Evaluating Spin-Orbit Effects on the Thermochemistry of Proton-Coupled Electron Transfer
Status PubMed-not-MEDLINE Jazyk angličtina Země Spojené státy americké Médium print-electronic
Typ dokumentu časopisecké články
PubMed
41429571
PubMed Central
PMC12801299
DOI
10.1021/acs.inorgchem.5c05144
Knihovny.cz E-zdroje
- Publikační typ
- časopisecké články MeSH
Many heavy transition metal compounds are active redox catalysts. Their redox potentials can be offset by differential spin-orbit coupling (SOC) effects in the case of strong perturbation of the ground-state energy of the oxidized or the reduced state. However, SOC effects are often considered negligible in the case of organometallic species, anticipating energetically well-separated, nondegenerate spin ground states for metal ions in strong ligand fields with low symmetry. We here report a rhenium(III) aminodiphosphine complex that undergoes proton-coupled electron transfer with a phenoxyl radical as a hydrogen abstractor. Experimental derivation of the PCET thermochemistry shows a deviation from coupled-cluster computations in the range of 6 kcal·mol-1. The deviation can be attributed to a sizable SOC contribution by the amine precursor, which is largely quenched in the rhenium(IV) amido product. Our case study emphasizes potential pitfalls for coupled-cluster benchmarking of the reaction energetics of heavy d-block catalysts.
Institute of Physics Charles University Ke Karlovu 5 Prague 121 16 Czech Republic
Laboratoire National des Champs Magnetiques Intenses 25 Rue des Martyrs Grenoble 38042 France
Universität Göttingen Institut für Anorganische Chemie Tammannstraße 4 Göttingen 37077 Germany
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Wang C. R., Stansberry J. M., Mukundan R., Chang H.-M. J., Kulkarni D., Park A. M., Plymill A. B., Firas N. M., Liu C. P., Lang J. T., Lee J. K., Tolouei N. E., Morimoto Y., Wang C. H., Zhu G., Brouwer J., Atanassov P., Capuano C. B., Mittelsteadt C., Peng X., Zenyuk I. V.. Proton Exchange Membrane (PEM) Water Electrolysis: Cell-Level Considerations for Gigawatt-Scale Deployment. Chem. Rev. 2025;125:1257–1302. doi: 10.1021/acs.chemrev.3c00904. PubMed DOI PMC
Garrido-Barros P., Derosa J., Chalkley M. J., Peters J. C.. Tandem electrocatalytic N2 fixation via proton-coupled electron transfer. Nature. 2022;609:71–77. doi: 10.1038/s41586-022-05011-6. PubMed DOI PMC
Mato M., Cornella J.. Bismuth in Radical Chemistry and Catalysis. Angew. Chem., Int. Ed. 2024;63:e202315046. doi: 10.1002/anie.202315046. PubMed DOI
Autschbach J.. Perspective: Relativistic effects. J. Chem. Phys. 2012;136:150902. doi: 10.1063/1.3702628. PubMed DOI
Heinemann C., Schwarz H., Koch W., Dyall K. G.. Relativistic effects in the cationic platinum carbene PtCH+ 2 . J. Chem. Phys. 1996;104:4642–4652. doi: 10.1063/1.471210. DOI
Fleig, T. Relativistic String-Based Electron Correlation Methods; Springer: Dordrecht, Heidelberg, London, NY, 2010. DOI: 10.1007/978-1-4020-9975-5_10. DOI
Srnec M., Chalupsky J., Fojta M., Zendlova L., Havran L., Hocek M., Kyvala M., Rulisek L.. Effect of Spin–Orbit Coupling on Reduction Potentials of Octahedral Ruthenium(II/III) and Osmium(II/III) Complexes. J. Am. Chem. Soc. 2008;130:10947–10954. doi: 10.1021/ja800616s. PubMed DOI
