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Mini-Review Article Section: Mathematics

Ab initio Valence Bond Theory with Density Functional

Author(s): Chen Zhou, Xun Wu, Peikun Zheng, Fuming Ying, Peifeng Su* and Wei Wu*

Volume 3, Issue 2, 2023

Published on: 08 December, 2022

Page: [141 - 153] Pages: 13

DOI: 10.2174/2210298103666221115115507

Price: $65

Abstract

The accurate description of strongly correlated systems, also known as multireference systems, requires a balanced treatment of static and dynamic correlations and is an important target for developing quantum chemical methods. An appealing treatment to economically describe strongly correlated systems is the multireference density function theory (MRDFT) approach, in which the static correlation is included in the multiconfigurational wave function, while the density functional includes the dynamic correlation. This mini-review focuses on the recent progress and applications of the density functional methods based on valence bond theory. A series of density functional valence bond (DFVB) methods are surveyed, including the dynamic correlation correction- based and Hamiltonian matrix correction-based DFVB methods, the hybrid one-parameter DFVB methods, the block-localized density functional theory and the multistate density functional theory. These methods have been applied to various chemical and physical property calculations of strongly correlated systems, including resonance energies, potential energy curves, spectroscopic constants, atomization energies, spin state energy gaps, excitation energies, and reaction barriers. Most of the test results show that the density functional methods based on VB theory give comparable accuracy but require lower computational cost than high-level quantum computational methods and thus provide a promising strategy for studying strongly correlated systems.

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[1]
Zhou, C.; Hermes, M.R.; Wu, D.; Bao, J.J.; Pandharkar, R.; King, D.S.; Zhang, D.; Scott, T.R.; Lykhin, A.O.; Gagliardi, L.; Truhlar, D.G. Electronic structure of strongly correlated systems: recent developments in multiconfiguration pair-density functional theory and multiconfiguration nonclassical-energy functional theory. Chem. Sci., 2022, 13(26), 7685-7706.
[http://dx.doi.org/10.1039/D2SC01022D] [PMID: 35865899]
[2]
Roos, B.O.; Taylor, P.R.; Sigbahn, P.E.M. A complete active space SCF method (CASSCF) using a density matrix formulated super-CI approach. Chem. Phys., 1980, 48(2), 157-173.
[http://dx.doi.org/10.1016/0301-0104(80)80045-0]
[3]
Olsen, J.; Roos, B.; Jorgensen, P.; Jensen, H.J. Determinant based configuration interaction algorithms for complete and restricted configuration interaction spaces. J. Chem. Phys., 1988, 89, 2185-2192.
[http://dx.doi.org/10.1063/1.455063]
[4]
Van Lenthe, J.H.; Balint-Kurti, G.G. The valence-bond self-consistent field method (VB–SCF): Theory and test calculations. J. Chem. Phys., 1983, 78(9), 5699-5713.
[http://dx.doi.org/10.1063/1.445451]
[5]
Van Lenthe, J.H.; Balint-Kurti, G.G. The valence-bond scf (VB SCF) method. Chem. Phys. Lett., 1980, 76(1), 138-142.
[http://dx.doi.org/10.1016/0009-2614(80)80623-3]
[6]
Andersson, K.; Malmqvist, P.Å.; Roos, B.O. Second-order perturbation theory with a complete active space self-consistent field reference function. J. Chem. Phys., 1992, 96(2), 1218-1226.
[http://dx.doi.org/10.1063/1.462209]
[7]
Siegbahn, P.E.M.; Almlöf, J.; Heiberg, A.; Roos, B.O. The complete active space SCF (CASSCF) method in a Newton–Raphson formulation with application to the HNO molecule. J. Chem. Phys., 1981, 74(4), 2384-2396.
[http://dx.doi.org/10.1063/1.441359]
[8]
Karach, I.; Botvinik, A.; Truhlar, D.G.; Wu, W.; Shurki, A. Assessing the performance of ab initio classical valence bond methods for hydrogen transfer reactions. Comput. Theor. Chem., 2017, 1116, 234-241.
