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The Effect of Hartree-Fock Exchange on Scaling Relations and Reaction Energetics for C–H Activation Catalysts


High-throughput computational catalyst studies are typically carried out using density functional theory (DFT) with a single, approximate exchange-correlation functional. In open shell transition metal complexes (TMCs) that are promising for challenging reactions (e.g., C–H activation), the predictive power of DFT has been challenged, and properties are known to be strongly dependent on the admixture of Hartree-Fock (HF) exchange. We carry out a large-scale study of the effect of HF exchange on the predicted catalytic properties of over 1200 mid-row (i.e., Cr, Mn, Fe, Co) 3d TMCs for direct methane-to-methanol conversion. Reaction energy sensitivities across this set depend both on the catalytic rearrangement and ligand chemistry of the catalyst. These differences in sensitivities change both the absolute energetics predicted for a catalyst and its relative performance. Previous observations of the poor performance of global linear free energy relationships (LFERs) hold with both semi-local DFT widely employed in heterogeneous catalysis and hybrid DFT. Narrower metal/oxidation/spin-state specific LFERs perform better and are less sensitive to HF exchange than absolute reaction energetics, except in the case of some intermediate/high-spin states. Importantly, the interplay between spin-state dependent reaction energetics and exchange effects on spin-state ordering means that the choice of DFT functional strongly influences whether the minimum energy pathway is spin-conserved. Despite these caveats, LFERs involving catalysts that can be expected to have closed shell intermediates and low-spin ground states retain significant predictive power.

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Data Availability

The data sets and codes generated during and/or analyzed during the current study are available in the “methane-to-methanol reaction energy sensitivities” repository, at The codes used in this work are also added to molSimplify.


  1. 1.

    Spivey JJ, Krishna KS, Kumar CSSR, Dooley KM, Flake JC, Haber LH, Xu Y, Janik MJ, Sinnott SB, Cheng YT, Liang T, Sholl DS, Manz TA, Diebold U, Parkinson GS, Bruce DA, de Jongh P (2014) Synthesis, characterization, and computation of catalysts at the center for atomic-level catalyst design. J Phys Chem C 118(35):20043–20069

    CAS  Article  Google Scholar 

  2. 2.

    Sperger T, Sanhueza IA, Kalvet I, Schoenebeck F (2015) Computational studies of synthetically relevant homogeneous organometallic catalysis involving Ni, Pd, Ir, and Rh: an overview of commonly employed DFT methods and mechanistic insights. Chem Rev 115(17):9532–9586

    CAS  PubMed  Article  Google Scholar 

  3. 3.

    Sperger T, Sanhueza IA, Schoenebeck F (2016) Computation and experiment: a powerful combination to understand and predict reactivities. Acc Chem Res 49(6):1311–1319

    CAS  PubMed  Article  Google Scholar 

  4. 4.

    Medford AJ, Vojvodic A, Hummelshoj JS, Voss J, Abild-Pedersen F, Studt F, Bligaard T, Nilsson A, Norskov JK (2015) From the Sabatier principle to a predictive theory of transition-metal heterogeneous catalysis. J Catal 328:36–42

    CAS  Article  Google Scholar 

  5. 5.

    Cheng GJ, Zhang XH, Chung LW, Xu LP, Wu YD (2015) Computational organic chemistry: bridging theory and experiment in establishing the mechanisms of chemical reactions. J Am Chem Soc 137(5):1706–1725

    CAS  PubMed  Article  Google Scholar 

  6. 6.

    Vogiatzis KD, Polynski MV, Kirkland JK, Townsend J, Hashemi A, Liu C, Pidko EA (2018) Computational approach to molecular catalysis by 3d transition metals: challenges and opportunities. Chem Rev 119(4):2453–2523

    PubMed  PubMed Central  Article  CAS  Google Scholar 

  7. 7.

    Raugei S, DuBois DL, Rousseau R, Chen S, Ho M-H, Bullock RM, Dupuis M (2015) Toward molecular catalysts by computer. Acc Chem Res 48(2):248–255

    CAS  PubMed  Article  Google Scholar 

  8. 8.

    Greeley J (2016) Theoretical heterogeneous catalysis: scaling relationships and computational catalyst design. Annu Rev Chem Biomol Eng 7:605–635

    PubMed  Article  Google Scholar 

  9. 9.

    Nørskov JK, Bligaard T, Rossmeisl J, Christensen CH (2009) Towards the computational design of solid catalysts. Nat Chem 1(1):37–46

    PubMed  Article  CAS  Google Scholar 

  10. 10.