Bím D., Rulisek L., Srnec M.. Accurate Prediction of One-Electron Reduction Potentials in Aqueous Solution by Variable-Temperature H-Atom Addition/Abstraction Methodology. J. Phys. Chem. Lett. 2016;7:7–13. doi: 10.1021/acs.jpclett.5b02452. PubMed DOI
Siegbahn P. E. M., Svensson M., Crabtree R. H.. A Theoretical Study of Mercury Photosensitized Reactions. J. Am. Chem. Soc. 1995;117:6758–6765. doi: 10.1021/ja00130a016. DOI
Carroll J. J., Weisshaar J. C., Siegbahn P. E. M., Wittborn C. A. M., Blomberg M. R. A.. An Experimental and Theoretical Study of the Gas Phase Reactions between Small Linear Alkanes and the Platinum and Iridium Atoms. J. Phys. Chem. 1995;99:14388–14396. doi: 10.1021/j100039a028. DOI
Chen K., Zhang G., Chen H., Yao J., Danovich D., Shaik S.. Spin–Orbit Coupling and Outer-Core Correlation Effects in Ir- and Pt-Catalyzed C–H Activation. J. Chem. Theory Comput. 2012;8:1641–1645. doi: 10.1021/ct3000537. PubMed DOI
Jerabek P., Vondung L., Schwerdtfeger P.. Tipping the Balance between Ligand and Metal Protonation due to Relativistic Effects: Unusually High Proton Affinity in Gold(I) Pincer Complexes. Chem.–Eur. J. 2018;24:6047–6051. doi: 10.1002/chem.201800755. PubMed DOI
Delony D., Kinauer M., Diefenbach M., Demeshko S., Würtele C., Holthausen M. C., Schneider S.. A Terminal Iridium Oxo Complex with a Triplet Ground State. Angew. Chem., Int. Ed. 2019;58:10971–10974. doi: 10.1002/anie.201905325. PubMed DOI
Tepaske M. A., Fitterer A., Verplancke H., Delony D., Neben M. C., de Bruin B., Holthausen M. C., Schneider S.. C–H Bond Activation by Iridium(III) and Iridium(IV)Oxo Complexes. Angew. Chem., Int. Ed. 2024;63:e202316729. doi: 10.1002/anie.202316729. PubMed DOI
Oelschlegel K., Heinz M., Maji S., Naumann R., Höhle Y. F. S., Alizadeh N., Finger M., Otte M., Heinze K., Holthausen M. C., Schneider S.. Photocatalytic Hydrogenation of an N2-Derived ReV Imido Complex. JACS Au. 2025;5(10):4706–4713. doi: 10.1021/jacsau.5c00525. PubMed DOI PMC
Warren J. J., Tronic T. A., Mayer J. M.. Thermochemistry of Proton-Coupled Electron Transfer Reagents and its Implications. Chem. Rev. 2010;110:6961–7001. doi: 10.1021/cr100085k. PubMed DOI PMC
Agarwal R. G., Coste S. C., Groff B. D., Heuer A. M., Noh H., Parada G. A., Wise C. F., Nichols E. M., Warren J. J., Mayer J. M.. Free Energies of Proton-Coupled Electron Transfer Reagents and Their Applications. Chem. Rev. 2022;122:1–49. doi: 10.1021/acs.chemrev.1c00521. PubMed DOI PMC
Schendzielorz F., Finger M., Abbenseth J., Würtele C., Krewald V., Schneider S.. Metal-Ligand Cooperative Synthesis of Benzonitrile by Electrochemical Reduction and Photolytic Splitting of Dinitrogen. Angew. Chem., Int. Ed. 2019;131:840–844. doi: 10.1002/ange.201812125. PubMed DOI
Fritz M., Rupp S., Kiene C. I., Kisan S., Telser J., Würtele C., Krewald V., Schneider S.. Photoelectrochemical Conversion of Dinitrogen to Benzonitrile: Selectivity Control by Electrophile- versus Proton-Coupled Electron Transfer. Angew. Chem., Int. Ed. 2022;61(35):e202205922. doi: 10.1002/anie.202205922. PubMed DOI PMC
Bertini I., Luchinat C.. Relaxation. Coord. Chem. Rev. 1996;150:77–110.
