Confined hydrogen atom: endohedrals H@C 36 and H@C 60

In this work, for the lowest states with angular momentum, $l = 0,1,2$ the energies and eigenfunctions of the endohedrals H@C36 and H@C60 are presented. The confining spherically-symmetric barrier was modeled by an inverted Gaussian function of depth ω0, width σ and centered at rc, $w(r) = -\,\omega_0\, \textrm{exp}[-(r-r_c)^2/\sigma^2]$. The spectra of the system as a function of the parameters ($\omega_0,\sigma,r_c$) is calculated using three distinct numerical methods: (i) Lagrange-mesh method, (ii) fourth order finite differences and (iii) the finite element method. Concrete results with not less than 11 significant figures are displayed. Also, within the Lagrange-mesh approach the corresponding eigenfunctions and the expectation value of r for the first six states of $s, p$, and d symmetries, respectively, are presented as well. Our accurate energies are taken as initial data to train an artificial neural network that generates faster and efficient numerical interpolation. The present numerical results improve and extend those reported in the literature.