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Compositional disorder is common in crystal compounds. In these compounds, some atoms are randomly distributed at some crystallographic sites. For such compounds, randomness forms many non-identical independent structures. Thus, calculating the energy of all structures using ordinary quantum ab initio methods can be significantly time-consuming. Machine learning can be a reliable alternative to ab initio methods. We calculate the energy of these compounds with an accuracy close to that of density functional theory calculations in a considerably shorter time using machine learning. In this study, we use kernel ridge regression and neural network to predict energy. In the KRR, we employ sine matrix, Ewald sum matrix, SOAP, ACSF, and MBTR. To implement the neural network, we use two important classes of application of the neural network in material science, including high-dimensional neural network and convolutional neural network based on crystal graph representation. We show that kernel ridge regression using MBTR and neural network using ACSF can provide better accuracy than other methods. [Display omitted] [ABSTRACT FROM AUTHOR]

The size-dependent properties of small pure copper and silver clusters and their alloys with one and two palladium atoms are studied by using full-potential density functional computations. The stable isomers of these clusters are identified and their magic numbers are determined via the analysis of the second difference of their minimized energy. We discuss that the doped Pd generally prefers the high coordination sites of the pure cluster. It is argued that Pd doping influences the structural cross over of these clusters. The GW correction is applied for more accurate determination of the electronic structure of the systems. [ABSTRACT FROM AUTHOR]