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

Liu, Junzi; Zheng, Xuechen; Asthana, Ayush; Zhang, Chaoqun; Cheng, Lan

doi:10.1063/5.0038779

Title: 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

Journal Article · 11 February 2021 · Journal of Chemical Physics

DOI: https://doi.org/10.1063/5.0038779 · OSTI ID:1777829

Liu, Junzi ^[1]; Zheng, Xuechen ^[2]; Asthana, Ayush ^[2]; Zhang, Chaoqun ^[2];

^[2]

Johns Hopkins Univ., Baltimore, MD (United States); Johns Hopkins University
Johns Hopkins Univ., Baltimore, MD (United States)

The paper reports 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. Here, the new development extends the applicability of relativistic coupled cluster methods for heavy-element chemistry and spectroscopy. 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 usefulness of the present analytic scheme.

View Accepted Manuscript (DOE)

Cite

Export

Save

Research Organization:: Johns Hopkins Univ., Baltimore, MD (United States)

Sponsoring Organization:: USDOE; USDOE Office of Science (SC), Basic Energy Sciences (BES)

Grant/Contract Number:: SC0020317

OSTI ID:: 1777829

Journal Information:: Journal of Chemical Physics, Journal Name: Journal of Chemical Physics Journal Issue: 6 Vol. 154; ISSN 0021-9606

Publisher:: American Institute of Physics (AIP)Copyright Statement

Country of Publication:: United States

Language:: English

References (124)

