Practical methods for including torsional anharmonicity in thermochemical calculations on complex molecules: The internal-coordinate multi-structural approximation

Many methods for correcting harmonic partition functions for the presence of torsional motions employ some form of one-dimensional torsional treatment to replace the harmonic contribution of a specific normal mode. However, torsions are often strongly coupled to other degrees of freedom, especially other torsions and low-frequency bending motions, and this coupling can make assigning torsions to specific normal modes problematic. Here, we present a new class of methods, called multi-structural (MS) methods, that circumvents the need for such assignments by instead adjusting the harmonic results by torsional correction factors that are determined using internal coordinates. We present three versions of the MS method: (i) MS-AS based on including all structures (AS), i.e., all conformers generated by internal rotations; (ii) MS-ASCB based on all structures augmented with explicit conformational barrier (CB) information, i.e., including explicit calculations of all barrier heights for internal-rotation barriers between the conformers; and (iii) MS-RS based on including all conformers generated from a reference structure (RS) by independent torsions. In the MS-AS scheme, one has two options for obtaining the local periodicity parameters, one based on consideration of the nearly separable limit and one based on strongly coupled torsions. The latter involves assigning the local periodicities on the basis of Voronoi volumes. The methods are illustrated with calculations for ethanol, 1-butanol, and 1-pentyl radical as well as two one-dimensional torsional potentials. The MS-AS method is particularly interesting because it does not require any information about conformational barriers or about the paths that connect the various structures.