Pitfalls in the n -mode representation of vibrational potentials

Abstract

Simulations of anharmonic vibrational motion rely on computationally expedient representations of the governing potential energy surface. The n-mode representation (n-MR)—effectively a many-body expansion in the space of molecular vibrations—is a general and efficient approach that is often used for this purpose in vibrational self-consistent field (VSCF) calculations and correlated analogues thereof. In the present analysis, a lack of convergence in many VSCF calculations is shown to originate from negative and unbound potentials at truncated orders of the n-MR expansion. For cases of strong anharmonic coupling between modes, the n-MR can both dip below the true global minimum of the potential surface and lead to effective single-mode potentials in VSCF that do not correspond to bound vibrational problems, even for bound total potentials. The present analysis serves mainly as a pathology report of this issue. Furthermore, this insight into the origin of VSCF non-convergence provides a simple, albeit ad hoc, route to correct the problem by “painting in” the full representation of groups of modes that exhibit these negative potentials at little additional computational cost. Somewhat surprisingly, this approach also reasonably approximates the results of the next-higher n-MR order and identifies groups of modes with particularly strong coupling. The method is shown to identify and correct problematic triples of modes—and restore SCF convergence—in two-mode representations of challenging test systems, including the water dimer and trimer, as well as protonated tropine.

The Near-Sightedness of Many-Body Interactions in Anharmonic Vibrational Couplings

“…This two-mode coupling approximation has been the most commonly employed approach for larger molecules 70 and is almost invariably the strongest coupling observed in molecular systems, although truncating the n-MR expansion at this order can sometimes lead to pathological potentials for large molecules and lowfrequency motions. 152 Nonetheless, it provides the most direct assessment of the role of many-body effects in vibrational anharmonicity. Only the values of these couplings were examined, and their overall role in the final spectrum has intentionally not been assessed, due to both the sensitivity of the latter effect to the choice of anharmonic simulation method (VSCF, VCI, etc.)…”

“…Anharmonic couplings were limited to pairwise (2-MR) terms for the sake of isolating many-body contributions in this first analysis. This two-mode coupling approximation has been the most commonly employed approach for larger molecules and is almost invariably the strongest coupling observed in molecular systems, although truncating the n -MR expansion at this order can sometimes lead to pathological potentials for large molecules and low-frequency motions . Nonetheless, it provides the most direct assessment of the role of many-body effects in vibrational anharmonicity.…”