Perturbatively Corrected Linear Response Selected Configuration Interaction

Abstract: Selected configuration interaction (SCI) methods have emerged as powerful, lower-cost alternatives to full configuration interaction (FCI) for ground- and excited-state energies. Still, calculating molecular response properties with SCI remains a significant challenge. In this work, we introduce perturbative corrections to the linear response selected configuration interaction (LR-SCI) framework, using an order-by-order Epstein-Nesbet perturbation expansion through second order. We demonstrate that in this theoretical framework, the finite-order perturbative treatment preserves the pole structure of the parent variational LR-SCI theory, which means that although the method can be useful for static properties, it is not suitable for frequency-dependent molecular response properties. Numerical benchmarks targeting the static polarizabilities of water, ethene, boron hydride, and hydrogen chloride demonstrate systematic convergence toward the FCI limit for both ground and excited electronic states. While first-order corrections yield marginal improvements, the inclusion of second-order corrections substantially enhances accuracy over underlying variational treatments and diminishes oscillatory convergence behavior present in the parent variational LR-SCI method. Combined with extrapolation techniques, LR-SCI-PT achieves excellent agreement with high-level coupled-cluster references, establishing a powerful route toward near-FCI quality molecular properties for systems otherwise inaccessible to exact FCI treatments.