A Master-Worker Type Eigensolver for Molecular Orbital Computations

We consider a parallel method for solving generalized eigenvalue problems that arise from molecular orbital computations. We use a moment-based method that finds several eigenvalues and their corresponding eigenvectors in a given domain, which is suitable for masterworker type parallel programming models. The computation of eigenvalues using explicit moments is sometimes numerically unstable. We show that a Rayleigh-Ritz procedure can be used to avoid the use of explicit moments. As a test problem, we use the matrices that arise in the calculation of molecular orbitals. We report the performance of the application of the proposed method with several PC clusters connected through a hybrid MPI and GridRPC system.