    Foscato M, Jensen VR (2020) Automated in silico design of homogeneous catalysts. ACS Catal 10(3):2354–2377

    CAS  Article  Google Scholar 

  11. 11.

    Nandy A, Zhu J, Janet JP, Duan C, Getman RB, Kulik HJ (2019) Machine learning accelerates the discovery of design rules and exceptions in stable metal-oxo intermediate formation. ACS Catal 9:8243–8255

    CAS  Article  Google Scholar 

  12. 12.

    Vogiatzis KD, Haldoupis E, Xiao DJ, Long JR, Siepmann JI, Gagliardi L (2016) Accelerated computational analysis of metal–organic frameworks for oxidation catalysis. J Phys Chem C 120(33):18707–18712.

    CAS  Article  Google Scholar 

  13. 13.

    Kim JY, Kulik HJ (2018) When is ligand pKa a good descriptor for catalyst energetics? In search of optimal CO2 hydration catalysts. J Phys Chem A 122(18):4579–4590

    CAS  PubMed  Article  Google Scholar 

  14. 14.

    Gani TZH, Kulik HJ (2018) Understanding and breaking scaling relations in single-site catalysis: methane to methanol conversion by FeIV=O. ACS Catal 8:975–986

    CAS  Article  Google Scholar 

  15. 15.

    Cramer CJ, Truhlar DG (2009) Density functional theory for transition metals and transition metal chemistry. Phys Chem Chem Phys 11(46):10757–10816

    CAS  PubMed  Article  Google Scholar 

  16. 16.

    Janet JP, Zhao Q, Ioannidis EI, Kulik HJ (2017) Density functional theory for modelling large molecular adsorbate-surface interactions: a mini-review and worked example. Mol Simul 43(5–6):327–345

    CAS  Article  Google Scholar 

  17. 17.

    Gaggioli CA, Stoneburner SJ, Cramer CJ, Gagliardi L (2019) Beyond density functional theory: the multiconfigurational approach to model heterogeneous catalysis. ACS Catal 9(9):8481–8502

    CAS  Article  Google Scholar 

  18. 18.

    Jimenez-Hoyos CA, Janesko BG, Scuseria GE (2009) Evaluation of range-separated hybrid and other density functional approaches on test sets relevant for transition metal-based homogeneous catalysts. J Phys Chem A 113(43):11742–11749

    CAS  PubMed  Article  Google Scholar 

  19. 19.

    Zhao Q, Kulik HJ (2019) Stable surfaces that bind too tightly: can range-separated hybrids or DFT + U improve paradoxical descriptions of surface chemistry? J Phys Chem Lett 10(17):5090–5098

    CAS  PubMed  PubMed Central  Article  Google Scholar 

  20. 20.

    Schimka L, Harl J, Stroppa A, Grüneis A, Marsman M, Mittendorfer F, Kresse G (2010) Accurate surface and adsorption energies from many-body perturbation theory. Nat Mater 9(9):741–744

    CAS  PubMed  Article  Google Scholar 

  21. 21.

    Kulik HJ (2015) Perspective: treating electron over-delocalization with the DFT plus U method. J Chem Phys 142(24):240901

  22. 22.

    Yu HS, Li SL, Truhlar DG (2016) Perspective: Kohn-Sham density functional theory descending a staircase. J Chem Phys 145(13):130901

    PubMed  Article  CAS  Google Scholar 

  23. 23.

    Cohen AJ, Mori-Sanchez P, Yang W (2008) Fractional charge perspective on the band gap in density-functional theory. Phys Rev B 77(11):115123

  24. 24.

    Perdew JP, Parr RG, Levy M, Balduz JL Jr (1982) Density-functional theory for fractional particle number - derivative discontinuities of the energy. Phys Rev Lett 49(23):1691–1694

    CAS  Article  Google Scholar 

  25. 25.

    Yang WT, Zhang YK, Ayers PW (2000) Degenerate ground states and a fractional number of electrons in density and reduced density matrix functional theory. Phys Rev Lett 84(22):5172–5175

    CAS  PubMed  Article  Google Scholar 

  26. 26.

    Cohen AJ, Mori-Sanchez P, Yang W (2008) Insights into current limitations of density functional theory. Science 321(5890):792–794

    CAS  PubMed  Article  Google Scholar 

  27. 27.

    Janesko BG, Proynov E, Kong J, Scalmani G, Frisch MJ (2017) Practical density functionals beyond the overdelocalization–underbinding zero-sum game. J Phys Chem Lett 8(17):4314–4318

    CAS  PubMed  Article  Google Scholar 

  28. 28.

