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

Abstract

ergy 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 because our cheaper 1D variant of anisotropic QHA, which gives free energies within within 0.02 kcal/mol of the fully anisotropic approach at all temperature 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.

Overcoming the difficulties of predicting conformational polymorph energetics in molecular crystals via correlated wavefunction methods

“…The differences between quasi-harmonic and molecular dynamics models are frequently (but not always) small. [102][103][104] In the end, combining information from the fully-relaxed 0 K structures and xed-cell room-temperature structures provides information regarding the topology of crystal energy landscapes that facilitates comparison with experiment.…”

Along the road to crystal structure prediction (CSP) of pharmaceutical-like molecules

“…Molecular crystals also manifest a large anisotropy in cell expansion, which can be particularly severe for flexible molecular units, further hindering application of QHA by considerably affecting the resulting Gibbs energy. 116 An alternative strategy invokes MD simulations, taking advantage of including anharmonic effects from the outset. This relies on the assumption that the statistical averages for lattice translation vectors and for atomic fractional coordinates are equivalent to structure relaxation at given pressure–temperature conditions.…”

Statistical mechanical approximations to more efficiently determine polymorph free energy differences for small organic molecules

“…For a given potential, we have shown that irreversible crystal restructuring away from direct minimization of the experimental crystal is a common phenomena when polymorphs are heated in MD. 30,32,56 Further investigation by Dybeck et al found that configurational ensembles obtained from MD include many static lattice minimum, being found in 8 of 12 polymorphic systems studied. 56 Approaches like QHA cannot overcome this barrier of restructuring, which can lead to inaccurate stability ranking or large errors (>1.0 kcal/mol) in the thermodynamics computed with QHA relative to MD.…”

“…But more recently free energy techniques that approximate the entropy using harmonic phonons have been used for CSPs 25,26 and a significant focused has been placed on developing and probing what free energy techniques are necessary. [27][28][29][30][31][32] The harmonic approximation (HA) is the easiest way to include entropy by computing the static lattice harmonic phonons, which can be improved by considering thermal expansion through the quasi-harmonic approximation (QHA). Given a lattice minimum crystal, the harmonic phonons can be computed to determine the free energy of the crystal at all temperatures of interest.…”

“…31 For a number of systems we have shown approximations that can be made to anisotropic QHA so that QHA only costs the user 7× the cost of performing isotropic QHA. 32 The simplicity and low computational cost of harmonic approaches is desirable in a CSP where 50-200 structures could exist within 2.5 kcal/mol of the global minimum and therefore screening at some level for entropy contributions to stability is useful.…”