O. Box 91, H-1521 Budapest, Hungary
| | - Gyula Samu
- Department of Physical Chemistry and Materials Science, Budapest University of Technology and Economics, P.O. Box 91, H-1521 Budapest, Hungary
| | - József Csontos
- Department of Physical Chemistry and Materials Science, Budapest University of Technology and Economics, P.O. Box 91, H-1521 Budapest, Hungary
| | - József Csóka
- Department of Physical Chemistry and Materials Science, Budapest University of Technology and Economics, P.O. Box 91, H-1521 Budapest, Hungary
| | - P. Bernát Szabó
- Department of Physical Chemistry and Materials Science, Budapest University of Technology and Economics, P.O. Box 91, H-1521 Budapest, Hungary
| | - László Gyevi-Nagy
- Department of Physical Chemistry and Materials Science, Budapest University of Technology and Economics, P.O. Box 91, H-1521 Budapest, Hungary
| | - Bence Hégely
- Department of Physical Chemistry and Materials Science, Budapest University of Technology and Economics, P.O. Box 91, H-1521 Budapest, Hungary
| | - István Ladjánszki
- Department of Physical Chemistry and Materials Science, Budapest University of Technology and Economics, P.O. Box 91, H-1521 Budapest, Hungary
| | - Lóránt Szegedy
- Department of Physical Chemistry and Materials Science, Budapest University of Technology and Economics, P.O. Box 91, H-1521 Budapest, Hungary
| | - Bence Ladóczki
- Department of Physical Chemistry and Materials Science, Budapest University of Technology and Economics, P.O. Box 91, H-1521 Budapest, Hungary
| | - Klára Petrov
- Department of Physical Chemistry and Materials Science, Budapest University of Technology and Economics, P.O. Box 91, H-1521 Budapest, Hungary
| | - Máté Farkas
- Department of Physical Chemistry and Materials Science, Budapest University of Technology and Economics, P.O. Box 91, H-1521 Budapest, Hungary
| | - Pál D. Mezei
- Department of Physical Chemistry and Materials Science, Budapest University of Technology and Economics, P.O. Box 91, H-1521 Budapest, Hungary
| | - Ádám Ganyecz
- Department of Physical Chemistry and Materials Science, Budapest University of Technology and Economics, P.O. Box 91, H-1521 Budapest, Hungary
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20
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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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21
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Yoshizawa T, Filatov M, Cremer D, Zou W. Calculation of contact densities and Mössbauer isomer shifts utilising the Dirac-exact two-component normalised elimination of the small component (2c-NESC) method. Mol Phys 2018. [DOI: 10.1080/00268976.2018.1530463] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/28/2022]
Affiliation(s)
- Terutaka Yoshizawa
- Department of Chemistry, Southern Methodist University, Dallas, Texas, USA
- Department of Chemistry and Biochemistry, Graduate School of Humanities and Sciences, Ochanomizu University, Bunkyo-ku, Tokyo, Japan
| | - Michael Filatov
- Department of Chemistry, Southern Methodist University, Dallas, Texas, USA
- Department of Chemistry, Kyungpook National University, Daegu, South Korea
| | - Dieter Cremer
- Department of Chemistry, Southern Methodist University, Dallas, Texas, USA
| | - Wenli Zou
- Department of Chemistry, Southern Methodist University, Dallas, Texas, USA
- Institute of Modern Physics, Northwest University, Xi'an, Shaanxi, People's Republic of China
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22
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Wang Z, Wang F. Equation-of-motion coupled-cluster method for ionised states with spin-orbit coupling using open-shell reference wavefunction. Mol Phys 2018. [DOI: 10.1080/00268976.2018.1439188] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/18/2022]
Affiliation(s)
- Zhifan Wang
- School of Electronic Engineering, Chengdu Technological University, Chengdu, P. R.China
| | - Fan Wang
- Institute of Atomic and Molecular Physics, Sichuan University, Chengdu, P. R. China
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23
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Cheng L, Wang F, Stanton JF, Gauss J. Perturbative treatment of spin-orbit-coupling within spin-free exact two-component theory using equation-of-motion coupled-cluster methods. J Chem Phys 2018; 148:044108. [DOI: 10.1063/1.5012041] [Citation(s) in RCA: 27] [Impact Index Per Article: 4.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/22/2022] Open
Affiliation(s)
- Lan Cheng
- Department of Chemistry, The Johns Hopkins University, Baltimore, Maryland 21218, USA
| | - Fan Wang
- Institute of Atomic and Molecular Physics, Key Laboratory of High Energy Density Physics and Technology, Ministry of Education, Sichuan University, Chengdu, China
| | - John F. Stanton
- Department of Chemistry, University of Florida, Gainesville, Florida 32611, USA
| | - Jürgen Gauss
- Institut für Physikalische Chemie, Universität Mainz, D-55099 Mainz, Germany
