Abstract
The interpretation of crystal structures in terms of intermolecular interaction energies enables phase stability and polymorphism to be rationalized in terms of quantitative thermodynamic models, while also providing insight into the origin of physical and chemical properties including solubility, compressibility and host-guest formation. The Pixel method is a semi-empirical procedure for the calculation of intermolecular interactions and lattice energies based only on crystal structure information. Molecules are represented as blocks of undistorted ab initio molecular electron and nuclear densities subdivided into small volume elements called pixels. Electrostatic, polarization, dispersion and Pauli repulsion terms are calculated between pairs of pixels and nuclei in different molecules, with the accumulated sum equating to the intermolecular interaction energy, which is broken down into physically meaningful component terms. The MrPIXEL procedure enables Pixel calculations to be carried out with minimal user intervention from the graphical interface of Mercury, which is part of the software distributed with the Cambridge Structural Database (CSD). Following initial setup of a crystallographic model, one module assigns atom types and writes necessary input files. A second module then submits the required electron-density calculation either locally or to a remote server, downloads the results, and submits the Pixel calculation itself. Full lattice energy calculations can be performed for structures with up to two molecules in the crystallographic asymmetric unit. For more complex cases, only molecule-molecule energies are calculated. The program makes use of the CSD Python API, which is also distributed with the CSD.
Highlights
Intermolecular interactions control an enormous diversity of chemical and physical properties in solid materials including the phase adopted under a given set of applied conditions, the solubility and melting point, and thermodynamic properties such as lattice energy, hardness, thermal expansion, heat capacity and so on
The Pixel method, which was originally devised by Gavezzotti (2005, 2007, 2011), adopts a semi-empirical approach in which molecules in a crystal structure are represented by blocks of electron and nuclear density sub-divided into small cubic volume elements referred to as ‘pixels’
The first, SetupPixel, is executed from within Mercury and interprets the crystal structure and generates the input files required for the Pixel calculation
Summary
Intermolecular interactions control an enormous diversity of chemical and physical properties in solid materials including the phase adopted under a given set of applied conditions, the solubility and melting point, and thermodynamic properties such as lattice energy, hardness, thermal expansion, heat capacity and so on. While most quantum mechanical methods provide a single intermolecular energy, some, including symmetry-adapted perturbation theory (Hohenstein & Sherrill, 2012; Szalewicz, 2012), break the energy down into constituent electrostatic, polarization, dispersion and Pauli repulsion terms, providing insight into the physical nature of an interaction. Though these methods are a gold standard in the field, they too are time consuming for large molecules when applied at the most accurate level
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