Oulette E. T., Estrada J. I. A., Lussier D. J., Chakarawet K., Lohrey T. D., Karon L., Bergman R. G., Arnold J.. Spectroscopic, Magnetic, and Computational Investigations on a Series of Rhenium(III) Cyclopentadienide β-diketiminate Halide and Pseudohalide Complexes. Organometallics. 2022;41:3128–3137. doi: 10.1021/acs.organomet.1c00516. DOI
Chatt J., Leigh G. J., Mingos D. M. P.. Configurations of some complexes of rhenium, ruthenium, osmium, rhodium, iridium, and platinum halides with mono(tertiary phosphines) and mono(tertiary arsines) J. Chem. Soc. A. 1969:1674–1680. doi: 10.1039/j19690001674. DOI
Randall E. W., Shaw D.. Nuclear magnetic resonance spectra of d4-cornplexes of rheniurn(iii) and osmium(iv) with phosphine and arsine ligands. J. Chem. Soc. A. 1969:2867–2872. doi: 10.1039/j19690002867. DOI
Mitsopoulou C. A., Mahiea N., Motevalli M., Randall E. W.. Second-order paramagnetic rhenium(III) complexes: solid-state structure and assignment of the carbon-13 magnetic resonance spectra in solution. J. Chem. Soc., Dalton Trans. 1996:4563–4566. doi: 10.1039/DT9960004563. DOI
Bertini I., Luchinat C.. The hyperfine shift. Coord. Chem. Rev. 1996;150:29–75.
Martin B., Autschbach J.. Temperature dependence of contact and dipolar NMR chemical shifts in paramagnetic molecules. J. Chem. Phys. 2015;142:054108. doi: 10.1063/1.4906318. PubMed DOI
Gunz B. H. P., Leigh G. J.. Magnetic Susceptibilities of Some Rhenium(iii) and Osmium(iv) Halide Complexes; Preparation of Some New d4 Complexes. J. Chem. Soc. A. 1971:2229–2233. doi: 10.1039/j19710002229. DOI
Figgis B. N., Lewis J.. The Magnetic Properties of Transition Metal Complexes. Prog. Inorg. Chem. 1964;6:37–239. doi: 10.1002/9780470166079.ch2. DOI
Uzelmeier C. E., Bartley S. L., Fourmigué M., Rogers R., Grandinetti G., Dunbar K. R.. Reaction of Octachlorodirhenate with a Redox-Active Tetrathiafulvalene Phosphine Ligand: Spectroscopic, Magnetic, and Structural Characterization of the Unusual Paramagnetic Salt [ReCl2(o-P2)2][Re2Cl6(o-P2)] (o-P2 = o-{P(C6H5)2}2(CH3)2TTF) Inorg. Chem. 1998;37:6706–6713. doi: 10.1021/ic9808192. PubMed DOI
Palion-Gazda J., Gryca I., Machura B., Lloret F., Julve M.. Synthesis, crystal structure and magnetic properties of the complex [ReCl 3 (tppz)]. MeCN. RSC Adv. 2015;5:101616–101622. doi: 10.1039/C5RA21466A. PubMed DOI
Cariati F., Sgamellotti A., Morazzoni F., Valenti V.. Electronic spectra and magnetic properties of some rhenium(IV) and rhenium(III) complexes. Inorg. Chim. Acta. 1971;5:531–535. doi: 10.1016/S0020-1693(00)95982-6. DOI
Hay-Motherwell R. S., Wilkinson G., Hussain-Bates B., Hursthouse M. B.. Synthesis and X-ray crystal structure of oxotrimesityliridium(V) Polyhedron. 1993;12:2009–2012. doi: 10.1016/S0277-5387(00)81474-6. DOI