An Introduction to Coupled Cluster Theory for Computational Chemists Crawford, T. Daniel; Schaefer, Henry F.; Lipkowitz, Kenny B. Reviews in Computational Chemistry: Lipkowitz/Reviews https://doi.org/10.1002/9780470125915.ch2	book	January 2000
Calculation of response properties with the normalized elimination of the small component method Filatov, Michael; Zou, Wenli; Cremer, Dieter International Journal of Quantum Chemistry, Vol. 114, Issue 15 https://doi.org/10.1002/qua.24578	journal	November 2013
Analytic energy derivatives in relativistic quantum chemistry Cheng, Lan; Stopkowicz, Stella; Gauss, Jürgen International Journal of Quantum Chemistry, Vol. 114, Issue 17 https://doi.org/10.1002/qua.24636	journal	February 2014
Theoretical models incorporating electron correlation Pople, John A.; Binkley, J. Stephen; Seeger, Rolf International Journal of Quantum Chemistry, Vol. 10, Issue S10 https://doi.org/10.1002/qua.560100802	journal	January 1976
Derivative studies in hartree-fock and møller-plesset theories Pople, J. A.; Krishnan, R.; Schlegel, H. B. International Journal of Quantum Chemistry, Vol. 16, Issue S13 https://doi.org/10.1002/qua.560160825	journal	March 1979
Analytical gradients for the coupled-cluster method Adamowicz, L.; Laidig, W. D.; Bartlett, R. J. International Journal of Quantum Chemistry, Vol. 26, Issue S18 https://doi.org/10.1002/qua.560260825	journal	March 1984
Kramers-restricted closed-shellCCSD theory Visscher, Lucas; Dyall, Kenneth G.; Lee, Timothy J. International Journal of Quantum Chemistry, Vol. 56, Issue S29 https://doi.org/10.1002/qua.560560844	journal	February 1995
Analytical derivatives, forces, force constants, molecular geometries, and related response properties in electronic structure theory: Analytical calculation of energy derivatives Pulay, Peter Wiley Interdisciplinary Reviews: Computational Molecular Science, Vol. 4, Issue 3 https://doi.org/10.1002/wcms.1171	journal	September 2013
Dirac–Fock Atomic Electronic Structure Calculations Using Different Nuclear Charge Distributions Visscher, L.; Dyall, K. G. Atomic Data and Nuclear Data Tables, Vol. 67, Issue 2 https://doi.org/10.1006/adnd.1997.0751	journal	November 1997
Four-Component Electronic Structure Methods for Molecules Saue, T.; Visscher, L.; Lipscomb, W. N. Theoretical Chemistry and Physics of Heavy and Superheavy Elements, Vol. 11, p. 211-267 https://doi.org/10.1007/978-94-017-0105-1_6	book	January 2003
Direct determination of pair natural orbitals: A new method to solve the multi-configuration hartree-fock problem for two-electron wave functions Ahlrichs, Reinhart; Driessler, Frank Theoretica Chimica Acta, Vol. 36, Issue 4 https://doi.org/10.1007/bf00549691	journal	January 1975
A relativistic 4-component general-order multi-reference coupled cluster method: initial implementation and application to HBr Fleig, Timo; Sørensen, Lasse K.; Olsen, Jeppe Theoretical Chemistry Accounts, Vol. 118, Issue 2 https://doi.org/10.1007/s00214-007-0265-y	journal	March 2007
Relativistic Gaussian basis sets for the elements K - Uuo Faegri Jr, Knut Theoretical Chemistry Accounts: Theory, Computation, and Modeling (Theoretica Chimica Acta), Vol. 105, Issue 3 https://doi.org/10.1007/s002140000209	journal	January 2001
Variational principles and linked-cluster exp S expansions for static and dynamic many-body problems Arponen, Jouko Annals of Physics, Vol. 151, Issue 2 https://doi.org/10.1016/0003-4916(83)90284-1	journal	December 1983
On the efficient evaluation of analytic energy gradients Rice, J. E.; Amos, R. D. Chemical Physics Letters, Vol. 122, Issue 6 https://doi.org/10.1016/0009-2614(85)87275-4	journal	December 1985
Analytical differentiation of the energy contribution due to triple excitations in quadratic configuration interaction theory Gauss, Jürgen; Cremer, Dieter Chemical Physics Letters, Vol. 163, Issue 6 https://doi.org/10.1016/0009-2614(89)85185-1	journal	November 1989
Analytic energy gradients for open-shell coupled-cluster singles and doubles (CCSD) calculations using restricted open-shell Hartree—Fock (ROHF) reference functions Gauss, Jürgen; Lauderdale, Walter J.; Stanton, John F. Chemical Physics Letters, Vol. 182, Issue 3-4 https://doi.org/10.1016/0009-2614(91)80203-a	journal	August 1991
A comparison of the efficiency and accuracy of the quadratic configuration interaction (QCISD), coupled cluster (CCSD), and Brueckner coupled cluster (BCCD) methods Hampel, Claudia; Peterson, Kirk A.; Werner, Hans-Joachim Chemical Physics Letters, Vol. 190, Issue 1-2 https://doi.org/10.1016/0009-2614(92)86093-w	journal	February 1992