[http://dx.doi.org/10.1016/j.comptc.2017.05.031]
[9]
Chen, Z.; Song, J.; Shaik, S.; Hiberty, P.C.; Wu, W. Valence bond perturbation theory. A valence bond method that incorporates perturbation theory. J. Phys. Chem. A, 2009, 113(43), 11560-11569.
[http://dx.doi.org/10.1021/jp903011j] [PMID: 19569658]
[10]
Chen, Z.; Chen, X.; Ying, F.; Gu, J.; Zhang, H.; Wu, W. Nonorthogonal orbital based n -body reduced density matrices and their applications to valence bond theory. III. Second-order perturbation theory using valence bond self-consistent field function as reference. J. Chem. Phys., 2014, 141(13), 134118.
[http://dx.doi.org/10.1063/1.4896534] [PMID: 25296795]
[11]
Wu, W.; Song, L.; Cao, Z.; Zhang, Q.; Shaik, S. Valence bond configuration interaction: A practical ab initio valence bond method that incorporates dynamic correlation. J. Phys. Chem. A, 2002, 106(11), 2721-2726.
[http://dx.doi.org/10.1021/jp0141272]
[12]
Song, L.; Wu, W.; Zhang, Q.; Shaik, S. A practical valence bond method: A configuration interaction method approach with perturbation theoretic facility. J. Comput. Chem., 2004, 25(4), 472-478.
[http://dx.doi.org/10.1002/jcc.10382] [PMID: 14735567]
[13]
Hohenberg, P.; Kohn, W. Inhomogeneous electron gas. Phys. Rev., 1964, 136(3B), B864-B871.
[http://dx.doi.org/10.1103/PhysRev.136.B864]
[14]
Kohn, W.; Sham, L.J. Self-consistent equations including exchange and correlation effects. Phys. Rev., 1965, 140(4A), A1133-A1138.
[http://dx.doi.org/10.1103/PhysRev.140.A1133]
[15]
Gritsenko, O.V.; Schipper, P.R.T.; Baerends, E.J. Exchange and correlation energy in density functional theory: Comparison of accurate density functional theory quantities with traditional Hartree–Fock based ones and generalized gradient approximations for the molecules Li2, N2, F2. J. Chem. Phys., 1997, 107(13), 5007-5015.
[http://dx.doi.org/10.1063/1.474864]
[16]
Cremer, D. Density functional theory: coverage of dynamic and non-dynamic electron correlation effects. Mol. Phys., 2001, 99(23), 1899-1940.
[http://dx.doi.org/10.1080/00268970110083564]
[17]
Handy, N.C.; Cohen, A.J. Left-right correlation energy. Mol. Phys., 2001, 99(5), 403-412.
[http://dx.doi.org/10.1080/00268970010018431]
[18]
Polo, V.; Kraka, E.; Cremer, D. Electron correlation and the self-interaction error of density functional theory. Mol. Phys., 2002, 100(11), 1771-1790.
[http://dx.doi.org/10.1080/00268970110111788]
[19]
Zhang, D.; Truhlar, D.G. Unmasking static correlation error in hybrid kohn–sham density functional theory. J. Chem. Theory Comput., 2020, 16(9), 5432-5440.
[http://dx.doi.org/10.1021/acs.jctc.0c00585] [PMID: 32693604]
[20]
Miehlich, B.B.U.R.K.H.A.R.D.; Stoll, H.; Savin, A. A correlation-energy density functional for multideterminantal wavefunctions. Mol. Phys., 1997, 91(3), 527-536.
[http://dx.doi.org/10.1080/002689797171418]
[21]
Filatov, M.; Shaik, S. Spin-restricted density functional approach to the open-shell problem. Chem. Phys. Lett., 1998, 288(5-6), 689-697.