    Johnson BG, Gonzales CA, Gill PMW, Pople JA (1994) A density-functional study of the simplest hydrogen abstraction reaction - effect of self-interaction correction. Chem Phys Lett 221(1–2):100–108

    CAS  Article  Google Scholar 

  29. 29.

    Ruzsinszky A, Perdew JP, Csonka GI, Vydrov OA, Scuseria GE (2006) Spurious fractional charge on dissociated atoms: pervasive and resilient self-interaction error of common density functionals. J Chem Phys 125(19):194112

    PubMed  Article  CAS  Google Scholar 

  30. 30.

    Ruzsinszky A, Perdew JP, Csonka GI, Vydrov OA, Scuseria GE (2007) Density functionals that are one- and two- are not always many-electron self-interaction-free, as shown for H-2(+), He-2(+), LiH+, and Ne-2(+). J Chem Phys 126(10):104102

    PubMed  Article  CAS  Google Scholar 

  31. 31.

    Dutoi AD, Head-Gordon M (2006) Self-interaction error of local density functionals for alkali-halide dissociation. Chem Phys Lett 422(1–3):230–233

    CAS  Article  Google Scholar 

  32. 32.

    Bally T, Sastry GN (1997) Incorrect dissociation behavior of radical ions in density functional calculations. J Phys Chem A 101(43):7923–7925

    CAS  Article  Google Scholar 

  33. 33.

    Zhang Y, Yang W (1998) A challenge for density functionals: self-interaction error increases for systems with a non integer number of electrons. J Chem Phys 109(7):2604–2608

    CAS  Article  Google Scholar 

  34. 34.

    Wilbraham L, Verma P, Truhlar DG, Gagliardi L, Ciofini I (2017) Multiconfiguration pair-density functional theory predicts spin state ordering in iron complexes with the same accuracy as complete active space second-order perturbation theory at a significantly reduced computational cost. J Phys Chem Lett 8(9):2026–2030

    CAS  PubMed  Article  Google Scholar 

  35. 35.

    Ioannidis EI, Kulik HJ (2017) Ligand-field-dependent behavior of meta-GGA exchange in transition-metal complex spin-state ordering. J Phys Chem A 121(4):874–884

    CAS  PubMed  Article  Google Scholar 

  36. 36.

    Ioannidis EI, Kulik HJ (2015) Towards quantifying the role of exact exchange in predictions of transition metal complex properties. J Chem Phys 143(3):034104

  37. 37.

    Mortensen SR, Kepp KP (2015) Spin propensities of octahedral complexes from density functional theory. J Phys Chem A 119(17):4041–4050

    CAS  PubMed  Article  Google Scholar 

  38. 38.

    Droghetti A, Alfe D, Sanvito S (2012) Assessment of density functional theory for iron(II) molecules across the spin-crossover transition. J Chem Phys 137(12):124303

  39. 39.

    Ganzenmuller G, Berkaine N, Fouqueau A, Casida ME, Reiher M (2005) Comparison of density functionals for differences between the high-(T-5(2 g)) and low-((1)A(1 g)) spin states of iron(II) compounds. IV. Results for the ferrous complexes [Fe(L)(‘NHS4’)]. J Chem Phys 122:23

    Article  CAS  Google Scholar 

  40. 40.

    Kulik HJ, Cococcioni M, Scherlis DA, Marzari N (2006) Density functional theory in transition-metal chemistry: a self-consistent Hubbard U approach. Phys Rev Lett 97(10):103001

    PubMed  Article  CAS  Google Scholar 

  41. 41.

    Tozer DJ, De Proft F (2005) Computation of the hardness and the problem of negative electron affinities in density functional theory. J Phys Chem A 109(39):8923–8929

    CAS  PubMed  Article  Google Scholar 

  42. 42.

    Teale AM, De Proft F, Tozer DJ (2008) Orbital energies and negative electron affinities from density functional theory: insight from the integer discontinuity. J Chem Phys 129(4):044110

    PubMed  Article  CAS  Google Scholar 

  43. 43.

    Peach MJG, Teale AM, Helgaker T, Tozer DJ (2015) Fractional electron loss in approximate DFT and Hartree-Fock theory. J Chem Theory Comput 11(11):5262–5268

    CAS  PubMed  Article  Google Scholar 

  44. 44.

    Mori-Sanchez P, Cohen AJ, Yang WT (2008) Localization and delocalization errors in density functional theory and implications for band-gap prediction. Phys Rev Lett 100:14

    Article  CAS  Google Scholar 

  45. 45.

    Mahler A, Janesko BG, Moncho S, Brothers EN (2018) When Hartree-Fock exchange admixture lowers DFT-predicted barrier heights: natural bond orbital analyses and implications for catalysis. J Chem Phys 148(24)

  46. 46.