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24
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Liu J, Shen Y, Asthana A, Cheng L. Two-component relativistic coupled-cluster methods using mean-field spin-orbit integrals. J Chem Phys 2018; 148:034106. [DOI: 10.1063/1.5009177] [Citation(s) in RCA: 34] [Impact Index Per Article: 5.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- Junzi Liu
- Department of Chemistry, The Johns Hopkins University, Baltimore, Maryland 21218, USA
| | - Yue Shen
- Department of Chemistry, The Johns Hopkins University, Baltimore, Maryland 21218, USA
| | - Ayush Asthana
- 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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25
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Mussard B, Sharma S. One-Step Treatment of Spin–Orbit Coupling and Electron Correlation in Large Active Spaces. J Chem Theory Comput 2017; 14:154-165. [DOI: 10.1021/acs.jctc.7b01019] [Citation(s) in RCA: 25] [Impact Index Per Article: 3.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/30/2022]
Affiliation(s)
- Bastien Mussard
- Department of Chemistry and
Biochemistry, University of Colorado Boulder, Boulder, Colorado 80302, United States
| | - Sandeep Sharma
- Department of Chemistry and
Biochemistry, University of Colorado Boulder, Boulder, Colorado 80302, United States
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26
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Lipparini F, Kirsch T, Köhn A, Gauss J. Internally Contracted Multireference Coupled Cluster Calculations with a Spin-Free Dirac–Coulomb Hamiltonian: Application to the Monoxides of Titanium, Zirconium, and Hafnium. J Chem Theory Comput 2017; 13:3171-3184. [DOI: 10.1021/acs.jctc.7b00110] [Citation(s) in RCA: 7] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Affiliation(s)
- Filippo Lipparini
- Institut
für Physikalische Chemie, Universität Mainz, Duesbergweg 10-14, D-55128 Mainz, Germany
| | - Till Kirsch
- Institut
für Physikalische Chemie, Universität Mainz, Duesbergweg 10-14, D-55128 Mainz, Germany
| | - Andreas Köhn
- Institut
für Theoretische Chemie, Universität Stuttgart, Pfaffenwaldring
55, D-70569 Stuttgart, Germany
| | - Jürgen Gauss
- Institut
für Physikalische Chemie, Universität Mainz, Duesbergweg 10-14, D-55128 Mainz, Germany
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27
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Akinaga Y, Nakajima T. Two-Component Relativistic Equation-of-Motion Coupled-Cluster Methods for Excitation Energies and Ionization Potentials of Atoms and Molecules. J Phys Chem A 2017; 121:827-835. [DOI: 10.1021/acs.jpca.6b10921] [Citation(s) in RCA: 20] [Impact Index Per Article: 2.9] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/30/2022]
Affiliation(s)
| | - Takahito Nakajima
- RIKEN Advanced Institute for Computational Science, Kobe 650-0047, Japan
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28
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Ghosh A, Chaudhuri RK, Chattopadhyay S. Relativistic state-specific multireference coupled cluster theory description for bond-breaking energy surfaces. J Chem Phys 2016; 145:124303. [DOI: 10.1063/1.4962911] [Citation(s) in RCA: 10] [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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29
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Lipparini F, Gauss J. Cost-Effective Treatment of Scalar Relativistic Effects for Multireference Systems: A CASSCF Implementation Based on the Spin-free Dirac–Coulomb Hamiltonian. J Chem Theory Comput 2016; 12:4284-95. [DOI: 10.1021/acs.jctc.6b00609] [Citation(s) in RCA: 18] [Impact Index Per Article: 2.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Affiliation(s)
- Filippo Lipparini
- Institut
für Physikalische
Chemie, Universität Mainz, Duesbergweg 10-14, D-55128 Mainz, Germany
| | - Jürgen Gauss
- Institut
für Physikalische
Chemie, Universität Mainz, Duesbergweg 10-14, D-55128 Mainz, Germany
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30
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Sørensen LK, Olsen J. Collecting all intermediates with an optimal scaling for the generalised-active-space coupled-cluster method with application to SbH. Mol Phys 2016. [DOI: 10.1080/00268976.2016.1195926] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/21/2022]
Affiliation(s)
- Lasse K. Sørensen
- Department of Chemistry, The qLEAP Center for Theoretical Chemistry, Aarhus University, Aarhus, Denmark
- Department of Chemistry, Ångström Laboratory, Uppsala University, Uppsala, Sweden
| | - Jeppe Olsen
- Department of Chemistry, The qLEAP Center for Theoretical Chemistry, Aarhus University, Aarhus, Denmark
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31
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Shiozaki T, Mizukami W. Relativistic Internally Contracted Multireference Electron Correlation Methods. J Chem Theory Comput 2015; 11:4733-9. [DOI: 10.1021/acs.jctc.5b00754] [Citation(s) in RCA: 29] [Impact Index Per Article: 3.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Affiliation(s)
