Intensity‐carrying modes important for vibrational polarizabilities and hyperpolarizabilities of molecules: Derivation from the algebraic properties of formulas and applications

Abstract

The intensity-carrying mode (ICM) theory is developed for analyzing the vibrational motions that mainly contribute to vibrational polarizabilities and hyperpolarizabilities, which are important for describing intermolecular electrostatic interactions and nonlinear optical properties of molecules. The ICMs are derived from dipole derivatives, polarizability derivatives, and first hyperpolarizability derivatives by using algebraic properties of intensity formulas. The way to obtain explicit forms of ICMs, including the optimization method of the basis of the ICM vector space, is discussed in detail. One- and two-dimensional models are constructed on the basis of the ICMs. The theory is applied to three molecules (a push-pull type polyene, a streptocyanine dye cation, and a symmetric neutral polyene) taken as typical examples. It is shown that the ICM theory provides a reasonable picture on the vibrational polarization properties of these molecules. On the basis of this result, the validity of the valence-bond charge transfer (VB-CT) model, which is a one-dimensional model and is widely used to describe the electronic and vibrational properties of dye molecules, is also discussed.

Theoretical study of the polymer molecules (TeO2)n as model systems for the local structure in TeO2 glass

“…This is in line with the results of Ref. [13] in which the correlation between the high c values and the high Raman activity was found for organic conjugated polymer molecules.…”

MOVIPAC: Vibrational spectroscopy with a robust meta‐program for massively parallel standard and inverse calculations

“…These ICMs have been found by Torii et al [70] and in an alternative derivation by us. [31] In a similar way, the ICMs can be derived for Raman intensities where the Cartesian gradients of the electric-dipole-electric-dipole polarizability tensor are required [71,32] for the eigenvalue equation. This concept has also been extended to Raman Optical Activity (ROA) spectroscopy, where, in addition to the electric-dipole-electric-dipole polarizability tensor, the electric-dipole-magnetic-dipole and electric-dipole-electric-quadrupole polarizability tensors are necessary.…”

Intensity‐Carrying Modes in Raman and Raman Optical Activity Spectroscopy

“…The polarizability has six independent components, and therefore we get these six intense modes as has also been found by Torii. [11] However, Torii determined the Raman ICMs by employing an iterative procedure, projecting out an optimized ICM from the vector space and optimizing another ICM in the new vector space.…”

“…An interesting aspect in this context is the concept of the so-called intensity-carrying modes (ICMs), [10,11] which are collective distortions of the molecular structure that carry all intensity and are in general not equal to normal modes. They allow one to understand which movements in the molecule bring about high intensity.…”

“…[10] Three years later the concept was extended to (hyper)-polarizabilities. [11] Herein, we derive the ICMs for Raman and ROA spectroscopy in analogy to the determination of IR ICMs described in ref. [12].…”