    Janet JP, Kulik HJ (2017) Predicting electronic structure properties of transition metal complexes with neural networks. Chem Sci 8:5137–5152.

    CAS  Article  PubMed  PubMed Central  Google Scholar 

  47. 47.

    Reiher M, Salomon O, Hess BA (2001) Reparameterization of hybrid functionals based on energy differences of states of different multiplicity. Theor Chem Acc 107(1):48–55

    CAS  Article  Google Scholar 

  48. 48.

    Coskun D, Jerome SV, Friesner RA (2016) Evaluation of the performance of the B3LYP, PBE0, and M06 DFT functionals, and DBLOC-corrected versions, in the calculation of redox potentials and spin splittings for transition metal containing systems. J Chem Theory Comput 12(3):1121–1128

    CAS  PubMed  Article  Google Scholar 

  49. 49.

    Haunschild R, Henderson TM, Jimenez-Hoyos CA, Scuseria GE (2010) Many-electron self-interaction and spin polarization errors in local hybrid density functionals. J Chem Phys 133(13):134116

    PubMed  Article  CAS  Google Scholar 

  50. 50.

    Mori-Sanchez P, Cohen AJ, Yang WT (2006) Many-electron self-interaction error in approximate density functionals. J Chem Phys 125(20)

  51. 51.

    Schmidt T, Kummel S (2016) One- and many-electron self-interaction error in local and global hybrid functionals. Phys Rev B 93(16)

  52. 52.

    Kim MC, Sim E, Burke K (2013) Understanding and reducing errors in density functional calculations. Phys Rev Lett 111:7

    Google Scholar 

  53. 53.

    Zheng X, Liu M, Johnson ER, Contreras-Garcia J, Yang W (2012) Delocalization error of density-functional approximations: a distinct manifestation in hydrogen molecular chains. J Chem Phys 137(21):214106

    PubMed  Article  CAS  Google Scholar 

  54. 54.

    Simm GN, Reiher M (2016) Systematic error estimation for chemical reaction energies. J Chem Theory Comput 12(6):2762–2773

    CAS  PubMed  Article  Google Scholar 

  55. 55.

    Sutton JE, Guo W, Katsoulakis MA, Vlachos DG (2016) Effects of correlated parameters and uncertainty in electronic-structure-based chemical kinetic modelling. Nat Chem 8(4):331–337

    CAS  PubMed  Article  Google Scholar 

  56. 56.

    Walker E, Ammal SC, Terejanu GA, Heyden A (2016) Uncertainty quantification framework applied to the water–gas shift reaction over Pt-based catalysts. J Phys Chem C 120(19):10328–10339

    CAS  Article  Google Scholar 

  57. 57.

    Wellendorff J, Lundgaard KT, Mogelhoj A, Petzold V, Landis DD, Norskov JK, Bligaard T, Jacobsen KW (2012) Density functionals for surface science: exchange-correlation model development with Bayesian error estimation. Phys Rev B 85(23):235149

    Article  CAS  Google Scholar 

  58. 58.

    Medford AJ, Wellendorff J, Vojvodic A, Studt F, Abild-Pedersen F, Jacobsen KW, Bligaard T, Nørskov JK (2014) Assessing the reliability of calculated catalytic ammonia synthesis rates. Science 345(6193):197–200

    CAS  PubMed  Article  Google Scholar 

  59. 59.

    Sumaria V, Krishnamurthy D, Viswanathan V (2018) Quantifying confidence in DFT predicted surface Pourbaix diagrams and associated reaction pathways for chlorine evolution. ACS Catal 8(10):9034–9042

    CAS  Article  Google Scholar 

  60. 60.

    Christensen R, Hansen HA, Vegge T (2015) Identifying systematic DFT errors in catalytic reactions. Catal Sci Technol 5(11):4946–4949

    CAS  Article  Google Scholar 

  61. 61.

    Wellendorff J, Silbaugh TL, Garcia-Pintos D, Norskov JK, Bligaard T, Studt F, Campbell CT (2015) A benchmark database for adsorption bond energies to transition metal surfaces and comparison to selected DFT functionals. Surf Sci 640:36–44

    CAS  Article  Google Scholar 

  62. 62.

    Houchins G, Viswanathan V (2017) Quantifying confidence in density functional theory predictions of magnetic ground states. Phys Rev B 96(13):134426

    Article  Google Scholar 

  63. 63.

