On the use of a volume constraint to account for thermal expansion effects on the low-frequency vibrations of molecular crystals

Abstract

A volume-constraint method is presented as a means to capture the influence of thermal expansion on the low-frequency vibrations in molecular crystals. In particular, the room-temperature terahertz absorption spectra of L-tartaric acid, α-lactose monohydrate, and α-para-aminobenzoic acid (PABA) have been simulated using dispersion-corrected, solid-state density functional theory (DFT-D). By comparing the normal modes obtained with a unit cell optimised without constraints to those obtained with a unit cell optimised while constrained to keep its experimental volume, wholesale improvements to the resultant spectrum is achieved when using the constrained geometry by inhibiting cell contraction. These improvements are demonstrated over a range of popular density functionals and basis sets up to triple-zeta complexity. A correlation method is then presented as a means to quantitatively compare the vibrational pattern of normal modes obtained from both unit cells. This analysis reveals that thermal expansion can effect the character and relative frequency of normal modes, with the choice of geometry ultimately affecting the assignment of the experimental absorptions. The sensibility of using the experimental volume as an approximation is then discussed, where it is speculated that large basis sets or hybrid functionals are necessary to ensure that the thermal expansion effect is not overestimated. The low-frequency absorption spectrum of PABA is then fully characterised using the PBE-D3BJ/6-311G(2d,2p) method.