Integer programming for crystal structure prediction

The task of finding a periodic allocation of atoms on a grid in space that minimises their pairwise interaction energy can be encoded as an integer program. Such integer program can be solved either using advanced solvers to obtain provably optimal solutions or using quantum annealers (or any other Ising machine) for a potential speed-up or energy efficiency. Subsequently, solutions of the periodic lattice allocation problems can be used to predict crystal structures of materials or perform other investigations of the potential energy surfaces.

This package provides implementation of this encoding for uniform grids in cubic unit cells, where the interaction energy is a sum of periodic Coulombic interaction computed using Ewald summation method and Buckingham repulsion. An example of interaction potential is provided for Ca-Al-Si-O phase field. In the current implementation, the resulting integer programs can be solved either using Gurobi or D-Wave quantum annealer.

If the package is run as a module, then crystal structure prediction of several well-known crystal structures is performed. Solutions of integer programs are reported alongside the outcomes of subsequent local minimisations and the expected outcomes.

Installation

Dependencies

On top of the commonly used python packages, the code relies on:

• Gurobi to solve integer programs on classical computers (tested with v9.5). Academic licence is available free of charge.
• D-Wave Leap and its SDK to solve quadratic unconstrained binary problems (tested with dwave-ocean-sdk v2.0.1 and v5.0.0). A limited time on a quantum annealer is available each month for free. Classical simulation annealing algorithm is available as well in the same package for testing purposes and requires no registration.
• GULP for subsequent local minimisations of periodic lattice allocations (tested with 5.2).
• Atomic Simulation Environment to run GULP calculations and handle crystal files.

Package

It can be installed using pip:

pip install -e [email protected]:lrcfmd/ipcsp.git#egg=ipcsp

It will create a local copy of the repository and install the package. Alternatively, you can clone it as well.

Usage

The code can be run as a module:

python -m ipcsp

It will perform prediction of a variety of cubic crystal structures. The corresponding experimentally determined structures are stored in data/structures. Crystal structure prediction problems to run can be selected by modifying test key in the settings dictionary defined in __main__.py as well as other parameters of the corresponding lattice allocation problems.

For every phase field, grid and unit cell sizes the package will store the interaction values between different pairs of atoms and positions for subsequent use. Thus, repeated runs for another space group or composition are usually faster.

Citation

This research code is written to accompany the paper "Optimality guarantees for crystal structure prediction" and this version will not be further updated except for minor corrections.