The ground state energy and structural properties of a model two‐electron system (Zee), bound via screened Coulomb interaction with nuclear charge Z, have been studied under the variational framework. Hylleraas type basis has been adopted for explicit incorporation of the electron–electron correlation. Critical nuclear charges (Zc) of Zee system have been reported for different screening parameters (μ). Expectation values of different structural properties have been estimated to predict the internal structure of the Zee system. The variation of the structural properties with respect to Z for different μ reveals the signature of quantum phase transition (QPT) in the vicinity of Zc. Moreover, the nature of variation of these properties with respect to Z in case of bare Coulomb or free system (μ = 0) is completely opposite to those of screened system (μ ≠ 0). Radial two‐particle density (TPD) confirms the symmetry breaking of the electronic structure and therefore QPT in the vicinity of Zc.

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