[http://dx.doi.org/10.1016/S0009-2614(98)00364-9]
[22]
Filatov, M.; Shaik, S. Application of spin-restricted open-shell Kohn–Sham method to atomic and molecular multiplet states. J. Chem. Phys., 1999, 110(1), 116-125.
[http://dx.doi.org/10.1063/1.477941]
[23]
Grimme, S.; Waletzke, M. A combination of Kohn–Sham density functional theory and multi-reference configuration interaction methods. J. Chem. Phys., 1999, 111(13), 5645-5655.
[http://dx.doi.org/10.1063/1.479866]
[24]
Gräfenstein, J.; Cremer, D. The combination of density functional theory with multi-configuration methods – CAS-DFT. Chem. Phys. Lett., 2000, 316(5-6), 569-577.
[http://dx.doi.org/10.1016/S0009-2614(99)01326-3]
[25]
Gräfenstein, J.; Cremer, D. Can density functional theory describe multi-reference systems? Investigation of carbenes and organic biradicals. Phys. Chem. Chem. Phys., 2000, 2(10), 2091-2103.
[http://dx.doi.org/10.1039/a909905k]
[26]
Pérez-Jiménez, Á.J.; Pérez-Jordá, J.M.; Illas, F. Density functional theory with alternative spin densities: Application to magnetic systems with localized spins. J. Chem. Phys., 2004, 120(1), 18-25.
[http://dx.doi.org/10.1063/1.1630021] [PMID: 15267256]
[27]
Head-Gordon, M. Characterizing unpaired electrons from the one-particle density matrix. Chem. Phys. Lett., 2003, 372(3-4), 508-511.
[http://dx.doi.org/10.1016/S0009-2614(03)00422-6]
[28]
Gräfenstein, J.; Cremer, D. Development of a CAS-DFT method covering non-dynamical and dynamical electron correlation in a balanced way. Mol. Phys., 2005, 103(2-3), 279-308.
[http://dx.doi.org/10.1080/00268970512331318858]
[29]
Fromager, E.; Toulouse, J.; Jensen, H.J.A. On the universality of the long-/short-range separation in multiconfigurational density-functional theory. J. Chem. Phys., 2007, 126(7), 074111.
[http://dx.doi.org/10.1063/1.2566459] [PMID: 17328597]
[30]
Cembran, A.; Song, L.; Mo, Y.; Gao, J. Block-localized density functional theory (BLDFT), diabatic coupling, and their use in valence bond theory for representing reactive potential energy surfaces. J. Chem. Theory Comput., 2009, 5(10), 2702-2716.
[http://dx.doi.org/10.1021/ct9002898] [PMID: 20228960]
[31]
Fromager, E.; Réal, F.; Wåhlin, P.; Wahlgren, U.; Jensen, H.J.A. On the universality of the long-/short-range separation in multiconfigurational density-functional theory. II. Investigating f[sup 0] actinide species. J. Chem. Phys., 2009, 131(5), 054107.
[http://dx.doi.org/10.1063/1.3187032] [PMID: 19673551]
[32]
Kurzweil, Y.; Lawler, K.V.; Head-Gordon, M. Analysis of multi-configuration density functional theory methods: theory and model application to bond-breaking. Mol. Phys., 2009, 107(20), 2103-2110.
[http://dx.doi.org/10.1080/00268970903160597]
[33]
Mo, Y.; Bao, P.; Gao, J. Energy decomposition analysis based on a block-localized wavefunction and multistate density functional theory. Phys. Chem. Chem. Phys., 2011, 13(15), 6760-6775.
[http://dx.doi.org/10.1039/c0cp02206c] [PMID: 21369567]
[34]
Sharkas, K.; Savin, A.; Jensen, H.J.A.; Toulouse, J. A multiconfigurational hybrid density-functional theory. J. Chem. Phys., 2012, 137(4), 044104.
