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We present two open-source implementations of the Locally Optimal BlockPreconditioned Conjugate Gradient (LOBPCG) algorithm to find a few eigenvaluesand eigenvectors of large, possibly sparse matrices. We then test LOBPCG forvarious quantum chemistry problems, encompassing medium to large, dense tosparse, wellbehaved to ill-conditioned ones, where the standard methodtypically used is Davidson's diagonalization. Numerical tests show that, whileDavidson's method remains the best choice for most applications in quantumchemistry, LOBPCG represents a competitive alternative, especially when memoryis an issue, and can even outperform Davidson for ill-conditioned, nondiagonally dominant problems.

A robust, open-source implementation of the locally optimal block  preconditioned conjugate gradient for large eigenvalue problems in quantum  chemistry