Open-shell analytical energy gradients for triple excitation many-body, coupled-cluster methods: MBPT(4), CCSD+T(CCSD), CCSD(T),and QCISD(T) Watts, John D.; Gauss, Jürgen; Bartlett, Rodney J. Chemical Physics Letters, Vol. 200, Issue 1-2 https://doi.org/10.1016/0009-2614(92)87036-o	journal	November 1992
The millimeter and sub-millimeter spectrum of the BaOH radical Anderson, M. A.; Allen, M. D.; Barcaly, W. L. Chemical Physics Letters, Vol. 205, Issue 4-5 https://doi.org/10.1016/0009-2614(93)87144-r	journal	April 1993
A direct atomic orbital driven implementation of the coupled cluster singles and doubles (CCSD) model Koch, Henrik; Christiansen, Ove; Kobayashi, Rika Chemical Physics Letters, Vol. 228, Issue 1-3 https://doi.org/10.1016/0009-2614(94)00898-1	journal	September 1994
On the construction of double group molecular symmetry functions Visscher, Lucas Chemical Physics Letters, Vol. 253, Issue 1-2 https://doi.org/10.1016/0009-2614(96)00234-5	journal	April 1996
Stability conditions and nuclear rotations in the Hartree-Fock theory Thouless, D. J. Nuclear Physics, Vol. 21 https://doi.org/10.1016/0029-5582(60)90048-1	journal	November 1960
Formation, microwave spectrum and molecular constants of bismuth monochloride Kuijpers, P.; Törring, T.; Dymanus, A. Chemical Physics, Vol. 18, Issue 3-4 https://doi.org/10.1016/0301-0104(76)87121-2	journal	December 1976
Millimeter wave spectrum of gaseous bismuth monofluoride (BiF) Kuijpers, P.; Dymanus, A. Chemical Physics, Vol. 24, Issue 1 https://doi.org/10.1016/0301-0104(77)85082-9	journal	August 1977
Rotational spectrum and hyperfine structure of the 2Σ radicals BaF and BaCl Ryzlewicz, Ch.; Schütze-Pahlmann, H. -U.; Hoeft, J. Chemical Physics, Vol. 71, Issue 3 https://doi.org/10.1016/0301-0104(82)85045-3	journal	October 1982
First-order MP2 molecular properties in a relativistic framework van Stralen, Joost N. P.; Visscher, Lucas; Larsen, Christoffer Vaaben Chemical Physics, Vol. 311, Issue 1-2 https://doi.org/10.1016/j.chemphys.2004.10.018	journal	April 2005
Optical Stark spectroscopy of the (000)← (000) system of barium monohydroxide, BaOH Frey, Sarah E.; Steimle, Timothy C. Chemical Physics Letters, Vol. 512, Issue 1-3 https://doi.org/10.1016/j.cplett.2011.06.070	journal	August 2011
Broadband velocity modulation spectroscopy of HfF+: Towards a measurement of the electron electric dipole moment Cossel, Kevin C.; Gresh, Daniel N.; Sinclair, Laura C. Chemical Physics Letters, Vol. 546 https://doi.org/10.1016/j.cplett.2012.06.037	journal	September 2012
The pure rotational spectrum of YbOH Nakhate, Sanjay; Steimle, Timothy C.; Pilgram, Nickolas H. Chemical Physics Letters, Vol. 715 https://doi.org/10.1016/j.cplett.2018.11.030	journal	January 2019
On the dipole moments of some excited electronic states of HfS and HfO Hansson, Annie; Pettersson, Anders; Royen, Peder Journal of Molecular Spectroscopy, Vol. 224, Issue 2 https://doi.org/10.1016/j.jms.2004.01.010	journal	April 2004
The rotational spectrum of BiO radical in its X1 2Π1/2 and X2 2Π3/2 states Cohen, E. A.; Goodridge, D. M.; Kawaguchi, K. Journal of Molecular Spectroscopy, Vol. 239, Issue 1 https://doi.org/10.1016/j.jms.2006.05.011	journal	September 2006
Microwave spectra, nuclear field shift effects, geometries and hyperfine constants of bismuth mononitride, BiN, and bismuth monophosphide, BiP Cooke, Stephen A.; Michaud, Julie M.; Gerry, Michael C. L. Journal of Molecular Structure, Vol. 695-696 https://doi.org/10.1016/j.molstruc.2003.10.049	journal	June 2004
A fifth-order perturbation comparison of electron correlation theories Raghavachari, Krishnan; Trucks, Gary W.; Pople, John A. Chemical Physics Letters, Vol. 157, Issue 6 https://doi.org/10.1016/s0009-2614(89)87395-6	journal	May 1989
Restricted Møller—Plesset theory for open-shell molecules Knowles, Peter J.; Andrews, Jamie S.; Amos, Roger D. Chemical Physics Letters, Vol. 186, Issue 2-3 https://doi.org/10.1016/s0009-2614(91)85118-g	journal	November 1991
Spin-orbit effects calculated by two-component coupled-cluster methods: test calculations on AuH, Au2, TlH and Tl2 Lee, Hyo-Sug; Han, Young-Kyu; Kim, Myeong Cheol Chemical Physics Letters, Vol. 293, Issue 1-2 https://doi.org/10.1016/s0009-2614(98)00760-x	journal	August 1998