Earnshaw A., Figgis B. N., Lewis J., Peacock R. D.. The magnetic properties of some d4-complexes. J. Chem. Soc. 1961:3132–3138. doi: 10.1039/jr9610003132. DOI
Abbenseth J., Delony D., Neben M. C., Würtele C., de Bruin B., Schneider S.. Interconversion of Phosphinyl Radical and Phosphinidene Complexes by Proton Coupled Electron Transfer. Angew. Chem., Int. Ed. 2019;58:6338–6341. doi: 10.1002/anie.201901470. PubMed DOI PMC
Connor G. P., Delony D., Weber J. E., Mercado B. Q., Curley J. B., Schneider S., Mayer J. M., Holland P. L.. Facile conversion of ammonia to a nitride in a rhenium system that cleaves dinitrogen. Chem. Sci. 2022;13:4010–4018. doi: 10.1039/D1SC04503B. PubMed DOI PMC
Lever A. B. P.. Electrochemical Parametrization of Metal Complex Redox Potentials, Using the Ruthenium(III)/Ruthenium(II) Couple To Generate a Ligand Electrochemical Series. Inorg. Chem. 1990;29:1271–1285. doi: 10.1021/ic00331a030. DOI
van Alten R. S., Wieser P. A., Finger M., Abbenseth J., Demeshko S., Würtele C., Siewert I., Schneider S.. Halide Effects in Reductive Splitting of Dinitrogen with Rhenium Pincer Complexes. Inorg. Chem. 2022;61:11581–11591. doi: 10.1021/acs.inorgchem.2c00973. PubMed DOI
Tshepelevitsh S., Kütt A., Lõkov M., Kaljurand I., Saame J., Heering A., Plieger P. G., Vianello R., Leito I.. On the Basicity of Organic Bases in Different Media. Eur. J. Org. Chem. 2019;2019:6735–6748. doi: 10.1002/ejoc.201900956. DOI
Mader E. A., Manner V. W., Markle T. F., Wu A., Franz J. A., Mayer J. M.. Trends in Ground-State Entropies for Transition Metal Based Hydrogen Atom Transfer Reactions. J. Am. Chem. Soc. 2009;131:4335–4345. doi: 10.1021/ja8081846. PubMed DOI PMC
Wise C. F., Agarwal R. G., Mayer J. M.. Determining Proton-Coupled Standard Potentials and X–H Bond Dissociation Free Energies in Nonaqueous Solvents Using Open-Circuit Potential Measurements. J. Am. Chem. Soc. 2020;142:10681–10691. doi: 10.1021/jacs.0c01032. PubMed DOI
Manner V. W., Markle T. F., Freudenthal J. H., Roth J. P., Mayer J. M.. The first crystal structure of a monomeric phenoxyl radical: 2, 4, 6-tri-tert-butylphenoxyl radical. Chem. Commun. 2008;246:256–258. doi: 10.1039/B712872J. PubMed DOI
LeMardele, FieldOptic, FieldOptic https://github.com/LeMardele/FieldOptic. 2024.
Kahn, O. Molecular Magnetism; VCH Publishers Inc.: New York, 1993.
Bill, E. ; JulX, Program for Simulation of Molecular Magnetic Data. Max-Planck Institute For Chemical Energy Conversion; JulX: Mülheim, Ruhr, 2008.
Frisch, M. J. ; Trucks, G. W. ; Schlegel, H. B. ; Scuseria, G. E. ; Robb, M. A. ; Cheeseman, J. R. ; Scalmani, G. ; Barone, V. ; Petersson, G. A. ; Nakatsuji, H. , et al. Gaussian 16, Revision B.01.; Gaussian, Inc.: Wallingford CT, 2016.
