Independent amplitude approximations in coupled cluster valence bond theory: Incorporation of 3-electron-pair correlation and application to spin frustration in the low-lying excited states of a ferredoxin-type tetrametallic iron-sulfur cluster

Small, David W.; Head-Gordon, Martin

doi:10.1063/1.5046318

Title: Independent amplitude approximations in coupled cluster valence bond theory: Incorporation of 3-electron-pair correlation and application to spin frustration in the low-lying excited states of a ferredoxin-type tetrametallic iron-sulfur cluster

Journal Article · Mon Oct 08 00:00:00 EDT 2018 · Journal of Chemical Physics

DOI:https://doi.org/10.1063/1.5046318· OSTI ID:1480819

Small, David W. ^[1];

^[1]

Univ. of California, Berkeley, CA (United States). Department of Chemsitry; Lawrence Berkeley National Lab. (LBNL), Berkeley, CA (United States). Chemical Sciences Division

We report that coupled cluster valence bond (CCVB) is a simple electronic structure method based on a perfect pairing (PP) reference with 2-pair recouplings for strong electron correlation problems. CCVB is spin-pure, size-consistent, and can exactly (in its active space) separate any molecule into atoms for which unrestricted Hartree-Fock (UHF) at dissociation is the sum of the ground state UHF energies of the atoms. However CCVB is far from a complete description of strong correlations. Its first failure to exactly describe spin-recouplings arises at the level of 3 electron pairs, such as the recoupling of 3 triplet oxygen atoms in the dissociation of singlet ozone. Such situations are often associated with spin frustration. To address this limitation, an extension of CCVB, termed CCVB+i3, is reported here that includes an independent (i) amplitude approximation to the 3-pair recouplings. CCVB+i3 thereby has the same basic computational requirements as those of CCVB, which has previously been shown to be an efficient method. CCVB+i3 correctly separates molecules that CCVB cannot. As a by-product, an independent 2-pair amplitude approximation to CCVB, called PP+i2, is also defined. Remarkably, PP+i2 can also correctly separate systems that CCVB cannot. CCVB+i3 is validated on the symmetric dissociation of D_3h ozone. CCVB+i3 is then used to explore the role of 3-pair recouplings in an [Fe₄S₄(SCH₃)₄]^2- cluster that has been used to model the iron-sulfur core of [Fe₄S₄] ferredoxins. Using localized PP orbitals, such recouplings are demonstrated to be large in some low-lying singlet excited states of the cluster. Lastly, significant 3 pair recoupling amplitudes include the usual triangular motif associated with spin frustration and other geometric arrangements of the 3 entangled pairs across the 4 iron centers.

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Research Organization:: Lawrence Berkeley National Laboratory (LBNL), Berkeley, CA (United States)

Sponsoring Organization:: USDOE Office of Science (SC), Basic Energy Sciences (BES). Chemical Sciences, Geosciences, and Biosciences Division

Grant/Contract Number:: AC02-05CH11231

OSTI ID:: 1480819

Alternate ID(s):: OSTI ID: 1476697

Journal Information:: Journal of Chemical Physics, Vol. 149, Issue 14; ISSN 0021-9606

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

Country of Publication:: United States

Language:: English

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Cited by: 7 works

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References (62)

