Extension of frozen natural orbital approximation to open-shell references: Theory, implementation, and application to single-molecule magnets

Pokhilko, Pavel; Izmodenov, Daniil; Krylov, Anna I.

doi:10.1063/1.5138643

Title: Extension of frozen natural orbital approximation to open-shell references: Theory, implementation, and application to single-molecule magnets

Journal Article · 20 January 2020 · Journal of Chemical Physics

DOI: https://doi.org/10.1063/1.5138643 · OSTI ID:1803467

^[1];

^[2];

^[3]

Univ. of Southern California, Los Angeles, CA (United States); OSTI
Univ. of Southern California, Los Angeles, CA (United States); Lomonosov Moscow State Univ. (Russia)
Univ. of Southern California, Los Angeles, CA (United States)

Natural orbitals are often used to achieve a more compact representation of correlated wave-functions. Using natural orbitals computed as eigenstates of the virtual–virtual block of the state density matrix instead of the canonical Hartree–Fock orbitals results in smaller errors when the same fraction of virtual space is frozen. This strategy, termed frozen natural orbital (FNO) approach, is effective in reducing the cost of regular coupled-cluster (CC) calculations and some multistate methods, such as EOM-IP-CC (equation-of-motion CC for ionization potentials). This contribution extends the FNO approach to the EOM-SF-CC ansatz (EOM-CC with spin-flip). In contrast to EOM-IP-CCSD, EOM-SF-CCSD relies on high-spin open-shell references. Using FNOs computed for an open-shell reference leads to an erratic behavior of the EOM-SF-CC energies and properties due to an inconsistent truncation of the α and β orbital spaces. A general solution to problems arising in the EOM-CC calculations utilizing open-shell references, termed OSFNO (open-shell FNO), is proposed. Furthermore, by means of singular value decomposition (SVD) of the overlap matrix of the α and β orbitals, the OSFNO algorithm identifies the corresponding orbitals and determines virtual orbitals corresponding to the singly occupied space. This is followed by SVD of the singlet part of the state density matrix in the remaining virtual orbital subspace. The so-computed FNOs preserve the spin purity of the open-shell orbital subspace to the extent allowed by the original reference, thus facilitating a safe truncation of the virtual space. The performance of OSFNO is benchmarked for selected diradicals and triradicals.

View Accepted Manuscript (DOE)

Cite

Export

Save

Research Organization:: Univ. of Southern California, Los Angeles, CA (United States)

Sponsoring Organization:: USDOE; USDOE Office of Science (SC)

Grant/Contract Number:: SC0018910

OSTI ID:: 1803467

Journal Information:: Journal of Chemical Physics, Journal Name: Journal of Chemical Physics Journal Issue: 3 Vol. 152; ISSN 0021-9606

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

Country of Publication:: United States

Language:: English

References (131)

