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Electronic structure of methyl radical photodissociation

  • Aiswarya M. Parameswaran , Dayou Zhang and Donald G. Truhlar ORCID logo EMAIL logo
Published/Copyright: August 27, 2025

Abstract

The calculation of accurate excitation energies and potential energy surfaces of photochemical reactions is a major challenge of current quantum chemistry, especially when one wants to keep the cost low enough to make detailed dynamical simulations affordable. Methods that might be affordable for large complex molecules can be tested against benchmark results for smaller molecules, where accurate benchmarks can be available. Here we report such testing for the excitation and dissociation of the methyl radical, yielding both singlet and triplet CH2. The emphasis is on multistate pair density functional theory using compressed-multistate (CMS-PDFT) and linearized (L-PDFT) formulations. We also consider the less affordable XMS-CASPT2 method with the same state-averaged-complete-active-space (SA-CASSCF) reference wave functions, which has seven active electrons in 10 active orbitals. The calculations use state averaging over seven states and a model space that spans the seven lowest SA-CASSCF eigenvectors. We study three on-top density functionals: tPBE, tPBE0, and MC23. Vertical excitation energies, adiabatic excitation energies, and dissociation energies, along with cuts through the potential surfaces along the dissociation coordinate, were computed with the (7, 10) active space. XMS-CASPT2 and L-PDFT with the MC23 functional show consistent and reliable performance for excitation energies, closely reproducing benchmark values, and producing smooth, physically reasonable potential energy surfaces essential for nonadiabatic dynamics simulations, but they are less accurate for bond energies. The L-PDFT calculations with the tPBE functional are more accurate for dissociation energies, but less accurate for excitation energies.


Corresponding author: Donald G. Truhlar, Department of Chemistry, Chemical Theory Center, and Supercomputing Institute, University of Minnesota, Minneapolis, MN 55455-0431, USA, e-mail:
Article note: A collection of invited papers to celebrate the UN’s proclamation of 2025 as the International Year of Quantum Science and Technology.

Award Identifier / Grant number: FA9550-20-1-0360

Acknowledgments

The authors are grateful to Yinan Shu, Matthew Hennefarth, Matthew Hermes, and Laura Gagliardi for valuable discussions.

  1. Research ethics: Not applicable.

  2. Informed consent: Not applicable.

  3. Author contributions: All authors have accepted responsibility for the entire content of this manuscript and approved its submission.

  4. Use of Large Language Models, AI and Machine Learning Tools: None declared.

  5. Conflict of interest: The authors declare no conflicts.

  6. Research funding: This work was supported in part by the Air Force Office of Scientific Research by grant FA9550-20-1-0360.

  7. Data availability: All data generated or analyzed during this study are included in this published article and its Supplementary information file.

References

1. Pauling, L. Nobel Lecture: Modern Structural Chemistry. Science 1956, 123, 255–258; https://doi.org/10.1126/science.123.3190.255.Search in Google Scholar PubMed

2. Mulliken, R. S. Nobel Lecture: Spectroscopy, Molecular Orbitals, and Chemical Bonding. Science 1967, 157, 13–24; https://doi.org/10.1126/science.157.3784.13.Search in Google Scholar PubMed

3. Stearn, A. E.; Eyring, H. Nonadiabatic Reactions. The Decomposition of N2O. J. Chem. Phys. 1935, 3, 778–785; https://doi.org/10.1063/1.1749592.Search in Google Scholar

4. Landau, L. D. Zur Theorie der Energieubertragung II. Phys. Z. Sowjetunion 1932, 2, 46–51.Search in Google Scholar

5. Zener, C. Non-Adiabatic Crossing of Energy Levels. Proc. R. Soc. London, Ser. A 1932, 137, 696–702; https://doi.org/10.1098/rspa.1932.0165.Search in Google Scholar

6. Teller, E. The Crossing of Potential Surfaces. J. Phys. Chem. 1937, 41, 109–116; https://doi.org/10.1021/j150379a010.Search in Google Scholar

7. Evans, M. G.; Eyring, H.; Kincaid, J. F. J. Chem. Phys. 1938, 6, 349–358; https://doi.org/10.1063/1.1750268.Search in Google Scholar

8. Tully, J. C.; Preston, R. K. Trajectory Surface Hopping Approach to Nonadiabatic Collisions: The Reaction of H+ with D2. J. Chem. Phys. 1971, 55, 562–572; https://doi.org/10.1063/1.1675788.Search in Google Scholar

9. Blais, N. C.; Truhlar, D. G. Trajectory-Surface-Hopping Study of Na(3p 2P) + H2 → Na(3s 2S) + H2(v´,j´, θ). J. Chem. Phys. 1983, 79, 1334–1342; https://doi.org/10.1063/1.445888.Search in Google Scholar