Applications of spin-coupled valence bond theory Cooper, David L.; Gerratt, Joseph.; Raimondi, Mario. Chemical Reviews, Vol. 91, Issue 5 https://doi.org/10.1021/cr00005a014	journal	July 1991
Theoretical studies of the first‐ and second‐row transition‐metal methyls and their positive ions Bauschlicher, Charles W.; Langhoff, Stephen R.; Partridge, Harry The Journal of Chemical Physics, Vol. 91, Issue 4 https://doi.org/10.1063/1.456998	journal	August 1989
Active-space two-electron reduced-density-matrix method: Complete active-space calculations without diagonalization of the N-electron Hamiltonian Gidofalvi, Gergely; Mazziotti, David A. The Journal of Chemical Physics, Vol. 129, Issue 13 https://doi.org/10.1063/1.2983652	journal	October 2008
Coupled-Cluster Valence-Bond Singles and Doubles for Strongly Correlated Systems: Block-Tensor Based Implementation and Application to Oligoacenes Lee, Joonho; Small, David W.; Epifanovsky, Evgeny Journal of Chemical Theory and Computation, Vol. 13, Issue 2 https://doi.org/10.1021/acs.jctc.6b01092	journal	January 2017
Cost-effective description of strong correlation: Efficient implementations of the perfect quadruples and perfect hextuples models Lehtola, Susi; Parkhill, John; Head-Gordon, Martin The Journal of Chemical Physics, Vol. 145, Issue 13 https://doi.org/10.1063/1.4964317	journal	October 2016
The Description of Chemical Bonding From AB Initio Calculations Goddard, W. A.; Harding, L. B. Annual Review of Physical Chemistry, Vol. 29, Issue 1 https://doi.org/10.1146/annurev.pc.29.100178.002051	journal	October 1978
Ab initio calculations on small hydrides including electron correlation: III. A study of the valence shell intrapair and interpair correlation energy of some first row hydrides Jungen, M.; Ahlrichs, R. Theoretica Chimica Acta, Vol. 17, Issue 5 https://doi.org/10.1007/bf00528569	journal	January 1970
Communication: An adaptive configuration interaction approach for strongly correlated electrons with tunable accuracy Schriber, Jeffrey B.; Evangelista, Francesco A. The Journal of Chemical Physics, Vol. 144, Issue 16 https://doi.org/10.1063/1.4948308	journal	April 2016
Tractable spin-pure methods for bond breaking: Local many-electron spin-vector sets and an approximate valence bond model Small, David W.; Head-Gordon, Martin The Journal of Chemical Physics, Vol. 130, Issue 8 https://doi.org/10.1063/1.3069296	journal	February 2009
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
Use of approximate integrals in ab initio theory. An application in MP2 energy calculations Feyereisen, Martin; Fitzgerald, George; Komornicki, Andrew Chemical Physics Letters, Vol. 208, Issue 5-6 https://doi.org/10.1016/0009-2614(93)87156-w	journal	June 1993
Auxiliary basis sets for density fitting–MP2 calculations: Nonrelativistic triple-ζ all-electron correlation consistent basis sets for the 3d elements Sc–Zn Hill, J. Grant; Platts, James A. The Journal of Chemical Physics, Vol. 128, Issue 4 https://doi.org/10.1063/1.2826348	journal	January 2008
Basis Set Exchange: A Community Database for Computational Sciences Schuchardt, Karen L.; Didier, Brett T.; Elsethagen, Todd Journal of Chemical Information and Modeling, Vol. 47, Issue 3 https://doi.org/10.1021/ci600510j	journal	March 2007
A tractable and accurate electronic structure method for static correlations: The perfect hextuples model Parkhill, John A.; Head-Gordon, Martin The Journal of Chemical Physics, Vol. 133, Issue 2 https://doi.org/10.1063/1.3456001	journal	July 2010
Direct Calculation of Approximate Natural Orbitals and Natural Expansion Coefficients of Atomic and Molecular Electronic Wavefunctions. II. Decoupling of the Pair Equations and Calculation of the Pair Correlation Energies for the Be and LiH Ground States Ahlrichs, Reinhart; Kutzelnigg, Werner The Journal of Chemical Physics, Vol. 48, Issue 4 https://doi.org/10.1063/1.1668917	journal	February 1968