    Gani TZH, Kulik HJ (2017) Unifying exchange sensitivity in transition metal spin-state ordering and catalysis through bond valence metrics. J Chem Theory Comput 13:5443–5457

    CAS  PubMed  Article  Google Scholar 

  64. 64.

    Busch M, Fabrizio A, Luber S, Hutter J, Corminboeuf C (2018) Exploring the limitation of molecular water oxidation catalysts. J Phys Chem C 122(23):12404–12412.

    CAS  Article  Google Scholar 

  65. 65.

    Janesko BG, Scuseria GE (2008) Hartree-Fock orbitals significantly improve the reaction barrier heights predicted by semi local density functionals. J Chem Phys 128(24):244112

    PubMed  PubMed Central  Article  CAS  Google Scholar 

  66. 66.

    Gani TZH, Kulik HJ (2016) Where does the density localize? Convergent behavior for global hybrids, range separation, and DFT + U. J Chem Theory Comput 12:5931–5945

    CAS  PubMed  Article  Google Scholar 

  67. 67.

    Liu F, Kulik HJ (2020) Impact of approximate DFT density delocalization error on potential energy surfaces in transition metal chemistry. J Chem Theory Comput 16(1):264–277.

    CAS  Article  PubMed  Google Scholar 

  68. 68.

    Oloo W, Que N Jr (2015) Bioinspired nonheme iron catalysts for C–H and C–C bond oxidation: insights into the nature of the metal-based oxidants. Acc Chem Res 48(9):2612–2621.

    CAS  Article  PubMed  Google Scholar 

  69. 69.

    Que L Jr, Tolman WB (2008) Biologically inspired oxidation catalysis. Nature 455(7211):333–340.

    CAS  Article  PubMed  Google Scholar 

  70. 70.

    Biswas AN, Puri M, Meier KK, Oloo WN, Rohde GT, Bominaar EL, Munck E, Que L Jr (2015) Modeling TauD-J: a high-spin nonheme oxoiron (IV) complex with high reactivity toward C–H bonds. J Am Chem Soc 137(7):2428–2431.

    CAS  Article  PubMed  Google Scholar 

  71. 71.

    Engelmann X, Monte-Perez I, Ray K (2016) Oxidation reactions with bioinspired mononuclear non-heme metal-oxo complexes. Angew Chem Int Ed 55(27):7632–7649.

    CAS  Article  Google Scholar 

  72. 72.

    Hammond C, Forde MM, Rahim A, Hasbi M, Thetford A, He Q, Jenkins RL, Dimitratos N, Lopez-Sanchez JA, Dummer NF (2012) Direct catalytic conversion of methane to methanol in an aqueous medium by using copper‐promoted Fe‐ZSM‐5. Angew Chem Int Ed 51(21):5129–5133

    CAS  Article  Google Scholar 

  73. 73.

    Jones C, Taube D, Ziatdinov VR, Periana RA, Nielsen RJ, Oxgaard J, Goddard WA (2004) Selective oxidation of methane to methanol catalyzed, with C-H activation, by homogeneous, cationic gold. Angew Chem Int Ed 116(35):4726–4729

    Article  Google Scholar 

  74. 74.

    Palkovits R, Antonietti M, Kuhn P, Thomas A, Schüth F (2009) Solid catalysts for the selective low-temperature oxidation of methane to methanol. Angew Chem Int Ed 48(37):6909–6912

    CAS  Article  Google Scholar 

  75. 75.

    Hull JF, Balcells D, Sauer EL, Raynaud C, Brudvig GW, Crabtree RH, Eisenstein O (2010) Manganese catalysts for C–H activation: an experimental/theoretical study identifies the stereoelectronic factor that controls the switch between hydroxylation and desaturation pathways. J Am Chem Soc 132(22):7605–7616.

    CAS  Article  PubMed  PubMed Central  Google Scholar 

  76. 76.

    Balcells D, Moles P, Blakemore JD, Raynaud C, Brudvig GW, Crabtree RH, Eisenstein O (2009) Molecular recognition in Mn-catalyzed C–H oxidation. Reaction mechanism and origin of selectivity from a DFT perspective. Dalton Trans 30:5989–6000

    Article  CAS  Google Scholar 

  77. 77.

    Latimer AA, Kulkarni AR, Aljama H, Montoya JH, Yoo JS, Tsai C, Abild-Pedersen F, Studt F, Nørskov JK (2017) Understanding trends in C-H bond activation in heterogeneous catalysis. Nat Mater 16(2):225–229.

    CAS  Article  PubMed  Google Scholar 

  78. 78.

    Christensen R, Hansen HA, Dickens CF, Nørskov JK, Vegge T (2016) Functional independent scaling relation for ORR/OER catalysts. J Phys Chem C 120(43):24910–24916.