10. Tully, J. C. Molecular Dynamics with Electronic Transitions. J. Chem. Phys. 1990, 93, 1061–1071; https://doi.org/10.1063/1.459170.Search in Google Scholar

11. Chapman, S. The Classical Trajectory−Surface Hopping Approach to Charge-Transfer Processes. Adv. Chem. Phys. 1992, 82, 423–483; https://doi.org/10.1002/9780470141403.ch7.Search in Google Scholar

12. Wolfsberg, M.; Helmholz, L. J. Chem. Phys. 1952, 20, 837–843; https://doi.org/10.1063/1.1700580.Search in Google Scholar

13. Pariser, R.; Parr, R. G. A Semi-Empirical Theory of the Electronic Spectra and Electronic Structure of Complex Unsaturated Molecules. II. J. Chem. Phys. 1953, 21, 767–776; https://doi.org/10.1063/1.1699030.Search in Google Scholar

14. Pople, J. A. Electron Interaction in Unsaturated Hydrocarbons. Trans. Faraday Soc. 1953, 49, 1375–1385; https://doi.org/10.1039/tf9534901375.Search in Google Scholar

15. Véril, M.; Scemama, A.; Caffarel, M.; Lipparini, F.; Boggio‐Pasqua, M.; Jacquemin, D.; Loos, P. F. QUESTDB: A Database of Highly Accurate Excitation Energies for the Electronic Structure Community. Wiley Interdiscip. Rev. Comput. Mol. Sci. 2021, 11, e1517; https://doi.org/10.1002/wcms.1517.Search in Google Scholar

16. Mielke, S. L.; Tawa, G. J.; Truhlar, D. G.; Schwenke, D. W. Quantum Photochemistry. Accurate Quantum Scattering Calculations for an Electronically Nonadiabatic Reaction. Chem. Phys. Lett. 1995, 234, 57–63; https://doi.org/10.1016/0009-2614(94)01515-w.Search in Google Scholar

17. Mielke, S. L.; Truhlar, D. G.; Schwenke, D. W. Quantum Photochemistry. the Competition Between Electronically Nonadiabatic Reaction and Electronic-to-Vibrational, Rotational, Translational Energy Transfer in Br* Collisions with H2. J. Phys. Chem. 1995, 99, 16210–16216; https://doi.org/10.1021/j100044a003.Search in Google Scholar

18. Balucani, N.; Skouteris, D.; Capozza, G.; Segoloni, E.; Casavecchia, P.; Alexander, M. H.; Capecchi, G.; Werner, H. J. The Dynamics of the Prototype Abstraction Reaction Cl (2P3/2,1/2)+ H2: A Comparison of Crossed Molecular Beam Experiments with Exact Quantum Scattering Calculations on Coupled Ab Initio Potential Energy Surfaces. Phys. Chem. Chem. Phys. 2004, 6, 5007–5017; https://doi.org/10.1039/b410119g.Search in Google Scholar

19. Xie, C.; Ma, J.; Zhu, X.; Zhang, D. H.; Yarkony, D. R.; Xie, D.; Guo, H. Full-Dimensional Quantum State-to-State Nonadiabatic Dynamics for Photodissociation of Ammonia in its A-Band. J. Phys. Chem. Lett. 2014, 5, 1055–1060; https://doi.org/10.1021/jz500227d.Search in Google Scholar PubMed

20. Born, M. Kopplung Der Elektronen- und Kernbewegung in Molekeln und Kristallen. Nachr. Akad. Wiss. Göttingen, Math.-Phys. 1951, 6, 1–3.10.1007/978-3-642-49913-5_1Search in Google Scholar

21. Ruedenberg, K.; Cheung, L. M.; Elbert, S. T. MCSCF Optimization Through Combined Use of Natural Orbitals and the Brillouin-Levy-Berthier Theorem. Int. J. Quantum Chem. 1979, 16, 1069–1101; https://doi.org/10.1002/qua.560160511.Search in Google Scholar

22. Roos, B.; Taylor, J. R.; Siegbahn, P. E. M. A Complete Active Space SCF Method (CASSCF) Using a Density Matrix Formulated Super-CI Approach. Chem. Phys. 1980, 48, 157–173; https://doi.org/10.1016/0301-0104(80)80045-0.Search in Google Scholar

23. Pople, J. A. Nobel Lecture: Quantum Chemical Methods. Rev. Mod. Phys. 1999, 71, 1267–1274; https://doi.org/10.1103/revmodphys.71.1267.Search in Google Scholar

