Charge Equilibration
hippynn has features for incorporating charge equilibration model (ChEQ)
to include long-range interactions.
These features can be found in cheq.
For a more detailed description, please see the paper [Li2025]
The HIPNN-ChEQ model learns short-range energy (\(V^{S}_{i}\)), electronegativity (\(\chi_{i}\)), and Hubbard-U (\(u_{i}\)) indirectly through training with total energy, forces, and dipole.
This is based on the second-order monopole charge equilibration model as following,
Here index i runs over the atomic centers, \(i = 1,2,\ldots N\), \({\bf q} = \{q_i\}\) are the net partial charges on each atom, \(V_i^{\rm S}({\bf R})\) are charge-independent, short-range energy terms for each atom at position, \({\bf R}_i\), and \(\chi_i({\bf R})\) and \(u_i({\bf R})\) are the atomic electronegativities and chemical hardness (or Hubbard-U) parameters, respectively. We assume that these depend not only on the atom type but also on their local atomic environments. The charge-independent energy terms, \(V_i^{\rm S}({\bf R})\), as well as \(\chi_i({\bf R})\) and \(u_i({\bf R})\) are parameterized using HIPNN that captures the local many-body interactions of each atom. This allows us to leverage HIPNN to parameterize their values based on reference data generated from first-principles theory.
We construct two HIPNN networks to predict the 1) short-range energy and 2) electronegativity and Hubbard-U separately. (Note: it is not absolutely necessary to use two different networks,
but we have found it to be effective–this way gradients are split to parameters in the same way as the energy is split.)
For the short-range energy, the node can be constructed using HEnergyNode:
network1 = networks.Hipnn("HIPNN2", network.parents, module_kwargs = network1_params)
henergy1 = targets.HEnergyNode("HEnergy",network1)
On the other hand, we build another HIP-NN network for the electronegativity and Hubbard-U predictions
using ChEQNode:
network = networks.Hipnn("HIPNN", (species, positions), module_kwargs = network_params)
henergy = ChEQNode("ChEQ", (network,), units={'energy':'kcal/mol', 'length':"Angstrom"}, lower_bound=0.01)
Then, we need to define the total energy, forces, and dipoles for training:
dipole = henergy.dipole
molecule_energy = henergy.coul_energy + henergy1.sys_energy
gradient = physics.GradientNode("Gradient", (molecule_energy, positions), sign=+1)
molecule_energy.db_name="energies"
gradient.db_name = "Grad"
dipole.db_name = "dipole"
In order to obtain a HIPNN-ChEQ model which can run stable molecular dynamcis, we emphasize the loss of forces and dipole more over the total energy:
loss_error = 1.0 * (rmse_energy + mae_energy) + 100.0 * (rmse_grad + mae_grad) +
10000.0 * (rmse_dipole + mae_dipole)
For a complete script, please take a look at examples/cheq_ani2x_training.py.