Molecular Electronic-Structure Theory Helgaker, Trygve; Jørgensen, Poul; Olsen, Jeppe https://doi.org/10.1002/9781119019572	book	August 2000
5-Dehydro-1,3-quinodimethane: A Hydrocarbon with an Open-Shell Doublet Ground State Slipchenko, Lyudmila V.; Munsch, Tamara E.; Wenthold, Paul G. Angewandte Chemie, Vol. 116, Issue 6 https://doi.org/10.1002/ange.200352990	journal	January 2004
5-Dehydro-1,3-quinodimethane: A Hydrocarbon with an Open-Shell Doublet Ground State Slipchenko, Lyudmila V.; Munsch, Tamara E.; Wenthold, Paul G. Angewandte Chemie International Edition, Vol. 43, Issue 6 https://doi.org/10.1002/anie.200352990	journal	January 2004
Spin-Flip Equation-of-Motion Coupled-Cluster Electronic Structure Method for a Description of Excited States, Bond Breaking, Diradicals, and Triradicals Krylov, Anna I. ChemInform, Vol. 37, Issue 17 https://doi.org/10.1002/chin.200617278	journal	April 2006
Reduced-cost sparsity-exploiting algorithm for solving coupled-cluster equations: Reduced-Cost Sparsity-Exploiting Algorithm for Solving CC Equations Brabec, Jiri; Yang, Chao; Epifanovsky, Evgeny Journal of Computational Chemistry, Vol. 37, Issue 12 https://doi.org/10.1002/jcc.24293	journal	January 2016
A study of the convergence in iterative natural orbital procedures: CONVERGENCE IN TWO PROCEDURES Thunemann, K. H.; Römelt, J.; Peyerimhoff, S. D. International Journal of Quantum Chemistry, Vol. 11, Issue 5 https://doi.org/10.1002/qua.560110506	journal	May 1977
Simplifications in the generation and transformation of two-electron integrals in molecular calculations Beebe, Nelson H. F.; Linderberg, Jan International Journal of Quantum Chemistry, Vol. 12, Issue 4 https://doi.org/10.1002/qua.560120408	journal	October 1977
Q-Chem: an engine for innovation: Q-Chem: an engine for innovation Krylov, Anna I.; Gill, Peter M. W. Wiley Interdisciplinary Reviews: Computational Molecular Science, Vol. 3, Issue 3 https://doi.org/10.1002/wcms.1122	journal	November 2012
Reduced‐scaling coupled cluster response theory: Challenges and opportunities Crawford, T. Daniel; Kumar, Ashutosh; Bazanté, Alexandre P. Wiley Interdisciplinary Reviews: Computational Molecular Science, Vol. 9, Issue 4 https://doi.org/10.1002/wcms.1406	journal	January 2019
Coupled-cluster theory and its equation-of-motion extensions: Coupled-cluster theory Bartlett, Rodney J. Wiley Interdisciplinary Reviews: Computational Molecular Science, Vol. 2, Issue 1 https://doi.org/10.1002/wcms.76	journal	July 2011
Excited state coupled cluster methods: Excited state coupled cluster methods Sneskov, Kristian; Christiansen, Ove Wiley Interdisciplinary Reviews: Computational Molecular Science, Vol. 2, Issue 4 https://doi.org/10.1002/wcms.99	journal	November 2011
Cholesky Decomposition Techniques in Electronic Structure Theory Aquilante, Francesco; Boman, Linus; Boström, Jonas Challenges and Advances in Computational Chemistry and Physics https://doi.org/10.1007/978-90-481-2853-2_13	book	January 2011
Orbital-invariant formulation and second-order gradient evaluation in M�ller-Plesset perturbation theory Pulay, Peter; Saeb�, Svein Theoretica Chimica Acta, Vol. 69, Issue 5-6 https://doi.org/10.1007/bf00526697	journal	June 1986
Exploiting regularity in systematic sequences of wavefunctions which approach the full CI limit Cave, Robert J.; Xantheas, Sotiris S.; Feller, David Theoretica Chimica Acta, Vol. 83, Issue 1-2 https://doi.org/10.1007/bf01113242	journal	January 1992
Individualized configuration selection in CI calculations with subsequent energy extrapolation Buenker, Robert J.; Peyerimhoff, Sigrid D. Theoretica Chimica Acta, Vol. 35, Issue 1 https://doi.org/10.1007/bf02394557	journal	August 1974
Deadwood in configuration spaces. II. Singles + doubles and singles + doubles + triples + quadruples spaces Ivanic, Joseph; Ruedenberg, Klaus Theoretical Chemistry Accounts: Theory, Computation, and Modeling (Theoretica Chimica Acta), Vol. 107, Issue 4 https://doi.org/10.1007/s00214-002-0326-1	journal	April 2002
Density fitting with auxiliary basis sets from Cholesky decompositions Pedersen, Thomas Bondo; Aquilante, Francesco; Lindh, Roland Theoretical Chemistry Accounts, Vol. 124, Issue 1-2 https://doi.org/10.1007/s00214-009-0608-y	journal	July 2009
Resolution of the Identity and Cholesky Representation of EOM-MP2 Approximation: Implementation, Accuracy and Efficiency Kumar, Dinesh; Dutta, Achintya Kumar; Manohar, Prashant Uday Journal of Chemical Sciences, Vol. 129, Issue 10 https://doi.org/10.1007/s12039-017-1378-z	journal	October 2017
Localizability of dynamic electron correlation Pulay, Peter Chemical Physics Letters, Vol. 100, Issue 2 https://doi.org/10.1016/0009-2614(83)80703-9	journal	September 1983
Local configuration interaction: An efficient approach for larger molecules Sæbø, Svein; Pulay, Peter Chemical Physics Letters, Vol. 113, Issue 1 https://doi.org/10.1016/0009-2614(85)85003-x	journal	January 1985
Selection of the reduced virtual space for correlated calculations. An application to the energy and dipole moment of H2O Sosa, Carlos; Geertsen, Jan; Trucks, Gary W. Chemical Physics Letters, Vol. 159, Issue 2-3 https://doi.org/10.1016/0009-2614(89)87399-3	journal	July 1989
Economical triple excitation equation-of-motion coupled-cluster methods for excitation energies Watts, John D.; Bartlett, Rodney J. Chemical Physics Letters, Vol. 233, Issue 1-2 https://doi.org/10.1016/0009-2614(94)01434-w	journal	February 1995
