Many‐Body Dispersion Interactions in Molecular Crystal Polymorphism

Abstract

Polymorphs of molecular crystals are often very close in energy, yet they may possess very different physical and chemical properties. The understanding of polymorphism is therefore of great importance for a variety of applications, ranging from drug design to nonlinear optics and hydrogen storage. While the crystal structure prediction blind tests conducted by the Cambridge Crystallographic Data Centre have shown steady progress toward reliable structure prediction for molecular crystals, several challenges remain, including molecular salts, hydrates, and flexible molecules with several stable conformers. The ability to identify and rank all of the relevant polymorphs of a given molecular crystal hinges on an accurate description of their relative energetic stability. Hence, a first-principles quantum mechanical method that can attain the required accuracy of around 0.1–0.2 kcalmol 1 would clearly be an indispensable tool for polymorph prediction. In this work, we show that accounting for the nonadditive many-body dispersion (MBD) energy beyond the standard pairwise approximation is crucial for the correct qualitative and quantitative description of polymorphism in molecular crystals. We demonstrate this through three fundamental and stringent benchmark examples: glycine, oxalic acid, and tetrolic acid. These systems represent a broad class of molecular crystals, comprising hydrogenbonded (H-bonded) networks of amino acids and carboxylic acids. Among the first-principles methods, density functional theory (DFT) is the most widely used approach in the study of polymorphism in molecular crystals. However, most common exchange-correlation functionals (including hybrid functionals) are based on semi-local electron correlation, and thereby fail to capture the contribution of dispersion interactions to the stability of molecular crystals. These ubiquitous noncovalent interactions are quantum mechanical in nature and correspond to the multipole moments induced in response to instantaneous fluctuations in the electron density. To incorporate these long-range electron correlation effects within DFT, significant progress has been made by using the standard C6/R 6 pairwise additive expression for the dispersion energy. Indeed, DFT with pairwise dispersion terms can yield accurate results when the energy differences between molecular crystal polymorphs are sufficiently large. Notably, Neumann et al. have achieved the highest success rate in the last two blind tests using such methods. However, these pairwise dispersion approaches, even when used in conjunction with state-of-the-art functionals, are still unable to reach the level of accuracy required to describe polymorphism in many relevant molecular crystals, including glycine and oxalic acid. Recently, a novel and efficient method for describing the many-body dispersion (MBD) energy has been developed, building upon the Tkatchenko–Scheffler (TS) pairwise method. Within the TS approach, the effective dispersion coefficients (C6) are calculated from the DFTelectron density, hence the effect of the local environment of an atom in a molecule is accurately accounted for by construction. The MBD method presents a two-fold improvement over the TS approach by including: 1) the long-range electrodynamic screening through the self-consistent solution of the dipole– dipole electric-field coupling equations for the effective polarizability, and 2) the non-pairwise-additive many-body dispersion energy to infinite order through diagonalization of the Hamiltonian corresponding to a system of coupled fluctuating dipoles. The inclusion of the MBD energy in DFT leads to a significant improvement in the binding energies between organic molecules, and for the cohesion of the benzene and oligoacene molecular crystals. The MBD energy, like the TS energy, can be added to any DFT functional, requiring only the adjustment of a single rangeseparation parameter per functional. [*] N. Marom, J. R. Chelikowsky Center for Computational Materials Institute for Computational Engineering and Sciences The University of Texas at Austin Austin, TX 78712 (USA) E-mail: noa@ices.utexas.edu