The Dose Makes the Poison: Perturbative Steps Toward the Ultimate Linearized Coupled Cluster Method

TL;DR

The paper tackles the difficulty of accurately describing strongly correlated systems with single-reference coupled cluster methods by augmenting a linearized CCD framework. It introduces xlinCCD(2), a linearized external CC perturbation theory that reintroduces ring and crossed-ring correlation on top of a linLCCD reference via a dressed Hamiltonian, yielding a regular, CCD-like description across challenging regimes. The approach demonstrates robust performance on diverse systems, including diatomics, transition metals, and model Hamiltonians, and shows size-consistency with potential one-shot implementations and extensions to xlinCCSD(2). This work broadens the applicability of linearized CC methods to strongly correlated chemistry, offering a practical path to balanced dynamical and static correlation at reduced cost.

Abstract

"Addition-by-subtraction" coupled cluster (CC) approaches provide a promising approach to treating the difficult strong correlation problem by simplifying the standard CC equations. In a separate vein, linearized CC methods have drawn interest for their lower computational cost, increased parallelizability, and favorable properties for extension to the excited state--but the inclusion of ring/crossed-ring terms causes singularities even for single bond breaking. A linearized, addition-by-subtraction CC method called linearized ladder CCD (linLCCD) removes these terms to avoid divergences, but linLCCD under-estimates dynamical correlation. Herein we resolve this deficiency of linLCCD by introducing a linearized external coupled cluster perturbation theory that adds a second-order ring/crossed-ring correction back into a linLCCD reference wave function. Our resultant xlinCCD(2) method is regular and yields comparable results to linearized CCD in weakly-correlated regimes.

Figures (4)

• Figure 1: Ground state dissociation curves of (a) H$_2$, (b) FH, (c) CO$_2$ undergoing symmetric stretch, and (d) spatially symmetry-adapted N$_2$. The dotted horizontal lines indicate asymptotic limits estimated at 100 Å, except for the case of CCDf1, where the limit was estimated at 12 Å.
• Figure 2: Ground state dissociation curves for Cu$_2$. The dotted horizontal lines indicate the methods' asymptotic limits calculated at $100$ Å. The experimental dissociation energy is shown as a black line, with experimental uncertainty as a gray region.DroHon57
• Figure 3: Ground state energies as a function of interaction strength ($U/|t=-1.5|$) for a 10-site, half-filled Hubbard model with open boundary conditions. The exact reference is the FCI result.
• Figure 4: Root-mean-square error (eV) (colored bars) and maximum errors (gray bars) for the lowest energy singlet/triplet gaps of 25 transition metal diatomics as computed by $\Delta$CC and $\Delta$MP2 methods.