A method was proposed to derive the phonon density [g(ω)] of states of materials from their heat capacity data by using Real-Coded Genetic Algorithm (RCGA) with Just Generation Gap + Real-Coded Ensemble Crossover. The performance of the method was confirmed by testing whether or not the RCGA reproduces a reasonable g(ω) by analyzing the set of heat capacity data evaluated from an initially assumed model g 0 (ω) composed of Debye and optical modes. As an example, constantpressure heat capacities (C P s) were measured for soft molecular materials, diphenyl phosphate (DPP) and diphenylphosphinic acid, in the condensed state, and their g(ω)s were determined from the C P data by applying the RCGA. The unusual behavior that the C P value of glass was smaller than the one of the crystal in the temperature range from 10 to 70 K was observed in DPP; the behavior is contrary to that expected ordinarily for the glass as compared with the crystal. The g(ω)s determined by the RCGA demonstrated that the unusual behavior was attributed to the blue shift in g(ω) of ω = 30−240 K in the glass compared with the crystal. The blue shift and other effects were discussed reasonably as originating from the competitive concurrence of strong and weak intermolecular hydrogen bonds in DPP, with the help of determination of their intramolecular vibrations for the isolated molecule by the density functional theory calculation. It was concluded that the method using the RCGA is of value for obtaining the microscopic information of g(ω) from the precise heat capacity data and for investigating any difference between the details of g(ω)s in different phases of materials.

Constant-pressure heat capacities (C P s) of crystalline benzoic acid (BAh) and its deuterated analogue (C 6 H 5 COOD, BAd) were measured by adiabatic calorimetry, and the phonon density (g(ω)) of states was determined from their C P 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 C P s 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.

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Crystalline hypophosphorous acid, composed of strongly hydrogen-bonded chains, was investigated by adiabatic calorimetry in a temperature range between 20 and 306 K and by dielectrometry as a supplemental means. The heat-capacity curve showed subsequent phase transitions: a second-order one at 210.4 K followed by a first-order one at 159 K and the other two ones at 149 and 139.4 K with decreasing temperature. The total entropy of the transitions was assessed to be 0.35 J K–1 mol–1 by using the baseline heat capacities that were determined by means of a real-coded genetic algorithm. The small value was interpreted as the transitions were associated with displacements of the protons forming hydrogen bonds: namely, while they are located at the center between two oxygen atoms above 210.4 K, the protons are displaced close to one of the oxygen atoms with the bond length enlarged below it. Temperature dependence of dielectric constants displayed no sign, around 210 K, indicating the existence of (anti-)ferroelectricity. It was thus expected that the manner of off-center proton displacements along each hydrogen-bonded chain reveals a wave-like and incommensurate appearance below 210.4 K, referred to as the normal crystal lattice above it, and following locking to a wave-like but superlattice commensurate one at 159 K.