24. Karton, A. Benchmark Accuracy in Thermochemistry, Kinetics, and Noncovalent Interactions. In Comprehensive Computational Chemistry; Elsevier: Amsterdam, Vol. 1, 2023; pp. 47–68; https://doi.org/10.1016/b978-0-12-821978-2.00129-x.Search in Google Scholar

25. Hohenberg, P.; Kohn, W. Inhomogeneous Electron Gas. Phys. Rev. 1964, 136, B864–B871; https://doi.org/10.1103/physrev.136.b864.Search in Google Scholar

26. Becke, A. D. A New Mixing of Hartree–Fock and Local Density Functional Theories. J. Chem. Phys. 1993, 98, 1372–1377; https://doi.org/10.1063/1.464304.Search in Google Scholar

27. Leininger, T.; Stoll, H.; Werner, H.-J.; Savin, A. Combining Long-Range Configuration Interaction with Short-Range Density Functionals to Handle Near-Degeneracy in Atoms and Molecules. Chem. Phys. Lett. 1997, 275, 151–160; https://doi.org/10.1016/s0009-2614(97)00758-6.Search in Google Scholar

28. Zhao, Y.; Lynch, B. J.; Truhlar, D. G. Doubly Hybrid Meta DFT: New Multi-Coefficient Correlation and Density Functional Methods for Thermochemistry and Thermochemical Kinetics. J. Phys. Chem. A 2004, 108, 4786–4791; https://doi.org/10.1021/jp049253v.Search in Google Scholar

29. 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, 10158–10163; https://doi.org/10.1021/acs.jpclett.0c02956.Search in Google Scholar PubMed

30. Kohn, W.; Sham, L. J. Self-Consistent Equations Including Exchange and Correlation Effects. Phys. Rev. 1965, 140, A1133–A1138; https://doi.org/10.1103/physrev.140.a1133.Search in Google Scholar

31. Shiozaki, T.; Gyorffy, W.; Celani, P.; Werner, H.-J. Communication: Extended Multi-State Complete Active Space Second-Order Perturbation Theory: Energy and Nuclear Gradients. J. Chem. Phys. 2011, 135, 081106; https://doi.org/10.1063/1.3633329.Search in Google Scholar PubMed

32. Angeli, C.; Borini, S.; Cestari, M.; Cimiraglia, R. A Quasidegenerate Formulation of the Second Order n-Electron Valence State Perturbation Theory Approach. J. Chem. Phys. 2004, 121, 4043–4049; https://doi.org/10.1063/1.1778711.Search in Google Scholar PubMed

33. Andersson, K.; Malmqvist, P. A.; Roos, B. O.; Sadlej, A. J.; Wolinski, K. Second Order Perturbation Theory with a CASSCF Reference Function. J. Phys. Chem. 1990, 94, 5483–5488; https://doi.org/10.1021/j100377a012.Search in Google Scholar

34. 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; https://doi.org/10.1063/1.1361246.Search in Google Scholar

35. Szalay, P. G.; Müller, T.; Gidofalvi, G.; Lischka, H.; Shepard, R. Multiconfiguration Self-Consistent Field and Multireference Configuration Interaction Methods and Applications. Chem. Rev. 2012, 112, 108–181; https://doi.org/10.1021/cr200137a.Search in Google Scholar PubMed

36. Piecuch, P.; Oliphant, N.; Adamowicz, L. A State‐Selective Multireference Coupled‐Cluster Theory Employing the Single‐Reference Formalism. J. Chem. Phys. 1993, 99, 1875–1900; https://doi.org/10.1063/1.466179.Search in Google Scholar

37. Malmqvist, P. A.; Rendell, A.; Roos, B. O. The Restricted Active Space Self-Consistent-Field Method, Implemented with a Split Graph Unitary Group Approach. J. Phys. Chem. 1990, 94, 5477–5482; https://doi.org/10.1021/j100377a011.Search in Google Scholar

38. Sharma, P.; Truhlar, D. G.; Gagliardi, L. Magnetic Coupling in a Tris-Hydroxo-Bridged Chromium Dimer Occurs Through Ligand Mediated Superexchange in Conjunction with Through-Space Coupling. J. Am. Chem. Soc. 2020, 142, 16644–16650; https://doi.org/10.1021/jacs.0c06399.Search in Google Scholar PubMed

39. Presti, D.; Truhlar, D. G.; Gagliardi, L. Intramolecular Charge Transfer and Local Excitation in Organic Fluorescent Photoredox Catalysts Explained by RASCI-PDFT. J. Phys. Chem. C 2018, 122, 12061–12070; https://doi.org/10.1021/acs.jpcc.8b01844.Search in Google Scholar

