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Calculation of singlet and triplet energy states of the two-dimensional (2D) H– ion and 2D He atom


Physics & Astronomy International Journal
NI Kashirina,1 Ya O Kashyrina,2 OA Korol,3 OS Roik2

Abstract

Singlet and triplet energy states of the two-dimensional (2D) H–and 2D He ions were calculated. ? multi parameter system of Gaussian orbitals with exponentially correlated multipliers is used. An analog of the H–ion is a two-electron shallow D–center in covalent semiconductors. The energy of the lowest triplet term of 2D D–center coincides with the bottom of the conduction band, which is a numerical illustration of Hill’s theorem of the existence the only bound state for the hydrogen anion. The ground state energies and variational parameters for test wave functions are obtained. Useful limiting transition to the case of complete screening of the Coulomb repulsion Vee has been investigated. In this case, the Hamiltonian 2D H–transforms into a two-dimensional hydrogen-like atom with two noninteracting electrons. The distribution of electrons by energy levels is carried out according to the Pauli principle. In a singlet state, the energy of such atom corresponds to the doubled ground state energy, in triplet one it is the sum of the energies of the ground and first excited states of the 2D hydrogen atom. The results are compared with the calculations performed by other authors. The energies obtained in the work with the use of Gaussian orbitals are the lowest in comparison with th results that have already been calculate by other authors for Slater type orbitals. This indicates a high accuracy of calculations with using Gaussian orbitals.

Keywords

Gaussian orbitals, ground state energies, hydrogen anion, noninteracting electrons, Hamiltonian 2D ??

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