Atoms and molecules in soft confinement potentials
Résumé
We present a detailed non-relativistic study of the atoms H, He, C and K and the molecule CH4 in the center 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 analyzed. We find that, for increasing stiffness parameter N , the convergence towards the basis-set limit becomes problematic. As an application, we report dipole polarizabilities 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 2s 2 2p 2 to 2s 0 2p 4 is observed with decreasing r0, while, for potassium, we observe a change from the 2 S to 2 D 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 discussed. Dedicated to Prof. Jürgen Gauss on the occasion of his 60th birthday
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