Auxiliary basis sets to approximate Coulomb potentials Eichkorn, Karin; Treutler, Oliver; Öhm, Holger Chemical Physics Letters, Vol. 240, Issue 4 https://doi.org/10.1016/0009-2614(95)00621-a	journal	June 1995
Iterative and non-iterative triple excitation corrections in coupled-cluster methods for excited electronic states: the EOM-CCSDT-3 and EOM-CCSD(T̃) methods Watts, John D.; Bartlett, Rodney J. Chemical Physics Letters, Vol. 258, Issue 5-6 https://doi.org/10.1016/0009-2614(96)00708-7	journal	August 1996
Efficient, approximate and parallel Hartree–Fock and hybrid DFT calculations. A ‘chain-of-spheres’ algorithm for the Hartree–Fock exchange Neese, Frank; Wennmohs, Frank; Hansen, Andreas Chemical Physics, Vol. 356, Issue 1-3 https://doi.org/10.1016/j.chemphys.2008.10.036	journal	February 2009
Singlet stabilization of oxazole- and isoxazolenitrene-n-oxides by radical delocalization Hossain, Ekram; Wenthold, Paul G. Computational and Theoretical Chemistry, Vol. 1020 https://doi.org/10.1016/j.comptc.2013.07.028	journal	September 2013
Electronic structure of the two dehydro-meta-xylylene triradicals and their derivatives Wang, Tao; Krylov, Anna I. Chemical Physics Letters, Vol. 425, Issue 4-6 https://doi.org/10.1016/j.cplett.2006.05.035	journal	July 2006
Natural transition orbitals for the calculation of correlation and excitation energies Höfener, Sebastian; Klopper, Wim Chemical Physics Letters, Vol. 679 https://doi.org/10.1016/j.cplett.2017.04.083	journal	July 2017
Local perturbative triples correction (T) with linear cost scaling Schütz, Martin; Werner, Hans-Joachim Chemical Physics Letters, Vol. 318, Issue 4-5 https://doi.org/10.1016/s0009-2614(00)00066-x	journal	February 2000
Size-consistent wave functions for bond-breaking: the equation-of-motion spin-flip model Krylov, Anna I. Chemical Physics Letters, Vol. 338, Issue 4-6 https://doi.org/10.1016/s0009-2614(01)00287-1	journal	April 2001
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
The Configuration Interaction Method: Advances in Highly Correlated Approaches David Sherrill, C.; Schaefer, III, Henry F. Advances in Quantum Chemistry https://doi.org/10.1016/s0065-3276(08)60532-8	book	January 1999
Tensor Hypercontraction Second-Order Møller–Plesset Perturbation Theory: Grid Optimization and Reaction Energies Kokkila Schumacher, Sara I. L.; Hohenstein, Edward G.; Parrish, Robert M. Journal of Chemical Theory and Computation, Vol. 11, Issue 7 https://doi.org/10.1021/acs.jctc.5b00272	journal	June 2015
Multiconfigurational Second-Order Perturbation Theory with Frozen Natural Orbitals Extended to the Treatment of Photochemical Problems Segarra-Martí, Javier; Garavelli, Marco; Aquilante, Francesco Journal of Chemical Theory and Computation, Vol. 11, Issue 8 https://doi.org/10.1021/acs.jctc.5b00479	journal	July 2015
Spin-Adapted Formulation and Implementation of Density Cumulant Functional Theory with Density-Fitting Approximation: Application to Transition Metal Compounds Wang, Xiao; Sokolov, Alexander Yu.; Turney, Justin M. Journal of Chemical Theory and Computation, Vol. 12, Issue 10 https://doi.org/10.1021/acs.jctc.6b00589	journal	September 2016
Using Higher-Order Singular Value Decomposition To Define Weakly Coupled and Strongly Correlated Clusters: The n -Body Tucker Approximation Mayhall, Nicholas J. Journal of Chemical Theory and Computation, Vol. 13, Issue 10 https://doi.org/10.1021/acs.jctc.7b00696	journal	September 2017
Characterizing Bonding Patterns in Diradicals and Triradicals by Density-Based Wave Function Analysis: A Uniform Approach Orms, Natalie; Rehn, Dirk R.; Dreuw, Andreas Journal of Chemical Theory and Computation, Vol. 14, Issue 2 https://doi.org/10.1021/acs.jctc.7b01012	journal	January 2018
State-Averaged Pair Natural Orbitals for Excited States: A Route toward Efficient Equation of Motion Coupled-Cluster Peng, Chong; Clement, Marjory C.; Valeev, Edward F. Journal of Chemical Theory and Computation, Vol. 14, Issue 11 https://doi.org/10.1021/acs.jctc.8b00171	journal	September 2018
Double Precision Is Not Needed for Many-Body Calculations: Emergent Conventional Wisdom Pokhilko, Pavel; Epifanovsky, Evgeny; Krylov, Anna I. Journal of Chemical Theory and Computation, Vol. 14, Issue 8 https://doi.org/10.1021/acs.jctc.8b00321	journal	June 2018
Optimization of the Linear-Scaling Local Natural Orbital CCSD(T) Method: Improved Algorithm and Benchmark Applications Nagy, Péter R.; Samu, Gyula; Kállay, Mihály Journal of Chemical Theory and Computation, Vol. 14, Issue 8 https://doi.org/10.1021/acs.jctc.8b00442	journal	June 2018
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
Massive-Parallel Implementation of the Resolution-of-Identity Coupled-Cluster Approaches in the Numeric Atom-Centered Orbital Framework for Molecular Systems Shen, Tonghao; Zhu, Zhenyu; Zhang, Igor Ying Journal of Chemical Theory and Computation, Vol. 15, Issue 9 https://doi.org/10.1021/acs.jctc.8b01294	journal	July 2019
Frozen Virtual Natural Orbitals for Coupled-Cluster Linear-Response Theory Kumar, Ashutosh; Crawford, T. Daniel The Journal of Physical Chemistry A, Vol. 121, Issue 3 https://doi.org/10.1021/acs.jpca.6b11410	journal	January 2017
