Nuclear Energy

The output properties
for the GPR models are atomic properties calculated using ab initio methods. In our previous work using active learning,
the atomic property being modeled was the IQA energy. The IQA energy
is used in atomic simulations for intramolecular interaction, that
is, taking care of the internal energy balance of a flexible molecule.
The IQA energy captures the intra-atomic energy along with the interaction
energy with all atoms other than a given atom A in
the molecule, where E_intra^A is the intra-atomic
energy of atom A, V_cl^AB is the classical
potential energy between atoms A and B, and V_xc^A is the exchange-correlation potential energy
between atoms A and B. Explicit
formulae defining these energies can be found in the original IQA
publication^{44 (link)} and in work^{62 (link)} that made IQA compatible with DFT, for the first time.
In an MD simulation, the forces to apply to each atom can be calculated
from the derivative of the predicted energy allowing the modeling
of a single molecule in vacuo.
FFLUX is a polarizable
force field, which requires electrostatic information to cover intermolecular
interactions. Short-range electrostatics are captured by the IQA energy,
specifically in the interaction energy (E_inter^AB) of the IQA energy. For long-range electrostatic interactions,
FFLUX uses multipole moment predictions^{63 (link)−65 (link)} from GPR models as an
input^{45 (link)} to the SPME method.^{48 (link)} This allows FFLUX to capture monopole–monopole,
monopole–dipole, dipole–dipole, etc. interactions using
multipole moments up to hexadecapole moments (L′
= 4).
Training multipole moment models is similar to training
IQA energies.
In fact, the training process is identical, other than for the replacement
of the training outputs by the specific multipole moment being trained.
It is important to note that it is required that the multipole moments
are in the ALF because the features are expressed with respect to
the ALF. The multipole moments are typically computed in the global
frame so a rotation to the ALF is needed prior to training. Then,
when using the GPR multipole moment models in a simulation, the multipole
moments must be expressed with respect to the global frame. Thus,
the multipole moments must be rotated from the predicted local frame
moments back to the global frame.
Quantum chemical calculations
were carried out using the program⁶⁶ GAUSSIAN09
at B3LYP/6-31+G(d,p) level of theory,
while the QTAIM calculations were carried out using the external program⁶⁷ AIMAll19.
Numerical errors in the computation
of the atomic properties cause
an integration error to the training input. Certain geometries may
result in an especially large integration error and may not be suitable
for use in the GPR model. Such geometries must thus be removed from
the training set prior to training, in a process known as scrubbing.
Points are scrubbed from the training set if the point’s integration
error is greater than the threshold of 0.001.

We trained a machine-learning neural network potential for the Mg–O–H system using the NEP and GPUMD⁷¹ method, which directly uses relative atomic coordinates to describe local atomic environments to obtain atomic energies, while forces are obtained by taking the derivatives of the energies. Our dataset was built by choosing 16,000 configures in the trajectories from AIMD in the NVT ensemble in the pressure range from 300 GPa to 800 GPa with a temperature step of 1000 K from 3000 to 7000 K.