MBD-ML: Many-body dispersion from machine learning for molecules and materials

TL;DR

MBD-ML offers a practical and streamlined tool that simplifies the incorporation of state-of-the-art vdW interactions into any electronic structure code, as well as empirical and machine-learned force fields.

Abstract

Van der Waals (vdW) interactions are essential for describing molecules and materials, from drug design and catalysis to battery applications. These omnipresent interactions must also be accurately included in machine-learned force fields. The many-body dispersion (MBD) method stands out as one of the most accurate and transferable approaches to capture vdW interactions, requiring only atomic $C_6$ coefficients and polarizabilities as input. We present MBD-ML, a pretrained message passing neural network that predicts these atomic properties directly from atomic structures. Through seamless integration with libMBD, our method enables the immediate calculation of MBD-inclusive total energies, forces, and stress tensors. By eliminating the need for intermediate electronic structure calculations, MBD-ML offers a practical and streamlined tool that simplifies the incorporation of state-of-the-art vdW interactions into any electronic structure code, as well as empirical and machine-learned force fields.

Figures (6)

• Figure 1: Overview of the training and the validation of the MBD-ML model: (top left) MBD-ML was trained on the QCML molecular data set spanning almost the entire periodic system (top right; Reproduced from Ref. ganscha2025qcml under CC BY 4.0). (middle) The model has been integrated into the libMBD python interface, pymbd, to allow direct calculation of MBD properties from the atomic structure. (bottom) The model was validated on both molecules and molecular crystals in predicting fundamental properties including total energy and force contributions and -- in the case of organic crystals -- to perform geometry optimizations and recover the energy ranking of different polymorphs
• Figure 2: Performance of PBE0+MBD-ML in predicting the $C_6$ and $\alpha_0$ ratios and the MBD contribution to the total energy and atomic forces of the QCML test set
• Figure 3: Performance of PBE0+MBD-ML in predicting the $C_6$ and $\alpha_0$ ratios and the MBD contribution to the total energy, atomic forces and stress tensor components in the OMC25 test set
• Figure 4: Comparison of MBD-ML and DFT-D performance on predicting vdW force contributions compared to MBD-NL. Polar representation of atomic force deviations computed from the MBD-ML (a), D3 (b) and D4 method (c). The radial coordinate specifies the relative magnitude deviation of the atomic force vector to the MBD-NL reference in percent. The angular coordinate corresponds to the angular deviation from the reference in degrees. The point colour encodes the absolute magnitude of the MBD-NL atomic force As a guide to the eye the radial $100\%$ mark is highlighted in red
• Figure 5: Structural comparison of polymorphs relaxed with PBE and PBE+MBD-ML compared to the PBE+MBD-NL relaxed structures: (top) RMSD and maximum atomic displacement and (bottom) ratio of the unit cell volume of the relaxed structures with respect to the PBE+MBD-NL-relaxed structure. Blue crosses represent cases where the PBE geometry optimization did not converge. The RMSD and volume ratio is shown for every polymorph of each molecular crystal. ANP refers to 2-amino-5-nitropyrimidine. Numerical values are tabulated in Table S4