Computational Quantum Chemistry for Multiple-Site Heisenberg Spin Couplings Made Simple: Still Only One Spin–Flip Required Mayhall, Nicholas J.; Head-Gordon, Martin The Journal of Physical Chemistry Letters, Vol. 6, Issue 10 https://doi.org/10.1021/acs.jpclett.5b00733	journal	May 2015
Spin-Flip Equation-of-Motion Coupled-Cluster Electronic Structure Method for a Description of Excited States, Bond Breaking, Diradicals, and Triradicals Krylov, Anna I. Accounts of Chemical Research, Vol. 39, Issue 2 https://doi.org/10.1021/ar0402006	journal	February 2006
Efficient Structure Optimization with Second-Order Many-Body Perturbation Theory: The RIJCOSX-MP2 Method Kossmann, Simone; Neese, Frank Journal of Chemical Theory and Computation, Vol. 6, Issue 8 https://doi.org/10.1021/ct100199k	journal	July 2010
High-Multiplicity Natural Orbitals in Multireference Configuration Interaction for Excited States Lu, Zhen; Matsika, Spiridoula Journal of Chemical Theory and Computation, Vol. 8, Issue 2 https://doi.org/10.1021/ct200832u	journal	January 2012
Accurate Noncovalent Interaction Energies Using Truncated Basis Sets Based on Frozen Natural Orbitals DePrince, A. Eugene; Sherrill, C. David Journal of Chemical Theory and Computation, Vol. 9, Issue 1 https://doi.org/10.1021/ct300780u	journal	December 2012
Photoelectron Spectroscopy Study of Quinonimides Hossain, Ekram; Deng, Shihu M.; Gozem, Samer Journal of the American Chemical Society, Vol. 139, Issue 32 https://doi.org/10.1021/jacs.7b05197	journal	August 2017
Spin-State Dependent Radical Stabilization in Nitrenes: The Unusually Small Singlet–Triplet Splitting in 2-Furanylnitrene Wenthold, Paul G. The Journal of Organic Chemistry, Vol. 77, Issue 1 https://doi.org/10.1021/jo2016967	journal	November 2011
Bonding Patterns in Benzene Triradicals from Structural, Spectroscopic, and Thermochemical Perspectives Cristian, Ana-Maria C.; Shao, Yihan; Krylov, Anna I. The Journal of Physical Chemistry A, Vol. 108, Issue 31 https://doi.org/10.1021/jp049007j	journal	August 2004
Triradicals Krylov, Anna I. The Journal of Physical Chemistry A, Vol. 109, Issue 47 https://doi.org/10.1021/jp0528212	journal	December 2005
High-Multiplicity Natural Orbitals in Multireference Configuration Interaction for Excited State Potential Energy Surfaces Lu, Zhen; Matsika, Spiridoula The Journal of Physical Chemistry A, Vol. 117, Issue 32 https://doi.org/10.1021/jp401444c	journal	May 2013
Tensor Hypercontraction Equation-of-Motion Second-Order Approximate Coupled Cluster: Electronic Excitation Energies in O(N4) Time Hohenstein, Edward G.; Kokkila, Sara I. L.; Parrish, Robert M. The Journal of Physical Chemistry B, Vol. 117, Issue 42 https://doi.org/10.1021/jp4021905	journal	July 2013
Effect of a Heteroatom on Bonding Patterns and Triradical Stabilization Energies of 2,4,6-Tridehydropyridine versus 1,3,5-Tridehydrobenzene Manohar, Prashant U.; Koziol, Lucas; Krylov, Anna I. The Journal of Physical Chemistry A, Vol. 113, Issue 11 https://doi.org/10.1021/jp810522e	journal	March 2009
Singlet–triplet energy gaps and the degree of diradical character in binuclear copper molecular magnets characterized by spin-flip density functional theory Orms, Natalie; Krylov, Anna I. Physical Chemistry Chemical Physics, Vol. 20, Issue 19 https://doi.org/10.1039/c7cp07356a	journal	January 2018
Distinguishing artificial and essential symmetry breaking in a single determinant: approach and application to the C ₆₀ , C ₃₆ , and C ₂₀ fullerenes Lee, Joonho; Head-Gordon, Martin Physical Chemistry Chemical Physics, Vol. 21, Issue 9 https://doi.org/10.1039/c8cp07613h	journal	January 2019
Spin-contamination of coupled-cluster wave functions Krylov, Anna I. The Journal of Chemical Physics, Vol. 113, Issue 15 https://doi.org/10.1063/1.1308557	journal	October 2000
Low-order scaling local correlation methods II: Splitting the Coulomb operator in linear scaling local second-order Møller–Plesset perturbation theory Hetzer, Georg; Schütz, Martin; Stoll, Hermann The Journal of Chemical Physics, Vol. 113, Issue 21 https://doi.org/10.1063/1.1321295	journal	December 2000
Low-order scaling local electron correlation methods. III. Linear scaling local perturbative triples correction ( T ) Schütz, Martin The Journal of Chemical Physics, Vol. 113, Issue 22 https://doi.org/10.1063/1.1323265	journal	December 2000
Low-order scaling local electron correlation methods. IV. Linear scaling local coupled-cluster (LCCSD) Schütz, Martin; Werner, Hans-Joachim The Journal of Chemical Physics, Vol. 114, Issue 2 https://doi.org/10.1063/1.1330207	journal	January 2001
A second-order perturbative correction to the coupled-cluster singles and doubles method: CCSD(2) Gwaltney, Steven R.; Head-Gordon, Martin The Journal of Chemical Physics, Vol. 115, Issue 5 https://doi.org/10.1063/1.1383589	journal	August 2001
New type of noniterative energy corrections for excited electronic states: Extension of the method of moments of coupled-cluster equations to the equation-of-motion coupled-cluster formalism Kowalski, Karol; Piecuch, Piotr The Journal of Chemical Physics, Vol. 115, Issue 7 https://doi.org/10.1063/1.1386794	journal	August 2001
Low-order scaling local electron correlation methods. V. Connected triples beyond (T): Linear scaling local CCSDT-1b Schütz, Martin The Journal of Chemical Physics, Vol. 116, Issue 20 https://doi.org/10.1063/1.1470497	journal	May 2002
Singlet-triplet gaps in diradicals by the spin-flip approach: A benchmark study Slipchenko, Lyudmila V.; Krylov, Anna I. The Journal of Chemical Physics, Vol. 117, Issue 10 https://doi.org/10.1063/1.1498819	journal	September 2002