Analytic Gradients of Approximate Coupled Cluster Methods with Quadruple Excitations Matthews, Devin A. Journal of Chemical Theory and Computation https://doi.org/10.1021/acs.jctc.0c00522	journal	September 2020
Relativistic effects on chemical properties Pitzer, Kenneth S. Accounts of Chemical Research, Vol. 12, Issue 8 https://doi.org/10.1021/ar50140a001	journal	August 1979
Relativity and the periodic system of elements Pyykko, Pekka; Desclaux, Jean Paul Accounts of Chemical Research, Vol. 12, Issue 8 https://doi.org/10.1021/ar50140a002	journal	August 1979
Relativistic effects in structural chemistry Pyykko, Pekka Chemical Reviews, Vol. 88, Issue 3 https://doi.org/10.1021/cr00085a006	journal	May 1988
Factors Contributing to the Accuracy of Harmonic Force Field Calculations for Water Cortez, Michael H.; Brinkmann, Nicole R.; Polik, William F. Journal of Chemical Theory and Computation, Vol. 3, Issue 4 https://doi.org/10.1021/ct600347e	journal	May 2007
Main Group Atoms and Dimers Studied with a New Relativistic ANO Basis Set Roos, Björn O.; Lindh, Roland; Malmqvist, Per-Åke https://doi.org/10.1021/jp031064+		December 2003
New Relativistic ANO Basis Sets for Transition Metal Atoms Roos, Björn O.; Lindh, Roland; Malmqvist, Per-Åke The Journal of Physical Chemistry A, Vol. 109, Issue 29 https://doi.org/10.1021/jp0581126	journal	July 2005
Basis Set Limit CCSD(T) Harmonic Vibrational Frequencies ^† Tew, David P.; Klopper, Wim; Heckert, Miriam The Journal of Physical Chemistry A, Vol. 111, Issue 44 https://doi.org/10.1021/jp070851u	journal	November 2007
Analytic first and second derivatives for the CCSDT-n (n = 1–3) models: a first step towards the efficient calculation of CCSDT properties Gauss, Jürgen; Stanton, John F. Physical Chemistry Chemical Physics, Vol. 2, Issue 10 https://doi.org/10.1039/a909820h	journal	January 2000
The accurate determination of molecular equilibrium structures Bak, Keld L.; Gauss, Jürgen; Jørgensen, Poul The Journal of Chemical Physics, Vol. 114, Issue 15 https://doi.org/10.1063/1.1357225	journal	April 2001
Fourier transform microwave spectroscopy of the 2Σ+ ground states of YbX (X=F, Cl, Br): Characterization of hyperfine effects and determination of the molecular geometries Dickinson, C. S.; Coxon, J. A.; Walker, N. R. The Journal of Chemical Physics, Vol. 115, Issue 15 https://doi.org/10.1063/1.1404146	journal	October 2001
Interfacing relativistic and nonrelativistic methods. IV. One- and two-electron scalar approximations Dyall, Kenneth G. The Journal of Chemical Physics, Vol. 115, Issue 20 https://doi.org/10.1063/1.1413512	journal	November 2001
Analytic gradients for the coupled-cluster singles, doubles, and triples (CCSDT) model Gauss, Jürgen; Stanton, John F. The Journal of Chemical Physics, Vol. 116, Issue 5 https://doi.org/10.1063/1.1429244	journal	February 2002
Linear response at the 4-component relativistic level: Application to the frequency-dependent dipole polarizabilities of the coinage metal dimers Saue, T.; Jensen, H. J. Aa. The Journal of Chemical Physics, Vol. 118, Issue 2 https://doi.org/10.1063/1.1522407	journal	January 2003
Analytic first derivatives for general coupled-cluster and configuration interaction models Kállay, Mihály; Gauss, Jürgen; Szalay, Péter G. The Journal of Chemical Physics, Vol. 119, Issue 6 https://doi.org/10.1063/1.1589003	journal	August 2003
Force Constants and Dipole‐Moment Derivatives of Molecules from Perturbed Hartree–Fock Calculations. I Gerratt, J.; Mills, I. M. The Journal of Chemical Physics, Vol. 49, Issue 4 https://doi.org/10.1063/1.1670299	journal	August 1968
Hyperfine Interaction and Chemical Bonding in MgF, CaF, SrF, and BaF molecules Knight, L. B.; Easley, W. C.; Weltner, W. The Journal of Chemical Physics, Vol. 54, Issue 1 https://doi.org/10.1063/1.1674610	journal	January 1971
Coupled-cluster methods including noniterative corrections for quadruple excitations Bomble, Yannick J.; Stanton, John F.; Kállay, Mihály The Journal of Chemical Physics, Vol. 123, Issue 5 https://doi.org/10.1063/1.1950567	journal	August 2005
The accuracy of ab initio molecular geometries for systems containing second-row atoms Coriani, Sonia; Marchesan, Domenico; Gauss, Jürgen The Journal of Chemical Physics, Vol. 123, Issue 18 https://doi.org/10.1063/1.2104387	journal	November 2005
Nuclear electric quadrupole moment of gold Belpassi, Leonardo; Tarantelli, Francesco; Sgamellotti, Antonio The Journal of Chemical Physics, Vol. 126, Issue 6 https://doi.org/10.1063/1.2436881	journal	February 2007
