Method for energy ranking of molecular crystals using dft calculations and empirical van der waals potentials

A method for the efficient numerical optimization of a molecular crystal structure using an advantageous crystal coordinate system, comprising the steps of:

• providing a starting crystal lattice described by an initial coordinate system comprising lattice parameters and atomic positions in said crystal;
• defining a so-called natural coordinate system and representing said starting crystal lattice in said natural coordinate system, said natural coordinate system comprising:
• first coordinates describing symmetry-allowed lattice changes and defined in such a way that changes of said first coordinates do not cause changes of the molecular geometry or a rotation of molecules with respect to each other and leave fractional coordinates of molecular centres constant;
• second coordinates describing symmetry-allowed translations of said molecules in said crystal;
• third coordinates describing symmetry-allowed rotations of said molecules in said crystal;
• fourth coordinates describing symmetry-allowed changes of the molecular geometry;
• transforming coordinates from said natural coordinate system to said initial coordinate system;
• calculating the lattice energy and energy derivatives with respect to said initial coordinate system;
• and
• transforming said energy derivatives from said initial coordinate system to said natural coordinate system,
• wherein a minimization algorithm is used for minimizing said lattice energy with respect to said natural coordinate system.

A method for the energy ranking of polymorphic crystal structures, comprising the steps of:

• providing rough estimate models of each of said crystal structures;
• numerically simulating each of said crystal structures based on density functional theory (DFT) calculations combined with a potential energy term representing Van der Waals interactions
• obtaining accurate crystal structures and energies as a result of said numerical simulation;
• and
• ranking said accurate crystal structures according to their respective accurate energies.