Adding Anisotropy to the Standard Quasi-Harmonic Approximation Still Fails in Several Ways to Capture Organic Crystal Thermodynamics

We
evaluate the accuracy of varying thermal expansion models for
the quasi-harmonic approximation (QHA) relative to molecular dynamics
(MD) for 10 sets of enantiotropic organic polymorphs. Relative to
experiment we find that MD, using an off-the-shelf point charge potential,
gets the sign of the enthalpic contributions correct for 6 of the
10 pairs of polymorphs and the sign of the entropic contributions
correct for all pairs. We find that anisotropic QHA provides little
improvement to the error in free energy differences from MD relative
to isotropic QHA, but does a better job capturing the thermal expansion
of the crystals. A form of entropy–enthalpy compensation allows
the free energy differences of QHA to deviate less than 0.1 kcal/mol
from MD for most polymorphic pairs, despite errors up to 0.4 kcal/mol
in the entropy and enthalpy. Deviations in the free energy of QHA
and MD do not clearly correlate with molecular flexibility, clarifying
a previously published finding. Much of the error previously found
between QHA and MD for these flexible molecules is reduced when QHA
is run from a lattice minimum consistent with the same basin as MD,
rather than the energy-minimized experimental crystal structure. Specifically,
performing anisotropic QHA on lattice minimum quenched from low-temperature
replica exchange simulations reduced the error previously found by
0.2 kcal/mol on average. However, these conformationally flexible
molecules can have many low-temperature conformational minima, and
the choice of an inconsistent minima causes free energies estimated
from QHA to deviate from MD at temperatures as low as 10 K. We also
find finite size errors in the polymorph free energy differences using
anisotropic QHA, with free energy differences as large as 0.5 kcal/mol
between unit and supercells loosely correlated with differences in
anisotropic thermal expansion. These larger system sizes are computationally
more accessible using our cheaper 1D variant of anisotropic QHA, which
gives free energies within 0.02 kcal/mol of the fully anisotropic
approach at all temperatures studied. The errors between MD and experiment
are 1–2 orders of magnitude larger than those seen between
QHA and MD, so the quality of the force field used is still of primary
concern, but this study illustrates a number of other important factors
that must be considered to obtain quantitative organic crystal thermodynamics.