MERCE: Method-Space Correlation Energy Extrapolation toward High-Rank Coupled Cluster Accuracy
Abstract
Energy extrapolation is a well-established strategy for approaching quantum-chemical limits without performing prohibitively expensive calculations. Complete basis set extrapolation is widely used, whereas extrapolation across electronic structure methods remains much less developed. Method-Space Effective-Rank Correlation Energy Extrapolation (MERCE) is introduced as an adaptive effective-rank framework for estimating high-rank finite-basis correlation energies from second-order Moller-Plesset perturbation theory (MP2), coupled cluster with single and double excitations (CCSD), and CCSD with perturbative triples [CCSD(T)]. The method assigns adaptive effective ranks to MP2 and CCSD(T) from the local MP2-CCSD-CCSD(T) correlation energy pattern and fits a compact three-point extrapolation form for each system. A hierarchical model-selection protocol balances cross-dataset transferability, maximum dataset-level mean absolute error (MAE) ratios, robustness on developmental sets referenced to full configuration interaction (FCI), size-consistency defects, and performance for A24 noncovalent interaction energies. Across the chemically diverse benchmarks used during model development, the selected MERCE model substantially reduces CCSD(T) errors and frequently improves upon the tested higher-rank coupled cluster baselines. Transferability is further assessed using calculations performed only after the functional form and parameters were frozen. Formal nonadditivity is quantified using artificial noninteracting pairs and the actual A24 and selected S66 component calculations.
Related
- Coupled Cluster Amplitude Extrapolation in Geometry Optimization
- Bringing coupled‑cluster theory to the strong-correlation frontier
- Absorption and Emission Spectra in Aqueous Solution with Coupled-Cluster Accuracy
- Tailored coupled cluster method with sample-based quantum diagonalization: Application to titanium-based metallocene catalytic reactions for 1-hexene production
- Reduced scaling implementation of the coupled cluster-based static embedding method, MPCC with density fitting
BibTeX
@misc{witkowski2026merce,
title = {{MERCE: Method-Space Correlation Energy Extrapolation toward High-Rank Coupled Cluster Accuracy}},
author = {Mateusz Witkowski and Szymon Śmiga and Pavlo O. Dral and Ireneusz Grabowski},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.12315},
eprint = {2610.12315},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.12315},
}
RIS
TY - UNPB
TI - MERCE: Method-Space Correlation Energy Extrapolation toward High-Rank Coupled Cluster Accuracy
AU - Mateusz Witkowski
AU - Szymon Śmiga
AU - Pavlo O. Dral
AU - Ireneusz Grabowski
PY - 2026
DA - 2026/10/08
PB - arXiv
DO - 10.48550/arxiv.2610.12315
UR - https://arxiv.org/abs/2610.12315
AB - Energy extrapolation is a well-established strategy for approaching quantum-chemical limits without performing prohibitively expensive calculations. Complete basis set extrapolation is widely used, whereas extrapolation across electronic structure methods remains much less developed. Method-Space Effective-Rank Correlation Energy Extrapolation (MERCE) is introduced as an adaptive effective-rank framework for estimating high-rank finite-basis correlation energies from second-order Moller-Plesset perturbation theory (MP2), coupled cluster with single and double excitations (CCSD), and CCSD with perturbative triples [CCSD(T)]. The method assigns adaptive effective ranks to MP2 and CCSD(T) from the local MP2-CCSD-CCSD(T) correlation energy pattern and fits a compact three-point extrapolation form for each system. A hierarchical model-selection protocol balances cross-dataset transferability, maximum dataset-level mean absolute error (MAE) ratios, robustness on developmental sets referenced to full configuration interaction (FCI), size-consistency defects, and performance for A24 noncovalent interaction energies. Across the chemically diverse benchmarks used during model development, the selected MERCE model substantially reduces CCSD(T) errors and frequently improves upon the tested higher-rank coupled cluster baselines. Transferability is further assessed using calculations performed only after the functional form and parameters were frozen. Formal nonadditivity is quantified using artificial noninteracting pairs and the actual A24 and selected S66 component calculations.
ER -