Closed-shell coupled-cluster theory with spin-orbit coupling Wang, Fan; Gauss, Jürgen; van Wüllen, Christoph The Journal of Chemical Physics, Vol. 129, Issue 6 https://doi.org/10.1063/1.2968136	journal	August 2008
Analytic energy gradients in closed-shell coupled-cluster theory with spin-orbit coupling Wang, Fan; Gauss, Jürgen The Journal of Chemical Physics, Vol. 129, Issue 17 https://doi.org/10.1063/1.3000010	journal	November 2008
Exact two-component Hamiltonians revisited Liu, Wenjian; Peng, Daoling The Journal of Chemical Physics, Vol. 131, Issue 3 https://doi.org/10.1063/1.3159445	journal	July 2009
General implementation of the relativistic coupled-cluster method Nataraj, Huliyar S.; Kállay, Mihály; Visscher, Lucas The Journal of Chemical Physics, Vol. 133, Issue 23 https://doi.org/10.1063/1.3518712	journal	December 2010
Fourth-order relativistic corrections to electrical first-order properties using direct perturbation theory Stopkowicz, Stella; Gauss, Jürgen The Journal of Chemical Physics, Vol. 134, Issue 20 https://doi.org/10.1063/1.3587633	journal	May 2011
Analytical evaluation of first-order electrical properties based on the spin-free Dirac-Coulomb Hamiltonian Cheng, Lan; Gauss, Jürgen The Journal of Chemical Physics, Vol. 134, Issue 24 https://doi.org/10.1063/1.3601056	journal	June 2011
Development and application of the analytical energy gradient for the normalized elimination of the small component method Zou, Wenli; Filatov, Michael; Cremer, Dieter The Journal of Chemical Physics, Vol. 134, Issue 24 https://doi.org/10.1063/1.3603454	journal	June 2011
Symmetry exploitation in closed-shell coupled-cluster theory with spin-orbit coupling Tu, Zheyan; Yang, Dong-Dong; Wang, Fan The Journal of Chemical Physics, Vol. 135, Issue 3 https://doi.org/10.1063/1.3611052	journal	July 2011
Analytic energy gradients for the spin-free exact two-component theory using an exact block diagonalization for the one-electron Dirac Hamiltonian Cheng, Lan; Gauss, Jürgen The Journal of Chemical Physics, Vol. 135, Issue 8 https://doi.org/10.1063/1.3624397	journal	August 2011
Theory of self‐consistent electron pairs. An iterative method for correlated many‐electron wavefunctions Meyer, Wilfried The Journal of Chemical Physics, Vol. 64, Issue 7 https://doi.org/10.1063/1.432551	journal	April 1976
A full coupled‐cluster singles and doubles model: The inclusion of disconnected triples Purvis, George D.; Bartlett, Rodney J. The Journal of Chemical Physics, Vol. 76, Issue 4 https://doi.org/10.1063/1.443164	journal	February 1982
On the evaluation of analytic energy derivatives for correlated wave functions Handy, Nicholas C.; Schaefer, Henry F. The Journal of Chemical Physics, Vol. 81, Issue 11 https://doi.org/10.1063/1.447489	journal	December 1984
An efficient reformulation of the closed‐shell self‐consistent electron pair theory Pulay, Péter; Saebo/, Svein; Meyer, Wilfried The Journal of Chemical Physics, Vol. 81, Issue 4 https://doi.org/10.1063/1.447863	journal	August 1984
Hyperfine structure and electric dipole moment of BaF X ² Σ ⁺ Ernst, W. E.; Kändler, J.; Törring, T. The Journal of Chemical Physics, Vol. 84, Issue 9 https://doi.org/10.1063/1.449961	journal	May 1986
Rotational analysis of the B ̃ ² Σ ⁺ – X ̃ ² Σ ⁺ transition of BaOH and BaOD Kinsey‐Nielsen, S.; Brazier, C. R.; Bernath, P. F. The Journal of Chemical Physics, Vol. 84, Issue 2 https://doi.org/10.1063/1.450566	journal	January 1986
Property evaluation and orbital relaxation in coupled cluster methods Salter, E. A.; Sekino, Hideo; Bartlett, Rodney J. The Journal of Chemical Physics, Vol. 87, Issue 1 https://doi.org/10.1063/1.453596	journal	July 1987
Analytic evaluation of energy gradients for the single and double excitation coupled cluster (CCSD) wave function: Theory and application Scheiner, Andrew C.; Scuseria, Gustavo E.; Rice, Julia E. The Journal of Chemical Physics, Vol. 87, Issue 9 https://doi.org/10.1063/1.453655	journal	November 1987
Mo/ller–Plesset energy derivatives Jo/rgensen, Poul; Helgaker, Trygve The Journal of Chemical Physics, Vol. 89, Issue 3 https://doi.org/10.1063/1.455152	journal	August 1988
Analytic energy derivatives in many‐body methods. I. First derivatives Salter, E. A.; Trucks, Gary W.; Bartlett, Rodney J. The Journal of Chemical Physics, Vol. 90, Issue 3 https://doi.org/10.1063/1.456069	journal	February 1989
Gaussian basis sets for use in correlated molecular calculations. I. The atoms boron through neon and hydrogen Dunning, Thom H. The Journal of Chemical Physics, Vol. 90, Issue 2 https://doi.org/10.1063/1.456153	journal	January 1989