Adamo C., Barone V.. Toward reliable density functional methods without adjustable parameters: The PBE0 model. J. Chem. Phys. 1999;110:6158–6170. doi: 10.1063/1.478522. DOI
Grimme S., Antony J., Ehrlich S., Krieg H.. A consistent and accurate ab initio parametrization of density functional dispersion correction (DFT-D) for the 94 elements H-Pu. J. Chem. Phys. 2010;132:154104. doi: 10.1063/1.3382344. PubMed DOI
Grimme S., Ehrlich S., Goerigk L.. Effect of the damping function in dispersion corrected density functional theory. J. Comput. Chem. 2011;32:1456–1465. doi: 10.1002/jcc.21759. PubMed DOI
Weigend F., Ahlrichs R.. Balanced basis sets of split valence, triple zeta valence and quadruple zeta valence quality for H to Rn: Design and assessment of accuracy. Phys. Chem. Chem. Phys. 2005;7:3297–3305. doi: 10.1039/b508541a. PubMed DOI
Andrae D., Häußermann U., Dolg M., Stoll H., Preuß H.. Energy-adjustedab initio pseudopotentials for the second and third row transition elements. Theor. Chim. Acta. 1990;77:123–141. doi: 10.1007/BF01114537. DOI
Neese F.. The ORCA program system. WIREs Comput. Mol. Sci. 2012;2:73–78. doi: 10.1002/wcms.81. DOI
Neese F., Wennmohs F., Becker U., Riplinger C.. The ORCA quantum chemistry program package. J. Chem. Phys. 2020;152:224108. doi: 10.1063/5.0004608. PubMed DOI
Neese F.. Software Update: The ORCA Program SystemVersion 6.0. WIREs Comput. Mol. Sci. 2025;15:e70019. doi: 10.1002/wcms.70019. DOI
Riplinger C., Neese F.. An efficient and near linear scaling pair natural orbital based local coupled cluster method. J. Chem. Phys. 2013;138:034106. doi: 10.1063/1.4773581. PubMed DOI
Saitow M., Becker U., Riplinger C., Valeev E. F., Neese F.. A new near-linear scaling, efficient and accurate, open-shell domain-based local pair natural orbital coupled cluster singles and doubles theory. J. Chem. Phys. 2017;146:164105. doi: 10.1063/1.4981521. PubMed DOI
Guo Y., Riplinger C., Becker U., Liakos D. G., Minenkov Y., Cavallo L., Neese F.. Communication: An improved linear scaling perturbative triples correction for the domain based local pair-natural orbital based singles and doubles coupled cluster method [DLPNO-CCSD(T)] J. Chem. Phys. 2018;148:011101. doi: 10.1063/1.5011798. PubMed DOI
Altun A., Neese F., Bistoni G.. Extrapolation to the Limit of a Complete Pair Natural Orbital Space in Local Coupled-Cluster Calculations. J. Chem. Theory Comput. 2020;16:6142–6149. doi: 10.1021/acs.jctc.0c00344. PubMed DOI PMC
Schwenke D. W.. The extrapolation of one-electron basis sets in electronic structure calculations: How it should work and how it can be made to work. J. Chem. Phys. 2005;122:014107. doi: 10.1063/1.1824880. PubMed DOI
Karton A., Martin J. M. L.. Comment on: “Estimating the Hartree–Fock limit from finite basis set calculations” [Jensen F (2005) Theor Chem Acc 113: 267] Theor. Chem. Acc. 2006;115:330–333. doi: 10.1007/s00214-005-0028-6. DOI
Neese F., Valeev E. F.. Revisiting the Atomic Natural Orbital Approach for Basis Sets: Robust Systematic Basis Sets for Explicitly Correlated and Conventional Correlated ab initio Methods? J. Chem. Theory Comput. 2011;7:33–43. doi: 10.1021/ct100396y. PubMed DOI
