Double configuration interaction singles: Scalable and size-intensive approach for orbital relaxation in excited...

We present a novel theoretical scheme for orbital relaxation in configuration interaction singles (CIS) based on a perturbative treatment of its electronic Hessian, whose analytical derivation is also established in this work. The proposed method, which can be interpreted as a "CIS-then-CIS" scheme, variationally accounts for orbital relaxation in excited states, thus significantly reducing the overestimation of charge-transfer excitation energies commonly associated with standard CIS. In addition, by incorporating de-excitation effects from CIS, we demonstrate that our approach effectively describes single bond dissociation. Notably, all these improvements are achieved at a mean-field cost, with the pre-factor further reduced with the efficient algorithm introduced here, while preserving the size-intensive property of CIS.