Pulsed‐nozzle Fourier‐transform microwave spectroscopy of laser‐vaporized metal oxides: Rotational spectra and electric dipole moments of YO, LaO, ZrO, and HfO Suenram, R. D.; Lovas, F. J.; Fraser, G. T. The Journal of Chemical Physics, Vol. 92, Issue 8 https://doi.org/10.1063/1.457690	journal	April 1990
Coupled cluster energy derivatives. Analytic Hessian for the closed‐shell coupled cluster singles and doubles wave function: Theory and applications Koch, Henrik; Jensen, Hans Jo/rgen Aa.; Jo/rgensen, Poul The Journal of Chemical Physics, Vol. 92, Issue 8 https://doi.org/10.1063/1.457710	journal	April 1990
Analytic evaluation of energy gradients for the singles and doubles coupled cluster method including perturbative triple excitations: Theory and applications to FOOF and Cr ₂ Scuseria, Gustavo E. The Journal of Chemical Physics, Vol. 94, Issue 1 https://doi.org/10.1063/1.460359	journal	January 1991
An efficient formulation and implementation of the analytic energy gradient method to the single and double excitation coupled‐cluster wave function: Application to Cl ₂ O ₂ Rendell, Alistair P.; Lee, Timothy J. The Journal of Chemical Physics, Vol. 94, Issue 9 https://doi.org/10.1063/1.460410	journal	May 1991
Analytic gradients for coupled‐cluster energies that include noniterative connected triple excitations: Application to c i s ‐ and t r a n s ‐HONO Lee, Timothy J.; Rendell, Alistair P. The Journal of Chemical Physics, Vol. 94, Issue 9 https://doi.org/10.1063/1.460411	journal	May 1991
A direct product decomposition approach for symmetry exploitation in many‐body methods. I. Energy calculations Stanton, John F.; Gauss, Jürgen; Watts, John D. The Journal of Chemical Physics, Vol. 94, Issue 6 https://doi.org/10.1063/1.460620	journal	March 1991
Coupled‐cluster open‐shell analytic gradients: Implementation of the direct product decomposition approach in energy gradient calculations Gauss, Jürgen; Stanton, John F.; Bartlett, Rodney J. The Journal of Chemical Physics, Vol. 95, Issue 4 https://doi.org/10.1063/1.460915	journal	August 1991
Analytic evaluation of energy gradients at the coupled‐cluster singles and doubles level using quasi‐restricted Hartree–Fock open‐shell reference functions Gauss, Jürgen; Stanton, John F.; Bartlett, Rodney J. The Journal of Chemical Physics, Vol. 95, Issue 4 https://doi.org/10.1063/1.460916	journal	August 1991
Coupled‐cluster methods with noniterative triple excitations for restricted open‐shell Hartree–Fock and other general single determinant reference functions. Energies and analytical gradients Watts, John D.; Gauss, Jürgen; Bartlett, Rodney J. The Journal of Chemical Physics, Vol. 98, Issue 11 https://doi.org/10.1063/1.464480	journal	June 1993
Coupled‐cluster calculations of nuclear magnetic resonance chemical shifts Gauss, Jürgen; Stanton, John F. The Journal of Chemical Physics, Vol. 103, Issue 9 https://doi.org/10.1063/1.470240	journal	September 1995
Laser‐rf double resonance spectroscopy of ¹⁷⁴ YbF in the X ² Σ ⁺ state: Spin‐rotation, hyperfine interactions, and the electric dipole moment Sauer, B. E.; Wang, Jun; Hinds, E. A. The Journal of Chemical Physics, Vol. 105, Issue 17 https://doi.org/10.1063/1.472569	journal	November 1996
Formulation and implementation of a relativistic unrestricted coupled‐cluster method including noniterative connected triples Visscher, Lucas; Lee, Timothy J.; Dyall, Kenneth G. The Journal of Chemical Physics, Vol. 105, Issue 19 https://doi.org/10.1063/1.472655	journal	November 1996
The prediction of molecular equilibrium structures by the standard electronic wave functions Helgaker, Trygve; Gauss, Jürgen; Jo/rgensen, Poul The Journal of Chemical Physics, Vol. 106, Issue 15 https://doi.org/10.1063/1.473634	journal	April 1997
Interfacing relativistic and nonrelativistic methods. I. Normalized elimination of the small component in the modified Dirac equation Dyall, Kenneth G. The Journal of Chemical Physics, Vol. 106, Issue 23 https://doi.org/10.1063/1.473860	journal	June 1997
A point-charge model for the nuclear quadrupole moment: Coupled-cluster, Dirac–Fock, Douglas–Kroll, and nonrelativistic Hartree–Fock calculations for the Cu and F electric field gradients in CuF Pernpointner, Markus; Seth, Michael; Schwerdtfeger, Peter The Journal of Chemical Physics, Vol. 108, Issue 16 https://doi.org/10.1063/1.476088	journal	April 1998