- Toru Shiozaki
- Department
of Chemistry, Northwestern University, 2145 Sheridan Rd., Evanston, Illinois 60208, United States
| | - Wataru Mizukami
- Department
of Energy and Material Sciences, Faculty of Engineering Sciences, Kyushu University, 6-1 Kasuga-Park, Fukuoka, 816-8580, Japan
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32
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Eriksen JJ, Matthews DA, Jørgensen P, Gauss J. Communication: The performance of non-iterative coupled cluster quadruples models. J Chem Phys 2015; 143:041101. [DOI: 10.1063/1.4927247] [Citation(s) in RCA: 13] [Impact Index Per Article: 1.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/14/2022] Open
Affiliation(s)
- Janus J. Eriksen
- Department of Chemistry, qLEAP Center for Theoretical Chemistry, Aarhus University, DK-8000 Aarhus C, Denmark
| | - Devin A. Matthews
- The Institute for Computational Engineering and Sciences, The University of Texas at Austin, Austin, Texas 78712, USA
| | - Poul Jørgensen
- Department of Chemistry, qLEAP Center for Theoretical Chemistry, Aarhus University, DK-8000 Aarhus C, Denmark
| | - Jürgen Gauss
- Institut für Physikalische Chemie, Johannes Gutenberg-Universität Mainz, D-55128 Mainz, Germany
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33
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MacLeod MK, Shiozaki T. Communication: Automatic code generation enables nuclear gradient computations for fully internally contracted multireference theory. J Chem Phys 2015; 142:051103. [DOI: 10.1063/1.4907717] [Citation(s) in RCA: 78] [Impact Index Per Article: 8.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/04/2023] Open
Affiliation(s)
- Matthew K. MacLeod
- Department of Chemistry, Northwestern University, 2145 Sheridan Rd., Evanston, Illinois 60208, USA
| | - Toru Shiozaki
- Department of Chemistry, Northwestern University, 2145 Sheridan Rd., Evanston, Illinois 60208, USA
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34
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Hedegård ED, Knecht S, Ryde U, Kongsted J, Saue T. Theoretical 57Fe Mössbauer spectroscopy: isomer shifts of [Fe]-hydrogenase intermediates. Phys Chem Chem Phys 2014; 16:4853-63. [DOI: 10.1039/c3cp54393e] [Citation(s) in RCA: 19] [Impact Index Per Article: 1.9] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/21/2022]
Abstract
A computational protocol for 57Fe isomer shifts, based on the relativistic eXact 2-Component Hamiltonian (X2C), is applied to discriminate between proposed intermediates of [Fe]-hydrogenase. Detailed analysis reveals that the difference in isomer shifts between two intermediates is due to an overlap effect.
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Affiliation(s)
- Erik Donovan Hedegård
- Department of Physics
- Chemistry and Pharmacy
- University of Southern Denmark
- Odense 5420 M, Denmark
| | - Stefan Knecht
- Department of Physics
- Chemistry and Pharmacy
- University of Southern Denmark
- Odense 5420 M, Denmark
| | - Ulf Ryde
- Department of Theoretical Chemistry
- Lund University
- Chemical Centre
- S-221 00 Lund, Sweden
| | - Jacob Kongsted
- Department of Physics
- Chemistry and Pharmacy
- University of Southern Denmark
- Odense 5420 M, Denmark
| | - Trond Saue
- Laboratoire de Chimie et Physique Quantiques (UMR 5626)
- CNRS/Université Toulouse III – Paul Sabatier
- F-31062 Toulouse cedex, France
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35
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Cheng L, Stopkowicz S, Gauss J. Spin-free Dirac-Coulomb calculations augmented with a perturbative treatment of spin-orbit effects at the Hartree-Fock level. J Chem Phys 2013; 139:214114. [DOI: 10.1063/1.4832739] [Citation(s) in RCA: 13] [Impact Index Per Article: 1.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022] Open
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36
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Hubert M, Olsen J, Loras J, Fleig T. General active space commutator-based coupled cluster theory of general excitation rank for electronically excited states: Implementation and application to ScH. J Chem Phys 2013; 139:194106. [DOI: 10.1063/1.4827638] [Citation(s) in RCA: 10] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/20/2022] Open
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37
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Csontos B, Nagy B, Csontos J, Kállay M. Dissociation of the Fluorine Molecule. J Phys Chem A 2013; 117:5518-28. [DOI: 10.1021/jp403387n] [Citation(s) in RCA: 21] [Impact Index Per Article: 1.9] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/23/2022]
Affiliation(s)
- Botond Csontos
- Department of Physical Chemistry and Materials
Science, Budapest University of Technology and Economics, P.O. Box 91, Budapest H-1521, Hungary
| | - Balázs Nagy
