Probing vibrational coupling via a grid‐based quantum approach—an efficient strategy for accurate calculations of localized normal modes in solid‐state systems

Abstract

In this work an approach to investigate the properties of strongly localized vibrational modes of functional groups in bulk material and on solid‐state surfaces is presented. The associated normal mode vectors are approximated solely on the basis of structural information and obtained via diagonalization of a reduced Hessian. The grid‐based Numerov procedure in one and two dimensions is then applied to an adequate scan of the respective potential surface yielding the associated vibrational wave functions and energy eigenvalues. This not only provides a detailed description of anharmonic effects but also an accurate inclusion of the coupling between the investigated vibrational states on a quantum mechanical level. All results obtained for the constructed normal modes are benchmarked against their analytical counterparts obtained from the diagonalization of the total Hessian of the entire system. Three increasingly complex systems treated at quantum chemical level of theory have been considered, namely the symmetric and asymmetric stretch vibrations of an isolated water molecule, hydroxyl groups bound to the surface of GeO2 (001), α‐quartz(001) and Rutil (001) as well as crystalline Li2NH serving as an example for a bulk material. While the data obtained for the individual systems verify the applicability of the proposed methodology, comparison to experimental data demonstrates the accuracy of this methodology despite the restriction to limit this methodology to a few selected vibrational modes. The possibility to investigate vibrational phenomena of localized normal modes without the requirement of executing costly harmonic frequency calculations of the entire system enables the application of this method to cases in which the determination of normal modes is prohibitively expensive or not available for a particular level of theory. © 2018 Wiley Periodicals, Inc.

MC-QTAIM analysis reveals an exotic bond in coherently quantum superposed malonaldehyde

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Spectra–Structure Correlations in Isotopomers of Ethanol (CX3CX2OX; X = H, D): Combined Near-Infrared and Anharmonic Computational Study

“…Considerable efforts have been undertaken in order to develop anharmonic approaches applicable to even larger molecular systems [31,32,33,34]. On the other hand, meticulous probing of vibrational potential capable of yielding nearly-exact results is also available [35,36,37,38]. Recent advances in this field include the development of multi-dimensional approaches that provide complete information on mode couplings in linear triatomic molecules [39].…”

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

“…The origin of this vibrational coupling is the central focus of the present study. Existing routes to alleviate this computational challenge include (1) new approaches to the numerical quadrature of the potential surface, − (2) the development of analytical representations of potential energy surfaces, − and (3) new physical insights into the nature of vibrational-coupling behavior. ,,− The present analysis focuses on the latter approach, which has received relatively less attention but holds the potential to open entirely new avenues for the simulation and understanding of vibrational phenomena. The same analysis will exploit tools that have been provided by the second approach, however, including modern many-body potentials.…”