[http://dx.doi.org/10.1063/1.4733672] [PMID: 22852594]
[35]
Ying, F.; Su, P.; Chen, Z.; Shaik, S.; Wu, W. DFVB: A density-functional-based valence bond method. J. Chem. Theory Comput., 2012, 8(5), 1608-1615.
[http://dx.doi.org/10.1021/ct200803h] [PMID: 26593654]
[36]
Fromager, E.; Knecht, S.; Jensen, H.J.A. Multi-configuration time-dependent density-functional theory based on range separation. J. Chem. Phys., 2013, 138(8), 084101.
[http://dx.doi.org/10.1063/1.4792199] [PMID: 23464134]
[37]
Stoyanova, A.; Teale, A.M.; Toulouse, J.; Helgaker, T.; Fromager, E. Alternative separation of exchange and correlation energies in multi-configuration range-separated density-functional theory. J. Chem. Phys., 2013, 139(13), 134113.
[http://dx.doi.org/10.1063/1.4822135] [PMID: 24116558]
[38]
Li, Manni G.; Carlson, R.K.; Luo, S.; Ma, D.; Olsen, J.; Truhlar, D.G.; Gagliardi, L. Multiconfiguration pair-density functional theory. J. Chem. Theory Comput., 2014, 10(9), 3669-3680.
[http://dx.doi.org/10.1021/ct500483t] [PMID: 26588512]
[39]
Gao, J.; Grofe, A.; Ren, H.; Bao, P. Beyond Kohn–Sham Approximation: Hybrid multistate wave function and density functional theory. J. Phys. Chem. Lett., 2016, 7(24), 5143-5149.
[http://dx.doi.org/10.1021/acs.jpclett.6b02455] [PMID: 27973892]
[40]
Zhou, C.; Zhang, Y.; Gong, X.; Ying, F.; Su, P.; Wu, W. Hamiltonian matrix correction based density functional valence bond method. J. Chem. Theory Comput., 2017, 13(2), 627-634.
[http://dx.doi.org/10.1021/acs.jctc.6b01144] [PMID: 27992721]
[41]
Ying, F. Zhou, C.; Zheng, P.; Luan, J.; Su, P.; Wu, W. λ-density functional valence bond: A valence bond-based multiconfigurational density functional theory with a single variable hybrid parameter. Front Chem., 2019, 7, 225.
[http://dx.doi.org/10.3389/fchem.2019.00225] [PMID: 31041304]
[42]
Mostafanejad, M.; Liebenthal, M.D.; DePrince, A.E., III Global hybrid multiconfiguration pair-density functional theory. J. Chem. Theory Comput., 2020, 16(4), 2274-2283.
[http://dx.doi.org/10.1021/acs.jctc.9b01178] [PMID: 32101416]
[43]
Qu, Z.; Ma, Y.; Gao, J. Variational multistate density functional theory for a balanced treatment of static and dynamic correlations. J. Chem. Theory Comput., 2020, 16(8), 4912-4922.
[http://dx.doi.org/10.1021/acs.jctc.0c00208] [PMID: 32672966]
[44]
Ying, F. Ji, C.; Su, P.; Wu, W. λ-DFCAS: A hybrid density functional complete active space self consistent field method. Chem. J. Chin. Univ., 2021, 42, 2218-2226.
[45]
Zhang, D.; Hermes, M.R.; Gagliardi, L.; Truhlar, D.G. Multiconfiguration density-coherence functional theory. J. Chem. Theory Comput., 2021, 17(5), 2775-2782.
[http://dx.doi.org/10.1021/acs.jctc.0c01346] [PMID: 33818081]
[46]
Zheng, P.; Ji, C.; Ying, F.; Su, P.; Wu, W. A valence-bond-based multiconfigurational density functional theory: The λ-DFVB method revisited. Molecules, 2021, 26(3), 521.