- Department of Physical Chemistry and Materials
Science, Budapest University of Technology and Economics, P.O. Box 91, Budapest H-1521, Hungary
| | - József Csontos
- Department of Physical Chemistry and Materials
Science, Budapest University of Technology and Economics, P.O. Box 91, Budapest H-1521, Hungary
| | - Mihály Kállay
- Department of Physical Chemistry and Materials
Science, Budapest University of Technology and Economics, P.O. Box 91, Budapest H-1521, Hungary
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38
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Kelley MS, Shiozaki T. Large-scale Dirac–Fock–Breit method using density fitting and 2-spinor basis functions. J Chem Phys 2013; 138:204113. [DOI: 10.1063/1.4807612] [Citation(s) in RCA: 35] [Impact Index Per Article: 3.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/15/2023] Open
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39
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Le A, Steimle TC, Skripnikov L, Titov AV. The molecular frame electric dipole moment and hyperfine interactions in hafnium fluoride, HfF. J Chem Phys 2013; 138:124313. [DOI: 10.1063/1.4794049] [Citation(s) in RCA: 14] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/16/2023] Open
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40
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Liang YN, Wang F, Guo J. Theoretical study on low-lying electronic states of Kr2(+), Xe2(+), and Rn2(+). J Chem Phys 2013; 138:094319. [PMID: 23485306 DOI: 10.1063/1.4792435] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
In this work, the equation-of-motion coupled-cluster approach with spin-orbit coupling (SOC) for ionization potentials (IP) at the singles and doubles level (EOMIP-CCSD) is employed to calculate spectroscopic constants of low-lying states of rare gas dimer ions Kr2(+), Xe2(+), and Rn2(+). Two approaches are proposed to include contributions of triples: (1) energies of these states are calculated by adding the IPs from EOMIP-CCSD and the CCSD(T) energy of the rare gas dimers and (2) CCSD(T) energies without SOC for Rg2(+) are first calculated and energies of these states with SOC are determined subsequently using the SOC matrix between these states. The first approach can provide accurate results for the three most stable states, while overestimates bond lengths for the other states. The second approach has been adopted previously and the SOC matrix element between (2)Σ1∕2 (+) and (2)Π1∕2 states was set to be 1/2 times that of the SOC constant. In our work, the SOC matrix elements are determined from the calculated IPs and reasonable results for these states can be achieved with this approach, which could be useful for experimental works.
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Affiliation(s)
- Yan-Ni Liang
- Key Laboratory of Chemical Laser, Dalian Institute of Chemical Physics, Chinese Academy of Sciences, Dalian 116023, People's Republic of China
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41
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Wang Z, Wang F. Spin–orbit coupling and electron correlation at various coupled-cluster levels for closed-shell diatomic molecules. Phys Chem Chem Phys 2013; 15:17922-8. [DOI: 10.1039/c3cp51749g] [Citation(s) in RCA: 8] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/15/2023]
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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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Peterson KA, Krause C, Stoll H, Hill JG, Werner HJ. Application of explicitly correlated coupled-cluster methods to molecules containing post-3d main group elements. Mol Phys 2011. [DOI: 10.1080/00268976.2011.624129] [Citation(s) in RCA: 27] [Impact Index Per Article: 2.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/16/2022]
Affiliation(s)
- Kirk A. Peterson
- a Department of Chemistry , Washington State University , Pullman , Washington 99164-4630 , USA
| | - Christine Krause
- b Institut für Theoretische Chemie, Universität Stuttgart , Pfaffenwaldring 55, D-70569 Stuttgart , Germany
| | - Hermann Stoll
- b Institut für Theoretische Chemie, Universität Stuttgart , Pfaffenwaldring 55, D-70569 Stuttgart , Germany
| | - J. Grant Hill
- a Department of Chemistry , Washington State University , Pullman , Washington 99164-4630 , USA
| | - Hans-Joachim Werner
- b Institut für Theoretische Chemie, Universität Stuttgart , Pfaffenwaldring 55, D-70569 Stuttgart , Germany
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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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Sørensen LK, Olsen J, Fleig T. Two- and four-component relativistic generalized-active-space coupled cluster method: Implementation and application to BiH. J Chem Phys 2011; 134:214102. [DOI: 10.1063/1.3592148] [Citation(s) in RCA: 24] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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