Research ArticleMATERIALS SCIENCE

Reliable and practical computational description of molecular crystal polymorphs

See allHide authors and affiliations

Science Advances  11 Jan 2019:
Vol. 5, no. 1, eaau3338
DOI: 10.1126/sciadv.aau3338
  • Fig. 1 General overview of a CSP protocol.

    Starting with the 2D chemical formula for each molecule, this procedure generates molecular crystal structures and (free) energy rankings for all thermodynamically relevant polymorphs. In this work, we combine the crystal structure sampling strategy provided by the GRACE software package with the highly accurate (free) energy ranking strategy provided by the first principles–based DFT + MBD framework.

  • Fig. 2 Obtained polymorphic energy landscapes.

    Relative stabilities for all steps in the present CSP stability ranking procedure for systems: (A) XXII, (B) XXIII, (C) XXIV, (D) XXV, and (E) XXVI. For each ranking, the energy of the most stable crystal structure defines the zero of the energy. Experimentally observed structures are highlighted in color, while all other structures are in gray. The final ranking for each system corresponds to the Helmholtz free energies at the PBE0 + MBD + Fvib level, computed at the corresponding experimental temperatures: 150 K for XXII, 240 K for XXIV, and 300 K for XXIII, XXV, and XXVI. All relative energies are reported per chemical unit, i.e., for XXII, XXIII, and XXVI, the energies are normalized per molecule, and for XXIV and XXV, the energies are given per trimer and dimer, respectively. (F) Unit cells for all highlighted structures.

  • Fig. 3 Accuracy of structures.

    Overlay between the experimentally determined structures (element-specific colors) and the corresponding PBE + TS–optimized structures (green) for systems: (A) XXII, (B) XXIII-A, (C) XXIII-B, (D) XXIII-C, (E) XXIII-D, (F) XXIII-E, (G) XXIV, (H) XXV, and (I) XXVI. These overlays are shown for the molecules constituting the respective unit cell.

  • Fig. 4 Stability rankings for thermally expanded structures.

    Energetic rankings for all experimentally observed (forms A, B, C, D, and E) and theoretically predicted (N18, N31, N42, and N70) structures for system XXIII. All energies were evaluated using thermally expanded PBE + TS structures optimized at 300 K with the QHA. The last two rankings include harmonic (Fvib) and Morse anharmonic (Embedded Image) vibrational free energy contributions.

Supplementary Materials

  • Supplementary material for this article is available at http://advances.sciencemag.org/cgi/content/full/5/1/eaau3338/DC1

    Supplementary Text

    Fig. S1. Rank 1 (XXIII-N70) and form A (XXIII-N85) share a sheet structure (red boxes), in which the molecules are arranged according to the same pattern, but the sheets are stacked differently.

    Table S1. Relative energies of a benchmark set of structures with small unit cells calculated with different methods.

    Table S2. Convergence of relative stabilities with basis set and grid settings.

    Table S3. This table shows the MAD and the maximum absolute deviation (MAX) for all possible relative energies (within a system) from table S1 with regard to PBE0 + MBD calculations with tight settings for basis set and grids.

    Table S4. Stability ranking for system XXII in kilojoules per mole per molecule.

    Table S5. Stability ranking for system XXIII in kilojoules per mole per molecule.

    Table S6. Stability ranking for system XXIV in kilojoules per mole per trimer.

    Table S7. Stability ranking for system XXV in kilojoules per mole per dimer.

    Table S8. Stability ranking for system XXVI in kilojoules per mole per molecule.

    Table S9. Errors of PBE + TS–optimized structures with regard to experimental structures.

    Table S10. Errors of the thermally expanded structures (corresponding to 300 K within the QHA) with regard to experimental structures.

    Data S1. All PBE + TS–optimized structures (light settings) and the thermally expanded structures for system XXIII.

  • Supplementary Materials

    The PDF file includes:

    • Supplementary Text
    • Fig. S1. Rank 1 (XXIII-N70) and form A (XXIII-N85) share a sheet structure (red boxes), in which the molecules are arranged according to the same pattern, but the sheets are stacked differently.
    • Table S1. Relative energies of a benchmark set of structures with small unit cells calculated with different methods.
    • Table S2. Convergence of relative stabilities with basis set and grid settings.
    • Table S3. This table shows the MAD and the maximum absolute deviation (MAX) for all possible relative energies (within a system) from table S1 with regard to PBE0 + MBD calculations with tight settings for basis set and grids.
    • Table S4. Stability ranking for system XXII in kilojoules per mole per molecule.
    • Table S5. Stability ranking for system XXIII in kilojoules per mole per molecule.
    • Table S6. Stability ranking for system XXIV in kilojoules per mole per trimer.
    • Table S7. Stability ranking for system XXV in kilojoules per mole per dimer.
    • Table S8. Stability ranking for system XXVI in kilojoules per mole per molecule.
    • Table S9. Errors of PBE + TS–optimized structures with regard to experimental structures.
    • Table S10. Errors of the thermally expanded structures (corresponding to 300 K within the QHA) with regard to experimental structures.
    • Legend for data S1

    Download PDF

    Other Supplementary Material for this manuscript includes the following:

    • Data S1 (.cif format). All PBE + TS–optimized structures (light settings) and the thermally expanded structures for system XXIII.

    Files in this Data Supplement:

Stay Connected to Science Advances

Navigate This Article