A comparison of polarized double-zeta basis sets and natural orbitals for full configuration interaction benchmarks Abrams, Micah L.; Sherrill, C. David The Journal of Chemical Physics, Vol. 118, Issue 4 https://doi.org/10.1063/1.1532313	journal	January 2003
Electronic structure of the 1,3,5-tridehydrobenzene triradical in its ground and excited states Slipchenko, Lyudmila V.; Krylov, Anna I. The Journal of Chemical Physics, Vol. 118, Issue 21 https://doi.org/10.1063/1.1569845	journal	June 2003
Reduced scaling in electronic structure calculations using Cholesky decompositions Koch, Henrik; Sánchez de Merás, Alfredo; Pedersen, Thomas Bondo The Journal of Chemical Physics, Vol. 118, Issue 21 https://doi.org/10.1063/1.1578621	journal	June 2003
New coupled-cluster methods with singles, doubles, and noniterative triples for high accuracy calculations of excited electronic states Kowalski, Karol; Piecuch, Piotr The Journal of Chemical Physics, Vol. 120, Issue 4 https://doi.org/10.1063/1.1632474	journal	January 2004
Coulombic potential energy integrals and approximations Whitten, J. L. The Journal of Chemical Physics, Vol. 58, Issue 10 https://doi.org/10.1063/1.1679012	journal	May 1973
Theoretical Calculation of the Potential Curves of the Be2 Molecule Bender, Charles F.; Davidson, Ernest R. The Journal of Chemical Physics, Vol. 47, Issue 12 https://doi.org/10.1063/1.1701748	journal	December 1967
Report on Notation for the Spectra of Polyatomic Molecules Mulliken, Robert S. The Journal of Chemical Physics, Vol. 23, Issue 11 https://doi.org/10.1063/1.1740655	journal	November 1955
The effect of substituents on electronic states’ ordering in meta -xylylene diradicals: Qualitative insights from quantitative studies Wang, Tao; Krylov, Anna I. The Journal of Chemical Physics, Vol. 123, Issue 10 https://doi.org/10.1063/1.2018645	journal	September 2005
Unbiased auxiliary basis sets for accurate two-electron integral approximations Aquilante, Francesco; Lindh, Roland; Bondo Pedersen, Thomas The Journal of Chemical Physics, Vol. 127, Issue 11 https://doi.org/10.1063/1.2777146	journal	September 2007
Frozen natural orbital coupled-cluster theory: Forces and application to decomposition of nitroethane Taube, Andrew G.; Bartlett, Rodney J. The Journal of Chemical Physics, Vol. 128, Issue 16 https://doi.org/10.1063/1.2902285	journal	April 2008
Charge localization and Jahn–Teller distortions in the benzene dimer cation Pieniazek, Piotr A.; Bradforth, Stephen E.; Krylov, Anna I. The Journal of Chemical Physics, Vol. 129, Issue 7 https://doi.org/10.1063/1.2969107	journal	August 2008
Method specific Cholesky decomposition: Coulomb and exchange energies Boman, Linus; Koch, Henrik; Sánchez de Merás, Alfredo The Journal of Chemical Physics, Vol. 129, Issue 13 https://doi.org/10.1063/1.2988315	journal	October 2008
A noniterative perturbative triples correction for the spin-flipping and spin-conserving equation-of-motion coupled-cluster methods with single and double substitutions Manohar, Prashant U.; Krylov, Anna I. The Journal of Chemical Physics, Vol. 129, Issue 19 https://doi.org/10.1063/1.3013087	journal	November 2008
Double spin-flip approach within equation-of-motion coupled cluster and configuration interaction formalisms: Theory, implementation, and examples Casanova, David; Slipchenko, Lyudmila V.; Krylov, Anna I. The Journal of Chemical Physics, Vol. 130, Issue 4 https://doi.org/10.1063/1.3066652	journal	January 2009
Efficient and accurate local approximations to coupled-electron pair approaches: An attempt to revive the pair natural orbital method Neese, Frank; Wennmohs, Frank; Hansen, Andreas The Journal of Chemical Physics, Vol. 130, Issue 11 https://doi.org/10.1063/1.3086717	journal	March 2009
Atomic Cholesky decompositions: A route to unbiased auxiliary basis sets for density fitting approximation with tunable accuracy and efficiency Aquilante, Francesco; Gagliardi, Laura; Pedersen, Thomas Bondo The Journal of Chemical Physics, Vol. 130, Issue 15 https://doi.org/10.1063/1.3116784	journal	April 2009
Systematic truncation of the virtual space in multiconfigurational perturbation theory Aquilante, Francesco; Todorova, Tanya Kumanova; Gagliardi, Laura The Journal of Chemical Physics, Vol. 131, Issue 3 https://doi.org/10.1063/1.3157463	journal	July 2009
Efficient and accurate approximations to the local coupled cluster singles doubles method using a truncated pair natural orbital basis Neese, Frank; Hansen, Andreas; Liakos, Dimitrios G. The Journal of Chemical Physics, Vol. 131, Issue 6 https://doi.org/10.1063/1.3173827	journal	January 2009
Analytic evaluation of the nonadiabatic coupling vector between excited states using equation-of-motion coupled-cluster theory Tajti, Attila; Szalay, Péter G. The Journal of Chemical Physics, Vol. 131, Issue 12 https://doi.org/10.1063/1.3232011	journal	September 2009
Frozen natural orbitals for ionized states within equation-of-motion coupled-cluster formalism Landau, Arie; Khistyaev, Kirill; Dolgikh, Stanislav The Journal of Chemical Physics, Vol. 132, Issue 1 https://doi.org/10.1063/1.3276630	journal	January 2010
An efficient local coupled cluster method for accurate thermochemistry of large systems Werner, Hans-Joachim; Schütz, Martin The Journal of Chemical Physics, Vol. 135, Issue 14 https://doi.org/10.1063/1.3641642	journal	October 2011
