We present a model to explain the mechanism behind enantiomeric separation under either shear flow or local rotational motion in a fluid. Local vorticity of the fluid imparts molecular rotation that couples to translational motion, sending enantiomers in opposite directions. Translation-rotation coupling of enantiomers is explored using the molecular hydrodynamic resistance tensor, and a molecular equivalent of the pitch of a screw is introduced to describe the degree of translation-rotation coupling. Molecular pitch is a structural feature of the molecules and can be easily computed, allowing rapid estimation of the pitch of 85 drug-like molecules. Simulations of model enantiomers in a range of fluids such as $\Lambda$- and $\Delta$-Ru(bpy)_3]Cl_2 in water and (R,R)- and (S,S)-atorvastatin in methanol support predictions made using molecular pitch values.A competition model and continuum drift diffusion equations are developed to predict separation of realistic racemic mixtures. We find that enantiomeric separation on a centimeter length scale can be achieved in hours, using experimentally-achievable vorticities. Additionally, we find that certain achiral objects can also exhibit a non-zero molecular pitch.
Supporting Information: Separation of Enantiomers through Local Vorticity: A Screw Model Mechanism
The supporting documentation contains hydrodynamic and Green-Kubo derivations of the resistance and diffusion tensors, theoretical development of the overlapping bead and rough shell models for the resistance tensors, a version of the molecular pitch using diffusion tensors, screw model pitch predictions for 85 drug-like molecules, details and simulation parameters for the RNEMD and coupled drift-diffusion simulations, and an examination of pitch values for certain achiral molecules that naturally emerge from mirror image properties of the hydrodynamic tensors. A accompanying set of text files provide the rigid body molecular geometries and force field parameters for all molecules (and solvents).
Geometries, force field parameters, and code
Text files providing the rigid body molecular geometries and force field parameters for all molecules (and solvents), as well as python-based routines to compute resistance tensors and molecular pitch values.