On the spin separation of algebraic two-component relativistic Hamiltonians: Molecular properties Li, Zhendong; Xiao, Yunlong; Liu, Wenjian The Journal of Chemical Physics, Vol. 141, Issue 5 https://doi.org/10.1063/1.4891567	journal	August 2014
Analytic energy gradients for the coupled-cluster singles and doubles method with the density-fitting approximation Bozkaya, Uğur; Sherrill, C. David The Journal of Chemical Physics, Vol. 144, Issue 17 https://doi.org/10.1063/1.4948318	journal	May 2016
Correlation consistent basis sets for lanthanides: The atoms La–Lu Lu, Qing; Peterson, Kirk A. The Journal of Chemical Physics, Vol. 145, Issue 5 https://doi.org/10.1063/1.4959280	journal	August 2016
Analytic one-electron properties at the 4-component relativistic coupled cluster level with inclusion of spin-orbit coupling Shee, Avijit; Visscher, Lucas; Saue, Trond The Journal of Chemical Physics, Vol. 145, Issue 18 https://doi.org/10.1063/1.4966643	journal	November 2016
Coupled-cluster method for open-shell heavy-element systems with spin-orbit coupling Cao, Zhanli; Wang, Fan; Yang, Mingli The Journal of Chemical Physics, Vol. 146, Issue 13 https://doi.org/10.1063/1.4979491	journal	April 2017
Communication: Theoretical study of HfF ⁺ cation to search for the T,P-odd interactions Skripnikov, L. V. The Journal of Chemical Physics, Vol. 147, Issue 2 https://doi.org/10.1063/1.4993622	journal	July 2017
Two-component relativistic coupled-cluster methods using mean-field spin-orbit integrals Liu, Junzi; Shen, Yue; Asthana, Ayush The Journal of Chemical Physics, Vol. 148, Issue 3 https://doi.org/10.1063/1.5009177	journal	January 2018
Analytical energy gradients for explicitly correlated wave functions. II. Explicitly correlated coupled cluster singles and doubles with perturbative triples corrections: CCSD(T)-F12 Győrffy, Werner; Werner, Hans-Joachim The Journal of Chemical Physics, Vol. 148, Issue 11 https://doi.org/10.1063/1.5020436	journal	March 2018
An atomic mean-field spin-orbit approach within exact two-component theory for a non-perturbative treatment of spin-orbit coupling Liu, Junzi; Cheng, Lan The Journal of Chemical Physics, Vol. 148, Issue 14 https://doi.org/10.1063/1.5023750	journal	April 2018
Exact two-component equation-of-motion coupled-cluster singles and doubles method using atomic mean-field spin-orbit integrals Asthana, Ayush; Liu, Junzi; Cheng, Lan The Journal of Chemical Physics, Vol. 150, Issue 7 https://doi.org/10.1063/1.5081715	journal	February 2019
Analytic evaluation of first-order properties within the mean-field variant of spin-free exact two-component theory Kirsch, Till; Engel, Franziska; Gauss, Jürgen The Journal of Chemical Physics, Vol. 150, Issue 20 https://doi.org/10.1063/1.5095698	journal	May 2019
Implementation of analytic gradients for CCSD and EOM-CCSD using Cholesky decomposition of the electron-repulsion integrals and their derivatives: Theory and benchmarks Feng, Xintian; Epifanovsky, Evgeny; Gauss, Jürgen The Journal of Chemical Physics, Vol. 151, Issue 1 https://doi.org/10.1063/1.5100022	journal	July 2019
A study of non-iterative triples contributions in relativistic equation-of-motion coupled-cluster calculations using an exact two-component Hamiltonian with atomic mean-field spin-orbit integrals: Application to uranyl and other heavy-element compounds Cheng, Lan The Journal of Chemical Physics, Vol. 151, Issue 10 https://doi.org/10.1063/1.5113796	journal	September 2019
The MRCC program system: Accurate quantum chemistry from water to proteins Kállay, Mihály; Nagy, Péter R.; Mester, Dávid The Journal of Chemical Physics, Vol. 152, Issue 7 https://doi.org/10.1063/1.5142048	journal	February 2020
Coupled-cluster techniques for computational chemistry: The CFOUR program package Matthews, Devin A.; Cheng, Lan; Harding, Michael E. The Journal of Chemical Physics, Vol. 152, Issue 21 https://doi.org/10.1063/5.0004837	journal	June 2020
Molecular equilibrium geometries based on coupled-cluster calculations including quadruple excitations Heckert, Miriam; KÁllay ‡, MihÁly; Gauss †, Jürgen Molecular Physics, Vol. 103, Issue 15-16 https://doi.org/10.1080/00268970500083416	journal	August 2005
Relativistic coupled-cluster calculations of the ¹⁷³ Yb nuclear quadrupole coupling constant for the YbF molecule Pašteka, L. F.; Mawhorter, R. J.; Schwerdtfeger, P. Molecular Physics, Vol. 114, Issue 7-8 https://doi.org/10.1080/00268976.2016.1139206	journal	February 2016
