Structural Properties and Quantum Information Theoretic Measures of a Harmonically Trapped Two-Electron Quantum Dot

Accurate estimation of structural properties is essential for understanding the behavior of atomic systems, particularly in confined environments where they display unique physical phenomena. Amongst these, the correlation energy plays a pivotal role in shaping the overall dynamics of the system. In this study, we investigate the influence of external confinement on both correlation energy and Collins' conjecture by evaluating different quantum information and quantum entanglement entropies. For this purpose, we model a two-electron quantum dot using an isotropic harmonic potential to explore these effects. Various geometrical properties are estimated to showcase the acceptability and viability of the present method. Additionally, we investigate the impact of harmonic confinement on the quantum similarity measures e.g. quantum similarity index and quantum dissimilarity between He${\hspace{0.17em}}^{+}$(1$s{}^{2}S$) and He(1$s^2{}^{1}S$ and 1$s2s{}^{1,3}S$), as well as between He(1$s2s{}^{1}S$) and He(1$s2s{}^{3}S$). These results for both ground and singly excited states of two-electron system are reported here for first time.