Analytic gradients for the single-reference driven similarity renormalization group second-order perturbation theory

Wang, Shuhe; Li, Chenyang; Evangelista, Francesco A.

doi:10.1063/1.5100175

Title: Analytic gradients for the single-reference driven similarity renormalization group second-order perturbation theory

Journal Article · 31 July 2019 · Journal of Chemical Physics

DOI: https://doi.org/10.1063/1.5100175 · OSTI ID:1612370

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Emory Univ., Atlanta, GA (United States)

Herein we derive and implement analytic energy gradients for the single-reference driven similarity renormalization group second-order perturbation theory (DSRG-PT2). The resulting equations possess an asymptotic scaling that is identical to that of the second-order Møller–Plesset perturbation theory (MP2), indicating that the exponential regularizer in the DSRG equations does not introduce formal difficulties in the gradient theory. We apply the DSRG-PT2 method to optimizing the geometries of 15 small molecules. The equilibrium bond lengths computed with DSRG-PT2 are found similar to those of MP2, yielding a mean absolute error of 0.0033 Å and a standard deviation of 0.0045 Å when compared with coupled cluster with singles, doubles, and perturbative triples.

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Research Organization:: Emory Univ., Atlanta, GA (United States)

Sponsoring Organization:: USDOE Office of Science (SC)

Grant/Contract Number:: SC0016004

OSTI ID:: 1612370

Alternate ID(s):: OSTI ID: 1545915

Journal Information:: Journal of Chemical Physics, Vol. 151, Issue 4; ISSN 0021-9606

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

Country of Publication:: United States

Language:: English

References (79)

