Here large values of r signify the distances where both the electron density and its gradients are very small. As a result, our computed g(r) is also susceptible to numerical inaccuracies. On the other hand, g E (r) (blue solid line) shows very different profile while it is more well-behaved at large values of r. It appears that, although simpler in form, g L (r) produces better shell-structures than the more complicated g E (r) contrary to bulk systems . for open-shell atoms. For such systems, we examined g L (r), g α L (r) and g β L (r) for the total density, α spin density and β spin density, respectively (Fig. ). For all four cases, g β L (r) showed the highest peak followed by g α L (r) and g L (r). This trend indicates that the peak height is inversely proportional to the number of electrons considered. This is also corroborated by Fig. For C atom, g α L (r) is very similar to that of g L (r). While the shell structure is clearly visible for all four atoms, note that the g L values sometimes fall below zero, rendering the corresponding Pauli potential negative. This is a serious drawback of this g L (r). Next, we analyze the effects of g E (r) for open-shell atoms (Fig. ). Similar to the cases discussed in the previous section, we considered g E (r), g α E (r) and g β E (r) for the total density, α spin density and β spin density, respectively. Following the same trend already observed in sectionIII B, we find that g E (r) is well-behaved for large r. However, the absence of any clear shell structures, akin to g L (r), obscures the applicability of Eq.( ) in Pauli potential. Unlike the divergence observed for g β L (r) for Li, here we see that the g β E (r) settles to zero for r ≥ 1.2. The problem of negative values for g E (r) is more prominent here compared to g L (r). The other features are shown by g α E and g β E are not very clear at present. A more careful analysis of Eqs. ( ) and ( ) is therefore required to develop better Pauli potentials in the future. To achieve this we employed Green's function technique to obtain a well-defined but infinite series expression for density matrix. We found that the Pauli potentials derived from previously used enhancement factors does not always meet the expected asymptotic behaviors. Also, the linear enhancement factor produces the atomic shell structure better compared to the more complicated Gaussian enhancement factors. However, both of these functions fail to provide a correct description of g(r) near the nucleus. Further studies are required to understand the reasons and remedies for this problem. Moreover, we have found that the shell structure in g(r) corresponding to linear enhancement factor is very sensitive to spin multiplicity. This work raises some new questions as well. The possibility to derive adequately accurate yet analytically closed forms of enhancement factor and Pauli potential is the most significant among them. While the Green's function method is promising, the convergence of the infinite series remains an open question. Description of Pauli potential for molecular systems is another problem that may be taken up in the future. Furthermore, the effect of the bond-breaking and bond-making process on these quantities are yet to be explored. We will be addressing these questions in our future works.