Machine-Learned
Force Fields for
Improved Materials
Modeling
Machine-learned force fields (MLFFs) are designed to improve upon traditional
force fields by incorporating machine learning models to accurately model
the interactions between atoms and molecules. This technique is based ona neural network potential energy surface (NN-PES) architecture, where themodel is trained to reproduce the total electronic energy of the system tochemical accuracy.
The NN-PES architecture is computationally efficient and utilizes local atomic
descriptors to account for the surrounding environment. The model is trainedby minimizing prediction errors against electronic energy obtained fromany theory, such as density functional theory (DFT). This method enables
simulations on larger length and time scales when compared to ab initio
molecular dynamics (AIMD) methods, but with similar accuracy.
Previously, MLFF methods were limited to short-range interactions, but recent
efforts have incorporated complex neural network architecture, charge
recursive neural network (QRNN), that includes training of atomic charges tocapture long-range interactions1. As a result, complex systems such as battery
electrolytes can now be more accurately modeled with MLFFs.
Our combination of OPLS4 for initial structure generation, fast DFT and MD
engines, and leading MLFF methods makes Schrödinger the leading partner
for MLFF generation. In this application note, we showcase the applicationsof QRNN technology in three different areas of materials science, namely themodeling of liquid electrolytes, polymers, and ionic liquids.

HΨ = EΨ
Activelearning

Accuracy

QRNN
Speed

Accuracy

DFT
Speed

APPLICATION NOTE

Figure 1: Machine-learned force field workflow

Advantages of MLFF
One limitation of classical force fields is theinability to adjust for changing partial charges
and polarization of atoms, leading to inaccurate
electrostatic interactions. On the other hand,
MLFF methods enable the dynamic adjustmentof partial charges and polarization, resulting in
more accurate dynamics. Since MLFF models
are trained on DFT data, they offer a higher
level of accuracy that is similar to ab initio
calculations. Empirical parameters-basedclassical force fields also breakdown whenmodeling interactions in complex inorganic andorganic systems, while MLFF can effectively learn
the underlying potential energy surface thatgoverns these interactions. Moreover, with theuse of Desmond (Schrödinger’s GPU-accelerated
molecular dynamics engine), MLFF simulations
can be performed at a rate of 1ns/day for a
10,000 atom system, allowing for larger systems
to be simulated for sufficient periods to obtain
converged bulk properties.

APPLICATION

High-Dimensional
Neural Network
Force Field for Liquid
Electrolytes 2
Liquid electrolytes are one of the most importantcomponents of Li-ion batteries, which are a criticaltechnology of the modern world. However, it ischallenging to obtain molecular-level insights into thestructure of liquid electrolytes and its impact on thebulk properties. Additionally, we lack the computational
tools required to quantitatively calculate key propertiesof the materials (viscosity, ionic diffusivity) from firstprinciples necessary to design next-generation batterymaterials. The optimization of battery electrolyte
formulation is a complex multi-objective problem.

Approach
In this work, we developed MLFF for liquid electrolyte
simulations which bridges the gap between the accuracyof range-separated hybrid DFT and the efficiency ofclassical force fields. Our training dataset consists of LiPF6salt and 7 common carbonates.* We trained the MLFF
to a dataset of ~360K molecular clusters using sevenrounds of active learning. The performance of the MLFF
was validated by comparing the predicted values to theexperimental bulk thermodynamic and transport properties
over a range of temperatures and salt concentrations.
*Carbonates used in this study: ethylene carbonate (EC), propylene carbonate(PC), vinylene carbonate (VC), fluoroethylene carbonate (FEC), dimethylcarbonate (DMC), diethyl carbonate (DEC), and ethyl methyl carbonate (EMC)

Results
We evaluated the MLFF model performance byconstructing an independently sampled test set of 2.5K
cluster data points extracted from the production MD
trajectories of pure carbonate solvents and electrolyte
mixtures (Figure 2a). Predictions of material properties
made with this force field are quantitatively accuratecompared to experimental data. Such highly accurate
MLFF models are critical to optimize complex electrolyte
formulations needed for advancing battery technology.

Figure 2:a) Comparison of MLFF predicted energies with DFT energies;b) comparison of the computed viscosity of solvents with experiments;c) comparison of the diffusivity of Li+ ions in DEC solvent with increasing temperature.