[http://dx.doi.org/10.3390/molecules26030521] [PMID: 33498268]
[47]
Pandharkar, R.; Hermes, M.R.; Truhlar, D.G.; Gagliardi, L. A new mixing of nonlocal exchange and nonlocal correlation with multiconfiguration pair-density functional theory. J. Phys. Chem. Lett., 2020, 11(23), 10158-10163.
[http://dx.doi.org/10.1021/acs.jpclett.0c02956] [PMID: 33196208]
[48]
Zheng, P. Gan, Z.; Zhou, C.; Su, P.; Wu, W. λ-DFVB(U): A hybrid density functional valence bond method based on unpaired electron density. J. Chem. Phys., 2022, 156(20), 204103.
[http://dx.doi.org/10.1063/5.0091592] [PMID: 35649821]
[49]
Becke, A.D.; Savin, A.; Stoll, H. Extension of the local-spin-density exchange-correlation approximation to multiplet states. Theor. Chim. Acta, 1995, 91(3-4), 147-156.
[http://dx.doi.org/10.1007/BF01114982]
[50]
Yamaguchi, K.; Fueno, T. Correlation effects in singlet biradical species. Chem. Phys., 1977, 19(1), 35-42.
[http://dx.doi.org/10.1016/0301-0104(77)80004-9]
[51]
Moscardó, F.; San-Fabián, E. Density-functional formalism and the two-body problem. Phys. Rev. A, 1991, 44(3), 1549-1553.
[http://dx.doi.org/10.1103/PhysRevA.44.1549] [PMID: 9906119]
[52]
Perdew, J.P.; Savin, A.; Burke, K. Escaping the symmetry dilemma through a pair-density interpretation of spin-density functional theory. Phys. Rev. A, 1995, 51(6), 4531-4541.
[http://dx.doi.org/10.1103/PhysRevA.51.4531] [PMID: 9912142]
[53]
Garza, A.J.; Jiménez-Hoyos, C.A.; Scuseria, G.E. Capturing static and dynamic correlations by a combination of projected Hartree-Fock and density functional theories. J. Chem. Phys., 2013, 138(13), 134102.
[http://dx.doi.org/10.1063/1.4796545] [PMID: 23574203]
[54]
Garza, A.J.; Jiménez-Hoyos, C.A.; Scuseria, G.E. Electronic correlation without double counting via a combination of spin projected Hartree-Fock and density functional theories. J. Chem. Phys., 2014, 140(24), 244102.
[http://dx.doi.org/10.1063/1.4883491] [PMID: 24985613]
[55]
Staroverov, V.N.; Davidson, E.R. A density functional method for degenerate spin-multiplet components. Chem. Phys. Lett., 2001, 340(1-2), 142-150.
[http://dx.doi.org/10.1016/S0009-2614(01)00390-6]
[56]
Gusarov, S.; Malmqvist, P.; Lindh, R.; Roos, B.O. Correlation potentials for a multiconfigurational-based density functional theory with exact exchange. Theor. Chem. Acc., 2004, 112(2), 84-94.
[http://dx.doi.org/10.1007/s00214-004-0568-1]
[57]
Lie, G.C.; Clementi, E. Study of the electronic structure of molecules. XXI. Correlation energy corrections as a functional of the Hartree-Fock density and its application to the hydrides of the second row atoms. J. Chem. Phys., 1974, 60(4), 1275-1287.
[http://dx.doi.org/10.1063/1.1681192]
[58]
Lie, G.C.; Clementi, E. Study of the electronic structure of molecules. XXII. Correlation energy corrections as a functional of the Hartree-Fock type density and its application to the homonuclear diatomic molecules of the second row atoms. J. Chem. Phys., 1974, 60(4), 1288-1296.
[http://dx.doi.org/10.1063/1.1681193]
[59]
Filatov, M.; Shaik, S. A spin-restricted ensemble-referenced Kohn–Sham method and its application to diradicaloid situations. Chem. Phys. Lett., 1999, 304(5-6), 429-437.
