Characterizing vibrational motion beyond internal coordinates

Abstract

We present a procedure for the decomposition of the normal modes of a composite system, including its rotations and translations, into those of fragments. The method permits-by the cross-contraction of dyads of mass-weighted displacement vectors, without recourse to valence coordinates-the direct comparison of nuclear motions of structurally similar but otherwise arbitrary fragments of molecules, and it leads to a quantitative definition of the similarity and the overlap of nuclear motions. We illustrate its usefulness by the quantification of the mixing of the normal modes of formic acid monomers upon the formation of a dimer, by the comparison of the overlap of the intermolecular normal vibrations of the water dimer computed with different ab initio schemes, and by the comparison of similarity and overlap of vibrations of (4S,7R)-galaxolide and (4S)-4-methylisochromane. The approach is expected to become a standard tool in vibrational analysis.

A New Method to Describe the Multimode Jahn–Teller Effect Using Density Functional Theory

“…These vibrations are illustrated in Fig. 8, using the vibrational energy distribution representation [44]. The analysis shows, that the contribution of low energy skeletal vibrations (1 to 3) and the high energy vibrations (C-H stretch 14 to 16) is almost negligible.…”

“…There is a unitary transformation between the normal coordinates of HS and LS points: The visual inspection can be used for small molecules, but for larger molecules this is impossible. Alternatively, it is possible to use the method developed by Hug [44], for the comparison of nuclear motions of structurally similar fragments of molecules. We applied it for the correlation of the normal modes of the same molecule in different conformations belonging to different point groups.…”

Density functional theory study of the Jahn-Teller effect in cobaltocene

“…For the energies, LDA and the generalized gradient approximation (GGA) in the form given by Perdew-Wang (PW91) [39,40] have been compared. Analytical harmonic frequencies were calculated [41][42][43] and analyzed with the aid of PyVib2 1.1 [44,45]. For the detailed discussion of potential energy surface, the IRC method [22,23] as implemented in the Amsterdam density functional (ADF) [24,25] has been used.…”

“…More details about this approach will be published shortly [49]. (15) The set of normal modes q = (q 1 , q 2 , …, q n ), n being the number of the totally symmetric vibrations in low symmetry, are orthonormal, that is, q i ؒ q j = δ ij : (16) (17) In order to be consistent with the usual treatments [2] and the previous qualitative arguments, we correlate the vibrations in the minimum-energy conformation of low symmetry to the ones in high symmetry by the method developed by Hug et al [44,45], using overlap and similarities of the massweighted Cartesian displacements of the two different configurations.…”

Density Functional Theory Study of the Multimode Jahn-Teller Effect – Ground State Distortion of Benzene Cation

“…The normal coordinates in the LS are not identical with the normal coordinates in the HS, so the idea of using LS structure as a reference point is in contrast with usual treatment of the JT effect which starts from the HS configuration. Still, we can easily correlate the normal modes of the LS structure to the HS ones, using the method of Hug [23], thus having the connection with the common exploration of the JT effect. Our model is based on the symmetry rules developed by Bader [24][25][26] and Pearson [27,28] for chemical reactions.…”