Computational Methods for the Assignment of Vibrational Modes in Crystalline Materials

Abstract

In this chapter we provide a description of the computational tools used for the calculation of the terahertz absorption spectrum of a crystalline material, with a particular focus on molecular crystals. We explain using examples why it is not correct to use the normal modes of vibration of an isolated molecule to understand the vibrational spectrum of a material in the terahertz range, but that the features in this spectral region are largely related to intermolecular interactions. It is, therefore, necessary to use methods that consider the periodicity of the crystal structure. We describe the two main methods used for the calculation of the vibrational frequencies and their absorption intensities of a crystal: lattice dynamics and molecular dynamics, providing examples showing the benefits and limitations of each method.

Terahertz Time-Domain and Low-Frequency Raman Spectroscopy of Organic Materials

“…For example, using the THz-TDS spectra of cysteine three modes were observed between 40 and 93 cm –1 , yet Gaussian predicted only a single feature. 186 As Tomerini and Day explained in their recent article, 206 the use of single modes to explain the origin of features in the terahertz spectrum can be dangerous. A classic example is the analysis of the low-frequency modes of 3,4-methylenedioxymethamphetamine (MDMA, or ecstasy) performed by Allis et al 207 and Hakey et al, 208 in which three modes at 37.0, 59.3, and 86.6 cm –1 were identified from the experimental spectrum.…”

Polymorph Characterization of Active Pharmaceutical Ingredients (APIs) Using Low-Frequency Raman Spectroscopy

“…14,28,29 Only recently have these experimental and theoretical tools been applied to the larger complex aromatic molecules characteristic of APIs. 8,9,22,27,30 We first review a few fundamentals necessary to understand vibrational spectroscopy in the low-frequency spectral region.…”

“…Molecular crystals are characterized by vibrations as well as translational oscillations and rotational oscillations (librations), which are hindered by the crystalline structure. 14,27–29 Typically, we consider the vibrational spectrum in terms of the molecular vibration (i.e., internal modes). The characteristic intramolecular and intermolecular vibrations observed in the low-frequency region vary as a function of the state of matter.…”

“…As a first approximation in theoretical treatments of external vibrations of a crystalline lattice, we can treat the molecules as rigid blocks that can undergo translation, libration, or mixed translation-libration oscillations. 27–29 The motions of the molecules in the crystal are coupled to form a wave in the crystalline lattice with a defined wavevector ( K ) and frequency (Ω). Two types of phonon modes result: the acoustic phonons, which are IR and Raman inactive, and the optical phonons, which are IR and Raman active.…”

“…However, computational methodologies are increasingly being applied to develop an understanding of the characteristic vibrations below 200 cm −1 of organic molecular solids. 27…”