Importance of Vibrational Zero-Point Energy Contribution to the Relative Polymorph Energies of Hydrogen-Bonded Species

The relative stability of polymorphic crystal forms is a challenging conceptual problem of considerable technical interest. Current estimates of relative polymorph energies concentrate on lattice energy. In this work the contribution of differences in zero-point energy and vibrational enthalpy to the enthalpy difference for polymorphs is investigated. The specific case investigated is that of alpha-and gamma-glycine, for which the experimental enthalpy difference is known. Periodic lattice density functional theory (DFT) computations are used to provide the vibrational spectrum at the F-point. It is confirmed that these methods provide reasonable descriptions of the inelastic neutron scattering spectra of these two crystals. It is found that the difference in the zero-point energy is about 1.9 kJ/mol and that the vibrational thermal population difference is 0.9 kJ/mol in the opposite sense. The overall vibrational contributions to the enthalpy difference are much larger than the observed value of ca. 0.3 kJ/mol. The vibrational contribution must be largely compensated by the lattice energy difference. The polymorphs of glycine differ in the pattern of their hydrogen bonds, a feature common to many polymorphs of interest. The consequent difference in the N-H stretching frequencies is a contributor to the zero-point correction, but the major effect stems from changes in the bending vibrations.