Second-Order Orbital Optimization with Large Active Spaces Using Adaptive Sampling Configuration Interaction (ASCI) and Its Application to Molecular Geometry Optimization.

Recently, selected configuration interaction (SCI) methods that enable calculations with several tens of active orbitals have been developed. With the SCI subspace embedded in the mean field, molecular orbitals with an accuracy comparable to that of the complete active space self-consistent field method can be obtained. Here, we implement the analytical gradient theory for the single-state adaptive sampling CI (ASCI) SCF method to enable molecular geometry optimization. The resulting analytical gradient is inherently approximate due to the dependence on the sampled determinants, but its accuracy was sufficient for performing geometry optimizations with large active spaces. To obtain the tight convergence needed for accurate analytical gradients, we combine the augmented Hessian (AH) and Werner-Meyer-Knowles (WMK) second-order orbital optimization methods with the ASCI-SCF method. We test these algorithms for orbital and geometry optimizations, demonstrate applications of the geometry optimizations of polyacenes and periacenes, and discuss the geometric dependence of the characteristics of singlet ASCI wave functions.