Atoms and molecules in soft confinement potentials

Abstract

ABSTRACT We present a detailed non-relativistic study of the atoms H, He, C and K and the molecule CH in the centre of a spherical soft confinement potential of the form with stiffness parameter N and confinement radius . The soft confinement potential approaches the hard-wall limit as , giving a more detailed picture of spherical confinement. The confined hydrogen atom is considered as a base model: it is treated numerically to obtain ground- and excited-state energies and nodal positions of the eigenstates to study the convergence towards the hard-wall limit. We also derive some important analytical relations. The use of Gaussian basis sets is analysed. We find that, for increasing stiffness parameter N, the convergence towards the basis-set limit becomes problematic. As an application, we report dipole polarisabilities for different values of N and of hydrogen. For helium, we determine electron correlation effects with varying N and , and discuss the virial theorem for both soft and hard confinements in the limit . For carbon, a change in the orbital population from 2s2p to 2s2 is observed with decreasing , while, for potassium, we observe a change from the S to D ground state at small values. For CH, we show that the one-particle density becomes more spherical with increasing confinement. A possible application of soft confinement to atoms and molecules under high pressure is discussed Prof. Jürgen Gauss observing Schrödinger's cat under quantum confinement.