    CAS  Article  Google Scholar 

  79. 79.

    Fajin JLC, Vines F, Cordeiro MNDS, Illas F, Gomes JRB (2016) Effect of the exchange-correlation potential on the transferability of Bronsted-Evans-Polanyi relationships in heterogeneous catalysis. J Chem Theory Comput 12(5):2121–2126

    CAS  PubMed  Article  Google Scholar 

  80. 80.

    Curnan MT, Kitchin JR (2015) Investigating the energetic ordering of stable and metastable TiO2 polymorphs using DFT + U and hybrid functionals. J Phys Chem C 119(36):21060–21071

    CAS  Article  Google Scholar 

  81. 81.

    Rosen AS, Notestein JM, Snurr RQ (2019) Structure–activity relationships that identify metal–organic framework catalysts for methane activation. ACS Catal 9(4):3576–3587.

    CAS  Article  Google Scholar 

  82. 82.

    Liao P, Getman RB, Snurr RQ (2017) Optimizing open iron sites in metal – organic frameworks for ethane oxidation: a first-principles study. ACS Appl Mater Interfaces 9(39):33484–33492.

    CAS  Article  PubMed  Google Scholar 

  83. 83.

    Pellizzeri S, Jones IA, Doan HA, Snurr RQ, Getman RB (2016) Using gas-phase clusters to screen porphyrin-supported nanocluster catalysts for ethane oxidation to ethanol. Catal Lett 146(12):2566–2573.

    CAS  Article  Google Scholar 

  84. 84.

    Wodrich MD, Sawatlon B, Busch M, Corminboeuf C (2021) The genesis of molecular volcano plots. Acc Chem Res 54(5):1107–1117

    CAS  PubMed  Article  Google Scholar 

  85. 85.

    Anand M, Rohr B, Statt MJ, Nørskov JK (2020) Scaling relationships and volcano plots in homogeneous catalysis. J Phys Chem Lett 11(20):8518–8526

    CAS  PubMed  Article  Google Scholar 

  86. 86.

    Busch M, Wodrich MD, Corminboeuf C (2015) Linear scaling relationships and volcano plots in homogeneous catalysis–revisiting the Suzuki reaction. Chem Sci 6(12):6754–6761

    CAS  PubMed  PubMed Central  Article  Google Scholar 

  87. 87.

    Andrikopoulos PC, Michel C, Chouzier S, Sautet P (2015) In silico screening of iron-oxo catalysts for CH bond cleavage. ACS Catal 5(4):2490–2499

    CAS  Article  Google Scholar 

  88. 88.

    Nandy A, Kulik HJ (2020) Why conventional design rules for C–H activation fail for open-shell transition-metal catalysts. ACS Catal 10(24):15033–15047.

    CAS  Article  Google Scholar 

  89. 89.

    Szécsényi Á, Khramenkova E, Chernyshov IY, Li G, Gascon J, Pidko EA (2019) Breaking linear scaling relationships with secondary interactions in confined space: a case study of methane oxidation by Fe/ZSM-5 zeolite. ACS Catal 9(10):9276–9284.

    CAS  Article  Google Scholar 

  90. 90.

    Pérez-Ramírez J, López N (2019) Strategies to break linear scaling relationships. Nat Catal 2(11):971–976

    Article  Google Scholar 

  91. 91.

    Marshall-Roth T, Libretto NJ, Wrobel AT, Anderton KJ, Pegis ML, Ricke ND, Van Voorhis T, Miller JT, Surendranath Y (2020) A pyridinic Fe-N 4 macrocycle models the active sites in Fe/N-doped carbon electrocatalysts. Nat Commun 11(1):1–14

    Article  CAS  Google Scholar 

  92. 92.

    Liu F, Yang T, Yang J, Xu E, Bajaj A, Kulik HJ (2019) Bridging the homogeneous-heterogeneous divide: modeling spin and reactivity in single atom catalysis. Front Chem 7:219

    CAS  PubMed  PubMed Central  Article  Google Scholar 

  93. 93.

    Xu H, Cheng D, Cao D, Zeng XC (2018) A universal principle for a rational design of single-atom electrocatalysts. Nat Catal 1(5):339–348

    CAS  Article  Google Scholar 

  94. 94.

    Sours T, Patel A, Nørskov J, Siahrostami S, Kulkarni A (2020) Circumventing scaling relations in oxygen electrochemistry using metal–organic frameworks. J Phys Chem Lett 11(23):10029–10036

    CAS  PubMed  Article  Google Scholar 

  95. 95.

