A simple approximate solution for the H3+ ion

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1 Citation (Scopus)


Here I derive analytical expressions for the total energy of the (Formula presented.) cation in its equilateral and linear geometries. The theoretical model consists of a simple variational trial wavefunction made of the sum of three 1S Gaussian functions, each centered on each nucleus. Detailed derivations are presented and the advantages and limitations of this simple model are discussed. The correctness of the results was verified independently via Monte Carlo integration. This simple model correctly predicts and rationalizes the preference of (Formula presented.) for the equilateral geometry rather than the linear configuration. Despite its simplicity, the calculated H-H bond length (R = 0.9088 Å) and breathing vibrational frequency (ν1 = 3276.59 cm−1) for equilateral (Formula presented.) ion are in good agreement with high-level ab initio methods and the experiment, respectively.

Original languageEnglish
Article numbere27015
JournalInternational Journal of Quantum Chemistry
Issue number2
Publication statusPublished - Jan 15 2023


  • electronic structure
  • quantum Monte Carlo
  • trihydrogen cation
  • variational method

ASJC Scopus subject areas

  • Atomic and Molecular Physics, and Optics
  • Condensed Matter Physics
  • Physical and Theoretical Chemistry


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