Psi4 1.1: An Open-Source Electronic Structure Program Emphasizing Automation, Advanced Libraries, and Interoperability Parrish, Robert M.; Burns, Lori A.; Smith, Daniel G. A. Journal of Chemical Theory and Computation, Vol. 13, Issue 7 https://doi.org/10.1021/acs.jctc.7b00174	journal	June 2017
An improved algorithm for analytical gradient evaluation in resolution-of-the-identity second-order Møller-Plesset perturbation theory: Application to alanine tetrapeptide conformational analysis Distasio, Robert A.; Steele, Ryan P.; Rhee, Young Min Journal of Computational Chemistry, Vol. 28, Issue 5 https://doi.org/10.1002/jcc.20604	journal	April 2007
Multiconfigurational perturbation theory with level shift — the Cr2 potential revisited Roos, Björn O.; Andersson, Kerstin Chemical Physics Letters, Vol. 245, Issue 2-3 https://doi.org/10.1016/0009-2614(95)01010-7	journal	October 1995
Multireference Theories of Electron Correlation Based on the Driven Similarity Renormalization Group Li, Chenyang; Evangelista, Francesco A. Annual Review of Physical Chemistry, Vol. 70, Issue 1 https://doi.org/10.1146/annurev-physchem-042018-052416	journal	June 2019
Driven similarity renormalization group: Third-order multireference perturbation theory Li, Chenyang; Evangelista, Francesco A. The Journal of Chemical Physics, Vol. 146, Issue 12 https://doi.org/10.1063/1.4979016	journal	March 2017
Molecular Electronic-Structure Theory Helgaker, Trygve; Jørgensen, Poul; Olsen, Jeppe https://doi.org/10.1002/9781119019572	book	August 2000
Oscillator strengths, first-order properties, and nuclear gradients for local ADC(2) Schütz, Martin The Journal of Chemical Physics, Vol. 142, Issue 21 https://doi.org/10.1063/1.4921839	journal	June 2015
Molpro: a general-purpose quantum chemistry program package: Molpro Werner, Hans-Joachim; Knowles, Peter J.; Knizia, Gerald Wiley Interdisciplinary Reviews: Computational Molecular Science, Vol. 2, Issue 2 https://doi.org/10.1002/wcms.82	journal	July 2011
Direct Use of the Gradient for Investigating Molecular Energy Surfaces Pulay, Péter Applications of Electronic Structure Theory https://doi.org/10.1007/978-1-4684-8541-7_4	book	January 1977
Efficient distance-including integral screening in linear-scaling Møller-Plesset perturbation theory Maurer, Simon A.; Lambrecht, Daniel S.; Kussmann, Jörg The Journal of Chemical Physics, Vol. 138, Issue 1 https://doi.org/10.1063/1.4770502	journal	January 2013
A companion perturbation theory for state-specific multireference coupled cluster methods Evangelista, Francesco A.; Simmonett, Andrew C.; Schaefer III, Henry F. Physical Chemistry Chemical Physics, Vol. 11, Issue 23 https://doi.org/10.1039/b822910d	journal	January 2009
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
Orbital-optimized third-order Møller-Plesset perturbation theory and its spin-component and spin-opposite scaled variants: Application to symmetry breaking problems Bozkaya, Uğur The Journal of Chemical Physics, Vol. 135, Issue 22 https://doi.org/10.1063/1.3665134	journal	December 2011
Multiconfiguration Self-Consistent Field and Multireference Configuration Interaction Methods and Applications Szalay, Péter G.; Müller, Thomas; Gidofalvi, Gergely Chemical Reviews, Vol. 112, Issue 1 https://doi.org/10.1021/cr200137a	journal	December 2011
Towards numerically robust multireference theories: The driven similarity renormalization group truncated to one- and two-body operators Li, Chenyang; Evangelista, Francesco A. The Journal of Chemical Physics, Vol. 144, Issue 16 https://doi.org/10.1063/1.4947218	journal	April 2016
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
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
Second‐order perturbation theory with a complete active space self‐consistent field reference function Andersson, Kerstin; Malmqvist, Per‐Åke; Roos, Björn O. The Journal of Chemical Physics, Vol. 96, Issue 2 https://doi.org/10.1063/1.462209	journal	January 1992
Introduction of n -electron valence states for multireference perturbation theory Angeli, C.; Cimiraglia, R.; Evangelisti, S. The Journal of Chemical Physics, Vol. 114, Issue 23 https://doi.org/10.1063/1.1361246	journal	June 2001
Orbital-optimized opposite-spin scaled second-order correlation: An economical method to improve the description of open-shell molecules Lochan, Rohini C.; Head-Gordon, Martin The Journal of Chemical Physics, Vol. 126, Issue 16 https://doi.org/10.1063/1.2718952	journal	April 2007
