Hindered-rotor harmonic oscillator model

Concerning the proper treatment of torsional anharmonicity, which still represents a challenging aspect for accurate thermochemical calculations of complex molecules [257-265], a hindered-rotor anharmonic oscilattor (HRAO) model has been shown to provide accurate results[62, 72, 117, 204]. The HRAO model is based on a generalization to anharmonic force fields of the hindered-rotor harmonic oscillator (HRHO) model [257] that automatically identifies internal rotation modes and rotating groups during the normal-mode vibrational analysis. 

The vibrational and rotational components can be calculated from the harmonic oscillator and rigid rotor models, for example, whose expressions can be found in many textbooks of statistical thermodynamics [20]. If a more sophisticated correction is needed, vibrational anharmonic corrections and the hindered rotor are also valid models to be considered. The translational component can be calculated from the respective partition function or approximated, for example, by 3I2RT, the value found for an ideal monoatomic gas. 

The above treatment of hindered rotors assumes that a given mode can be approximated as a one-dimensional rigid rotor, and studies for small systems have shown that this is generally a reasonable assumption in those cases (82). However, for larger molecules, the various motions become increasingly coupled, and a (considerably more complex) multidimensional treatment may be needed in those cases. When coupling is significant, the use of a one-dimensional hindered rotor model may actually introduce more error than the (fully decoupled) harmonic oscillator treatment. Hence, in these cases, the one-dimensional hindered rotor model should be used cautiously. 

---