Tuning vibrational mode localization with frequency windowing.

Local-mode coordinates have previously been shown to be an effective starting point for anharmonic vibrational spectroscopy calculations. This general approach borrows techniques from localized-orbital machinery in electronic structure theory and generates a new set of spatially localized vibrational modes. These modes exhibit a well-behaved spatial decay of anharmonic mode couplings, which, in turn, allows for a systematic, a priori truncation of couplings and increased computational efficiency. Fully localized modes, however, have been found to lead to unintuitive mixtures of characteristic motions, such as stretches and bends, and accordingly large bilinear couplings. In this work, a very simple, tunable localization frequency window is introduced, in order to realize the transition from normal modes to fully localized modes. Partial localization can be achieved by localizing only pairs of modes within this traveling frequency window, which allows for intuitive interpretation of modes. The optimal window size is suggested to be a few hundreds of wave numbers, based on small- to medium-sized test systems, including water clusters and polypeptides. The new sets of partially localized coordinates retain their spatial coupling decay behavior while providing a reduced number of potential energy evaluations for convergence of anharmonic spectra.