40. Odoh, Samuel O.; Manni, G. L.; Carlson, R. K.; Truhlar, D. G.; Gagliardi, L. Separated-Pair Approximation and Separated-Pair Pair-Density Functional Theory. Chem. Sci. 2016, 7, 2399–2413; https://doi.org/10.1039/c5sc03321g.Search in Google Scholar PubMed PubMed Central

41. Ghosh, S.; Cramer, C. J.; Truhlar, D. G.; Gagliardi, L. Generalized-Active-Space Pair-Density Functional Theory: An Efficient Method to Study Large, Strongly Correlated, Conjugated Systems. Chem. Sci. 2017, 8, 2741–2750; https://doi.org/10.1039/c6sc05036k.Search in Google Scholar PubMed PubMed Central

42. Bender, C. F.; Davidson, E. R. Studies in Configuration Interaction: the First-Row Diatomic Hydrides. Phys. Rev. 1969, 183, 23–30; https://doi.org/10.1103/physrev.183.23.Search in Google Scholar

43. Whitten, J. L.; Hackmeyer, M. Configuration Interaction Studies of Ground and Excited States of Polyatomic Molecules. I. The CI Formulation and Studies of Formaldehyde. J. Chem. Phys. 1969, 51, 5584–5596; https://doi.org/10.1063/1.1671985.Search in Google Scholar

44. Chan, G. K.-L.; Sharma, S. The Density Matrix Renormalization Group in Quantum Chemistry. Annu. Rev. Phys. Chem. 2011, 62, 465–481; https://doi.org/10.1146/annurev-physchem-032210-103338.Search in Google Scholar PubMed

45. Baiardi, A.; Reiher, M. The Density Matrix Renormalization Group in Chemistry and Molecular Physics: Recent Developments and New Challenges. J. Chem. Phys. 2020, 152, 040903; https://doi.org/10.1063/1.5129672.Search in Google Scholar PubMed

46. Sharma, P.; Bernales, V.; Knecht, S.; Truhlar, D. G.; Gagliardi, L. Density Matrix Renormalization Group Pair-Density Functional Theory (DMRG-PDFT): Singlet–Triplet Gaps in Polyacenes and Polyacetylenes. Chem. Sci. 2019, 10, 1716–1723; https://doi.org/10.1039/c8sc03569e.Search in Google Scholar PubMed PubMed Central

47. Jasper, A. W.; Kendrick, B. K.; Mead, C. A.; Truhlar, D. G. Non-Born-Oppenheimer Chemistry: Potential Surfaces, Couplings, and Dynamics. In Modern Trends in Chemical Reaction Dynamics: Experiment and Theory (Part 1); Yang, X.; Liu, K., Eds.; World Scientific: Singapore, 2004; pp. 329–391.10.1142/9789812565426_0008Search in Google Scholar

48. Bao, J. J.; Zhou, C.; Truhlar, D. G. Compressed-State Multistate Pair-Density Functional Theory. J. Chem. Theory Comput. 2020, 16, 7444–7452; https://doi.org/10.1021/acs.jctc.0c00908.Search in Google Scholar PubMed

49. 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, 3669–3680; https://doi.org/10.1021/ct500483t.Search in Google Scholar PubMed

50. Gagliardi, L.; Truhlar, D. G.; Li Manni, G.; Carlson, R. K.; Hoyer, C. E.; Bao, J. L. Multiconfiguration Pair-Density Functional Theory: A New Way to Treat Strongly Correlated Systems. Acc. Chem. Res. 2017, 50, 66–73; https://doi.org/10.1021/acs.accounts.6b00471.Search in Google Scholar PubMed

51. 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, 7685–7706; https://doi.org/10.1039/d2sc01022d.Search in Google Scholar PubMed PubMed Central

52. Hennefarth, M. R.; Hermes, M. R.; Truhlar, D. G.; Gagliardi, L. Linearized Pair-Density Functional Theory. J. Chem. Theory Comput. 2023, 19, 3172–3183; https://doi.org/10.1021/acs.jctc.3c00207.Search in Google Scholar PubMed

53. Hennefarth, M. R.; King, D. S.; Gagliardi, L. Linearized Pair-Density Functional Theory for Vertical Excitation Energies. J. Chem. Theory Comput. 2023, 19, 7983–7988; https://doi.org/10.1021/acs.jctc.3c00863.Search in Google Scholar PubMed

54. Hennefarth, M. R.; Truhlar, D. G.; Gagliardi, L. Semiclassical Nonadiabatic Molecular Dynamics Using Linearized Pair-Density Functional Theory. J. Chem. Theory Comput. 2024, 20, 8741–8748; https://doi.org/10.1021/acs.jctc.4c01061.Search in Google Scholar PubMed

