EquiDTB: Equivariant many-body $\Delta_{\rm TB}$ potentials for molecular simulations

About

We introduce the EquiDTB framework, which leverages physics-inspired equivariant neural networks to parameterize scalable and transferable many-body $\Delta_{\rm TB}$ potentials, replacing the standard pairwise repulsive potential in the DFTB method. This advancement extends the applicability of our previous ML-corrected DFTB approach NNrep to compute energetic, structural, vibrational, and dynamics properties of larger molecules and non-covalent systems at DFT-PBE0 accuracy supplemented with a many-body dispersion treatment for van der Waals interactions.

QM datasets

The quantum-mechanical property data used to train the EquiDTB models can be downloaded from the ZENODO repository https://zenodo.org/records/17433999.

Computing with EquiDTB framework

Installation

Install MACE following the instructions in MACE GitHub.

pip install --upgrade pip
pip install mace-torch

Install DFTB+ code and ASE python package to combine the MACE and DFTB calculators.

conda install -n equidtb mamba
mamba install 'dftbplus=*=mpi_openmpi_*'

# additional components like the dptools and the Python API

mamba install dftbplus-tools dftbplus-python
conda install conda-forge::ase

For more information regarding DFTB+ installation, you can visit DFTB+ Recipes.

Note1: It is necessary to replace the dftb.py file from the calculators directory in the ASE package with the one provided in this repository (see ase_calc_dftb.py). This modified ASE-DFTB calculator includes the reference values for Hubbard Derivatives.

cp ase_calc_dftb.py /path/to/.conda/envs/qued/lib/python3.9/site-packages/ase/calculators/dftb.py

Note2: If you encounter any conflicts after installing these packages, you can check the package versions in the environment.yml file.

Setting up DFTB+ ASE calculator

The current version of EquiDTB models consider only C, N, O, and H elements. To run calculations using these models and ASE calculator, you should first download the Slater-Koster parameters corresponding to the 3ob set (visit dft.org). Moreover, you must add the following environment variables to your shell (e.g., in .bashrc, .zshrc, or your job script), replacing the placeholder paths with your own installation paths:

# Path to your DFTB+ executable (MPI-enabled if available)
export DFTB_COMMAND='mpiexec -n 1 /path/to/dftb+/bin/dftb+'
# Path to the DFTB+ parameter set (e.g., 3ob-3-1 directory)
export DFTB_PREFIX='/path/to/slater-koster-files/3ob-3-1/'
# Set number of OpenMP threads (must be 1 if running under MPI)
export OMP_NUM_THREADS=1

Single point calculation

This is a simple python script file that combines the developed EquiDTB3 model with the DFTB3 electronic components. We have also considered the flags related to many-body dispersion interactions; however, you can remove them if it is not required for your calculations.

from ase.io import read, write
from ase.calculators.dftb import Dftb
import ase.calculators.mixing

# Load MACE calculator
from mace.calculators import MACECalculator
MLcalc = MACECalculator(model_path="/path/to/model/EquiDTB3.model", device='cpu', default_dtype="float32")

# Read structure file
atoms = read("xyz_file.xyz")

# Load DFTB calculator with MBD
DFTBcalc = Dftb(label='current_dftb',
                atoms=atoms,
                Hamiltonian_SCC = 'Yes',
                Hamiltonian_ThirdOrderFull = 'Yes',
                Hamiltonian_PolynomialRepulsive_ = '',
                Hamiltonian_PolynomialRepulsive_setForAll = '{Yes}',
                Hamiltonian_Dispersion_ = 'MBD',
                Hamiltonian_Dispersion_KGrid = '1 1 1',
                Hamiltonian_Dispersion_Beta = 0.83, 
                Hamiltonian_Dispersion_NOmegaGrid = 25,
                Hamiltonian_Dispersion_ReferenceSet = 'ts',
                ParserOptions_ParserVersion = '13')

# Mixing calculators
QMMLcalc =  ase.calculators.mixing.SumCalculator([DFTBcalc,MLcalc])

atoms.set_calculator(QMMLcalc)

energy = atoms.get_total_energy()
forces = atoms.get_forces()

print('Energy and forces in ASE')
print('Energy = ', energy)
print('Forces = ', forces)

To run calculations using the EquiDTB1 model, you should change the settings only in the ASE-DFTB calculator,

DFTBcalc = Dftb(label='current_dftb',
                atoms=atoms,
                Hamiltonian_SCC = 'No',
                Hamiltonian_PolynomialRepulsive_ = '',
                Hamiltonian_PolynomialRepulsive_setForAll = '{Yes}',
                Hamiltonian_Dispersion_ = 'MBD',
                Hamiltonian_Dispersion_KGrid = '1 1 1',
                Hamiltonian_Dispersion_Beta = 0.83,
                Hamiltonian_Dispersion_NOmegaGrid = 25,
                Hamiltonian_Dispersion_ReferenceSet = 'ts',
                ParserOptions_ParserVersion = '13')

Validation benchmarks

We have considered several challenging calculations to validate the performance of the EquiDTB models. Among them,

• S66x8 molecular dimers: Calculation of interaction energy and atomic forces.
• Nudged elastic band (NEB) calculations: Determination of the minimum energy path between conformers of large molecules.
• Molecular dynamics simulations: Conformational sampling at constant temperature of flexible molecules.
• Vibrational properties: Computation of vibrational frequencies of amino acids.
• Energetic ranking: Predicting energetic ranking and atomic forces of Aquamarine molecules.

Reference data were computed using PBE0+MBD level, as implemented in the FHI-aims code. Python scripts and reference data to perform these validations can be found in the ./Validations/ folder.

Citation

If you use parts of the code please cite

@Article{equidtb,
author ="Medrano Sandonas, Leonardo and Puleva, Mirela and Erarslan, Zekiye and Parra Payano, Ricardo and Stöhr, Martin and Cuniberti, Gianaurelio and Tkatchenko, Alexandre",
title  ="Advancing density functional tight-binding method for large organic molecules through equivariant neural networks",
journal  ="Phys. Chem. Chem. Phys.",
year  ="2026",
pages  ="-",
publisher  ="The Royal Society of Chemistry",
doi  ="10.1039/D6CP00038J",
url  ="http://dx.doi.org/10.1039/D6CP00038J",
}

@article{stoehr20,
author = {Stöhr, Martin and Medrano Sandonas, Leonardo and Tkatchenko, Alexandre},
title = {Accurate Many-Body Repulsive Potentials for Density-Functional Tight Binding from Deep Tensor Neural Networks},
journal = {The Journal of Physical Chemistry Letters},
volume = {11},
number = {16},
pages = {6835-6843},
year = {2020},
doi = {10.1021/acs.jpclett.0c01307},
}