Converging the n-Mode Representation of Anharmonic Molecular Vibrations via Local Modes

The inclusion of anharmonic vibrational effects is critical for the interpretation of modern vibrational spectra and accurate thermodynamic quantities. Generalized techniques to computationally simulate anharmonicity include the vibrational self-consistent field (VSCF) method and correlated analogues thereof. The "n-mode representation" is a commonly used approximation for representing the vibrational potential in VSCF computations and includes pairwise (and higher) mode-coupling terms that dominate both the anharmonic effects and the computational cost. Localized vibrational coordinates are known to accelerate simulations involving pairwise couplings, but many systems require three- and four-mode couplings both for the convergence of the n-mode representation and to avoid spurious pathologies involving low-frequency modes. In this analysis, the convergence of this potential representation─and its distance dependence─is explored in the context of local modes. Convergence of the n-mode representation's impact on vibrational spectra is shown to be attainable in full vibrational dimensionality for water clusters and biomolecules. Furthermore, the requisite distance cutoffs are allowed to be successively more aggressive for three- and four-mode coupling terms, which further enhances the ensuing computational efficiency. For the Z-alanine molecule and (H₂O)₁₇ cluster, 290- and 590-fold computational accelerations, respectively, were observed, and these accelerations should increase for larger systems. This computational efficiency was achieved while retaining subwavenumber fidelity with the results of cutoff-free simulations.