mploying Virial Coefficients for Optimal Solutions in Variational Calculations

In this study, virial coefficients for one and two-electron hydrogen and helium-like quantum dot structures confined in an infinite potential well were calculated. The virial coefficients were determined based on the dot radius using the Quantum Genetic Algorithm (QGA) method. Calculations were performed using Fernandez's expression; however, due to calculation errors in confined systems, this equivalent expression was found unsuitable as a direct stopping criterion. Instead, virial coefficients were calculated using the ⟨T⟩/⟨V⟩ relationship, and the results were plotted. The fitting function obtained for the virial coefficients is proposed as an effective cutoff criterion for electronic structure calculations of quantum dot systems.