Random phase approximation-based local natural orbital coupled cluster theory

TL;DR

The paper replaces MP2 with random phase approximation (RPA) as the low-level theory in local natural orbital CC (LNO-CC) embedding, using direct ring CCD (drCCD) amplitudes and an external correction scheme. RPA-based LNO-CCSD and LNO-CCSD(T) reproduce MP2-based results for systems with sizable gaps while delivering notably faster convergence toward the canonical CC limit for metallic systems, particularly as the thermodynamic limit is approached; applying SOSEX as the external correction often yields chemical accuracy with far fewer active LNOs. Benchmark results on coronene dimer, anthracene crystal, and bulk metals (Li and Cu) show that RPA-derived LNOs are competitive in short-range correlation, and that composite corrections based on RPA and SOSEX outperform MP2-based corrections in many metallic cases. The study highlights the critical influence of the chosen low-level theory on fragment-embedding performance and positions RPA as a compelling alternative to MP2 for efficient, accurate high-level calculations in complex molecular and condensed-phase systems.

Abstract

Practical applications of fragment embedding and closely related local correlation methods critically depend on a judicious choice of a low-level theory to define the local embedding subspace and to capture long-range electrostatic and correlation effects outside the embedding region. Second-order Møller-Plesset perturbation theory (MP2) is by far the most widely used correlated low-level theory; however, its applicability becomes questionable in systems where MP2 is known to fail either quantitatively or qualitatively. In this work, we present the random phase approximation (RPA) as a promising alternative low-level theory to MP2 within the local natural orbital-based coupled-cluster (LNO-CC) framework. We demonstrate that RPA-based LNO-CC closely matches the performance of its MP2-based counterpart for systems with sizable energy gaps, while delivering significantly faster convergence toward the canonical coupled-cluster limit for metallic systems, particularly as the thermodynamic limit is approached. These results highlight the critical role of the low-level theory in fragment embedding and local correlation methods and identify RPA as a compelling alternative to the commonly used MP2.

Figures (3)

• Figure 1: (A--C) Convergence of MP2- and RPA-based LNO-CCSD(T) correlation energies (A), binding energies (B), and extrapolated binding energies (C) for the coronene dimer in the parallel-displaced (C2C2PD) configuration as a function of the maximum LAS size, measured by the number of active LNOs. (D--F) Corresponding results for the anthracene molecular crystal with $\Gamma$-point Brillouin zone sampling, where the lattice energy replaces the binding energy. In (A,B,D,E), open and filled symbols denote LNO-CCSD(T) results obtained without and with the external correction $\Delta E_{\mathrm{c}}^{\mathrm{ext}}$, respectively. In (C,F), extrapolated values are obtained using \ref{['eq:Ec_extrap_ext']} based on two adjacent LNO thresholds; the abscissa indicates the LAS size associated with the tighter threshold. The best estimate of the canonical CCSD(T) result, obtained by averaging the best extrapolations from both MP2- and RPA-based LNO constructions, is shown as a horizontal dashed line in each panel. The gray shaded region in each panel represents an error window of $\pm 1$ kcal/mol relative to the corresponding reference value. All calculations employ all-electron cc-pVTZ basis sets with the $1s^2$ core electrons of carbon frozen. The total orbital count (excluding frozen orbitals) is $1776$ for C2C2PD and $1120$ per unit cell of the anthracene crystal. The binding energy $E_{\mathrm{bind}}$ and lattice energy $E_{\mathrm{lat}}$ are counterpoise-corrected.
• Figure 2: Convergence of MP2-, RPA-, and SOSEX-based LNO-CCSD correlation energies per atom as a function of the maximum LAS size for (A) body-centered cubic (BCC) Li with a $3\times3\times3$$k$-mesh and a lattice constant of $3.51$ Å, and (B) face-centered cubic (FCC) Cu with a $2\times2\times2$$k$-mesh and a lattice constant of $3.615$ Å. The Li calculations employ the GTH-cc-pVTZ basis sets, while the Cu calculations use the all-electron cc-pVTZ basis sets optimized in this work. Open and filled symbols denote LNO-CCSD results obtained without and with the external energy correction, respectively. The uncorrected SOSEX-based LNO-CCSD results are identical to the uncorrected RPA-based results and are therefore not shown. The best estimate of the canonical CCSD correlation energy, obtained by averaging the best extrapolated values from all three methods using \ref{['eq:Ec_extrap_ext']}, is indicated by a horizontal dashed line in each panel. The gray shaded region represents an error window of $\pm 1$ kcal/mol relative to the corresponding reference value.
• Figure 3: Convergence of LNO-CCSD correlation energies for BCC Li as a function of the maximum LAS size using RPA-derived LNOs with different external corrections $\Delta E_{\mathrm{c}}^{\mathrm{ext}}$, for (A) $2\times2\times2$, (B) $3\times3\times3$, and (C) $4\times4\times4$$k$-point meshes. All $k$-meshes are shifted from the $\Gamma$ point by $\bm{k}^* = \frac{2\pi}{L}(\frac{1}{4},\frac{1}{4},\frac{1}{4})$, where $L = N_k^{1/3} a$ and $a=3.51$ Å is the lattice constant. All calculations employ the GTH-cc-pVDZ basis sets. In panels (A) and (B), the horizontal solid lines indicate reference values obtained from canonical $k$-point CCSD calculations. In panel (C), the horizontal dashed line denotes our best extrapolated estimate obtained using \ref{['eq:Ec_extrap_ext']} with the SOSEX external correction [\ref{['eq:Ec_ext_SOSEX']}]. The gray shaded region in each panel represents an error window of $\pm 1$ kcal/mol relative to the corresponding reference value.