Year-2017 nuclear quadrupole moments Pyykkö, Pekka Molecular Physics, Vol. 116, Issue 10 https://doi.org/10.1080/00268976.2018.1426131	journal	February 2018
On the orbital contribution to analytical derivatives of perturbation theory energies Lee, Timothy J.; Racine, Stephen C.; Rice, Julia E. Molecular Physics, Vol. 85, Issue 3 https://doi.org/10.1080/00268979500101301	journal	June 1995
Analytic second derivatives in high-order many-body perturbation and coupled-cluster theories: Computational considerations and applications Stanton, John F.; Gauss, Jurgen International Reviews in Physical Chemistry, Vol. 19, Issue 1 https://doi.org/10.1080/014423500229864	journal	January 2000
Enhancement of the electric dipole moment of the electron in the YbF molecule Kozlov, M. G. Journal of Physics B: Atomic, Molecular and Optical Physics, Vol. 30, Issue 18 https://doi.org/10.1088/0953-4075/30/18/003	journal	September 1997
Precision Measurement of the Electron’s Electric Dipole Moment Using Trapped Molecular Ions Cairncross, William B.; Gresh, Daniel N.; Grau, Matt Physical Review Letters, Vol. 119, Issue 15 https://doi.org/10.1103/PhysRevLett.119.153001	journal	October 2017
Nuclear Quadrupole Moments of Bismuth Bieroń, Jacek; Pyykkö, Pekka Physical Review Letters, Vol. 87, Issue 13 https://doi.org/10.1103/PhysRevLett.87.133003	journal	September 2001
Hyperfine Structure of Bi 209 Hull, Robert J.; Brink, Gilbert O. Physical Review A, Vol. 1, Issue 3 https://doi.org/10.1103/physreva.1.685	journal	March 1970
Fine and hyperfine interaction in YbF 173 Wang, Hailing; Le, Anh T.; Steimle, Timothy C. Physical Review A, Vol. 100, Issue 2 https://doi.org/10.1103/physreva.100.022516	journal	August 2019
Field-free, Stark, and Zeeman spectroscopy of the A ̃ 2 Π 1 / 2 − X ̃ 2 Σ + transition of ytterbium monohydroxide Steimle, Timothy C.; Linton, Colan; Mengesha, Ephriem Tadesse Physical Review A, Vol. 100, Issue 5 https://doi.org/10.1103/physreva.100.052509	journal	November 2019
Nuclear electric quadrupole moment of bismuth from the molecular method Teodoro, Tiago Quevedo; Haiduke, Roberto Luiz Andrade Physical Review A, Vol. 88, Issue 5 https://doi.org/10.1103/physreva.88.052504	journal	November 2013
P , T -odd and magnetic hyperfine-interaction constants and excited-state lifetime for HfF + Fleig, Timo Physical Review A, Vol. 96, Issue 4 https://doi.org/10.1103/physreva.96.040502	journal	October 2017
Evaluation of CP violation in HfF + Petrov, A. N.; Skripnikov, L. V.; Titov, A. V. Physical Review A, Vol. 98, Issue 4 https://doi.org/10.1103/physreva.98.042502	journal	October 2018
Enhancement factor for the electric dipole moment of the electron in the BaOH and YbOH molecules Denis, Malika; Haase, Pi A. B.; Timmermans, Rob G. E. Physical Review A, Vol. 99, Issue 4 https://doi.org/10.1103/physreva.99.042512	journal	April 2019
Precision Measurement of Time-Reversal Symmetry Violation with Laser-Cooled Polyatomic Molecules Kozyryev, Ivan; Hutzler, Nicholas R. Physical Review Letters, Vol. 119, Issue 13 https://doi.org/10.1103/physrevlett.119.133002	journal	September 2017
Measurement of the Electron Electric Dipole Moment Using YbF Molecules Hudson, J. J.; Sauer, B. E.; Tarbutt, M. R. Physical Review Letters, Vol. 89, Issue 2 https://doi.org/10.1103/physrevlett.89.023003	journal	June 2002
Coupled-cluster theory in quantum chemistry Bartlett, Rodney J.; Musiał, Monika Reviews of Modern Physics, Vol. 79, Issue 1 https://doi.org/10.1103/revmodphys.79.291	journal	February 2007

Similar Records

Geometry optimizations with spinor-based relativistic coupled-cluster theory

Journal Article · 2022 · Journal of Chemical Physics · OSTI ID:1868359

Zheng, Xuechen; Zhang, Chaoqun; Liu, Junzi; +1 more

Analytic Gradients for Equation-of-Motion Coupled Cluster with Single, Double, and Perturbative Triple Excitations

Journal Article · 2024 · Journal of Chemical Theory and Computation · OSTI ID:2549295

Zhao, Tingting; Matthews, Devin. A.

Coupled-cluster singles, doubles, and triples calculations with Hartree-Fock and Brueckner orbital reference determinants: A comparative study

Conference · 1994 · OSTI ID:107043

Watts, J D; Bartlett, R J

Related Subjects

97 MATHEMATICS AND COMPUTING
Coupled-cluster methods
Electrical properties and parameters
Electronic correlation
Molecular properties
Relativistic effects
Spin-orbit interactions

Title: 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

Citation Formats

References (124)

Similar Records

Related Subjects