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Methylene: a turning point in the history of quantum chemistry and an enduring paradigm

  • Ashley M. Allen ORCID logo , Allison C. Sargent ORCID logo and Henry F. Schaefer ORCID logo EMAIL logo
Published/Copyright: October 20, 2025
Pure and Applied Chemistry
From the journal Pure and Applied Chemistry Volume 97 Issue 11

Abstract

Prior to 1970, no successful ab initio electronic structure predictions were made that challenged experiment for polyatomic molecules. For diatomics, the work of Ernest Davidson stands out, in 1960 explaining that two spectroscopically known but misunderstood electronic states of H2 were in fact part of the very same potential energy curve. Another diatomic example was the startling 1968 overturn by Kolos and Wolniewicz of the “known” experimental dissociation energy of H2. Moving to polyatomics, the research in 1970 concerning the structure of triplet methylene captured the imagination of many chemists, and the 1982 success of theory for the singlet-triplet separation of methylene confirmed for many the great usefulness of ab initio theory. In the second half of this paper, the utility of methods based on single Slater determinant reference wavefunctions for both singlet and triplet methylene is demonstrated. In particular, we examine how the optimized geometries and harmonic vibrational frequencies of triplet and singlet CH2 evolve with systematic improvements in basis set size and valence electron correlation treatment. To accurately pinpoint the geometric structures and singlet-triplet splitting of methylene, we perform comprehensive focal point analyses (FPA) that push the level of theory to new heights, leveraging core-valence basis sets up to sextuple-zeta quality and all-electron coupled-cluster methods through CCSDTQ(P) appended with relativistic (MVD1) and non-Born-Oppenheimer (DBOC) corrections. Our final FPA prediction for the singlet-triplet splitting is 9.01 kcal mol−1, in complete agreement with the best empirical estimate of 9.00 ± 0.01 kcal mol−1. The corresponding optimized FPA geometries are [r e(H–C), θ e(H–C–H)] = (1.1063 Å, 102.35°) for ã1A1 CH2 and (1.0756 Å, 133.94°) for X̃3B1 CH2, in close agreement with the best existing experimental and theoretical structures but with a little finer precision. Our outcomes not only affirm the validity of the contemporary single-reference coupled-cluster theory pushed to high order but also provide definitive resolutions for a paradigmatic molecule that has long been emblematic of the challenges and triumphs that have shaped a century of quantum chemistry.

Keywords: Electronic structures; quantum chemistry; quantum science and technology
Corresponding author: Henry F. Schaefer, III, Center for Computational Quantum Chemistry, University of Georgia, Athens, GA 30602, 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. Ashley M. Allen and Allison C. Sargent: authors contributed equally and share primary authorship.

Funding source: U.S. Department of Energy, Basic Energy Sciences, Division of Chemistry, Computational and Theoretical Chemistry (CTC) Program

Award Identifier / Grant number: DE-SC0018412

  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 state no conflict of interest.

  6. Research funding: This research was supported by the U.S. Department of Energy, Basic Energy Sciences, Division of Chemistry, Computational and Theoretical Chemistry (CTC) Program under Contract No. DE-SC0018412.

  7. Data availability: Not applicable. (All raw data is included in text).

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Received: 2025-08-15
Accepted: 2025-10-01
Published Online: 2025-10-20
Published in Print: 2025-11-25

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  6. FAIRSpec-ready spectroscopic data collections – advice for researchers, authors, and data managers (IUPAC Technical Report)
  7. Review Articles
  8. Are the Lennard-Jones potential parameters endowed with transferability? Lessons learnt from noble gases
  9. Quantum mechanics and human dynamics
  10. Quantum chemistry and large systems – a personal perspective
  11. The organic chemist and the quantum through the prism of R. B. Woodward
  12. Relativistic quantum theory for atomic and molecular response properties
  13. A chemical perspective of the 100 years of quantum mechanics
  14. Methylene: a turning point in the history of quantum chemistry and an enduring paradigm
  15. Quantum chemistry – from the first steps to linear-scaling electronic structure methods
  16. Nonadiabatic molecular dynamics on quantum computers: challenges and opportunities
  17. Research Articles
  18. Alzheimer’s disease – because β-amyloid cannot distinguish neurons from bacteria: an in silico simulation study
  19. Molecular electrostatic potential as a guide to intermolecular interactions: challenge of nucleophilic interaction sites
  20. Photophysical properties of functionalized terphenyls and implications to photoredox catalysis
  21. Combining molecular fragmentation and machine learning for accurate prediction of adiabatic ionization potentials
  22. Thermodynamic and kinetic insights into B10H14 and B10H14 2−
  23. Quantum origin of atoms and molecules – role of electron dynamics and energy degeneracy in atomic reactivity and chemical bonding
  24. Clifford Gaussians as Atomic Orbitals for periodic systems: one and two electrons in a Clifford Torus
  25. First-principles modeling of structural and RedOx processes in high-voltage Mn-based cathodes for sodium-ion batteries
  26. Erratum
  27. Erratum to: Furanyl-Chalcones as antimalarial agent: synthesis, in vitro study, DFT, and docking analysis of PfDHFR inhibition
https://doi.org/10.1515/pac-2025-0586
Keywords for this article
Electronic structures; quantum chemistry; quantum science and technology

Articles in the same Issue

  1. Frontmatter
  2. IUPAC Recommendations
  3. Experimental methods and data evaluation procedures for the determination of radical copolymerization reactivity ratios from composition data (IUPAC Recommendations 2025)
  4. IUPAC Technical Reports
  5. Kinetic parameters for thermal decomposition of commercially available dialkyldiazenes (IUPAC Technical Report)
  6. FAIRSpec-ready spectroscopic data collections – advice for researchers, authors, and data managers (IUPAC Technical Report)
  7. Review Articles
  8. Are the Lennard-Jones potential parameters endowed with transferability? Lessons learnt from noble gases
  9. Quantum mechanics and human dynamics
  10. Quantum chemistry and large systems – a personal perspective
  11. The organic chemist and the quantum through the prism of R. B. Woodward
  12. Relativistic quantum theory for atomic and molecular response properties
  13. A chemical perspective of the 100 years of quantum mechanics
  14. Methylene: a turning point in the history of quantum chemistry and an enduring paradigm
  15. Quantum chemistry – from the first steps to linear-scaling electronic structure methods
  16. Nonadiabatic molecular dynamics on quantum computers: challenges and opportunities
  17. Research Articles
  18. Alzheimer’s disease – because β-amyloid cannot distinguish neurons from bacteria: an in silico simulation study
  19. Molecular electrostatic potential as a guide to intermolecular interactions: challenge of nucleophilic interaction sites
  20. Photophysical properties of functionalized terphenyls and implications to photoredox catalysis
  21. Combining molecular fragmentation and machine learning for accurate prediction of adiabatic ionization potentials
  22. Thermodynamic and kinetic insights into B10H14 and B10H14 2−
  23. Quantum origin of atoms and molecules – role of electron dynamics and energy degeneracy in atomic reactivity and chemical bonding
  24. Clifford Gaussians as Atomic Orbitals for periodic systems: one and two electrons in a Clifford Torus
  25. First-principles modeling of structural and RedOx processes in high-voltage Mn-based cathodes for sodium-ion batteries
  26. Erratum
  27. Erratum to: Furanyl-Chalcones as antimalarial agent: synthesis, in vitro study, DFT, and docking analysis of PfDHFR inhibition
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