Neural network and ReaxFF comparison for Au properties
Jacob R. Boes, Mitchell C. Groenenboom, John A. Keith and John R. Kitchin, “Neural network and ReaxFF comparison for Au properties”, International Journal of Quantum Chemistry 116, 979–987 (2016). https://doi.org/10.1002/qua.25115
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Question
Many nanoscale systems are too large for first-principles simulation and need atomistic potentials, which come in two broad kinds: physical potentials with analytical forms built on known bonding physics, and mathematical potentials that learn the potential energy surface with no built-in physics. This paper asks how a widely used physical reactive potential, ReaxFF, and a Behler–Parrinello neural network (BPNN) should be trained to be accurate and tractable across bulk, surface and cluster regimes of a single element, using gold as the test case because it has many known nanoscale structures and screened long-range interactions (Boes et al. 2016).
Approach
The reference data were 9,972 VASP calculations with the PBE functional and PAW potentials: 905 bulk, 1,022 surface and 8,045 cluster configurations, most of them (9,076) intermediate steps of geometry relaxations. The bulk set covered equations of state of several lattices, vacancy formation and vacancy diffusion; the surface set covered fcc(111) slabs and fcc(100) adatom diffusion pathways taken from earlier ReaxFF work and recomputed as single points; the cluster set held ordered, planar and disordered clusters of up to 126 atoms. A fixed validation set of 238 calculations was held out. ReaxFF (bond, overcoordination and van der Waals terms plus three-body valence-angle terms) was parameterized with the Monte Carlo MCFFopt tool in ADF on 848 ground-state geometries split roughly equally among regimes, because fitting to larger sets raised the objective function and biased predictions. The BPNN was trained with the AMP code in ASE on 9,734 calculations, using a 6.5 Å cutoff and four hidden layers of 40 tanh nodes, a large network for a BPNN. The DFT data and trained network are shared in the Supporting Information (Boes et al. 2016).
Key findings
The BPNN reached a training RMSE of 0.017 eV/atom with normally distributed residuals, and validation errors of similar size, except for underrepresented fcc(100) diffusion pathways. ReaxFF gave an overall RMSE of 0.136 eV against the full dataset. For fcc, simple cubic and diamond equations of state, the BPNN nearly reproduced DFT (fcc minimum volume 17.99 versus 17.97 ų, bulk modulus 145 versus 147 GPa), while ReaxFF underpredicted bulk moduli by roughly 20 to 30 GPa (122 GPa for fcc) and showed an unphysical convex region in its bond energy at large volumes, giving residuals near 1 eV/atom far from equilibrium. DFT vacancy formation energies agreed with other PBE values (about 0.42 eV) but fell well below experiment (0.93 eV); the BPNN overestimated them systematically by about 0.4 eV and ReaxFF underestimated them by about 0.3 eV. The bulk vacancy diffusion barrier was 0.56 eV in DFT, 0.60 eV with the BPNN and 0.50 eV with ReaxFF, errors an order of magnitude smaller than for vacancy formation because of cancellation with similar reference states.
On surfaces, ReaxFF predicted an untrained terrace diffusion barrier very well, while the BPNN had residuals of 0.2 to 0.3 eV there but did well on an untrained dimer diffusion path where ReaxFF erred by 0.1 to 0.2 eV. Across 144 fcc(100) diffusion images, 86.1% of ReaxFF and 52.1% of BPNN predictions fell within 0.1 eV of DFT, which the authors connect to the larger share of surface data in the ReaxFF training set. Both potentials reproduced the single-layer fcc(111) slipping barrier within 0.05 eV, although ReaxFF showed a spurious metastable intermediate. For clusters, BPNN-driven Born–Oppenheimer MD of a six-atom cluster cooled from 800 K to 300 K found the planar triangular global minimum (not in the training set) with residuals below 0.05 eV/atom, whereas ReaxFF did not identify that minimum. In minima hopping of a 38-atom cluster, neither potential found the lowest DFT minimum, and ReaxFF energies were systematically offset by about 0.11 eV/atom; adding cluster data to ReaxFF degraded its bulk and surface accuracy. ReaxFF in LAMMPS ran 6,700 MD steps per second on the six-atom cluster versus 15 for the Python BPNN in ASE (Boes et al. 2016).
Some numbers in the extracted text have garbled minus and plus-minus signs; values above were read in the sense the surrounding text makes clear, and the validation-set standard deviation is omitted because it is not legible.
Significance
This is an early head-to-head test of a physics-based reactive force field against a machine-learned potential on a common, openly shared DFT dataset. It shows that a single ReaxFF parameterization struggles to cover bulk, surfaces and small clusters at once, with an optimal training set size beyond which it overfits, while a BPNN can absorb nearly 10,000 calculations and, by the authors’ overall assessment, perform comparably or better across regimes, at much higher data and run-time cost. The authors recommend against standard ReaxFF for clusters under 126 atoms without extensive validation and argue that open data and methods speed potential development (Boes et al. 2016).