55. Smyth, K. C.; Taylor, P. H. Detection of the Methyl Radical in a Methane/Air Diffusion Flame by Multiphoton Ionization Spectroscopy. Chem. Phys. Lett. 1985, 122, 518–522; https://doi.org/10.1016/0009-2614(85)87257-2.Search in Google Scholar

56. Wayne, R. P. Chemistry of Atmospheres, 3rd ed.; Oxford University Press: Oxford, 2000.Search in Google Scholar

57. Feuchtgruber, H.; Helmich, F. P.; Van Dishoeck, E. F.; Wright, C. M. Detection of Interstellar CH3. Astrophys. J. 2000, 535, L111–L114; https://doi.org/10.1086/312711.Search in Google Scholar PubMed

58. Herzberg, G. The Bakerian Lecture. The Spectra and Structures of Free Methyl and Free Methylene. Proc. R. Soc. London. Ser. A. Math. Phys. Sci. 1961, 262, 291–317.10.1098/rspa.1961.0120Search in Google Scholar

59. Herzberg, G. Spectroscopic Studies of Molecular Structure (Nobel Lecture). Science 1972, 177, 123–138; https://doi.org/10.1126/science.177.4044.123.Search in Google Scholar PubMed

60. Hudgens, J. W.; DiGiuseppe, T. G.; Lin, M. C. Two Photon Resonance Enhanced Multiphoton Ionization Spectroscopy and State Assignments of the Methyl Radical. J. Chem. Phys. 1983, 79, 571–582; https://doi.org/10.1063/1.445857.Search in Google Scholar

61. North, S. W.; Blank, D. A.; Chu, P. M.; Lee, Y. T. Photodissociation Dynamics of the Methyl Radical 3s Rydberg State. J. Chem. Phys. 1995, 102, 792–798; https://doi.org/10.1063/1.469193.Search in Google Scholar

62. Westre, S. G.; Kelly, P. B.; Zhang, Y. P.; Ziegler, L. D. Subpicosecond Predissociation Dynamics of the Methyl Radical Rydberg 3s State. J. Chem. Phys. 1991, 94, 270–276; https://doi.org/10.1063/1.460394.Search in Google Scholar

63. Westre, S. G.; Gansberg, T. E.; Kelly, P. B.; Ziegler, L. D. Structure and Dynamics of Higher Vibronic Levels in the Methyl Radical Rydberg 3s State. J. Phys. Chem. 1992, 96, 3610–3615; https://doi.org/10.1021/j100188a012.Search in Google Scholar

64. Wu, G.; Jiang, B.; Ran, Q.; Zhang, J.; Harich, S. A.; Yang, X. Photodissociation Dynamics of the Methyl Radical at 212.5 nm: Effect of Parent Internal Excitation. J. Chem. Phys. 2004, 120, 2193–2198; https://doi.org/10.1063/1.1635363.Search in Google Scholar PubMed

65. Balerdi, G.; Woodhouse, J.; Zanchet, A.; de Nalda, R.; Senent, M. L.; García-Vela, A.; Bañares, L.; Senent, M. L.; García-Vela, A.; Bañares, L. Femtosecond Predissociation Dynamics of the Methyl Radical from the 3pz Rydberg State. Phys. Chem. Chem. Phys. 2016, 18, 110–118; https://doi.org/10.1039/c5cp05710h.Search in Google Scholar PubMed

66. Marggi Poullain, S.; Chicharro, D. V.; Zanchet, A.; González, M. G.; Rubio-Lago, L.; Senent, M. L.; García-Vela, A.; Bañares, L. Imaging the Photodissociation Dynamics of the Methyl Radical from the 3s and 3pz Rydberg States. Phys. Chem. Chem. Phys. 2016, 18, 17054–17061; https://doi.org/10.1039/c6cp01558a.Search in Google Scholar PubMed PubMed Central

67. García-Vela, A. Photodissociation of the Methyl Radical: the Role of Nonadiabatic Couplings in Enhancing the Variety of Dissociation Mechanisms. Phys. Chem. Chem. Phys. 2021, 23, 25911–25924; https://doi.org/10.1039/d1cp03293c.Search in Google Scholar PubMed

68. Zanchet, A.; Bañares, L.; Senent, M. L.; García-Vela, A.; García-Vela, A. An Ab Initio Study of the Ground and Excited Eectronic States of the Methyl Radical. Phys. Chem. Chem. Phys. 2016, 18, 33195–33203; https://doi.org/10.1039/c6cp05960k.Search in Google Scholar PubMed PubMed Central

