Multireference Second-Order Perturbation Theories Based on Iterative Configuration Interaction with Selection
Abstract
Under the assumption that the static correlation can well be described by selected configuration interaction, to the extent that the residual dynamic correlation can be accounted for accurately by a second-order perturbation theory (PT2), a family of multireference PT2s (iCI-MRPT2) based on the iterative configuration interaction with selection are proposed and compared. The first step is to partition a large complete active space (CAS) P into the direct sum of a primary (Pm) and a secondary (Ps) subspace via a parameter Cmin. The former serves as the actual reference space, whereas the latter is treated via Epstein-Nesbet PT2. An MRPT2 is then invoked to account for the dynamic correction of the Q=1−P space to the Pm space. Different MRPT2s are distinguished by the underlying zeroth-order Hamiltonians. To circumvent the prohibitive computational cost and memory footprint associated with high-order reduced density matrices in the fully internally contracted scheme and the exponential growth of external functions (XF) in the uncontracted scheme, a partial contraction strategy is employed for constructing the XFs: those involving one or two inactive (core or virtual) orbitals are kept uncontracted, whereas those involving three or four inactive orbitals are internally contracted. They span the uncontracted (Qu) and contracted (Qc) portions of Q, respectively. The former is further split into two subspaces Quc and Quu via a parameter Qmin, which are to be treated in coupled and uncoupled manners, respectively. Extrapolations to zero Qmin and Cmin can be performed, so as to approach CAS-based MRPT2. Calculations with active spaces as large as CAS(56e,58o) can now be performed. The size-consistency of the iCI-MRPT2s is also analyzed in detail.
Related
- State-specific perturbation theory for configuration interaction singles: Theoretical analysis, benchmarks, and improvement with size-intensive level shifts
- Accelerated Quantum-Assisted Selected Configuration Interaction via Fast-Annealing-Based Determinant Selection
- Multireference perturbation theory with nonorthogonal determinants
- Universal Interatomic Potentials as Configuration-Space Generators for One-Shot and Iterative Fine-Tuning of Ab Initio-Accurate Material-Specific Models
- Basis pruning in rovibrational configuration interaction (RVCI) calculations
BibTeX
@misc{zhang2026multireference,
title = {{Multireference Second-Order Perturbation Theories Based on Iterative Configuration Interaction with Selection}},
author = {Ning Zhang and Wenjian Liu},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.37221},
eprint = {2610.37221},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.37221},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Multireference Second-Order Perturbation Theories Based on Iterative Configuration Interaction with Selection
AU - Ning Zhang
AU - Wenjian Liu
PY - 2026
DA - 2026/10/27
PB - arXiv
DO - 10.48550/arxiv.2610.37221
UR - https://arxiv.org/abs/2610.37221
AB - Under the assumption that the static correlation can well be described by selected configuration interaction, to the extent that the residual dynamic correlation can be accounted for accurately by a second-order perturbation theory (PT2), a family of multireference PT2s (iCI-MRPT2) based on the iterative configuration interaction with selection are proposed and compared. The first step is to partition a large complete active space (CAS) P into the direct sum of a primary (P_m) and a secondary (P_s) subspace via a parameter C_min. The former serves as the actual reference space, whereas the latter is treated via Epstein-Nesbet PT2. An MRPT2 is then invoked to account for the dynamic correction of the Q=1−P space to the P_m space. Different MRPT2s are distinguished by the underlying zeroth-order Hamiltonians. To circumvent the prohibitive computational cost and memory footprint associated with high-order reduced density matrices in the fully internally contracted scheme and the exponential growth of external functions (XF) in the uncontracted scheme, a partial contraction strategy is employed for constructing the XFs: those involving one or two inactive (core or virtual) orbitals are kept uncontracted, whereas those involving three or four inactive orbitals are internally contracted. They span the uncontracted (Q_u) and contracted (Q_c) portions of Q, respectively. The former is further split into two subspaces Q_u^c and Q_u^u via a parameter Q_min, which are to be treated in coupled and uncoupled manners, respectively. Extrapolations to zero Q_min and C_min can be performed, so as to approach CAS-based MRPT2. Calculations with active spaces as large as CAS(56e,58o) can now be performed. The size-consistency of the iCI-MRPT2s is also analyzed in detail.
ER -