A direct MP2 gradient method Frisch, Michael J.; Head-Gordon, Martin; Pople, John A. Chemical Physics Letters, Vol. 166, Issue 3 https://doi.org/10.1016/0009-2614(90)80029-d	journal	February 1990
GVVPT2 energy gradient using a Lagrangian formulation Theis, Daniel; Khait, Yuriy G.; Hoffmann, Mark R. The Journal of Chemical Physics, Vol. 135, Issue 4 https://doi.org/10.1063/1.3611049	journal	July 2011
Improved virtual orbitals in state specific multireference perturbation theory for prototypes of quasidegenerate electronic structure Sinha Ray, Suvonil; Ghosh, Pradipta; Chaudhuri, Rajat K. The Journal of Chemical Physics, Vol. 146, Issue 6 https://doi.org/10.1063/1.4975322	journal	February 2017
Estimates of the Ab Initio Limit for π−π Interactions: The Benzene Dimer Sinnokrot, Mutasem Omar; Valeev, Edward F.; Sherrill, C. David Journal of the American Chemical Society, Vol. 124, Issue 36 https://doi.org/10.1021/ja025896h	journal	September 2002
Comparative study of multireference perturbative theories for ground and excited states Hoffmann, Mark R.; Datta, Dipayan; Das, Sanghamitra The Journal of Chemical Physics, Vol. 131, Issue 20 https://doi.org/10.1063/1.3265769	journal	November 2009
Improved second-order Møller–Plesset perturbation theory by separate scaling of parallel- and antiparallel-spin pair correlation energies Grimme, Stefan The Journal of Chemical Physics, Vol. 118, Issue 20 https://doi.org/10.1063/1.1569242	journal	May 2003
Interaction Energy of Large Molecules from Restrained Denominator MP2-F12 Ohnishi, Yu-ya; Ishimura, Kazuya; Ten-no, Seiichiro Journal of Chemical Theory and Computation, Vol. 10, Issue 11 https://doi.org/10.1021/ct500738g	journal	October 2014
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-scaling atomic orbital-based second-order Møller–Plesset perturbation theory by rigorous integral screening criteria Doser, Bernd; Lambrecht, Daniel S.; Kussmann, Jörg The Journal of Chemical Physics, Vol. 130, Issue 6 https://doi.org/10.1063/1.3072903	journal	February 2009
Toward a systematic molecular orbital theory for excited states Foresman, James B.; Head-Gordon, Martin; Pople, John A. The Journal of Physical Chemistry, Vol. 96, Issue 1 https://doi.org/10.1021/j100180a030	journal	January 1992
Analytic gradients for Mukherjee’s multireference coupled-cluster method using two-configurational self-consistent-field orbitals Jagau, Thomas-C.; Prochnow, Eric; Evangelista, Francesco A. The Journal of Chemical Physics, Vol. 132, Issue 14 https://doi.org/10.1063/1.3370847	journal	April 2010
Nuclear Energy Gradients for Internally Contracted Complete Active Space Second-Order Perturbation Theory: Multistate Extensions Vlaisavljevich, Bess; Shiozaki, Toru Journal of Chemical Theory and Computation, Vol. 12, Issue 8 https://doi.org/10.1021/acs.jctc.6b00572	journal	July 2016
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
A derivation of the frozen-orbital unrestricted open-shell and restricted closed-shell second-order perturbation theory analytic gradient expressions Aikens, Christine M.; Webb, Simon P.; Bell, Rob L. Theoretical Chemistry Accounts: Theory, Computation, and Modeling (Theoretica Chimica Acta), Vol. 110, Issue 4 https://doi.org/10.1007/s00214-003-0453-3	journal	November 2003
Communication: Extended multi-state complete active space second-order perturbation theory: Energy and nuclear gradients Shiozaki, Toru; Győrffy, Werner; Celani, Paolo The Journal of Chemical Physics, Vol. 135, Issue 8 https://doi.org/10.1063/1.3633329	journal	August 2011
Analytic gradients for the state-specific multireference coupled cluster singles and doubles model Prochnow, Eric; Evangelista, Francesco A.; Schaefer, Henry F. The Journal of Chemical Physics, Vol. 131, Issue 6 https://doi.org/10.1063/1.3204017	journal	January 2009
A driven similarity renormalization group approach to quantum many-body problems Evangelista, Francesco A. The Journal of Chemical Physics, Vol. 141, Issue 5 https://doi.org/10.1063/1.4890660	journal	August 2014
Analytic energy gradients for the orbital-optimized second-order Møller–Plesset perturbation theory Bozkaya, Uğur; Sherrill, C. David The Journal of Chemical Physics, Vol. 138, Issue 18 https://doi.org/10.1063/1.4803662	journal	May 2013
Multireference Driven Similarity Renormalization Group: A Second-Order Perturbative Analysis Li, Chenyang; Evangelista, Francesco A. Journal of Chemical Theory and Computation, Vol. 11, Issue 5 https://doi.org/10.1021/acs.jctc.5b00134	journal	April 2015
