Theoretical Chemistry Accounts

, 133:1425 | Cite as

Accurate ab initio potential energy curves and spectroscopic properties of the four lowest singlet states of C2

  • Jeffery S. Boschen
  • Daniel Theis
  • Klaus Ruedenberg
  • Theresa L. Windus
Regular Article
Part of the following topical collections:
  1. Dunning Festschrift Collection


The diatomic carbon molecule has a complex electronic structure with a large number of low-lying electronic excited states. In this work, the potential energy curves (PECs) of the four lowest lying singlet states (\(X^{1} \Sigma^{ + }_{g}\), \(A^{1} \Pi_{u}\), \(B^{1} \Delta_{g}\), and \(B^{\prime1} \Sigma^{ + }_{g}\)) were obtained by high-level ab initio calculations. Valence electron correlation was accounted for by the correlation energy extrapolation by intrinsic scaling (CEEIS) method. Additional corrections to the PECs included core–valence correlation and relativistic effects. Spin–orbit corrections were found to be insignificant. The impact of using dynamically weighted reference wave functions in conjunction with CEEIS was examined and found to give indistinguishable results from the even weighted method. The PECs showed multiple curve crossings due to the \(B^{1} \Delta_{g}\) state as well as an avoided crossing between the two \(^{1} \Sigma^{ + }_{g}\) states. Vibrational energy levels were computed for each of the four electronic states, as well as rotational constants and spectroscopic parameters. Comparison between the theoretical and experimental results showed excellent agreement overall. Equilibrium bond distances are reproduced to within 0.05 %. The dissociation energies of the states agree with experiment to within ~0.5 kcal/mol, achieving “chemical accuracy.” Vibrational energy levels show average deviations of ~20 cm−1 or less. The \(B^{1} \Delta_{g}\) state shows the best agreement with a mean absolute deviation of 2.41 cm−1. Calculated rotational constants exhibit very good agreement with experiment, as do the spectroscopic constants.


Diatomic carbon Ab initio electronic structure Dissociation Configuration interaction Spectroscopic properties Multi-configurational wave functions 



The authors thank Dr. Laimutis Bytautas and Dr. Luke Roskop for helpful discussions related to this work. This research is supported by the US Department of Energy, Office of Basic Energy Sciences, Division of Chemical Sciences, Geosciences, and Biosciences through the Ames Laboratory. The Ames Laboratory is operated for the US Department of Energy by Iowa State University under Contract No. DE-AC02-07CH11358.

Supplementary material

214_2013_1425_MOESM1_ESM.docx (201 kb)
Supplementary material 1 (DOCX 200 kb)


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Copyright information

© Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  • Jeffery S. Boschen
    • 1
  • Daniel Theis
    • 1
  • Klaus Ruedenberg
    • 1
  • Theresa L. Windus
    • 1
  1. 1.Department of Chemistry and Ames Laboratory (USDOE)Iowa State UniversityAmesUSA

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