Tuning vibrational mode localization with frequency windowing

Abstract

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.

Theoretical and experimental investigations of complexation with BF3.Et2O effects on electronic structures, energies and photophysical properties of Anil and tetraphenyl (hydroxyl) imidazol

“…Figure shows the calculated IR spectrum with the experimental FT‐IR spectra of all compounds. After calculating the localized modes using the graphical interfaces Gabedit we can identify the different vibrations.…”

Isomeric Equilibria, Nuclear Quantum Effects, and Vibrational Spectra of M+(H2O)n=1−3 Clusters, with M = Li, Na, K, Rb, and Cs, Through Many-Body Representations

“…Instantaneous configurations for the M + (H 2 O) n clusters were extracted every 2 ps from each replica along the REMD simulations and quenched to identify possible isomers through geometry optimizations carried out by combining linear search and conjugate gradient methods, with a threshold of 10 −8 kcal mol −1Å−1 for the gradients. 89 To characterize how the presence of different alkali metal ions affect the spatial arrangements and HB network of the solvating water molecules, (anharmonic) infrared spectra of all isomers were calculated by combining the local-mode 90,91 and local-monomer 49 (LM) methods as described in Ref. 61.…”

“…By neglecting intermonomer, two-mode and higher-order anharmonic couplings, the LM method provides an approximate, yet accurate, solution to the vibrational Schrödinger equation. 91 For reference, harmonic spectra were also calculated to quantify the importance of nuclear quantum effects and anharmonicity (see Supporting Information). Harmonic frequencies obtained for both symmetric and asymmetric stretches of the water molecules were found to be blueshifted by ∼190 cm −1 and 150 cm −1 relative to the corresponding LM values, respectively.…”

Uncontracted core Pople basis sets in vibrational frequency calculations

“…The PES increases exponentially with the number of vibrational degrees of freedom a molecule has, which has led to the development of several methods to reduce the dimension of the PES needing to be sampled. These methods include the exclusion of energy derivatives involving more than a specific number of normal modes, referred to as an n‐mode representation (nMR), freezing vibrational degrees of freedom at both the harmonic and anharmonic level, and optimizing new coordinate systems to more compactly represent the important PES terms . Within these approximations the degree of PES sampling is further optimized over many energy evaluations or lower‐order analytical derivatives, depending on the level of analytical derivate available, all without considering changes in the method or basis set efficacy …”

“…coordinate systems to more compactly represent the important PES terms. [12][13][14][15][16][17][18][19][20] Within these approximations the degree of PES sampling is further optimized over many energy evaluations or lower-order analytical derivatives, depending on the level of analytical derivate available, [8] all without considering changes in the method or basis set efficacy. [20] The more recently developed meta-hybrid exchange-correlation functionals in density functional theory (DFT) often fail to provide as high quality vibrational frequencies as the previous generations, despite accurately predicting other molecular properties.…”