[http://dx.doi.org/10.1016/S0009-2614(99)00336-X]
[60]
Rapacioli, M.; Spiegelman, F.; Scemama, A.; Mirtschink, A. Modeling charge resonance in cationic molecular clusters: Combining DFT-tight binding with configuration interaction. J. Chem. Theory Comput., 2011, 7(1), 44-55.
[http://dx.doi.org/10.1021/ct100412f] [PMID: 26606217]
[61]
Wu, Q.; Cheng, C.L.; Van Voorhis, T. Configuration interaction based on constrained density functional theory: A multireference method. J. Chem. Phys., 2007, 127(16), 164119.
[http://dx.doi.org/10.1063/1.2800022] [PMID: 17979331]
[62]
Kraka, E. Homolytic dissociation energies from GVB-LSDC calculations. Chem. Phys., 1992, 161(1-2), 149-153.
[http://dx.doi.org/10.1016/0301-0104(92)80183-V]
[63]
Wu, W.; Zhong, S.; Shaik, S. VBDFT(s): a Hückel-type semi-empirical valence bond method scaled to density functional energies. Application to linear polyenes. Chem. Phys. Lett., 1998, 292(1-2), 7-14.
[http://dx.doi.org/10.1016/S0009-2614(98)00684-8]
[64]
Wu, W.; Luo, Y.; Song, L.; Shaik, S. VBDFT(s)—a semi-empirical valence bond method: Application to linear polyenes containing oxygen and nitrogen heteroatoms. Phys. Chem. Chem. Phys., 2001, 3(24), 5459-5465.
[http://dx.doi.org/10.1039/b107505e]
[65]
Wu, W.; Shaik, S.V.B-D.F.T. a nonempirical hybrid method combining valence bond theory and density functional energies. Chem. Phys. Lett., 1999, 301(1-2), 37-42.
[http://dx.doi.org/10.1016/S0009-2614(99)00011-1]
[66]
Mo, Y.; Song, L.; Lin, Y. Block-localized wavefunction (BLW) method at the density functional theory (DFT) level. J. Phys. Chem. A, 2007, 111(34), 8291-8301.
[http://dx.doi.org/10.1021/jp0724065] [PMID: 17655207]
[67]
Mo, Y.; Peyerimhoff, S.D. Theoretical analysis of electronic delocalization. J. Chem. Phys., 1998, 109(5), 1687-1697.
[http://dx.doi.org/10.1063/1.476742]
[68]
Ren, H.; Provorse, M.R.; Bao, P.; Qu, Z.; Gao, J. Multistate density functional theory for effective diabatic electronic coupling. J. Phys. Chem. Lett., 2016, 7(12), 2286-2293.
[http://dx.doi.org/10.1021/acs.jpclett.6b00915] [PMID: 27248004]
[69]
Lu, Y.; Gao, J. Multistate density functional theory of excited states. J. Phys. Chem. Lett., 2022, 13(33), 7762-7769.
[http://dx.doi.org/10.1021/acs.jpclett.2c02088] [PMID: 35969514]
[70]
Grofe, A.; Chen, X.; Liu, W.; Gao, J. Spin-multiplet components and energy splittings by multistate density functional theory. J. Phys. Chem. Lett., 2017, 8(19), 4838-4845.
[http://dx.doi.org/10.1021/acs.jpclett.7b02202] [PMID: 28914545]
[71]
Wu, W.; Su, P.; Shaik, S.; Hiberty, P.C. Classical valence bond approach by modern methods. Chem. Rev., 2011, 111(11), 7557-7593.
[http://dx.doi.org/10.1021/cr100228r] [PMID: 21848344]
[72]
Su, P.; Wu, W. Ab initio nonorthogonal valence bond methods. Wiley Interdiscip. Rev. Comput. Mol. Sci., 2013, 3(1), 56-68.
[http://dx.doi.org/10.1002/wcms.1105]
[73]
Chen, Z.; Wu, W. Ab initio valence bond theory: A brief history, recent developments, and near future. J. Chem. Phys., 2020, 153(9), 090902.
