### Abstract

The vibrational energy levels and partition functions of the nonrotating H_{3}^{+} molecular ion have been calculated by using second order perturbation theory, including constant, linear, and quadratic terms in the vibrational quantum numbers. Energy levels have been assigned to A′_{1}, A′_{2}, and E′ symmetry species up to 29 244 cm^{-1}, and perturbation theory energy levels have been compared with the results of accurate quantum calculations. The root-mean-square error in 141 energy levels is 4.0 cm^{-1}, as compared to 11.7 cm^{-1} in the harmonic approximation. Furthermore, perturbation-theory partition functions have errors of 7.4% or less over the factor-of-20 temperature range from 200 to 4000 K. The effect of the constant term in perturbation theory is also discussed; it improves the vibrational partition functions by ∼4% at 200 K.

Original language | English (US) |
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Pages (from-to) | 4948-4958 |

Number of pages | 11 |

Journal | The Journal of chemical physics |

Volume | 98 |

Issue number | 6 |

DOIs | |

State | Published - Jan 1 1993 |