Analytic energy gradients for the coupled-cluster singles and doubles with perturbative triples method with the density-fitting approximation Bozkaya, Uğur; Sherrill, C. David The Journal of Chemical Physics, Vol. 147, Issue 4 https://doi.org/10.1063/1.4994918	journal	July 2017
An orbital-invariant internally contracted multireference coupled cluster approach Evangelista, Francesco A.; Gauss, Jürgen The Journal of Chemical Physics, Vol. 134, Issue 11 https://doi.org/10.1063/1.3559149	journal	March 2011
Analytic gradients for excited states in the coupled-cluster model CC2 employing the resolution-of-the-identity approximation Köhn, Andreas; Hättig, Christof The Journal of Chemical Physics, Vol. 119, Issue 10 https://doi.org/10.1063/1.1597635	journal	September 2003
Canonical Van Vleck Quasidegenerate Perturbation Theory with Trigonometric Variables Hoffmann, Mark R. The Journal of Physical Chemistry, Vol. 100, Issue 15 https://doi.org/10.1021/jp952753r	journal	January 1996
Analytic energy gradients for multiconfigurational self-consistent field second-order quasidegenerate perturbation theory (MC-QDPT) Nakano, Haruyuki; Hirao, Kimihiko; Gordon, Mark S. The Journal of Chemical Physics, Vol. 108, Issue 14 https://doi.org/10.1063/1.475975	journal	April 1998
Erratum: “Driven similarity renormalization group: Third-order multireference perturbation theory” [J. Chem. Phys. 146, 124132 (2017)] Li, Chenyang; Evangelista, Francesco A. The Journal of Chemical Physics, Vol. 148, Issue 7 https://doi.org/10.1063/1.5023904	journal	February 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
Analytic formulation of derivative coupling vectors for complete active space configuration interaction wavefunctions with floating occupation molecular orbitals Hohenstein, Edward G. The Journal of Chemical Physics, Vol. 145, Issue 17 https://doi.org/10.1063/1.4966235	journal	November 2016
Intruder state avoidance multireference Møller-Plesset perturbation theory: Multireference Møller-Plesset Perturbation Theory Witek, Henryk A.; Choe, Yoong-Kee; Finley, James P. Journal of Computational Chemistry, Vol. 23, Issue 10 https://doi.org/10.1002/jcc.10098	journal	May 2002
Analytical energy gradients for internally contracted second-order multireference perturbation theory Celani, Paolo; Werner, Hans-Joachim The Journal of Chemical Physics, Vol. 119, Issue 10 https://doi.org/10.1063/1.1597672	journal	September 2003
The In-Medium Similarity Renormalization Group: A novel ab initio method for nuclei Hergert, H.; Bogner, S. K.; Morris, T. D. Physics Reports, Vol. 621 https://doi.org/10.1016/j.physrep.2015.12.007	journal	March 2016
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
Driven similarity renormalization group for excited states: A state-averaged perturbation theory Li, Chenyang; Evangelista, Francesco A. The Journal of Chemical Physics, Vol. 148, Issue 12 https://doi.org/10.1063/1.5019793	journal	March 2018
Imaginary Shift in CASPT2 Nuclear Gradient and Derivative Coupling Theory Park, Jae Woo; Al-Saadon, Rachael; Strand, Nils E. Journal of Chemical Theory and Computation, Vol. 15, Issue 7 https://doi.org/10.1021/acs.jctc.9b00368	journal	May 2019
Analytical gradients for tensor hyper-contracted MP2 and SOS-MP2 on graphical processing units Song, Chenchen; Martínez, Todd J. The Journal of Chemical Physics, Vol. 147, Issue 16 https://doi.org/10.1063/1.4997997	journal	October 2017
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
Regularized Orbital-Optimized Second-Order Møller–Plesset Perturbation Theory: A Reliable Fifth-Order-Scaling Electron Correlation Model with Orbital Energy Dependent Regularizers Lee, Joonho; Head-Gordon, Martin Journal of Chemical Theory and Computation, Vol. 14, Issue 10 https://doi.org/10.1021/acs.jctc.8b00731	journal	August 2018
Communication: Automatic code generation enables nuclear gradient computations for fully internally contracted multireference theory MacLeod, Matthew K.; Shiozaki, Toru The Journal of Chemical Physics, Vol. 142, Issue 5 https://doi.org/10.1063/1.4907717	journal	February 2015
Pilot applications of internally contracted multireference coupled cluster theory, and how to choose the cluster operator properly Hanauer, Matthias; Köhn, Andreas The Journal of Chemical Physics, Vol. 134, Issue 20 https://doi.org/10.1063/1.3592786	journal	May 2011
