Atoms and molecules in soft confinement potentials
Lukáš F. Pašteka, Trygve Helgaker, Trond Saue, Dage Sundholm, Hans‐Joachim Werner, Mustafa Hasanbulli, J. Major, Peter Schwerdtfeger
Abstract
We present a detailed non-relativistic study of the atoms H, He, C and K and the molecule CH4 in the centre of a spherical soft confinement potential of the form VN(r)=(r/r0)N with stiffness parameter N and confinement radius r0. The soft confinement potential approaches the hard-wall limit as N→∞, 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 r0 of hydrogen. For helium, we determine electron correlation effects with varying N and r0, and discuss the virial theorem for both soft and hard confinements in the limit r0→0. For carbon, a change in the orbital population from 2s22p2 to 2s02p4 is observed with decreasing r0, while, for potassium, we observe a change from the 2S to 2D ground state at small r0 values. For CH4, 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 discussedProf. Jürgen Gauss observing Schrödinger's cat under quantum confinement.