# Machine-Learning Interatomic Potentials Achieving CCSD(T) Accuracy for Systems with Extended Covalent Networks and van der Waals Interactions

## TL;DR

This paper introduces a machine-learning method to simulate complex materials with high accuracy, including covalent networks and van der Waals forces.

## Contribution

A novel Δ-learning strategy enables CCSD(T)-level accuracy for extended covalent systems using compact molecular fragments.

## Key findings

- The MLIP achieves root-mean-square energy errors below 0.4 meV/atom for training and test sets.
- The method accurately reproduces atomization energies, bond lengths, and intermolecular interactions.
- The approach successfully models a covalent organic framework with CCSD(T) accuracy.

## Abstract

Machine-learning interatomic potentials (MLIPs) enable
large-scale
atomistic simulations at moderate computational cost while retaining ab initio accuracy. In recent years, MLIPs trained on coupled-cluster
dataparticularly CCSD­(T), which includes single, double, and
perturbative triple excitationshave emerged as a promising
route to achieve chemical accuracy (1 kcal/mol) beyond the
limits of density functional theory (DFT) and to incorporate nonempirical
van der Waals (vdW) interactions. Most existing approaches are, however,
still not straightforwardly applicable for systems with extended covalent
networks such as covalent organic frameworks (COFs) due to the limited
availability of CCSD­(T) under periodic boundary conditions. Here we
present a methodology to train MLIPs with CCSD­(T) accuracy for systems
with extended covalent networks. The approach is based on the Δ-learning
method with a dispersion-corrected tight-binding baseline and an MLIP
trained on the differences of the target CCSD­(T) energies from the
baseline. This Δ-learning strategy enables training on compact
molecular fragments while preserving transferability toward the periodic
systems. Dispersion interactions are accounted for by including vdW-bound
multimers in the training set, and the combination with a vdW-aware
tight-binding baseline allows the formally local MLIP to attain CCSD­(T)-level
accuracy even for systems dominated by long-range vdW forces. The
resulting potential yields root-mean-square energy errors below 0.4 meV/atom
on both training and test sets and reproduces electronic total atomization
energies, bond lengths, harmonic vibrational frequencies, and intermolecular
interaction energies for benchmark molecular systems. We apply the
method to a prototypical quasi-two-dimensional covalent organic framework
(COF) composed of carbon and hydrogen. The COF structure, interlayer
binding energies, and hydrogen absorption are analyzed at CCSD­(T)
accuracy. Overall, the developed methodology opens a practical route
to large-scale atomistic simulations for systems with extended covalent
networks and vdW interactions with chemical accuracy.