CIS(2): a state-specific, size-intensive perturbative correction to configuration interaction singles

We present a state-specific second-order perturbation theory based on a configuration interaction singles (CIS) reference and its generalized Fock operator. Starting from a fully internally contracted construction, we retain the complete doubles space and internally contracted triples in the first-order wave function. We consider two partitions, Canonical and Block-diagonal, with reference excitation energies given by the Fock excitation gap $ω^{(0)}$ and the CIS excitation energy $ω_{\rm CIS}$, respectively. Our analysis establishes that strict size-intensivity is preserved when the contracted-triples denominators use bare Fock gaps and the occupied--virtual Fock block is projected to remove residual spectator coupling. Based on this observation, combining Canonical triples with Block-diagonal doubles yields a size-intensive Hybrid partition. These properties are verified for water with non-interacting helium atoms. Our formulation enables $O(o^3v^2)$ cost per matrix--vector product in a semicanonical basis. On the QUEST#1 benchmark, Canonical and Block-diagonal show opposite systematic biases, whereas Hybrid gives the best overall accuracy among the three partitions. Its mean absolute errors for singlets and triplets are 0.24 and 0.15eV, compared with 0.28 and 0.22eV for CIS(D). The improvement is largest for Rydberg excitations, although CIS(D) remains more accurate for valence singlets.

Source: arXiv:2610.03583v1 - http://arxiv.org/abs/2610.03583v1 PDF: https://arxiv.org/pdf/2610.03583v1 Original Link: http://arxiv.org/abs/2610.03583v1