Tailored multilevel approaches in vibrational structure theory: A route to quantum mechanical vibrational spectra for complex systems

Abstract

Vibrational spectroscopies have emerged as important tools to elucidate structures and processes in life sciences. The interpretation of vibrational spectra requires, in most cases, computational assistance and account for anharmonic effects. Pushing the size limitations of anharmonic vibrational structure calculations is therefore of great interest. Fortunately, interpretation of the experimental results often requires only a limited part of the vibrational spectrum. Hence, it can be expected that multilevel approaches, focusing computational effort on the relevant parts, are highly beneficial. Still, such approaches are rather sparse in the field of vibrational structure theory. In this perspective, we outline the present status on multilevel static vibrational wave functions and rectilinear vibrational coordinates. We further foresee how those ingredients can be combined to formulate a comprehensive multilevel vibrational structure framework.

Reduced Two-Electron Interactions in Anharmonic Molecular Vibrational Calculations Involving Localized Normal Coordinates

“…To quantify the impact of removing or reducing the two-electron terms when describing anharmonic mode coupling, the position of each mode p is defined as and the distance between two modes p and q is given by Coupling terms between modes that are centered beyond a certain cutoff distance can then be identified and modified as needed. Modifying aspects of the PES in this manner is conceptually similar to the multilevel methods used in multilevel quasi-Monte Carlo and recently for anharmonic molecular vibrational frequencies calculated through the single-to-all (STA)-in-VSCF and nonrelaxed (nr)-VCI-in-VSCF approaches . However, the distance decay of interactions between localized coordinates provides a natural basis for partitioning multilevel approaches and further motivates the investigation into these relationships.…”

“…Modifying aspects of the PES in this manner is conceptually similar to the multilevel methods used in multilevel quasi-Monte Carlo 82 and recently for anharmonic molecular vibrational frequencies calculated through the single-to-all (STA)-in-VSCF and nonrelaxed (nr)-VCI-in-VSCF approaches. 83 However, the distance decay of interactions between localized coordinates provides a natural basis for partitioning multilevel approaches and further motivates the investigation into these relationships.…”

Progress and Challenges in Ab Initio Simulations of Quantum Nuclei in Weakly Bonded Systems

“…Keeping with a quantum picture of nuclei, one route is to propose harmonic potentials that effectively capture anharmonic terms [45][46][47][48] . Another is to consider higher-order terms in a perturbative Taylor series expansion of the potential [48][49][50][51][52][53] or, for certain quantities, simply include anharmonic corrections from fitted potential forms to vibrational modes that are particularly anharmonic 54 . However, the cost of the more rigorous theories tends to have a very steep scaling with the number of degrees of freedom, making them feasible only for small systems or for larger systems if a small subset of essential degrees of freedom are sufficient.…”

Accelerating Anharmonic Spectroscopy Simulations via Local-Mode, Multilevel Methods

“…In multilevel approaches to anharmonic vibrational spectroscopy (also sometimes termed “multiresolution” or “hybrid” methods), at least some terms in the n -MR potential are representedor pre-screenedby more cost-efficient potential energy surfaces. These methods received their first systematic analyses in the early 2000s, ,,,,,,,,,, although examples of their use in Taylor series potentials occurred at least a decade prior, , and development has continued since. ,,,,,,, These approaches are considered in the context of local-mode methods in the present work as a particularly attractive means to distinguish the remnant short-range couplings that were discussed in the preceding section.…”