Electronic structure and crystalline electric field splitting of trivalent erbium in MgO

Here, we present an effective ab initio method of calculating crystal field coefficients of erbium, a rare earth, ion hosted in magnesium oxide (MgO) with Oh point group symmetry. The calculated band gap of MgO is 7.65 eV at Γ, which closely agrees with the experimentally observed value of 7.5±0.5 eV. Using thus calculated crystal field coefficients, which satisfy the Oh point group symmetry, we solve an effective Hamiltonian and calculate crystal field splitting of Er³⁺ for the ground and excited states. The calculated energy transitions are in good agreement with available experimental values within 15 cm⁻¹ error between the ground and first excited state. The long optical transition about 6506 cm⁻¹ of environmentally shielded 4f shell of Er3+ in MgO can have a potential application in quantum networks.