Feasibility of atomic calculations with singular confinement exponent n=4

Ascertain whether atomic electronic-structure calculations can be successfully converged for atoms confined by the generalized singular confinement potential V_c(r)=0 for r≤r_i; V_0·exp(−(r_c−r_i)/(r−r_i))/(r_c−r)^n for r_i<r<r_c; and V_c(r)=∞ for r≥r_c, when the exponent is n=4, given that calculations reported in the paper failed to converge despite asymptotic analysis suggesting fast orbital decay.

Background

In the Appendix, the authors derive asymptotic solutions for the generalized singular confinement potentials, including the case n=4, which yields ψ(x)∝x·exp(−√V1/x) and promises very fast decay near the boundary. Such behavior could be advantageous for generating strictly localized orbitals.

Despite the promising asymptotics, the authors explicitly report that calculations for atoms confined with n=4 failed to converge, leaving unresolved whether practical self-consistent atomic calculations with this potential are possible and under what conditions.