Correcting Systematic Errors in DFT Spin-Splitting Energetics for Transition Metal Complexes Hughes, Thomas F.; Friesner, Richard A. Journal of Chemical Theory and Computation, Vol. 7, Issue 1 https://doi.org/10.1021/ct100359x	journal	December 2010
Combining the Complete Active Space Self-Consistent Field Method and the Full Configuration Interaction Quantum Monte Carlo within a Super-CI Framework, with Application to Challenging Metal-Porphyrins Li Manni, Giovanni; Smart, Simon D.; Alavi, Ali Journal of Chemical Theory and Computation, Vol. 12, Issue 3 https://doi.org/10.1021/acs.jctc.5b01190	journal	February 2016
Coupled cluster valence bond theory for open-shell systems with application to very long range strong correlation in a polycarbene dimer Small, David W.; Head-Gordon, Martin The Journal of Chemical Physics, Vol. 147, Issue 2 https://doi.org/10.1063/1.4991797	journal	July 2017
The generalized active space concept in multiconfigurational self-consistent field methods Ma, Dongxia; Li Manni, Giovanni; Gagliardi, Laura The Journal of Chemical Physics, Vol. 135, Issue 4 https://doi.org/10.1063/1.3611401	journal	July 2011
A simple way to test for collinearity in spin symmetry broken wave functions: General theory and application to generalized Hartree Fock Small, David W.; Sundstrom, Eric J.; Head-Gordon, Martin The Journal of Chemical Physics, Vol. 142, Issue 9 https://doi.org/10.1063/1.4913740	journal	March 2015
The Density Matrix Renormalization Group in Quantum Chemistry Chan, Garnet Kin-Lic; Sharma, Sandeep Annual Review of Physical Chemistry, Vol. 62, Issue 1 https://doi.org/10.1146/annurev-physchem-032210-103338	journal	May 2011
Density Functional Theory of Electronic Structure Kohn, W.; Becke, A. D.; Parr, R. G. The Journal of Physical Chemistry, Vol. 100, Issue 31 https://doi.org/10.1021/jp960669l	journal	January 1996
Accurate first-principles structures and energies of diversely bonded systems from an efficient density functional Sun, Jianwei; Remsing, Richard C.; Zhang, Yubo Nature Chemistry, Vol. 8, Issue 9 https://doi.org/10.1038/nchem.2535	journal	June 2016
Self‐consistent molecular orbital methods. XXIII. A polarization‐type basis set for second‐row elements Francl, Michelle M.; Pietro, William J.; Hehre, Warren J. The Journal of Chemical Physics, Vol. 77, Issue 7, p. 3654-3665 https://doi.org/10.1063/1.444267	journal	October 1982
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
Coupled Cluster Valence Bond Method: Efficient Computer Implementation and Application to Multiple Bond Dissociations and Strong Correlations in the Acenes Small, David W.; Lawler, Keith V.; Head-Gordon, Martin Journal of Chemical Theory and Computation, Vol. 10, Issue 5 https://doi.org/10.1021/ct500112y	journal	April 2014
The complete active space SCF (CASSCF) method in a Newton–Raphson formulation with application to the HNO molecule Siegbahn, Per E. M.; Almlöf, Jan; Heiberg, Anders The Journal of Chemical Physics, Vol. 74, Issue 4 https://doi.org/10.1063/1.441359	journal	February 1981
The perfect quadruples model for electron correlation in a valence active space Parkhill, John A.; Lawler, Keith; Head-Gordon, Martin The Journal of Chemical Physics, Vol. 130, Issue 8 https://doi.org/10.1063/1.3086027	journal	February 2009
Size-consistent wave functions for nondynamical correlation energy: The valence active space optimized orbital coupled-cluster doubles model Krylov, Anna I.; Sherrill, C. David; Byrd, Edward F. C. The Journal of Chemical Physics, Vol. 109, Issue 24 https://doi.org/10.1063/1.477764	journal	December 1998
Are atoms intrinsic to molecular electronic wavefunctions? I. The FORS model Ruedenberg, Klaus; Schmidt, Michael W.; Gilbert, Mary M. Chemical Physics, Vol. 71, Issue 1 https://doi.org/10.1016/0301-0104(82)87004-3	journal	September 1982