    Abram S-L, Monte-Perez I, Pfaff FF, Farquhar ER, Ray K (2014) Evidence of two-state reactivity in alkane hydroxylation by Lewis-acid bound copper-nitrene complexes. Chem Commun 50(69):9852–9854

    CAS  Article  Google Scholar 

  96. 96.

    Zhu B, Guan W, Yan L-K, Su Z-M (2016) Two-state reactivity mechanism of benzene C–C activation by trinuclear titanium hydride. J Am Chem Soc 138(35):11069–11072

    CAS  PubMed  Article  Google Scholar 

  97. 97.

    Schwarz H (2017) Menage-a-trois: single-atom catalysis, mass spectrometry, and computational chemistry. Catal Sci Technol 7(19):4302–4314

    CAS  Article  Google Scholar 

  98. 98.

    Liu WG, Zhang LL, Liu X, Liu XY, Yang XF, Miao S, Wang WT, Wang AQ, Zhang T (2017) Discriminating catalytically active FeNx species of atomically dispersed Fe-N-C catalyst for selective oxidation of the C–H bond. J Am Chem Soc 139(31):10790–10798

    CAS  Article  Google Scholar 

  99. 99.

    Ricciarelli D, Belpassi L, Harvey JN, Belanzoni P (2020) Spin-forbidden reactivity of transition metal oxo species: exploring the potential energy surfaces. Chem Eur J 26(14):3080–3089.

    CAS  Article  PubMed  Google Scholar 

  100. 100.

    Harvey JN (2007) Understanding the kinetics of spin-forbidden chemical reactions. Phys Chem Chem Phys 9(3):331–343.

    CAS  Article  PubMed  Google Scholar 

  101. 101.

    Harvey JN (2014) Spin-forbidden reactions: computational insight into mechanisms and kinetics. Wiley Interdiscip Rev Comput Mol Sci 4(1):1–14.

    CAS  Article  Google Scholar 

  102. 102.

    Hirao H, Kumar D, Que L Jr, Shaik S (2006) Two-state reactivity in alkane hydroxylation by non-heme iron-oxo complexes. J Am Chem Soc 128(26):8590–8606.

    CAS  Article  PubMed  Google Scholar 

  103. 103.

    Shaik S, Danovich D, Fiedler A, Schroder D, Schwarz H (1995) 2-State reactivity in organometallic gas-phase ion chemistry. Helv Chim Acta 78(6):1393–1407

    CAS  Article  Google Scholar 

  104. 104.

    Schroder D, Shaik S, Schwarz H (2000) Two-state reactivity as a new concept in organometallic chemistry. Acc Chem Res 33(3):139–145

    CAS  PubMed  Article  Google Scholar 

  105. 105.

    Groves JT, McClusky GA (1976) Aliphatic hydroxylation via oxygen rebound. Oxygen transfer catalyzed by iron. J Am Chem Soc 98(3):859–861.

    CAS  Article  Google Scholar 

  106. 106.

    Ufimtsev IS, Martinez TJ (2009) Quantum chemistry on graphical processing units. 3. Analytical energy gradients, geometry optimization, and first principles molecular dynamics. J Chem Theory Comput 5(10):2619–2628

    CAS  PubMed  Article  Google Scholar 

  107. 107.

    Ioannidis EI, Gani TZH, Kulik HJ (2016) molSimplify: a toolkit for automating discovery in inorganic chemistry. J Comput Chem 37:2106–2117.

    CAS  Article  PubMed  Google Scholar 

  108. 108.

    O’Boyle NM, Banck M, James CA, Morley C, Vandermeersch T, Hutchison GR (2011) Open babel: an open chemical toolbox. J Cheminf 3:33.

    CAS  Article  Google Scholar 

  109. 109.

    O’Boyle NM, Morley C, Hutchison GR (2008) Pybel: a python wrapper for the open babel cheminformatics toolkit. Chem Cent J 2:5.

    CAS  Article  PubMed  PubMed Central  Google Scholar 

  110. 110.

    Nandy A, Duan C, Janet JP, Gugler S, Kulik HJ (2018) Strategies and software for machine learning accelerated discovery in transition metal chemistry. Ind Eng Chem Res 57(42):13973–13986

    CAS  Article  Google Scholar 

  111. 111.

    Lee C, Yang W, Parr RG (1988) Development of the Colle-Salvetti correlation-energy formula into a functional of the electron density. Phys Rev B 37:785–789

    CAS  Article  Google Scholar 

  112. 112.

    Becke AD (1993) Density-functional thermochemistry. III. The role of exact exchange. J Chem Phys 98(7):5648–5652

    CAS  Article  Google Scholar 

  113. 113.

