Analytic Gradients for Selected Configuration Interaction

We develop analytic gradients for selected configuration interaction wave functions. Despite all pairs of molecular orbitals now potentially having to be considered for the coupled perturbed Hartree-Fock equations, we show that degenerate orbital pairs belonging to different irreducible representations in the largest abelian subgroup do not need to be included and instabilities due to degeneracies are avoided. We introduce seminumerical gradients and use them to validate the analytic approach even when near degeneracies are present due to high-symmetry geometries being slightly distorted to break symmetry. The method is applied to carbon monoxide, ammonia, square planar H₄, hexagonal planar H₆, and methane for a range of bond lengths where we demonstrate that analytic gradients for selected configuration interaction can approach the quality of full configuration interaction yet only use a very small fraction of its determinants.