Reliability of the Phonon Density of States Determined by Real-Coded Genetic Algorithm from Heat Capacities of Benzoic Acid Crystals.

Constant-pressure heat capacities (CPs) of crystalline benzoic acid (BAh) and its deuterated analogue (C6H5COOD, BAd) were measured by adiabatic calorimetry, and the phonon density (g(ω)) of states was determined from their CP data using a real-coded genetic algorithm (RCGA) with just generation gap + real-coded ensemble cross-over. The distribution of g(ω) was in reasonable agreement with the spectroscopic one observed for molecular vibration modes, indicating sufficient reliability of g(ω) determined by the RCGA. Based on the fact that CPs reveals an inverse-isotope effect in the temperature range 30-130 K, the determined g(ω)s were used to investigate the molecular mechanism of the effect: g(ω) of BAd revealed blue shifts in the ranges of ω = 80-100 and 150-230 K, as referred to that of BAh. It was suggested from the combined considerations on g(ω) and spectroscopic results that an anticooperative correlation exists between O-H···O hydrogen bonds and interdimer interactions in BA.