The problem is formally equivalent to a nonlinear eigenvalue problem, where the matrix depends on the eigenvectors and eigenvalues. The matrix is a hermitian Hamilton operator. The use of the separable Kleinman-Bylander pseudopotentials allows us to efficiently compute the gradient, and avoids the storage of large matrices. When computing the gradient, a three-dimensional FFT is involved. The dimensionality of the search space for the conjugate-gradient minimization is very large.
Typical problems require a search space of dimensions from a few thousands to a few million.
The employed algorithms rank among the most efficient schemes known today. Paratec is used by about six members of our group, mainly to perform calculation s on fullerenes, ultra-hard materials research and computations of the NMR chemical shift. J. Ihm, A. Zunger, and M. L. Cohen, J. Phys. We use calls to native library routines to get high single-node performance. The code has been parallelized using explicit message passing with the MPI library.