Identification of Torsional Modes in Complex Molecules Using Redundant Internal Coordinates: The Multistructural Method with Torsional Anharmonicity with a Coupled Torsional Potential and Delocalized Torsions

Identification of internal-rotation modes in the normal-mode analysis of complex molecules is important for accurately describing the thermodynamic properties and kinetics of complex molecules when it is necessary to treat the anharmonicity of torsions and the multiconformer anharmonicity caused by the internal rotations. However, identifying and distinguishing torsional modes are very challenging because they are coupled to one another. In this work, we present a new strategy to automatically identify torsional vibrations and separate them from the other vibrational modes. By combining a redundant-internal-coordinate auto-generation procedure with torsional projection techniques, we automate the procedure of identifying and separating the coupled torsions, and we show that we can obtain robust and consistent results with various reasonable definitions of redundant-internal-coordinate sets. This model has been implemented in a new development version of the MSTor program to reduce the user input needed for multistructural and torsional anharmonicity (MS-T) calculations. The new method is called multistructural and torsional anharmonicity with a coupled torsional potential and delocalized torsions ([MS-T(CD)]. As example applications, we consider MS-T(CD) calculations on three molecules (2-hexyl radical, n-propylbenzene, and 5-hydroperoxy-6-oxohexanoylperoxy radical) that have multiple rotors and that provide challenges to choosing good sets of nonredundant-internal coordinates, and we compare the performance of the new strategy to five other torsion identification methods. The new strategy is demonstrated to be efficient in separating the torsional and nontorsional elements in the Hessian matrix, as well as in providing reasonable projected nontorsional frequencies to be used for calculations of partition function and thermochemistry.