Thermochemistry of Racemic and Enantiopure Organic Crystals for Predicting Enantiomer Separation

Abstract

The separation of an enantiomer from a racemic mixture is of primary relevance to the pharmaceutical industry. The thermochemical properties of organic enantiopure and racemate crystals can be exploited to design an enantioselective crystallization process. The thermodynamic difference between the two crystal forms is accessible by two cycles which give the eutectic composition in solution. The "sublimation cycle" requires calculating the lattice energy and phonon frequencies of the crystal structures. Experimental results from heat capacity and other thermodynamic measurements of enantiopure and racemic crystals are compared with a variety of molecular and crystal structure-based calculations. This is done for three prototypes of pharmaceutical-like molecules with different degrees of molecular flexibility. Differences in crystal packing result in varying temperature-dependent heat capacities and affect the sublimation thermodynamics, relative solubility, and eutectic composition. Many simplifying assumptions about the thermodynamics and solubilities of the racemic and enantiopure crystals are critically evaluated. We show that calculations and experimental information using the sublimation cycle can guide the design of processes to resolve enantiomers by crystallization.

Accurate lattice energies of organic molecular crystals from periodic turbomole calculations

“…can be derived from the lattice phonon modes as differences in molecular vibrations of isolated and crystallized compound would cancel out. In very flexible systems, this assumptions may not hold . Experimental vibrational lattice frequencies were used to calculate .…”

“…Lattice energy calculations have also been shown to be able to resolve energy differences between crystals of the crystallized pure enantiomer and the racemate . These lattice energy differences can be calculated accurately enough to be able to predict relative solubilities and thus the eutectic composition of a compound‐forming system in solution . However, it was recently shown that solely focusing on energy differences of the static lattice is not sufficient for modeling the thermochemistry of molecular crystals at ambient temperature and in solution but thermal corrections and solubilization need to be considered …”

Is zeroth order crystal structure prediction (CSP_0) coming to maturity? What should we aim for in an ideal crystal structure prediction code?

“…2 shows that if the lattice energy difference is large, you can condently predict which crystal will form by CSP_0, but if it is small, the outcome is horribly dependent on the energy difference and hence the cancellation of errors in all the other energy terms. Our recent comparison of measured heat capacities at low and ambient temperatures for three pairs of enantiopure and racemic crystals of diverse organic molecules, and other measured thermodynamic quantities, 25 shows that the approximations listed above are not good enough for any of these molecules. The contributions differ in their sensitivity to the molecular and structural differences, particularly the extent to which the molecular vibrational frequencies are unchanged on crystallisation.…”

“…Differences in the hydrogen bonding motif and consequent frequency shis in the IR spectra between the two crystals, can lead to a temperature dependence of the heat capacity difference around ambient. The performance of our attempts to predict thermal corrections using the harmonic approximation, 25 using rigid molecule J mol or J crys methods similar to those used for larger systems (DOI: 10.1039/c8fd00010g), shows the challenge of predicting free energies or relative solubility at a useful accuracy.…”

“…2 The proportion of enantiopure and racemic crystal structures as a function of their energy difference DG ¼ DG(RS) À DG(S), plotted for three temperatures. The asymmetry comes from the definition of one mole of the racemic crystal corresponding to 1/2 a mole of each enantiomer, as used often in experimental work 25 but not in CSP where the reference state is a mole independent of chirality. 26 The spread of energies that changes the crystallisation outcome is not dependent on the reference state.…”