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The Van der Waals Equation01:26

The Van der Waals Equation

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The ideal gas law is based on two simplifying assumptions: first, that there are no intermolecular attractions between gas molecules, and second, that the volume occupied by the molecules themselves is negligible compared with the volume of the container. However, these assumptions don't hold up under all conditions - specifically, at high pressures and low temperatures, as gas tends to deviate from ideal gas behavior.The van der Waals equation is an enhanced version of the ideal gas law,...
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The ideal gas law is an approximation that works well at high temperatures and low pressures. The van der Waals equation of state (named after the Dutch physicist Johannes van der Waals, 1837−1923) improves it by considering two factors.
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Network covalent solids contain a three-dimensional network of covalently bonded atoms as found in the crystal structures of nonmetals like diamond, graphite, silicon, and some covalent compounds, such as silicon dioxide (sand) and silicon carbide (carborundum, the abrasive on sandpaper). Many minerals have networks of covalent bonds.
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Machine-Learning Interatomic Potentials Achieving CCSD(T) Accuracy for Systems with Extended Covalent Networks and

Yuji Ikeda1, Axel Forslund1,2, Pranav Kumar1

  • 1Institute for Materials Science, University of Stuttgart, Pfaffenwaldring 55, 70569 Stuttgart, Germany.

Journal of Chemical Theory and Computation
|March 3, 2026
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Summary
This summary is machine-generated.

We developed a new method to train machine-learning interatomic potentials (MLIPs) for large, complex materials like covalent organic frameworks (COFs). This approach achieves high accuracy for simulations, including van der Waals interactions, enabling detailed analysis of material properties.

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Area of Science:

  • Computational materials science
  • Quantum chemistry
  • Machine learning

Background:

  • Machine-learning interatomic potentials (MLIPs) offer accurate, cost-effective atomistic simulations.
  • CCSD(T) calculations provide high accuracy but are computationally expensive, especially for periodic systems.
  • Existing MLIPs struggle with extended covalent networks and van der Waals (vdW) interactions.

Purpose of the Study:

  • To develop a methodology for training MLIPs with CCSD(T) accuracy for extended covalent networks.
  • To enable accurate large-scale atomistic simulations of systems with significant vdW interactions.
  • To apply the developed MLIPs to analyze the structure and properties of covalent organic frameworks (COFs).

Main Methods:

  • Utilized a Δ-learning approach with a dispersion-corrected tight-binding baseline.
  • Trained MLIPs on the energy differences between CCSD(T) and the baseline.
  • Incorporated vdW-bound multimers into the training set to capture dispersion interactions.
  • Combined vdW-aware tight-binding with a local MLIP for CCSD(T)-level accuracy.

Main Results:

  • Achieved root-mean-square energy errors below 0.4 meV/atom on training and test sets.
  • Accurately reproduced electronic total atomization energies, bond lengths, vibrational frequencies, and intermolecular interactions.
  • Successfully applied the method to a quasi-2D COF, analyzing its structure, interlayer binding, and hydrogen absorption at CCSD(T) accuracy.

Conclusions:

  • The developed methodology provides a practical route for large-scale atomistic simulations of extended covalent networks with vdW interactions.
  • This approach achieves chemical accuracy, significantly advancing the capabilities of computational materials science.
  • Enables in-depth analysis of complex materials like COFs, previously limited by computational constraints.