Metric-Based Assessment Method for MS-T Formalism with Small Subsets of Torsional Conformers

The multi-structural approximation with torsional anharmonicity (MS-T) method and its variants have been widely used for calculating conformational-rovibrational partition functions of large molecules. The present work aimed to propose a systematic method to assess and explain the performance of various variants of the MS-T method. First, we proposed the simplest variant MS-T(2NN) (two nearest neighborhood torsions are coupled) and systematically validated it for large alkanes n-CH₂ (n = 6-10) and their transition states of hydrogen abstraction reactions. Second, we proposed a metric-based method to explain the underlying reason for the good performance of MS-T(2NN)─it includes the torsional conformers that have dominant contributions to the partition function calculations. These conformers are closer to the lowest-energy conformer in the space of dihedral and energy metrics. Third, the same observation and explanation apply to the other two variants, MS-2DT (any two torsions are coupled) and MS-3DT (any three torsional are coupled), which contain increasingly more torsional conformers than MS-T(2NN) but are subsets of the complete set of torsional conformers considered by the MS-T method. Overall, the present method provides a mathematically rigorous and computationally effective diagnosis tool to assess various MS-T methods dealing with the torsional anharmonicity of large molecules in the partition function calculation.