Exploiting sparsity in the graphically contracted function configuration interaction method

Within the graphically contracted function configuration interaction method, the wave function and energy depend on a set of nonlinear variables known as arc factors. In previous work, an efficient algorithm for computing the energy gradient with respect to these variables has been presented. In this work we discuss further improvements of the algorithm by exploiting the sparsity of the orbital-level Hamiltonian matrices. For large wave function expansions, the new algorithm is faster and requires significantly less storage than the previous implementation. In addition, the implementation of a generalized Davidson method for computing optimal arc factors within a given orbital level is discussed. Although the orbital-level Hamiltonian matrices are in general not diagonally dominant, the iterative solver converges in a reasonable number of iterations and is several orders of magnitude faster than standard diagonalization methods.