Infrared Spectroscopy of Fluxional Molecules from (ab Initio) Molecular Dynamics: Resolving Large-Amplitude Motion, Multiple Conformations, and Permutational Symmetries

摘要

The computation of vibrational spectra of complex molecules from time correlation functions generated by ab initio , molecular dynamics simulations has made lively progress in recent years. However, the analysis of such spectra, i.e., the assignment of vibrational bands to atomic motions, is by no means straightforward. In a recent article [J. Chem. Theory Comput. 2011, 7, 2028-2039], Mathias and Baer presented a corresponding analysis method that derives generalized normal coordinates (GNCs) from molecular dynamics trajectories, which furnish band positions, band shapes, and infrared intensities of the separated vibrational modes. This vibrational analysis technique relies on the usual quasi-rigidity assumption; i.e., atomic motions are described by small Oscillations around a single reference structure. This assumption, however, breaks down if the molecule undergoes large-amplitude motion and visits different conformations along the trajectory or if the same conformation can be adopted by a different ordering of the atoms, i.e., if permutational symmetries have to be considered. Here, we present an extension of the GNC method that handles such cases by considering multiple reference structures, both for different conformations and for permutational symmetries. By introducing a projection technique and computing probabilities that assign the time frames of the trajectories to these reference structures, the vibrational spectra are split into conformational contributions via a consistent time correlation formalism. For each conformation, the permutational symmetries are resolved, which permits one to determine conformation-local GNCs for the band assignment. The working principle and the virtues of this generalization are demonstrated for the simple case of a methyl group rotation. This is followed by an application to a more intricate case: Upon replacing one proton by a deuteron in protonated methane, CH_S~+, significant changes of its infrared spectrum have been observed since the CH4D~+ isotopologue features five different isotopomers. Here, a total of 120 conformational and permutational references are required in the projection scheme in order to capture the frequent and versatile structural transitions of this small but utmost floppy molecule and to assign its infrared spectrum. The extended GNC method is general. Thus, it can be applied readily to systems that require more than one reference structure, and it can be transferred to other theoretical spectroscopies that are formulated in terms of time correlation functions.