CASTEP
CASTEP is a commercial software package which uses density functional theory with a plane wave basis set to calculate the electronic properties of crystalline solids, surfaces, molecules, liquids and amorphous materials from first principles. The abbreviation stands for Cambridge Serial Total Energy Package. CASTEP permits geometry optimisation and finite temperature molecular dynamics with implicit symmetry and geometry constraints, as well as calculation of a wide variety of derived properties of the electronic configuration. CASTEP has been completely written for use on parallel computers by researchers at the Universities of York, Durham, St. Andrews, Cambridge and Rutherford Labs.
Theory and approximations
Starting from the many-body wavefunction, an adiabatic approximation is made with respect to the nuclear and electronic coordinates (the Born–Oppenheimer approximation). The code also makes use of Bloch's Theorem which means a wavefunction of a periodic system has a cell-periodic factor and a phase factor. The phase factor is represented by a plane wave. From the usage of Bloch's Theorem, it is ideal to write the wavefunction in plane waves for the cell-periodic factor and the phase factor. From this the basis functions are orthogonal and it is easy to perform a Fourier transform from real to reciprocal space and vice versa. Fast Fourier Transforms are used throughout the CASTEP code, as is the Ewald summation method for Coulombic energies. Along with plane waves and conjugate gradient minimisation, pseudopotentials are essential to the CASTEP code for reducing the computational expense of the calculation. Pseudopotentials replace the atomic nucleus and the core electrons by an effective numeric potential.
Geometry optimisation
Castep is capable of optimising the atomic geometry of a system in several different ways. The default is BFGS, whereby an approximation to the Hessian matrix is built up over successive electronic minimisation steps and used to find a search direction at each. Damped molecular dynamics is also possible and often quick to converge, sometimes even faster than BFGS, due to wavefunction extrapolation. Damped MD is most often chosen over BFGS, however, due to the possibility for non-linear ion constraints. A further alternative is the FIRE scheme, which takes approximately the same approach as damped MD, but based on slightly different methodology.