PASPT2: a novel size-extensive and size-consistent partial-active-space multi-state multi-reference second-order perturbation theory for strongly correlated electrons

TL;DR

The paper introduces PASPT2, a size-extensive and size-consistent partial-active-space MS-MRPT2 built on the IN-GMS-SU-CCSD framework with an intermediate normalization and connectivity constraints. By employing a reference-specific zeroth-order Hamiltonian and a closed, connected intermediate Hamiltonian, PASPT2 achieves robust, intruder-free dynamic correlation corrections for strongly correlated systems. The approach is validated on prototypical systems, showing size-extensivity (e.g., He chains) and competitive accuracy for H$_2$O vertical excitations and N$_2$ potential-energy curves, with improved stability when using the extended intermediate space $\mathcal{M}_X$. The work highlights PASPT2 as a unique, spin-adaptation-ready method that combines PAS-based flexibility with rigorous size properties, paving the way for reliable treatments of large, strongly correlated electronic systems.

Abstract

A partial-active-space (PAS) multi-state (MS) multi-reference second-order perturbation theory (MRPT2) for the electronic structure of strongly correlated systems of electrons, dubbed PASPT2, is formulated by linearizing the intermediate normalization-based general-model-space state-universal coupled-cluster theory with singles and doubles [IN-GMS-SU-CCSD; J. Chem. Phys. 119, 5320 (2003)]. At variance with the existence of disconnected terms in the IN-GMS-SU-CCSD amplitude equations, the disconnected terms in the PASPT2 amplitude equations can be avoided completely by choosing a special reference-specific zeroth-order Hamiltonian. The corresponding effective/intermediate Hamiltonian can also be made connected and closed, so as to render the energies obtained by diagonalization fully connected. As such, PASPT2 is strictly size-extensive, in sharp contrast with the parent IN-GMS-SU-CCSD. It is also size-consistent when the PAS of a supermolecule is chosen to be the direct product of those of the physically separated, non-interacting fragments. Prototypical systems are taken as showcases to reveal the efficacy of PASPT2.

Figures (9)

• Figure 1: Classification of molecular spin orbitals with respect to the reference NED $|\alpha\rangle$.
• Figure 2: Diagrammatic representation of one-body cluster operators with $|\alpha\rangle$ as the Fermi vacuum. Up/down-going arrows denote particles/holes; double arrows denote active particles/holes.
• Figure 3: Diagrammatic representation of two-body cluster operators with $|\alpha\rangle$ as the Fermi vacuum. Up/down-going arrows denote particles/holes; double arrows denote active particles/holes. In parentheses are the degenerate manifolds of the diagrams.
• Figure 4: $Q$- and $P$-space couplings to the $t_l(\alpha)$-amplitudes of external excitations $\{\chi_{l\alpha}\}$ from the reference NED $|\alpha\rangle$ (i.e., processes for the dynamic correlation correction to $|\alpha\rangle$).
• Figure 5: Diagrammatic representation of $\bar{H}^{\mathrm{eff}[2]}_1$ [(1a)--(1g)], $\bar{H}^{\mathrm{eff}[2]}_2$ [(2a)--(2h)] and $\bar{H}^{\mathrm{eff}[2]}_3$ [(3a),(3b)] with $|\alpha\rangle$ as the Fermi vacuum. After the semicolons are the degenerate manifolds of the diagrams.