Speakers
Description
Polymorphism of elements or compounds means that these substances can exist in more than
one crystalline form. Due to the different mutual arrangement of molecules in these
polymorphs, both their static electron energies and their dynamic degrees of freedom vary.
As a result, different polymorphs of the same substance exhibit different physical properties.
Pharmaceutically active ingredients (APIs) often exhibit this polymorphism, rendering their
development significantly expensive and time consuming. At the same time, the
development of computational and predictive methods, together with the increased
availability of computational capacity, enables to predict crystal properties in silico,
bypassing part of the tedious experiments.
Quantum-chemical calculations for the solid state tend to use electron density functional
theory (DFT), which provide a relatively fair accuracy. Still, these DFT methods can be too
costly for complex molecular crystals, justifying the attempt to find some compromise
between the required accuracy and computational effort. Semi-empirical methods based on
the density functional tight binding (DFTB) could be this way, or at least could be helpful
for particular calculations. The lower computational demands of these methods are due to
the introduction of certain reference densities or pair-specific parameterizations. An
important step to predict the thermodynamically preferred polymorphic form is to know the
contributions of both the vibrational states and electron energy. For a sensible assessment of
the relative thermodynamic stability of the polymorphs, it is important too to take into
account the anharmonicity of vibrations in crystals. This is partially captured using the quasiharmonic approximation, which takes the energy of vibration with respect to the volume of
crystal.
A benchmark study, comparing the performance of DFT and DFTB calculations for
molecular crystals, is presented for several enantiopure or racemic crystals of APIs. DFT
calculations employ the PBE-D3/PAW level of theory implemented in the code VASP,
whereas the DFTB3 methods with the D4 dispersion correction method implemented in the
DFTB+ code is used as a DFTB representative. Both methods are used to calculate optimum
unit-cell geometries, their electron energies and the energy response to the variation of the
unit-cell volume. Phonon frequencies and densities of the phonon states are calculated in the
PHONOPY program at the both levels of theory. The aim of this procedure is to find an
efficient combination of DFTB and DFT methods for the individual computational steps
within the quasi-harmonic framework. Such a computational approach, validated through
reference experimental and DFT data, will enable to efficiently rank polymorphs also for
larger molecules in terms of their Gibbs energies at finite temperatures.