[http://dx.doi.org/10.1063/5.0019480] [PMID: 32891101]
[74]
Chirgwin, B.H.; Coulson, C.A.; Randall, J.T. The electronic structure of conjugated systems. VI. Proc. R. Soc. Lond. A Math. Phys. Sci., 1950, 201(1065), 196-209.
[http://dx.doi.org/10.1098/rspa.1950.0053]
[75]
Löwdin, P.O. Model of alkali haledes. Ark. Mat. Astron. Fys. A, 1947, 35, 30.
[76]
Ess, D.H.; Johnson, E.R.; Hu, X.; Yang, W. Singlet-triplet energy gaps for diradicals from fractional-spin density-functional theory. J. Phys. Chem. A, 2011, 115(1), 76-83.
[http://dx.doi.org/10.1021/jp109280y] [PMID: 21141988]
[77]
Huber, K.P.; Herzberg, G. Constants of diatomic molecules. Molecular Spectra and Molecular Structure: IV. Constants of Diatomic Molecules; Huber, K.P; Herzberg, G., Ed.; Springer US: Boston, MA, 1979, pp. 8-689.
[http://dx.doi.org/10.1007/978-1-4757-0961-2_2]
[78]
Harbison, G.S. The electric dipole polarity of the ground and low-lying metastable excited states of NF. J. Am. Chem. Soc., 2002, 124(3), 366-367.
[http://dx.doi.org/10.1021/ja0159261] [PMID: 11792193]
[79]
Li, X.; Paldus, J. Electronic structure of organic diradicals: Evaluation of the performance of coupled-cluster methods. J. Chem. Phys., 2008, 129(17), 174101.
[http://dx.doi.org/10.1063/1.2999560] [PMID: 19045327]
[80]
Guner, V.; Khuong, K.S.; Leach, A.G.; Lee, P.S.; Bartberger, M.D.; Houk, K.N. A standard set of pericyclic reactions of hydrocarbons for the benchmarking of computational methods: The Performance of ab Initio, Density Functional, CASSCF, CASPT2, and CBS-QB3 methods for the prediction of activation barriers, reaction energetics, and transition state geometries. J. Phys. Chem. A, 2003, 107(51), 11445-11459.
[http://dx.doi.org/10.1021/jp035501w]
[81]
Smith, J.E.T.; Mussard, B.; Holmes, A.A.; Sharma, S. Cheap and near exact CASSCF with large active Spaces. J. Chem. Theory Comput., 2017, 13(11), 5468-5478.
[http://dx.doi.org/10.1021/acs.jctc.7b00900] [PMID: 28968097]
[82]
Li, Manni G.; Alavi, A. understanding the mechanism stabilizing intermediate spin states in Fe(II)-Porphyrin. J. Phys. Chem. A, 2018, 122(22), 4935-4947.
[http://dx.doi.org/10.1021/acs.jpca.7b12710] [PMID: 29595978]
[83]
Kozlowski, P.M.; Spiro, T.G.; Bérces, A.; Zgierski, M.Z. Low-Lying Spin States of Iron(II). Porphine. J. Phys. Chem. B, 1998, 102(14), 2603-2608.
[http://dx.doi.org/10.1021/jp973346d]
[84]
Lemmon, E.W.; Bell, I.H.; Huber, M.L.; McLinden, M.O. Thermophysical properties of fluid systems. NIST Chemistry WebBook, NIST Standard Reference Database Number 69; Linstrom, P.J; Mallard, W.G., Ed.; National Institute of Standards and Technology: Gaithersburg, MD, 2019.
[85]
Leininger, M.L.; Sherrill, C.D.; Allen, W.D.; Schaefer, H.F. III Benchmark configuration interaction spectroscopic constants for X 1Σg+ C2 and X 1Σ+ CN+. J. Chem. Phys., 1998, 108(16), 6717-6721.
[http://dx.doi.org/10.1063/1.476087]

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