Truhlar D. G.. Basis set extrapolation. Chem. Phys. Lett. 1998;294:45–48. doi: 10.1016/S0009-2614(98)00866-5. DOI
Adalsteinsson H. M., Bjornsson R.. Ionization energies of metallocenes: a coupled cluster study of cobaltocene. Phys. Chem. Chem. Phys. 2023;25:4570–4587. doi: 10.1039/D2CP04715B. PubMed DOI
Adler T. B., Knizia G., Werner H.-J.. A simple and efficient CCSD(T)-F12 approximation. J. Chem. Phys. 2007;127:221106. doi: 10.1063/1.2817618. PubMed DOI
Peterson K. A., Adler T. B., Werner H.-J.. Systematically convergent basis sets for explicitly correlated wavefunctions: The atoms H, He, B–Ne, and Al–Ar. J. Chem. Phys. 2008;128:084102. doi: 10.1063/1.2831537. PubMed DOI
Figgen D., Peterson K. A., Dolg M., Stoll H.. Energy-consistent pseudopotentials and correlation consistent basis sets for the 5d elements Hf–Pt. J. Chem. Phys. 2009;130:164108. doi: 10.1063/1.3119665. PubMed DOI
Werner H.-J., Knowles P. J., Knizia G., Manby F. R., Schütz M.. Molpro: a general-purpose quantum chemistry program package. Wiley Interdiscip. Rev. :Comput. Mol. Sci. 2012;2:242–253. doi: 10.1002/wcms.82. DOI
Werner H.-J., Knowles P. J., Manby F. R., Black J. A., Doll K., Heßelmann A., Kats D., Köhn A., Korona T., Kreplin D. A.. et al. The Molpro quantum chemistry package. J. Chem. Phys. 2020;152:144107. doi: 10.1063/5.0005081. PubMed DOI
Werner, H.-J. ; Knowles, P. J. . MOLPRO, Version 2024, a package of ab initio programs. Molpro, 2025.
Knizia G., Adler T. B., Werner H.-J.. Simplified CCSD(T)-F12 methods: Theory and benchmarks. J. Chem. Phys. 2009;130:054104. doi: 10.1063/1.3054300. PubMed DOI
Weigend F.. Hartree–Fock exchange fitting basis sets for H to Rn. J. Comput. Chem. 2008;29:167–175. doi: 10.1002/jcc.20702. PubMed DOI
Hill J. G.. Auxiliary basis sets for density fitting second-order Møller-Plesset perturbation theory: correlation consistent basis sets for the 5d elements Hf-Pt. J. Chem. Phys. 2011;135:044105. doi: 10.1063/1.3615062. PubMed DOI
Yousaf K. E., Peterson K. A.. Optimized auxiliary basis sets for explicitly correlated Methods. J. Chem. Phys. 2008;129:184108. doi: 10.1063/1.3009271. PubMed DOI
Kritikou S., Hill J. G.. Auxiliary Basis Sets for Density Fitting in Explicitly Correlated Calculations: The Atoms H–Ar. J. Chem. Theory Comput. 2015;11:5269–5276. doi: 10.1021/acs.jctc.5b00816. PubMed DOI
Watts J. D., Gauss J., Bartlett R. J.. Coupled-cluster methods with noniterative triple excitations for restricted open-shell Hartree–Fock and other general single determinant reference functions Energies and analytical gradients. J. Chem. Phys. 1993;98:8718–8733. doi: 10.1063/1.464480. DOI
Hill J. G., Peterson K. A., Knizia G., Werner H.-J.. Extrapolating MP2 and CCSD explicitly correlated correlation energies to the complete basis set limit with first and second row correlation consistent basis sets. J. Chem. Phys. 2009;131:194105. doi: 10.1063/1.3265857. PubMed DOI