    Stephens PJ, Devlin FJ, Chabalowski CF, Frisch MJ (1994) Ab initio calculation of vibrational absorption and circular dichroism spectra using density functional force fields. J Phys Chem 98(45):11623–11627

    CAS  Article  Google Scholar 

  114. 114.

    Grimme S, Antony J, Ehrlich S, Krieg H (2010) A consistent and accurate ab initio parametrization of density functional dispersion correction (DFT-D) for the 94 elements H-Pu. J Chem Phys 132(15):154104

    Article  CAS  Google Scholar 

  115. 115.

    Becke AD, Johnson ER (2005) A density-functional model of the dispersion interaction. J Chem Phys 123(15):154101

    PubMed  Article  CAS  Google Scholar 

  116. 116.

    Wadt WR, Hay PJ (1985) Ab initio effective core potentials for molecular calculations. Potentials for main group elements Na to Bi. J Chem Phys 82(1):284–298.

    CAS  Article  Google Scholar 

  117. 117.

    Hay PJ, Wadt WR (1985) Ab initio effective core potentials for molecular calculations. Potentials for the transition metal atoms Sc to Hg. J Chem Phys 82(1):270–283

    CAS  Article  Google Scholar 

  118. 118.

    Ditchfield R, Hehre WJ, Pople JA (1971) Self-consistent molecular-orbital methods.9. Extended Gaussian-type basis for molecular-orbital studies of organic molecules. J Chem Phys 54(2):724–728

    CAS  Article  Google Scholar 

  119. 119.

    Wang L-P, Song C (2016) Geometry optimization made simple with translation and rotation coordinates. J Chem Phys 144(21):214108

    PubMed  Article  CAS  Google Scholar 

  120. 120.

    Saunders VR, Hillier IH (1973) A “Level-Shifting” method for converging closed shell Hartree-Fock wave functions. Int J Quantum Chem 7(4):699–705.

    Article  Google Scholar 

  121. 121.

    Nandy A, Chu DBK, Harper DR, Duan C, Arunachalam N, Cytter Y, Kulik HJ (2020) Large-scale comparison of 3d and 4d transition metal complexes illuminates the reduced effect of exchange on second-row spin-state energetics. Phys Chem Chem Phys 22(34):19326–19341.

    CAS  Article  PubMed  Google Scholar 

  122. 122.

    Latimer AA, Kakekhani A, Kulkarni AR, Nørskov JK (2018) Direct methane to methanol: the selectivity–conversion limit and design strategies. ACS Catal 8(8):6894–6907.

    CAS  Article  Google Scholar 

  123. 123.

    Bowman DN, Jakubikova E (2012) Low-spin versus high-spin ground state in pseudo-octahedral iron complexes. Inorg Chem 51(11):6011–6019

    CAS  PubMed  Article  Google Scholar 

  124. 124.

    Kepp KP (2016) Theoretical study of spin crossover in 30 iron complexes. Inorg Chem 55(6):2717–2727

    CAS  PubMed  Article  Google Scholar 

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The authors acknowledge primary support for the catalyst design screen by the National Science Foundation under Grant numbers CBET-1704266 and CBET-1846426. A.N. was partially supported by a National Science Foundation Graduate Research Fellowship under Grant #1122374. Initial conception and data set generation for this study was supported by the Department of Energy under Grant number DE-SC0012702. Algorithm and workflow development as well as data collection strategies were supported by the Office of Naval Research under Grant numbers N00014-17-1-2956, N00014-18-1-2434, and N00014-20-1-2150. This work was carried out in part using computational resources from the Extreme Science and Engineering Discovery Environment (XSEDE), which is supported by National Science Foundation Grant number ACI-1548562. H.J.K. holds a Career Award at the Scientific Interface from the Burroughs Wellcome Fund, an AAAS Marion Milligan Mason Award, and an Alfred P. Sloan Fellowship in Chemistry, which supported this work.

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All authors contributed to the study conception and design. Data collection and analysis were performed by VV and AN. The first draft of the manuscript was written by VV, revised by HJK, and all authors commented on and revised versions of the manuscript. All authors read and approved the final manuscript.

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Correspondence to Heather J. Kulik.

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Vennelakanti, V., Nandy, A. & Kulik, H.J. The Effect of Hartree-Fock Exchange on Scaling Relations and Reaction Energetics for C–H Activation Catalysts. Top Catal (2021).

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  • Density functional theory
  • Homogeneous catalysis
  • C–H activation
  • Methane conversion
  • Mid-row transition metals
  • Open shell transition metal catalysts