Related Experiment Video
Updated: Mar 29, 2026

Author Spotlight: Unveiling the Potential of VSFG Microscopy in Studying Mesoscopically Heterogeneous Self-Assembled Structures
Published on: December 1, 2023
Coarse Graining of Intermolecular Vibrations by a Karhunen-Loève Transformation of Atomic Displacement Vectors
1Institute of Industrial Science, University of Tokyo, 4-6-1 Komaba, Meguro-ku, Tokyo 153-8505, Japan.
Abstract:
We have formulated a procedure for evaluating the anisotropic stiffness of a molecular assembly. First, we show how to reduce the dimensions of the matrices that appear in a conventional Hessian analysis of mass-weighted coordination by using a 12-dimensional transverse-rotational basis set for expansion. This treatment yields matrix representations of the intermolecular force and inertial load of the constituent molecules. Next we applied this procedure to 2-aminopyridine dimers and numerically analyzed the low-frequency (∼THz region) normal-mode vibrations. By validating the elements of stiffness matrix, this study exemplifies a derivation of the parameters necessary for the normal-mode analysis of a large system like a crystal, without any explicit representation of the potential functions.
Related Concept Videos
IR Spectroscopy: Hooke's Law Approximation of Molecular Vibration
According to Hooke's law, the vibrational frequency is directly proportional to...
IR Spectroscopy: Molecular Vibration Overview
Stretching vibrations are vibrational motions that occur along the bond line, changing the bond length or distance between two bonded atoms. They are further distinguished as symmetric or asymmetric. In symmetric stretching, the...
IR Spectrum Peak Splitting: Symmetric vs Asymmetric Vibrations
¹H NMR: Interpreting Distorted and Overlapping Signals
As Δν decreases and the signals move closer, the doublets appear increasingly distorted. The intensities of the inner lines increase at the cost of those of the outer lines as the signals are...
Linear Approximation in Frequency Domain
In contrast, nonlinear systems do not inherently possess these properties. However, for small deviations around an operating point, a nonlinear system can often be approximated as linear....
Raman Spectroscopy: Overview
However, a small fraction of the scattered light exhibits a frequency shift due to the exchange of energy between the incident photons and...

