Deriving the equilibrium conformation in molecular crystals by the quasi-harmonic procedure: some critical remarks

Owing to progress in lattice-dynamical computing routines, free-energy calculations for perfect molecular crystals are no longer prohibitive in the quasi-harmonic approximation. Thus the consistent derivation of an equilibrium conformation at various temperatures and pressures, and even the stability range of various phases, may become a routine possibility, starting from semi-empirical potentials only. An example of such conformational calculations is given and discussed for the tetragonal phase of adamantane at 163 and 1 K. The effect of vibrational energy (even zero-point) and entropy upon molecular orientation and position in the unit cell is shown not to be negligible by several examples. This precludes the possibility of calculating the cell parameters on free-energy grounds and the molecular coordinates by considering the minimum packing energy. For crystals with molecules fixed by symmetry, the quasi-harmonic approximation becomes particularly appropriate, since in this case for any unit cell the first derivatives of energy with respect to any molecular shift are zero. Some critical steps of such calculations are examined and discussed, especially in connection with converging processes. No particular problem is encountered in sampling the Brillouin zone, because only a limited number of points is necessary. Convergence of lattice sums to obtain packing energy is more critical, although for most practical purposes a maximum packing distance of 15 Å is sufficient. The real difficulties of these calculations consist in the need of considering many degrees of freedom at once, and also in the inadequacy of present-day semi-empirical potentials.