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Reliable and Practical Computational Prediction of Molecular Crystal Polymorphs
Johannes Hoja, Hsin-Yu Ko, Marcus A. Neumann, Roberto Car, Robert A. DiStasio, Alexandre Tkatchenko
TL;DR
The study relaxes crystal structures with PBE+TS and ranks their relative stabilities using dispersion-corrected energies, hybrid-functional corrections, and vibrational free energies. The resulting approximations closely reproduce tighter-reference energies, while final rankings use PBE0+MBD+Fvib at experimental measurement temperatures.
Problem
The workflow addresses the need to distinguish relative crystal-structure stabilities accurately enough for polymorph ranking.
Method
Structures are relaxed with PBE+TS, then ranked using PBE+MBD, an approximated PBE0+MBD correction, and vibrational free energies, including anharmonic Γ-point contributions for selected structures.
Results
0.4 kJ/mol mean absolute deviation and 0.8 kJ/mol maximum deviation were obtained for the approximate PBE0+MBD energies versus tight PBE0+MBD reference energies.
Takeaways & Limitations
Final stability rankings are based on PBE0+MBD+Fvib energies evaluated at temperatures corresponding to the experimental crystal-structure measurements.
Abstract
from arXiv · showhide
The ability to reliably predict the structures and stabilities of a molecular crystal and its polymorphs without any prior experimental information would be an invaluable tool for a number of fields, with specific and immediate applications in the design and formulation of pharmaceuticals. In this case, detailed knowledge of the polymorphic energy landscape for an active pharmaceutical ingredient yields profound insight regarding the existence and likelihood of late-appearing polymorphs. However, the computational prediction of the structures and stabilities of molecular crystal polymorphs is particularly challenging due to the high dimensionality of conformational and crystallographic space accompanied by the need for relative (free) energies to within $\approx$ 1 kJ/mol per molecule. In this work, we combine the most successful crystal structure sampling strategy with the most accurate energy ranking strategy of the latest blind test of organic crystal structure prediction (CSP), organized by the Cambridge Crystallographic Data Centre (CCDC). Our final energy ranking is based on first-principles density functional theory (DFT) calculations that include three key physical contributions: (i) a sophisticated treatment of Pauli exchange-repulsion and electron correlation effects with hybrid functionals, (ii) inclusion of many-body van der Waals dispersion interactions, and (iii) account of vibrational free energies. In doing so, this combined approach has an optimal success rate in producing the crystal structures corresponding to the five blind-test molecules. With this practical approach, we demonstrate the feasibility of obtaining reliable structures and stabilities for molecular crystals of pharmaceutical importance, paving the way towards an enhanced fundamental understanding of polymorphic energy landscapes and routine industrial application of molecular CSP methods.
METHODS
The protocol relaxes and deduplicates candidate crystal structures, then ranks them with increasingly accurate electronic-structure and vibrational-free-energy calculations. Anharmonic vibrational effects are incorporated for system XXIII, while harmonic calculations provide the converged total vibrational free energies.
- Structure preparation: Candidate structures are fully relaxed with PBE+TS, deduplicated using crystal similarity criteria, and retained according to their relative PBE+TS energies.Similarity requires matching molecular distances and angles, RMSD20 below 0.5 Å, and PBE+TS energy agreement within 1 kJ/mol for identical structures.
- Electronic-structure ranking: Relative stabilities are evaluated hierarchically with PBE+TS, PBE+MBD, and an approximate tight-setting PBE0+MBD treatment.The approximation adds the light-level PBE0+MBD–PBE+MBD difference to tight-level PBE+MBD energies.
- Vibrational free energies: Vibrational free energies are computed with PHONOPY using finite differences, reciprocal-space q-points, and harmonic approximation at temperatures matching experimental measurements.Supercells and q-point meshes are selected to capture converged vibrational contributions, and all structures have no imaginary Γ-point frequencies.
- Anharmonic treatment: For system XXIII, anharmonic free energies replace harmonic oscillators with Morse oscillators for Γ-point phonon modes in cells containing four molecules.Morse potentials are fitted to displaced-structure energies sampled across a thermally accessible energy window.
- Anharmonic treatment: Total vibrational free energies combine fully converged harmonic contributions with an anharmonic Γ-point correction for the smaller cells.The correction uses the anharmonic Γ-point free energy relative to its harmonic Γ-point counterpart.