Calculation of the energy of a two-dimensional hydrogen molecule

Abstract

ABSTRACT The equilibrium distance and energies of singlet and triplet states of a two-dimensional (2D) hydrogen molecule are calculated. Variational calculations were carried out using a multiparameter system of Gaussian functions with correlation multipliers. The results are compared with the calculations performed by other authors. Currently, the most accurate values of the singlet and triplet states energy of the 2D-molecule in two-dimensional systems have been obtained: Es = –5.2843Eh , Et = –2.9277Eh ; the equilibrium state corresponds to the distance Rm = 0.36614ao , where Eh is the Hartree energy, and ao is the Bohr radius. In the mathematical sense, a 2D hydrogen molecule is a direct analog of a pair of shallow hydrogen-like paramagnetic centres in covalent two-dimensional crystals. The energies of the singlet and triplet states of 2DH2 are significantly lower than the corresponding values of the three-dimensional hydrogen molecule (3DH2), while the singlet–triplet splitting is much higher than that of 3DH2. In the equilibrium state, 2DH2 protons are much closer to each other, which leads to a significant increase in correlation effects associated with the direct dependence of the wave function on the interelectron distance compared to 3DH2.