CIS(2): a state-specific, size-intensive perturbative correction to configuration interaction singles
Abstract
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 ωCIS, 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(o3v2) 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 0.15~eV, compared with 0.28 and 0.22~eV for CIS(D). The improvement is largest for Rydberg excitations, although CIS(D) remains more accurate for valence singlets.
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BibTeX
@misc{tsuchimochi2026cis2,
title = {{CIS(2): a state-specific, size-intensive perturbative correction to configuration interaction singles}},
author = {Takashi Tsuchimochi},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.03583},
eprint = {2610.03583},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.03583},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - CIS(2): a state-specific, size-intensive perturbative correction to configuration interaction singles
AU - Takashi Tsuchimochi
PY - 2026
DA - 2026/10/02
PB - arXiv
DO - 10.48550/arxiv.2610.03583
UR - https://arxiv.org/abs/2610.03583
AB - 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_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 0.15~eV, compared with 0.28 and 0.22~eV for CIS(D). The improvement is largest for Rydberg excitations, although CIS(D) remains more accurate for valence singlets.
ER -