Lagrangian approach to molecular vibrational Raman intensities using time-dependent hybrid density functional theory Rappoport, Dmitrij; Furche, Filipp The Journal of Chemical Physics, Vol. 126, Issue 20 https://doi.org/10.1063/1.2744026	journal	May 2007
Analytical energy gradients for second-order multireference perturbation theory using density fitting Győrffy, Werner; Shiozaki, Toru; Knizia, Gerald The Journal of Chemical Physics, Vol. 138, Issue 10 https://doi.org/10.1063/1.4793737	journal	March 2013
Optimized spin-component scaled second-order Møller-Plesset perturbation theory for intermolecular interaction energies Distasio JR., Robert A.; Head-Gordon, Martin Molecular Physics, Vol. 105, Issue 8 https://doi.org/10.1080/00268970701283781	journal	April 2007
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
Derivative studies in configuration–interaction theory Krishnan, R.; Schlegel, H. B.; Pople, J. A. The Journal of Chemical Physics, Vol. 72, Issue 8 https://doi.org/10.1063/1.439708	journal	April 1980
Erratum: “Towards numerically robust multireference theories: The driven similarity renormalization group truncated to one- and two-body operators” [J. Chem. Phys. 144, 164114 (2016)] Li, Chenyang; Evangelista, Francesco A. The Journal of Chemical Physics, Vol. 148, Issue 7 https://doi.org/10.1063/1.5023493	journal	February 2018
Assessment of Orbital-Optimized, Spin-Component Scaled Second-Order Many-Body Perturbation Theory for Thermochemistry and Kinetics Neese, Frank; Schwabe, Tobias; Kossmann, Simone Journal of Chemical Theory and Computation, Vol. 5, Issue 11 https://doi.org/10.1021/ct9003299	journal	October 2009
Analytic energy gradients for the equation‐of‐motion coupled‐cluster method: Implementation and application to the HCN/HNC system Stanton, John F.; Gauss, Jürgen The Journal of Chemical Physics, Vol. 100, Issue 6 https://doi.org/10.1063/1.466253	journal	March 1994
A general multireference configuration interaction gradient program Shepard, R.; Lischka, H.; Szalay, P. G. The Journal of Chemical Physics, Vol. 96, Issue 3 https://doi.org/10.1063/1.462060	journal	February 1992
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
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
Analytic gradients for density cumulant functional theory: The DCFT-06 model Sokolov, Alexander Yu.; Wilke, Jeremiah J.; Simmonett, Andrew C. The Journal of Chemical Physics, Vol. 137, Issue 5 https://doi.org/10.1063/1.4739423	journal	August 2012
Analytic gradients for the spin-conserving and spin-flipping equation-of-motion coupled-cluster models with single and double substitutions Levchenko, Sergey V.; Wang, Tao; Krylov, Anna I. The Journal of Chemical Physics, Vol. 122, Issue 22 https://doi.org/10.1063/1.1877072	journal	June 2005
Comparison of low-order multireference many-body perturbation theories Chaudhuri, Rajat K.; Freed, Karl F.; Hose, Gabriel The Journal of Chemical Physics, Vol. 122, Issue 13 https://doi.org/10.1063/1.1863912	journal	April 2005
Scaled opposite-spin second order Møller–Plesset correlation energy: An economical electronic structure method Jung, Yousung; Lochan, Rohini C.; Dutoi, Anthony D. The Journal of Chemical Physics, Vol. 121, Issue 20 https://doi.org/10.1063/1.1809602	journal	November 2004
A Jeziorski-Monkhorst fully uncontracted multi-reference perturbative treatment. I. Principles, second-order versions, and tests on ground state potential energy curves Giner, Emmanuel; Angeli, Celestino; Garniron, Yann The Journal of Chemical Physics, Vol. 146, Issue 22 https://doi.org/10.1063/1.4984616	journal	June 2017
Multireference Møller—Plesset method Hirao, K. Chemical Physics Letters, Vol. 190, Issue 3-4 https://doi.org/10.1016/0009-2614(92)85354-d	journal	March 1992
A low-cost approach to electronic excitation energies based on the driven similarity renormalization group Li, Chenyang; Verma, Prakash; Hannon, Kevin P. The Journal of Chemical Physics, Vol. 147, Issue 7 https://doi.org/10.1063/1.4997480	journal	August 2017
A driven similarity renormalization group approach to quantum many-body problems Evangelista, Francesco A. arXiv https://doi.org/10.48550/arxiv.1406.0114	text	January 2014
The In-Medium Similarity Renormalization Group: A Novel Ab Initio Method for Nuclei Hergert, H.; Bogner, S. K.; Morris, T. D. arXiv https://doi.org/10.48550/arxiv.1512.06956	text	January 2015

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Title: Analytic gradients for the single-reference driven similarity renormalization group second-order perturbation theory

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