•The absolute energies, dipole components, and force
components are in good agreement to the reference
level of DFT theory.

•The MLFF predicted bulk properties (such as density,viscosity, heat of vaporization, etc.) are in excellent
agreement with experimental values, and provide
significant improvement in the predicted properties forthe pure liquid electrolytes as compared to the OPLS4.

•The MLFF computed diffusivities are in excellent
agreement with the experimental data.

2APPLICATIONAPPLICATION

Developmentof Scalable andGeneralizable MLFF
for Polymers 3

Machine Learning
Fitted Force Fields
for Ionic liquids

Classical force fields such as OPLS have been successful
for polymer systems in capturing some properties suchas density at a constant temperature, however, forcertain dynamic and thermodynamic properties such as
self-diffusivity, viscosity, and specific heat, it is limited toprimarily obtaining relative trends.

Ionic liquids represent an intermediate class of moleculesthat are liquid at room temperature, but are composed ofcompletely charged cation and anions. They are useful foradvanced batteries, biopharmaceuticals, and as industrial
solvents. The charged nature of ionic liquids make themdifficult to simulate and can only be correctly fitted withmore expensive polarizable force fields. DFT based
simulations are limited to only simulating 10s of molecules.

Approach

Approach

We developed an MLFF workflow for polymers anddemonstrated its scope by applying it to ethylene glycol
oligomers. We trained on samples containing monomers,dimers, and trimers of ethylene glycol to create an MLFF
model and evaluated the model by predicting the oligomer
properties (density, self-diffusivity, and specific heat) andcomparing them with DFT and experimental results.

We train an ML force field on DFT energies and forces forneutral organic molecules, charged organic molecules,dimers, and small clusters. We then run molecular
dynamics on a simulation box containing between 10003000 atoms for several classes of ionic liquids.

Results

MLFF ensemble models enable stable simulation
performance of simulations over 2ns. The diffusion
coefficients predicted by the MLFF agree with experimental
results over a wide range of ionic liquid chemistries (Figure4). These results demonstrate the first ab initio based
simulation of ionic liquids at such length and timescales.

We evaluated the MLFF model performance by comparing
the predicted energies with the DFT energies. The below
parity plot shows that the model is performing well. TheMLFF potentials accurately capture the diffusion dynamics
and surpass the capabilities of what the classical force field
can provide (Figure 3b).

Results

This demonstrates that our MLFF for polymers is scalable
and can be extended to compute complex properties
dependent on the chain dynamics, such as mechanicalproperties and thermophysical properties, including theglass transition temperature. Our work shows that theadvancing area of MLFF has application in a criticallyimportant materials area, polymers. This significant
advance was not possible with previous MLFFs and is
an important step toward simulations with the ideal
matching of accuracy and speed for key materials design
parameters.
Figure 4:
Comparison of MLFF predicted diffusion coefficients of ionic liquids with experimental data.

abFigure 3:a) snapshot from MLFF MD of 8000 atom system of PEG 1000 chains;b) comparison of diffusivity calculations with experiments.

3How we can help
Schrödinger provides research services focused on the development of advanced machinelearned force fields to facilitate accurate molecular dynamics simulations for a range ofapplications and to enable modeling of complex material systems with high speed and accuracy.

References
1.

Jacobson, L. D., Stevenson, J. M., Ramezanghorbani, F., Ghoreishi, D., Leswing, K., Harder, E. D., & Abel, R. (2022).
Transferable neural network potential energy surfaces for closed-shell organic molecules: Extension to ions.
Journal of Chemical Theory and Computation, 18(4), 2354-2366.

2.

Dajnowicz, S., Agarwal, G., Stevenson, J. M., Jacobson, L. D., Ramezanghorbani, F., Leswing, K., ... & Abel, R. (2022).
High-dimensional neural network potential for liquid electrolyte simulations. The Journal of Physical Chemistry B,126(33), 6271-6280.

3.

Mohanty, S., Stevenson, J., Browning, A., Jacobson, L., Leswing, K., Halls, M., & Afzal, M. (2023). Development ofScalable and Generalizable Machine Learned Force Field for Polymers. ChemRxiv. doi:10.26434/chemrxiv-20234z2bw This content is a preprint and has not been peer-reviewed.

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