# Accuracy and Limitations of the Pair‐Selected Multilevel Approach for DLPNO Coupled Cluster: Extensive Benchmark for Closed‐Shell Organic Reactions

## TL;DR

This paper evaluates a new computational method for predicting chemical reaction energies efficiently and accurately, with most results within chemical accuracy.

## Contribution

The study introduces a pair-selected multilevel approach for DLPNO-CCSD(T0) with semi-canonical triples correction, showing improved efficiency and accuracy for organic reactions.

## Key findings

- The pair-selected multilevel approach achieves chemical accuracy (within 4 kJ mol−1) for most closed-shell organic reactions.
- Significant time benefits are observed with the multilevel approach compared to standard methods.
- Error cancellation between DLPNO and multilevel contributions is observed in several cases.

## Abstract

Reliable approximations to coupled‐cluster (CC) methods are highly desirable for accurate yet efficient computations of barrier heights, reaction energies, and other molecular properties. Among these methods, domain‐based local pair natural orbital CC with singles, doubles, and perturbative triple excitations [DLPNO‐CCSD(T)] is widely used due to its formal linear scaling with the system size. However, since DLPNO‐CCSD(T) remains costly, the extension to multilevel (ML) variants becomes an obvious route. This strategy can be made even more economic with the pair‐selected ML ansatz [M. Bensberg and J. Neugebauer, J. Chem. Phys. 157, 064102 (2022)] to DLPNO‐CCSD(T0) with a semi‐canonical (SC) perturbative triples correction. This ansatz uses an automatic partitioning of orbital pairs according to their contribution to the overall correlation energy change in a chemical reaction. Herein, the advantages of this approach are demonstrated for closed‐shell organic reactions of the BH9 test set. The errors are nearly always within chemical accuracy (4 kJ mol−1) along with a significant time benefit. In rare cases, larger errors are observed. These are analyzed by comparison of SC and iterative perturbative triples, of different ML thresholds, and of ML and single‐level schemes. A beneficial error cancelation between DLPNO and ML contributions is also observed in several cases.

This graphic shows the error distribution for pericyclic reactions calculated with the multilevel approach under investigation and illustrates that outliers are critically analyzed using different approximations for the triples correction.© 2026 WILEY‐VCH GmbH