On first-row diatomic molecules and local density models Dunlap, B. I.; Connolly, J. W. D.; Sabin, J. R. The Journal of Chemical Physics, Vol. 71, Issue 12 https://doi.org/10.1063/1.438313	journal	January 1979
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
Fourth‐order Mo/ller–Plessett perturbation theory in the local correlation treatment. I. Method Saebo/, Svein; Pulay, Peter The Journal of Chemical Physics, Vol. 86, Issue 2 https://doi.org/10.1063/1.452293	journal	January 1987
The full CCSDT model for molecular electronic structure Noga, Jozef; Bartlett, Rodney J. The Journal of Chemical Physics, Vol. 86, Issue 12 https://doi.org/10.1063/1.452353	journal	June 1987
Pseudospectral full configuration interaction Martinez, Todd J.; Mehta, Aseem; Carter, Emily A. The Journal of Chemical Physics, Vol. 97, Issue 3 https://doi.org/10.1063/1.463176	journal	August 1992
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
The equation of motion coupled‐cluster method. A systematic biorthogonal approach to molecular excitation energies, transition probabilities, and excited state properties Stanton, John F.; Bartlett, Rodney J. The Journal of Chemical Physics, Vol. 98, Issue 9 https://doi.org/10.1063/1.464746	journal	May 1993
Pseudospectral Mo/ller–Plesset perturbation theory through third order Martinez, Todd J.; Carter, Emily A. The Journal of Chemical Physics, Vol. 100, Issue 5 https://doi.org/10.1063/1.466350	journal	March 1994
Analytic energy derivatives for ionized states described by the equation‐of‐motion coupled cluster method Stanton, John F.; Gauss, Jürgen The Journal of Chemical Physics, Vol. 101, Issue 10 https://doi.org/10.1063/1.468022	journal	November 1994
Equation of motion coupled cluster method for electron attachment Nooijen, Marcel; Bartlett, Rodney J. The Journal of Chemical Physics, Vol. 102, Issue 9 https://doi.org/10.1063/1.468592	journal	March 1995
Pseudospectral multireference single and double excitation configuration interaction Martinez, Todd J.; Carter, Emily A. The Journal of Chemical Physics, Vol. 102, Issue 19 https://doi.org/10.1063/1.469088	journal	May 1995
General formulation of spin-flip time-dependent density functional theory using non-collinear kernels: Theory, implementation, and benchmarks Bernard, Yves A.; Shao, Yihan; Krylov, Anna I. The Journal of Chemical Physics, Vol. 136, Issue 20 https://doi.org/10.1063/1.4714499	journal	May 2012
Tensor hypercontraction density fitting. I. Quartic scaling second- and third-order Møller-Plesset perturbation theory Hohenstein, Edward G.; Parrish, Robert M.; Martínez, Todd J. The Journal of Chemical Physics, Vol. 137, Issue 4 https://doi.org/10.1063/1.4732310	journal	July 2012
Tensor hypercontraction. II. Least-squares renormalization Parrish, Robert M.; Hohenstein, Edward G.; Martínez, Todd J. The Journal of Chemical Physics, Vol. 137, Issue 22 https://doi.org/10.1063/1.4768233	journal	December 2012
Communication: Tensor hypercontraction. III. Least-squares tensor hypercontraction for the determination of correlated wavefunctions Hohenstein, Edward G.; Parrish, Robert M.; Sherrill, C. David The Journal of Chemical Physics, Vol. 137, Issue 22 https://doi.org/10.1063/1.4768241	journal	December 2012
Energies and analytic gradients for a coupled-cluster doubles model using variational Brueckner orbitals: Application to symmetry breaking in O4+ Sherrill, C. David; Krylov, Anna I.; Byrd, Edward F. C. The Journal of Chemical Physics, Vol. 109, Issue 11 https://doi.org/10.1063/1.477023	journal	September 1998
An efficient and near linear scaling pair natural orbital based local coupled cluster method Riplinger, Christoph; Neese, Frank The Journal of Chemical Physics, Vol. 138, Issue 3 https://doi.org/10.1063/1.4773581	journal	January 2013
Low-order scaling local electron correlation methods. I. Linear scaling local MP2 Schütz, Martin; Hetzer, Georg; Werner, Hans-Joachim The Journal of Chemical Physics, Vol. 111, Issue 13 https://doi.org/10.1063/1.479957	journal	October 1999
General implementation of the resolution-of-the-identity and Cholesky representations of electron repulsion integrals within coupled-cluster and equation-of-motion methods: Theory and benchmarks Epifanovsky, Evgeny; Zuev, Dmitry; Feng, Xintian The Journal of Chemical Physics, Vol. 139, Issue 13 https://doi.org/10.1063/1.4820484	journal	October 2013
Natural triple excitations in local coupled cluster calculations with pair natural orbitals Riplinger, Christoph; Sandhoefer, Barbara; Hansen, Andreas The Journal of Chemical Physics, Vol. 139, Issue 13 https://doi.org/10.1063/1.4821834	journal	October 2013
Efficient and accurate treatment of weak pairs in local CCSD(T) calculations. II. Beyond the ring approximation Schütz, Martin; Masur, Oliver; Usvyat, Denis The Journal of Chemical Physics, Vol. 140, Issue 24 https://doi.org/10.1063/1.4884156	journal	June 2014
Sparse maps—A systematic infrastructure for reduced-scaling electronic structure methods. I. An efficient and simple linear scaling local MP2 method that uses an intermediate basis of pair natural orbitals Pinski, Peter; Riplinger, Christoph; Valeev, Edward F. The Journal of Chemical Physics, Vol. 143, Issue 3 https://doi.org/10.1063/1.4926879	journal	July 2015
