Build a Ruler to Measure Electron Localization Function with Machine Learning Models: S-Au bonds Quantification in Thiolate Protected Gold Nanoclusters

Complicated S-Au interaction patterns in thiolate-protected gold nanoclusters (TP-AuNCs) are important in the formation of versatility among clusters. In this study, the ELFnet, a novel convolutional neural network (CNN) model is trained and tested to bridge the electron localization function (ELF) images and the bond lengths. As believed to be a successful bond describer, a dataset of 3959 ELF images is obtained out of Density Functional Theory (DFT) simulations, followed by a series of model architecture and hyperparameter exploration. The ELFnet with its best performance shows its correct feature extraction ability to gain insights in the prediction of bond lengths. Besides, the ELFnet also possess 3 different "ELF reading modes" which inspires other possibilities in understanding ELF images. The ELFnet serves as an "ELF-ruler" to give precise bond type labels (or the predicted bond lengths). Such ELF-ruler measured bond types represent a particular bond when distorted by external factors with a quantitative indicator. With the help of such an ELF-ruler, the classification of chemical bonds in general may be extended to more precise types.