Verplancke H., Diefenbach M., Lienert J. N., Ugandi M., Kitsaras M.-P., Roemelt M., Stopkowicz S., Holthausen M. C.. Another Torture Track for Quantum Chemistry: Reinvestigation of the Benzaldehyde Amidation by Nitrogen-Atom Transfer from Platinum(II) and Palladium(II) Metallonitrenes. Isr. J. Chem. 2023;63:e202300060. doi: 10.1002/ijch.202300060. DOI
Radoń M., Drabik G., Hodorowicz M., Szklarzewicz J.. Performance of quantum chemistry methods for a benchmark set of spin-state energetics derived from experimental data of 17 transition metal complexes (SSE17) Chem. Sci. 2024;15:20189–20204. doi: 10.1039/D4SC05471G. PubMed DOI PMC
Chung L. W., Sameera W. M. C., Ramozzi R., Page A. J., Hatanaka M., Petrova G. P., Harris T. V., Li X., Ke Z., Liu F., Li H.-B., Ding L., Morokuma K.. The ONIOM Method and Its Applications. Chem. Rev. 2015;115:5678–5796. doi: 10.1021/cr5004419. PubMed DOI
Angeli C., Cimiraglia R., Evangelisti S., Leininger T., Malrieu J. P.. Introduction of n-electron valence states for multireference perturbation theory. J. Chem. Phys. 2001;114:10252–10264. doi: 10.1063/1.1361246. DOI
Angeli C., Cimiraglia R., Malrieu J. P.. N-electron valence state perturbation theory: a fast implementation of the strongly contracted variant. Chem. Phys. Lett. 2001;350:297–305. doi: 10.1016/S0009-2614(01)01303-3. DOI
Angeli C., Cimiraglia R., Malrieu J. P.. n-electron valence state perturbation theory: A spinless formulation and an efficient implementation of the strongly contracted and of the partially contracted variants. J. Chem. Phys. 2002;117:9138–9153. doi: 10.1063/1.1515317. DOI
Heß B. A., Marian C. M., Wahlgren U., Gropen O.. A mean-field spin-orbit method applicable to correlated wavefunctions. Chem. Phys. Lett. 1996;251:365–371. doi: 10.1016/0009-2614(96)00119-4. DOI
Van Lenthe E., Baerends E. J., Snijders J. G.. Relativistic regular two-component Hamiltonians. J. Chem. Phys. 1993;99:4597–4610. doi: 10.1063/1.466059. DOI
Van Lenthe E., Baerends E. J., Snijders J. G.. Relativistic total energy using regular approximations. J. Chem. Phys. 1994;101:9783–9792. doi: 10.1063/1.467943. DOI
Van Lenthe E., Snijders J. G., Baerends E. J.. The zero-order regular approximation for relativistic effects: The effect of spin–orbit coupling in closed shell molecules. J. Chem. Phys. 1996;105:6505–6516. doi: 10.1063/1.472460. DOI
Van Wüllen C.. Molecular density functional calculations in the regular relativistic approximation: Method, application to coinage metal diatomics, hydrides, fluorides and chlorides, and comparison with first-order relativistic calculations. J. Chem. Phys. 1998;109:392–399. doi: 10.1063/1.476576. DOI
Pantazis D. A., Chen X. Y., Landis C. R., Neese F.. All-Electron Scalar Relativistic Basis Sets for Third-Row Transition Metal Atoms. J. Chem. Theory Comput. 2008;4:908–919. doi: 10.1021/ct800047t. PubMed DOI
Weigend F.. A fully direct RI-HF algorithm: Implementation, optimized auxiliary basis sets, demonstration of accuracy and efficiency. Phys. Chem. Chem. Phys. 2002;4:4285–4291. doi: 10.1039/b204199p. DOI
Singh S. K., Eng J., Atanasov M., Neese F.. Covalency and chemical bonding in transition metal complexes: An ab initio based ligand field perspective. Coord. Chem. Rev. 2017;344:2–25. doi: 10.1016/j.ccr.2017.03.018. DOI