Efficient variable cell shape geometry optimization

A fast and reliable geometry optimization algorithm is presented that optimizes atomic positions and lattice vectors simultaneously. Using a series of benchmarks, it is shown that the method presented in this paper outperforms in most cases the standard optimization methods implemented in popular codes such as QUANTUM ESPRESSO and VASP. To motivate the variable cell shape optimization method presented in here, the eigenvalues of the lattice Hessian matrix are investigated thoroughly. It is shown that they change depending on the shape of the cell and the number of particles inside the cell. For certain cell shapes the resulting condition number of the lattice matrix can grow quadratically with respect to the number of particles. By a coordinate transformation which can be applied to all variable cell shape optimization methods, the undesirable conditioning of the lattice Hessian matrix is eliminated.