69. Rodríguez-Fernández, A.; Márquez-Mijares, M.; Rubayo-Soneira, J.; Zanchet, A.; García-Vela, A.; Bañares, L. Trajectory Surface Hopping Study of the Photodissociation Dynamics of Methyl Radical from the 3s and 3pz Rydberg States. Chem. Phys. Lett. 2018, 712, 171–176; https://doi.org/10.1016/j.cplett.2018.09.053.Search in Google Scholar

70. Yu, H. T.; Sevin, A.; Kassab, E.; Evleth, E. M. A Comparative Theoretical Analysis of the Photochemistry of the Methyl Radical and Related Systems. J. Chem. Phys. 1984, 80, 2049–2059; https://doi.org/10.1063/1.446969.Search in Google Scholar

71. Werner, H. J.; Knowles, P. J.; Knizia, G.; Manby, F. R.; Schütz, M. A General-Purpose Quantum Chemistry Program Package. Wiley Interdiscip. Rev. Comput. Mol. Sci. 2012, 2, 242–253; https://doi.org/10.1002/wcms.82.Search in Google Scholar

72. Li Manni, G.; Fdez Galván, I.; Alavi, A.; Aleotti, F.; Aquilante, F.; Autschbach, J.; Avagliano, D.; Baiardi, A.; Bao, J. J.; Battaglia, S.; Birnoschi, L.; Blanco-González, A.; Bokarev, S. I.; Broer, R.; Cacciari, R.; Calio, P. B.; Carlson, R. K.; Carvalho Couto, R.; Cerdán, L.; Chibotaru, L. F.; Chilton, N. F.; Church, J. R.; Conti, I.; Coriani, S.; Cuéllar-Zuquin, J.; Daoud, R. E.; Dattani, N.; Decleva, P.; de Graaf, C.; Delcey, M. G.; De Vico, L.; Dobrautz, W.; Dong, S. S.; Feng, R.; Ferré, N.; FilatovGulak, M.; Gagliardi, L.; Garavelli, M.; González, L.; Guan, Y.; Guo, M.; Hennefarth, M. R.; Hermes, M. R.; Hoyer, C. E.; Huix-Rotllant, M.; Jaiswal, V. K.; Kaiser, A.; Kaliakin, D. S.; Khamesian, M.; King, D. S.; Kochetov, V.; Krośnicki, M.; Kumaar, A. A.; Larsson, E. D.; Lehtola, S.; Lepetit, M. B.; Lischka, H.; López Ríos, P.; Lundberg, M.; Ma, D.; Mai, S.; Marquetand, P.; Merritt, I. C. D.; Montorsi, F.; Mörchen, M.; Nenov, A.; Nguyen, V. H. A.; Nishimoto, Y.; Oakley, M. S.; Olivucci, M.; Oppel, M.; Padula, D.; Pandharkar, R.; Phung, Q. M.; Plasser, F.; Raggi, G.; Rebolini, E.; Reiher, M.; Rivalta, I.; Roca-Sanjuán, D.; Romig, T.; Safari, A. A.; Sánchez-Mansilla, A.; Sand, A. M.; Schapiro, I.; Scott, T. R.; Segarra-Martí, J.; Segatta, F.; Sergentu, D. C.; Sharma, P.; Shepard, R.; Shu, Y.; Staab, J. K.; Straatsma, T. P.; Sørensen, L. K.; Tenorio, B. N. C.; Truhlar, D. G.; Ungur, L.; Vacher, M.; Veryazov, V.; Voß, T. A.; Weser, O.; Wu, D.; Yang, X.; Yarkony, D.; Zhou, C.; Zobel, J. P.; Lindh, R. The Openmolcas Web: a Community-Driven Approach to Advancing Computational Chemistry. J. Chem. Theory Comput. 2023, 19, 6933–6991; https://doi.org/10.1021/acs.jctc.3c00182.Search in Google Scholar PubMed PubMed Central

73. Sun, Q.; Zhang, X.; Banerjee, S.; Bao, P.; Barbry, M.; Blunt, N. S.; Bogdanov, N. A.; Booth, G. H.; Chen, J.; Cui, Z.-H.; Eriksen, J. J.; Gao, Y.; Guo, S.; Hermann, J.; Hermes, M. R.; Koh, K.; Koval, P.; Lehtola, S.; Li, Z.; Liu, J.; Mardirossian, N.; McClain, J. D.; Motta, M.; Mussard, B.; Pham, H. Q.; Pulkin, A.; Purwanto, W.; Robinson, P. J.; Ronca, E.; Sayfutyarova, E. R.; Scheurer, M.; Schurkus, H. F.; Smith, J. E. T.; Sun, C.; Sun, S. N.; Upadhyay, S.; Wagner, L. K.; Wang, X.; White, A.; Whitfield, J. D.; Williamson, M. J.; Wouters, S.; Yang, J.; Yu, J. M.; Zhu, T.; Berkelbach, T. C.; Sharma, S.; Sokolov, A. Y.; Chan, G. K. L. Recent Developments in the PySCF Program Package. J. Chem. Phys. 2020, 153, 024109; https://doi.org/10.1063/5.0006074.Search in Google Scholar PubMed