Restricted active space spin-flip configuration interaction: Theory and examples for multiple spin flips with odd numbers of electrons Zimmerman, Paul M.; Bell, Franziska; Goldey, Matthew The Journal of Chemical Physics, Vol. 137, Issue 16 https://doi.org/10.1063/1.4759076	journal	October 2012
Efficient use of the correlation consistent basis sets in resolution of the identity MP2 calculations Weigend, Florian; Köhn, Andreas; Hättig, Christof The Journal of Chemical Physics, Vol. 116, Issue 8 https://doi.org/10.1063/1.1445115	journal	February 2002
Thirty years of density functional theory in computational chemistry: an overview and extensive assessment of 200 density functionals Mardirossian, Narbe; Head-Gordon, Martin Molecular Physics, Vol. 115, Issue 19 https://doi.org/10.1080/00268976.2017.1333644	journal	April 2017
A look at the density functional theory zoo with the advanced GMTKN55 database for general main group thermochemistry, kinetics and noncovalent interactions Goerigk, Lars; Hansen, Andreas; Bauer, Christoph Physical Chemistry Chemical Physics, Vol. 19, Issue 48 https://doi.org/10.1039/c7cp04913g	journal	January 2017
A complete active space SCF method (CASSCF) using a density matrix formulated super-CI approach Roos, Björn O.; Taylor, Peter R.; Sigbahn, Per E. M. Chemical Physics, Vol. 48, Issue 2 https://doi.org/10.1016/0301-0104(80)80045-0	journal	May 1980
A deterministic alternative to the full configuration interaction quantum Monte Carlo method Tubman, Norm M.; Lee, Joonho; Takeshita, Tyler Y. The Journal of Chemical Physics, Vol. 145, Issue 4 https://doi.org/10.1063/1.4955109	journal	July 2016
General atomic and molecular electronic structure system Schmidt, Michael W.; Baldridge, Kim K.; Boatz, Jerry A. Journal of Computational Chemistry, Vol. 14, Issue 11, p. 1347-1363 https://doi.org/10.1002/jcc.540141112	journal	November 1993
The role of databases in support of computational chemistry calculations Feller, David Journal of Computational Chemistry, Vol. 17, Issue 13 https://doi.org/10.1002/jcc.9	journal	October 1996
Challenges for Density Functional Theory Cohen, Aron J.; Mori-Sánchez, Paula; Yang, Weitao Chemical Reviews, Vol. 112, Issue 1 https://doi.org/10.1021/cr200107z	journal	December 2011
Quantitative quantum chemistry Helgaker, Trygve; Klopper, Wim; Tew, David P. Molecular Physics, Vol. 106, Issue 16-18 https://doi.org/10.1080/00268970802258591	journal	August 2008
Robust and variational fitting Dunlap, Brett I. Physical Chemistry Chemical Physics, Vol. 2, Issue 10 https://doi.org/10.1039/b000027m	journal	January 2000
Application of the independent electron pair approach to the calculation of excitation energies, ionization potentials, and electron affinities of first row atoms Staemmler, Volker; Jungen, Martin Theoretica Chimica Acta, Vol. 38, Issue 4 https://doi.org/10.1007/bf00963469	journal	January 1975
Post-modern valence bond theory for strongly correlated electron spins Small, David W.; Head-Gordon, Martin Physical Chemistry Chemical Physics, Vol. 13, Issue 43 https://doi.org/10.1039/c1cp21832h	journal	January 2011
ω B97M-V: A combinatorially optimized, range-separated hybrid, meta-GGA density functional with VV10 nonlocal correlation Mardirossian, Narbe; Head-Gordon, Martin The Journal of Chemical Physics, Vol. 144, Issue 21 https://doi.org/10.1063/1.4952647	journal	June 2016
A fusion of the closed-shell coupled cluster singles and doubles method and valence-bond theory for bond breaking Small, David W.; Head-Gordon, Martin The Journal of Chemical Physics, Vol. 137, Issue 11 https://doi.org/10.1063/1.4751485	journal	September 2012
Spin states of (bio)inorganic systems: Successes and pitfalls Swart, Marcel International Journal of Quantum Chemistry, Vol. 113, Issue 1 https://doi.org/10.1002/qua.24255	journal	July 2012
Projected Hartree–Fock theory Jiménez-Hoyos, Carlos A.; Henderson, Thomas M.; Tsuchimochi, Takashi The Journal of Chemical Physics, Vol. 136, Issue 16 https://doi.org/10.1063/1.4705280	journal	April 2012
