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WIREs Comput Mol Sci
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First‐principles modeling of molecular crystals: structures and stabilities, temperature and pressure

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The understanding of the structure, stability, and response properties of molecular crystals at finite temperature and pressure is crucial for the field of crystal engineering and their application. For a long time, the field of crystal‐structure prediction and modeling of molecular crystals has been dominated by classical mechanistic force‐field methods. However, due to increasing computational power and the development of more sophisticated quantum‐mechanical approximations, first‐principles approaches based on density functional theory can now be applied to practically relevant molecular crystals. The broad transferability of first‐principles methods is especially imperative for polymorphic molecular crystals. This review highlights the current status of modeling molecular crystals from first principles. We give an overview of current state‐of‐the‐art approaches and discuss in detail the main challenges and necessary approximations. So far, the main focus in this field has been on calculating stabilities and structures without considering thermal contributions. We discuss techniques that allow one to include thermal effects at a first‐principles level in the harmonic or quasi‐harmonic approximation, and that are already applicable to realistic systems, or will be in the near future. Furthermore, this review also discusses how to calculate vibrational and elastic properties. Finally, we present a perspective on future uses of first‐principles calculations for modeling molecular crystals and summarize the many remaining challenges in this field. WIREs Comput Mol Sci 2017, 7:e1294. doi: 10.1002/wcms.1294

Schematic representation of intermolecular interactions.
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Spherical plots of the Young's modulus of ND3 (in GPa) obtained at the minima of E tot (opt) and at volumes corresponding to 194 K from the QHA for PBE and PBE+MBD, as well as experimental values at 194 K of Ref . MBD, many‐body dispersion; ND3 , phase‐I deutero ammonia; QHA, quasi‐harmonic approximation.
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Heat capacity at constant pressure (a) and linear thermal expansion coefficient (b) of solid ND3 obtained from the QHA compared to experimental values from Ref . ND3 , phase‐I deutero ammonia; QHA, quasi‐harmonic approximation.
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Quasi‐harmonic approximation for solid ND3 calculated with different methods at three different temperatures. The solid lines represent Murnaghan EOS fits and the red triangles mark the corresponding minima. EOS, equation of state; ND3 , phase‐I deutero ammonia.
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Phonon density of states of solid ND3 calculated with PBE at several unit‐cell volumes. ND3 , phase‐I deutero ammonia.
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Harmonicity of two phonon modes in ND3 calculated with PBE+MBD. The displacements are shown at a relative scale in which a displacement of 1 means that the norm of the eigenvectors is equal to one. MBD, many‐body dispersion; ND3 , phase‐I deutero ammonia.
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Full pDOS of ND3 (a), the low‐frequency region of the ND3 pDOS (b), and the low‐frequency region of the HMB pDOS (c). The gray lines in (a) show the location of the experimental internal modes as determined by Holt et al., and the gray lines in (c) mark the peak maxima of the experimental INS spectrum measured at 15 K by Ciezak et al. HMB, hexamethylbenzene; INS, inelastic neutron scattering; ND3 , phase‐I deutero ammonia; pDOS, phonon density of states.
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The temperature‐dependent factor in the second integral of Eq. .
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Calculated versus experimental densities for 91 polycyclic aromatic hydrocarbons. Structures obtained at room temperature are shown in red and structures obtained below room temperature are shown in blue. The black line marks perfect agreement, while the green dotted lines mark a deviation of ±5%. (Reprinted with permission from Ref . Copyright 2014 American Chemical Society).
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Relative error in the calculation of lattice energies for 22 molecular crystals for PBE+TS, PBE+MBD, PBE0+TS, and PBE0+MBD calculations. (Reprinted with permission from Ref . with the permission of AIP Publishing) MBD, many‐body dispersion; TS, Tkatchenko–Scheffler.
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Convergence of the pairwise (TS) and MBD vdW lattice energy with respect to the dipole–dipole cut off radius and MBD supercell cut off radius for ND3 and HMB. HMB, hexamethylbenzene; MBD, many‐body dispersion; ND3 , cubic deutero ammonia; TS, Tkatchenko–Scheffler; vdW, van der Waals.
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Structure and Mechanism > Computational Materials Science
Electronic Structure Theory > Ab Initio Electronic Structure Methods
Electronic Structure Theory > Density Functional Theory

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