Neural Network Approach for a Rapid Prediction of Metal-Supported Borophene Properties

We developed a high-dimensional neural network potential (NNP) to describe the structural and energetic properties of borophene deposited on silver. This NNP has the accuracy of density functional theory (DFT) calculations while achieving computational speedups of several orders of magnitude, allowing the study of extensive structures that may reveal intriguing moiré patterns or surface corrugations. We describe an efficient approach to constructing the training data set using an iterative technique known as the “adaptive learning approach”. The developed NNP is able to produce, with excellent agreement, the structure, energy, and forces obtained at the DFT level. Finally, the calculated stability of various borophene polymorphs, including those not initially included in the training data set, shows better stabilization for ν ∼ 0.1 hole density, and in particular for the allotrope α (ν=1/9). The stability of borophene on the metal surface is shown to depend on its orientation, implying structural corrugation patterns that can be observed only from long-time simulations on extended systems. The NNP also demonstrates its ability to simulate vibrational densities of states and produce realistic structures with simulated STM images closely matching the experimental ones.