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WIREs Comput Mol Sci
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Decoding chemical information from vibrational spectroscopy data: Local vibrational mode theory

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Abstract Modern vibrational spectroscopy is more than just an analytical tool. Information about the electronic structure of a molecule, the strength of its bonds, and its conformational flexibility is encoded in the normal vibrational modes. On the other hand, normal vibrational modes are generally delocalized, which hinders the direct access to this information, attainable only via local vibration modes and associated local properties. Konkoli and Cremer provided an ingenious solution to this problem by deriving local vibrational modes from the fundamental normal modes, obtained in the harmonic approximation of the potential, via mass‐decoupled Euler–Lagrange equations. This review gives a general introduction into the local vibrational mode theory of Konkoli and Cremer, elucidating how this theory unifies earlier attempts to obtain easy to interpret chemical information from vibrational spectroscopy: (a) the local mode theory furnishes bond strength descriptors derived from force constant matrices with a physical basis, (b) provides the highly sought after extension of the Badger rule to polyatomic molecules, (c) and offers a simpler way to derive localized vibrations compared to the complex route via overtone spectroscopy. Successful applications are presented, including a new measure of bond strength, a new detailed analysis of infrared/Raman spectra, and the recent extension to periodic systems, opening a new avenue for the characterization of bonding in crystals. At the end of this review the LMODEA software is introduced, which performs the local mode analysis (with minimal computational costs) after a harmonic vibrational frequency calculation optionally using measured frequencies as additional input. This article is categorized under: Structure and Mechanism > Molecular Structures Theoretical and Physical Chemistry > Spectroscopy Software > Quantum Chemistry Electronic Structure Theory > Ab Initio Electronic Structure Methods
Use of stretching force constants and frequencies as bond strength descriptors based on the Badger rule. A comprehensive overview is given in Table 4.1 of Reference 32
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Flowchart of the local mode program LMODEA
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MLEP(FeH) = BSO(FeH) for Fe─H and Fe─H2 derived from the local FeH stretching force constants k (FeH) via Equations (44)–(46). Low‐spin Fe(CO)5 was used as the reference molecule, in which one axial CO ligand was replaced by H2 ([1]) and H ([2]), respectively. (Reprinted with permission from Reference 254. Copyright 2019 from Springer Nature)
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Upper panel: Frequency of 16 different types of hydrogen bonds (BHs) (in %) found in the molecular dynamics simulations (MDS) of (H2O)1,000. The MDS simulations were carried out at two different temperatures to simulate warm water (90°C; red bars) and cold water (10°C; blue bars). The insert illustrates the four‐digit notation applied to identify the different hydrogen bond types. Lower panel: Explanation of the Mpemba effect.251
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(a) BSO (CC) determined from local CC force constants using Equations (44)–(45). (b) Correlation between CC bond lengths and local force constants. CC bonds analyzed are marked in red. For calculational details see Reference 223
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Structure of CH2O confined in a carbon nanotube; calculated at the B3LYP level of theory216–219 with Grimme's empirical D3 dispersion correction220 and Becke–Johnson (BJ) damping221 utilizing Pople's 6‐31G(d,p) basis set.222 Total number of atoms is 84. For details see Referenece [213]
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(a) Adiabatic connection scheme and (b) decomposition of normal modes into local mode contributions for CH3SCN; ωB97X‐D/aug‐cc‐pVDZ level of theory.185–187
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(a) Local mode versus overtone CH stretching frequencies; data was taken from Table 4.3 of Reference 32; (b) local mode versus isolated CH stretching frequencies, data was taken from Table 1 of Reference 140
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Development of bond strength descriptors based on the force constant matrix Fq
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Local modes and overtone spectroscopy
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Electronic Structure Theory > Ab Initio Electronic Structure Methods
Software > Quantum Chemistry
Theoretical and Physical Chemistry > Spectroscopy
Structure and Mechanism > Molecular Structures

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