How important is thermal expansion for predicting molecular crystal structures and thermochemistry at finite temperatures?

Abstract

Molecular crystals expand appreciably upon heating due to both zero-point and thermal vibrational motion, yet this expansion is often neglected in molecular crystal modeling studies. Here, a quasi-harmonic approximation is coupled with fragment-based hybrid many-body interaction calculations to predict thermal expansion and finite-temperature thermochemical properties in crystalline carbon dioxide, ice Ih, acetic acid and imidazole. Fragment-based second-order Möller-Plesset perturbation theory (MP2) and coupled cluster theory with singles, doubles and perturbative triples [CCSD(T)] predict the thermal expansion and the temperature dependence of the enthalpies, entropies and Gibbs free energies of sublimation in good agreement with experiment. The errors introduced by neglecting thermal expansion in the enthalpy and entropy cancel somewhat in the Gibbs free energy. The resulting ∼ 1-2 kJ mol(-1) errors in the free energy near room temperature are comparable to or smaller than the errors expected from the electronic structure treatment, but they may be sufficiently large to affect free-energy rankings among energetically close polymorphs.

Application of computational methods to the design and characterisation of porous molecular materials

“…Improvements to the energy models used in CSP include a recent move towards calculating relative free energies, rather than static lattice energies. 28,41,42 The energetic contribution to polymorph free energy differences from lattice vibrations has been shown to be potentially important in recent large-scale studies, re-ranking approximately 10% of observed polymorph pairs at room temperature compared to temperature-free lattice energy rankings. 19,43 Large potential density differences between porous and non-porous packings of molecules are expected to make entropy differences important in assessing relative stabilities of predicted structures for PMMs.…”

Introduction to the special issue on crystal structure prediction

“…present an evaluation of various quantum chemical methods on the target molecules in the sixth blind test, using both density functional theory (DFT) and semi-empirical methods, and suggest a set of these structures as a benchmark for testing such methods. Another developing trend in CSP is towards the evaluation of free energies in place of lattice energies, to allow thermal and pressure effects on the structural landscape to be evaluated; Heit & Beran's (2016) contribution addresses the question of whether including thermal expansion in the models is important for the energetic evaluation of structures.…”

Ab initiothermodynamic properties and their uncertainties for crystalline α-methanol

“…Several recent studies and reviews employ the quasi-harmonic approximation to calculate the thermodynamic properties of molecular crystals and emphasize the importance of the thermal terms for phenomena such as the thermal expansivity or polymorphism. 2,3,[17][18][19] The results of those studies indicate that the quasi-harmonic approximation sometimes enables calculation of temperature-dependent trends in properties such as molar volumes, sublimation enthalpies, or Gibbs energies for various molecular crystals with a semi-quantitative accuracy or better. This sometimes translates to sub-kJ mol À1 accuracy, which is important for polymorph stability ranking [18][19][20] and predicting of phase change properties.…”

“…Most computational studies of molecular crystals neglect thermal contributions to thermochemical properties at finite temperatures and pressures, since calculating static cohesive electronic energies is much simpler than rigorously accounting for all relevant vibrational and thermal terms. However, predicting the most stable phase or polymorph under certain thermodynamic conditions can require sub-kJ mol À1 accuracy, 2,3 in which case factors such as thermal expansion of the crystal and the temperature dependence of the isobaric heat capacity can play a key role. These effects can be captured only if the anharmonicity of the unit cell vibrations is included in the computational model.…”