The restricted active space self-consistent-field method, implemented with a split graph unitary group approach Malmqvist, Per Aake.; Rendell, Alistair.; Roos, Bjoern O. The Journal of Physical Chemistry, Vol. 94, Issue 14 https://doi.org/10.1021/j100377a011	journal	July 1990
Low-energy spectrum of iron–sulfur clusters directly from many-particle quantum mechanics Sharma, Sandeep; Sivalingam, Kantharuban; Neese, Frank Nature Chemistry, Vol. 6, Issue 10 https://doi.org/10.1038/nchem.2041	journal	August 2014
Gaussian Basis Set for Molecular Wavefunctions Containing Third‐Row Atoms Wachters, A. J. H. The Journal of Chemical Physics, Vol. 52, Issue 3 https://doi.org/10.1063/1.1673095	journal	February 1970
Large-Scale Variational Two-Electron Reduced-Density-Matrix-Driven Complete Active Space Self-Consistent Field Methods Fosso-Tande, Jacob; Nguyen, Truong-Son; Gidofalvi, Gergely Journal of Chemical Theory and Computation, Vol. 12, Issue 5 https://doi.org/10.1021/acs.jctc.6b00190	journal	April 2016
Modern valence bond theory Gerratt, J.; Cooper, D. L.; Karadakov, P. B. Chemical Society Reviews, Vol. 26, Issue 2 https://doi.org/10.1039/cs9972600087	journal	January 1997
Spin-coupled valence bond theory Cooper, D. L.; Gerratt, J.; Raimondi, M. International Reviews in Physical Chemistry, Vol. 7, Issue 1 https://doi.org/10.1080/01442358809353205	journal	January 1988
Quantum Mechanical Modeling of Catalytic Processes Bell, Alexis T.; Head-Gordon, Martin Annual Review of Chemical and Biomolecular Engineering, Vol. 2, Issue 1 https://doi.org/10.1146/annurev-chembioeng-061010-114108	journal	July 2011
Restricted active space spin-flip configuration interaction approach: theory, implementation and examples Casanova, David; Head-Gordon, Martin Physical Chemistry Chemical Physics, Vol. 11, Issue 42 https://doi.org/10.1039/b911513g	journal	January 2009
Efficient diffuse function-augmented basis sets for anion calculations. III. The 3-21+G basis set for first-row elements, Li-F Clark, Timothy; Chandrasekhar, Jayaraman; Spitznagel, G�nther W. Journal of Computational Chemistry, Vol. 4, Issue 3 https://doi.org/10.1002/jcc.540040303	journal	October 1983
Orbital optimization in the density matrix renormalization group, with applications to polyenes and β-carotene Ghosh, Debashree; Hachmann, Johannes; Yanai, Takeshi The Journal of Chemical Physics, Vol. 128, Issue 14 https://doi.org/10.1063/1.2883976	journal	April 2008
Self—Consistent Molecular Orbital Methods. XII. Further Extensions of Gaussian—Type Basis Sets for Use in Molecular Orbital Studies of Organic Molecules Hehre, W. J.; Ditchfield, R.; Pople, J. A. The Journal of Chemical Physics, Vol. 56, Issue 5, p. 2257-2261 https://doi.org/10.1063/1.1677527	journal	March 1972
An Antifungal Polycyclic Tetramate Macrolactam, Heat-Stable Antifungal Factor (HSAF), Is a Novel Oxidative Stress Modulator in Lysobacter enzymogenes Yu, Lingjun; Li, Hui; Zhou, Zaichun Applied and Environmental Microbiology, Vol. 87, Issue 10 https://doi.org/10.1128/aem.03105-20	journal	April 2021
Combining the Complete Active Space Self-Consistent Field Method and the Full Configuration Interaction Quantum Monte Carlo within a Super-CI Framework, with Application to Challenging Metal-Porphyrins Li Manni, Giovanni; Smart, Simon D.; Alavi, Ali Apollo - University of Cambridge Repository https://doi.org/10.17863/cam.21652	text	January 2016
Ab initio calculations on small hydrides including electron correlation: I. The BeH2 molecule in its ground state Ahlrichs, Reinhart; Kutzelnigg, Werner Theoretica Chimica Acta, Vol. 10, Issue 5 https://doi.org/10.1007/bf00528769	journal	January 1968
Cost-effective description of strong correlation: efficient implementations of the perfect quadruples and perfect hextuples models Lehtola, Susi; Parkhill, John; Head-Gordon, Martin arXiv https://doi.org/10.48550/arxiv.1609.00077	text	January 2016

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