Sparse maps—A systematic infrastructure for reduced-scaling electronic structure methods. II. Linear scaling domain based pair natural orbital coupled cluster theory Riplinger, Christoph; Pinski, Peter; Becker, Ute The Journal of Chemical Physics, Vol. 144, Issue 2 https://doi.org/10.1063/1.4939030	journal	January 2016
Speeding up equation of motion coupled cluster theory with the chain of spheres approximation Dutta, Achintya Kumar; Neese, Frank; Izsák, Róbert The Journal of Chemical Physics, Vol. 144, Issue 3 https://doi.org/10.1063/1.4939844	journal	January 2016
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
A new near-linear scaling, efficient and accurate, open-shell domain-based local pair natural orbital coupled cluster singles and doubles theory Saitow, Masaaki; Becker, Ute; Riplinger, Christoph The Journal of Chemical Physics, Vol. 146, Issue 16 https://doi.org/10.1063/1.4981521	journal	April 2017
Reduced-cost linear-response CC2 method based on natural orbitals and natural auxiliary functions Mester, Dávid; Nagy, Péter R.; Kállay, Mihály The Journal of Chemical Physics, Vol. 146, Issue 19 https://doi.org/10.1063/1.4983277	journal	May 2017
Correlated natural transition orbital framework for low-scaling excitation energy calculations (CorNFLEx) Baudin, Pablo; Kristensen, Kasper The Journal of Chemical Physics, Vol. 146, Issue 21 https://doi.org/10.1063/1.4984820	journal	June 2017
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
Tensor-decomposed vibrational coupled-cluster theory: Enabling large-scale, highly accurate vibrational-structure calculations Madsen, Niels Kristian; Godtliebsen, Ian H.; Losilla, Sergio A. The Journal of Chemical Physics, Vol. 148, Issue 2 https://doi.org/10.1063/1.5001569	journal	January 2018
Calculations of non-adiabatic couplings within equation-of-motion coupled-cluster framework: Theory, implementation, and validation against multi-reference methods Faraji, Shirin; Matsika, Spiridoula; Krylov, Anna I. The Journal of Chemical Physics, Vol. 148, Issue 4 https://doi.org/10.1063/1.5009433	journal	January 2018
A near-linear scaling equation of motion coupled cluster method for ionized states Dutta, Achintya Kumar; Saitow, Masaaki; Riplinger, Christoph The Journal of Chemical Physics, Vol. 148, Issue 24 https://doi.org/10.1063/1.5029470	journal	June 2018
An efficient algorithm for Cholesky decomposition of electron repulsion integrals Folkestad, Sarai D.; Kjønstad, Eirik F.; Koch, Henrik The Journal of Chemical Physics, Vol. 150, Issue 19 https://doi.org/10.1063/1.5083802	journal	May 2019
Rank reduced coupled cluster theory. I. Ground state energies and wavefunctions Parrish, Robert M.; Zhao, Yao; Hohenstein, Edward G. The Journal of Chemical Physics, Vol. 150, Issue 16 https://doi.org/10.1063/1.5092505	journal	April 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
General framework for calculating spin–orbit couplings using spinless one-particle density matrices: Theory and application to the equation-of-motion coupled-cluster wave functions Pokhilko, Pavel; Epifanovsky, Evgeny; Krylov, Anna I. The Journal of Chemical Physics, Vol. 151, Issue 3 https://doi.org/10.1063/1.5108762	journal	July 2019
Two new classes of non-iterative coupled-cluster methods derived from the method of moments of coupled-cluster equations Łoch, Marta W.; Lodriguito, Maricris D.; Piecuch†, Piotr Molecular Physics, Vol. 104, Issue 13-14 https://doi.org/10.1080/00268970600659586	journal	July 2006
The coupled-cluster revolution Bartlett, Rodney J. Molecular Physics, Vol. 108, Issue 21-23 https://doi.org/10.1080/00268976.2010.531773	journal	November 2010
Density-fitted singles and doubles coupled cluster on graphics processing units DePrince,, A. Eugene; Kennedy, Matthew R.; Sumpter, Bobby G. Molecular Physics, Vol. 112, Issue 5-6 https://doi.org/10.1080/00268976.2013.874599	journal	January 2014
Advances in molecular quantum chemistry contained in the Q-Chem 4 program package Shao, Yihan; Gan, Zhengting; Epifanovsky, Evgeny Molecular Physics, Vol. 113, Issue 2 https://doi.org/10.1080/00268976.2014.952696	journal	September 2014
Quantum Theory of Many-Particle Systems. I. Physical Interpretations by Means of Density Matrices, Natural Spin-Orbitals, and Convergence Problems in the Method of Configurational Interaction Löwdin, Per-Olov Physical Review, Vol. 97, Issue 6 https://doi.org/10.1103/physrev.97.1474	journal	March 1955
Nature of the Configuration-Interaction Method in Ab Initio Calculations. I. Ne Ground State Barr, Tery L.; Davidson, Ernest R. Physical Review A, Vol. 1, Issue 3 https://doi.org/10.1103/physreva.1.644	journal	March 1970
Frozen Natural Orbitals: Systematic Basis Set Truncation for Coupled-Cluster Theory Taube, Andrew G.; Bartlett, Rodney J. Collection of Czechoslovak Chemical Communications, Vol. 70, Issue 6 https://doi.org/10.1135/cccc20050837	journal	January 2005
Equation-of-Motion Coupled-Cluster Methods for Open-Shell and Electronically Excited Species: The Hitchhiker's Guide to Fock Space Krylov, Anna I. Annual Review of Physical Chemistry, Vol. 59, Issue 1 https://doi.org/10.1146/annurev.physchem.59.032607.093602	journal	May 2008
Distinguishing Artificial and Essential Symmetry Breaking in a Single Determinant: Approach and Application to the C$_{60}$, C$_{36}$, and C$_{20}$ Fullerenes Lee, Joonho; Head-Gordon, Martin arXiv https://doi.org/10.48550/arxiv.1812.05266	text	January 2018

