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