74. Bao, J. J.; Zhang, D.; Zhang, S.; Gagliardi, L.; Truhlar, D. G. A Hybrid Meta On-Top Functional for Multiconfiguration Pair-Density Functional Theory. Proc. Nat. Acad. Sci. 2025, 122, e2419413121; https://doi.org/10.1073/pnas.2419413121.Search in Google Scholar PubMed PubMed Central

75. Lynch, B. J.; Zhao, Y.; Truhlar, D. G. Effectiveness of Diffuse Basis Functions for Calculating Relative Energies by Density Functional Theory. J. Phys. Chem. A 2003, 107, 1384–1388; https://doi.org/10.1021/jp021590l.Search in Google Scholar

76. Loos, P. F.; Scemama, A.; Boggio-Pasqua, M.; Jacquemin, D. Mountaineering Strategy to Excited States: Highly Accurate Energies and Benchmarks for Exotic Molecules and Radicals. J. Chem. Theory Comput. 2020, 16, 3720–3736; https://doi.org/10.1021/acs.jctc.0c00227.Search in Google Scholar PubMed

77. Mebel, A. M.; Lin, S. H. Excited Electronic States of the Methyl Radical. Ab Initio Molecular Orbital Study of Geometries, Excitation Energies and Vibronic Spectra. Chem. Phys. 1997, 215, 329–341; https://doi.org/10.1016/s0301-0104(96)00363-1.Search in Google Scholar

78. Isegawa, M.; Peverati, R.; Truhlar, D. G. Performance of Recent and High-Performance Approximate Density Functionals for Time-Dependent Density Functional Theory Calculations of Valence and Rydberg Electronic Transition Energies. J. Chem. Phys. 2012, 137, 244104; https://doi.org/10.1063/1.4769078.Search in Google Scholar PubMed

79. Isegawa, M.; Truhlar, D. G. Valence Excitation Energies of Alkenes, Carbonyl Compounds, and Azabenzenes by Time-Dependent Density Functional Theory: Linear Response of the Ground State Compared to Collinear and Noncollinear Spin-Flip TDDFT with the Tamm-Dancoff Approximation. J. Chem. Phys. 2013, 138, 134111; https://doi.org/10.1063/1.4798402.Search in Google Scholar PubMed

80. Verma, P.; Truhlar, D. G. HLE16: a Local Kohn−Sham Gradient Approximation with Good Performance for Semiconductor Band Gaps and Molecular Excitation Energies. J. Phys. Chem. Lett. 2017, 8, 380–387; https://doi.org/10.1021/acs.jpclett.6b02757.Search in Google Scholar PubMed

81. Bao, J. J.; Truhlar, D. G. Automatic Active Space Selection for Calculating Electronic Excitation Energies Based on High-Spin Unrestricted Hartree−Fock Orbital. J. Chem. Theory Comput. 2019, 15, 5308–5318; https://doi.org/10.1021/acs.jctc.9b00535.Search in Google Scholar PubMed

82. Chien, A. D.; Holmes, A. A.; Otten, M.; Umrigar, C. J.; Sharma, S.; Zimmerman, P. M. Excited States of Methylene, Polyenes, and Ozone from Heat-Bath Configuration Interaction. J. Phys. Chem. A 2018, 122, 2714–2722; https://doi.org/10.1021/acs.jpca.8b01554.Search in Google Scholar PubMed

83. Sherrill, C. D.; Leininger, M. L.; Van Huis, T. J.; Schaefer, H. F.III Structures and Vibrational Frequencies in the Full Configuration Interaction Limit: Predictions for Four Electronic States of Methylene Using a Triple-Zeta Plus Double Polarization (TZ2P) Basis. J. Chem. Phys. 1998, 108, 1040–1049; https://doi.org/10.1063/1.475465.Search in Google Scholar

84. Ruscic, B.; Pinzon, R. E.; Morton, M. L.; von Laszevski, G.; Bittner, S. J.; Nijsure, S. G.; Amin, K. A.; Minkoff, M.; Wagner, A. F. Introduction to Active Thermochemical Tables: Several “Key” Enthalpies of Formation Revisited. J. Phys. Chem. A 2004, 108, 9979–9997; https://doi.org/10.1021/jp047912y.Search in Google Scholar