Cited By (1)

Spin-flip methods in quantum chemistry Casanova, David; Krylov, Anna I. Physical Chemistry Chemical Physics, Vol. 22, Issue 8 https://doi.org/10.1039/c9cp06507e	journal	January 2020

Similar Records

Equation-of-motion coupled-cluster method with double electron-attaching operators: Theory, implementation, and benchmarks

Journal Article · 2021 · Journal of Chemical Physics · OSTI ID:1852700

Gulania, Sahil; Kjønstad, Eirik F.; Stanton, John F.; +2 more

Higher-Order Equation-of-Motion Coupled-Cluster Methods for Ionization Processes

Journal Article · 2006 · Journal of Chemical Physics, 125:074111 · OSTI ID:899485

Kamiya, Muneaki; Hirata, So

Equation-of-motion coupled-cluster method for doubly ionized states with spin-orbit coupling

Journal Article · 2015 · Journal of Chemical Physics · OSTI ID:22415628

Wang, Zhifan; Hu, Shu; Guo, Jingwei; +1 more

Related Subjects

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CHEMISTRY
Chemistry
Coupled-cluster methods
Density-matrix
Free radicals
Nanomagnets
Physics
Spin contamination
Spin-orbit interactions

Title: Extension of frozen natural orbital approximation to open-shell references: Theory, implementation, and application to single-molecule magnets

Citation Formats

References (131)

Cited By (1)

Similar Records

Related Subjects