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arXiv · 2610.37221

Multireference Second-Order Perturbation Theories Based on Iterative Configuration Interaction with Selection

Ning Zhang·Wenjian Liu
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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 ($P_m$) and a secondary ($P_s$) subspace via a parameter $C_{\mathrm{min}}$. 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 $Q_{\mathrm{min}}$, which are to be treated in coupled and uncoupled manners, respectively. Extrapolations to zero $Q_{\mathrm{min}}$ and $C_{\mathrm{min}}$ 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.

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Ning Zhang, Wenjian Liu. 2026-10-27. Multireference Second-Order Perturbation Theories Based on Iterative Configuration Interaction with Selection. https://arxiv.org/abs/2610.37221

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