85. Ruscic, B.; Pinzon, R. E.; Laszewski, G. v.; Kodeboyina, D.; Burcat, A.; Leahy, D.; Montoy, D.; Wagner, A. F. Active Thermochemical Tables: Thermochemistry for the 21st Century. J. Phys. Conf. Ser. 2005, 16, 561–570; https://doi.org/10.1088/1742-6596/16/1/078.Search in Google Scholar

86. Ruscic, B.; Bross, D. H. Active Thermochemical Tables (ATcT) Values Based on Ver. 1.220 of the Thermochemical Network; Argonne National Laboratory: Lemont, Illinois, USA, 2025. available at ATcT.anl.gov.Search in Google Scholar

87. 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.; Li, X.; Caricato, M.; Marenich, A. V.; Bloino, J.; Janesko, B. G.; Gomperts, R.; Mennucci, B.; Hratchian, H. P.; Ortiz, J. V.; Izmaylov, A. F.; Sonnenberg, J. L.; Williams-Young, D.; Ding, F.; Lipparini, F.; Egidi, F.; Goings, J.; Peng, B.; Petrone, A.; Henderson, T.; Ranasinghe, D.; Zakrzewski, V. G.; Gao, J.; Rega, N.; Zheng, G.; Liang, W.; Hada, M.; Ehara, M.; Toyota, K.; Fukuda, R.; Hasegawa, J.; Ishida, M.; Nakajima, T.; Honda, Y.; Kitao, O.; Nakai, H.; Vreven, T.; Throssell, K.; Montgomery, J. A.; Peralta, J. E.; Ogliaro, F.; Bearpark, M. J.; Heyd, J. J.; Brothers, E. N.; Kudin, K. N.; Staroverov, V. N.; Keith, T. A.; Kobayashi, R.; Normand, J.; Raghavachari, K.; Rendell, A. P.; Burant, J. C.; Iyengar, S. S.; Tomasi, J.; Cossi, M.; Millam, J. M.; Klene, M.; Adamo, C.; Cammi, R.; Ochterski, J. W.; Martin, R. L.; Morokuma, K.; Farkas, O.; Foresman, J. B.; Fox, D. J. Gaussian 16, Revision C.01; Gaussian, Inc.: Wallingford CT, 2016.Search in Google Scholar

88. Alecu, I. M.; Zheng, J.; Zhao, Y.; Truhlar, D. G. Computational Thermochemistry: Scale Factor Databases and Scale Factors for Vibrational Frequencies Obtained from Electronic Model Chemistries. J. Chem. Theory Comput. 2010, 6, 2872–2887; https://doi.org/10.1021/ct100326h.Search in Google Scholar PubMed

89. Sand, A. M.; Truhlar, D. G.; Gagliardi, L. Efficient Algorithm for Multiconfiguration Pair-Density Functional Theory with Application to the Heterolytic Dissociation Energy of Ferrocene. J. Chem. Phys. 2017, 146, 034101; https://doi.org/10.1063/1.4973709.Search in Google Scholar PubMed

90. Sharkas, K.; Gagliardi, L.; Truhlar, D. G. Multiconfiguration Pair-Density Functional Theory and Complete Active Space Second Order Perturbation Theory. Bond Dissociation Energies of FeC, NiC, FeS, NiS, FeSe, and NiSe. J. Phys. Chem. A 2017, 121, 9392–9400; https://doi.org/10.1021/acs.jpca.7b09779.Search in Google Scholar PubMed

91. Presti, D.; Truhlar, D. G.; Gagliardi, L. Intramolecular Charge Transfer and Local Excitation in Organic Fluorescent Photoredox Catalysts Explained by RASCI-PDFT. J. Phys. Chem. C 2018, 122, 12061–12070; https://doi.org/10.1021/acs.jpcc.8b01844.Search in Google Scholar

92. Zhou, C.; Wu, D.; Gagliardi, L.; Truhlar, D. G. Calculation of the Zeeman Effect for Transition-Metal Complexes by Multiconfiguration Pair-Density Functional Theory. J. Chem. Theory Comput. 2021, 17, 5050–5063; https://doi.org/10.1021/acs.jctc.1c00208.Search in Google Scholar PubMed


Supplementary Material

This article contains supplementary material (https://doi.org/10.1515/pac-2025-0546).


Received: 2025-06-15
Accepted: 2025-08-14
Published Online: 2025-08-27
Published in Print: 2025-10-27

© 2025 IUPAC & De Gruyter

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