Electron density and its derivatives at the nucleus for spherically confined hydrogen atom

It is shown that the energy of a hydrogen‐like atom confined inside a spherical cavity of radius, R, and potential barrier, V₀, is quantitatively defined by the ratio . Here, the conventional spherical density (r) is scaled as η_l(r) = and the ratio of the second derivative η(r) to η_l(r) is evaluated at the nucleus. Numerical results of the ratios are presented for 1s, 2s, 2p, and 3d states at several values of V₀. For such states, the characteristic radii of confinement leading to the well‐defined values of energy are identified. © 2008 Wiley Periodicals, Inc. Int J Quantum Chem, 2009