Computational Modeling of Properties of Quantum Dots and Nanostructures: From First Principles to Artificial Intelligence (A Review)

Nanomaterials, including quantum dots, have gained more and more attention in the past few decades due to their extraordinary properties that make them useful for many applications, ranging from catalysis, energy generation and storage, biotechnology, and medicine to quantum informatics. Mathematical descriptions of the phenomena in which nanostructures are involved are of great demand because they may be utilized for the purpose of controlling these phenomena (e.g., the growth of nanostructures with certain sizes, shapes, and other properties). Such models may be of distinct nature, including calculations from first principles, ordinary and partial differential equations, and machine learning models (including artificial intelligence) as well. The aim of this article is to review the most important and useful computational and mathematical approaches for the description and control of processes involving nanostructures.