(192bf) Improved Thermal Gradient Quasiharmonic Approximations for Thermodynamic Properties of Organic Crystals with the Inclusion of Anisotropy

We explore the utility of variations in the quasi-harmonic approximation (QHA) to calculate the thermodynamic properties of small organic polymorphs and compare each approach to results for full molecular dynamics (MD). Due to the fact that crystalline structures of small organic molecules can vary in properties, fields such as as pharmaceutical formulation, organic electronics processing and explosives preservation have interest in fast and efficient methods to predict favorable structures. Common computational methods fail to include the dependence of temperature and importance of entropic effects on determining favorable crystal structures, while MD simulations are computationally costly. Quasi-harmonic (lattice dynamics) approximations provide a useful compromise to efficiently approximate entropy.

In QHA, it is standard to describe thermal expansion by constructing a stepwise array of isotropically expanded structures from the lattice minimum crystals and at any given temperature determine what structure minimizes the Gibbs free energy. We have developed an alternative method that determines the local gradient of thermal expansion and uses a 4th order Runge-Kutta method to efficiently determine the minimum free energy structure for thermal expansion. We have found that the gradient method produces smoother volumetric versus temperature curves and, generalizes easily to anisotropic expansion, which a more common in organic crystals. Between the two isotropic and one anisotropic method the vibrational spectra can be calculated in two ways; by directly solving the mass-weighted Hessian or to approximate the changes in the vibrational spectra due to thermal expansion with the Gruneisen parameter.

For 12 systems, with up to 60 atoms/molecule and 4 degrees of torsional freedom, this approach deviates by by less than 0.01 kcal/mol in the case of isotropic expansion. Therefore, using a Gruneisen parameter with the gradient approach could cut the computational time by 95%. Previous research has shown that isotropic QHA computes free energy curves within error of MD for small rigid molecules, but fails for systems with molecular flexibility. For these more flexible molecules, we can efficiently apply anisotropic QHA with the gradient method and determine how much of this deviation is due to anisotropic expansion and how much is due to other anharmonic sources.