A parameter-free analytical representation for the Pauli potential is presented. Minimization with respect to the energy yields a single minimum for H and He atoms, while for atoms from Li to C the energy landscape exhibits two separate minima with the proposed ansatz for the Pauli potential. Here, one of the local minima results in structured electron densities, while the other minimum is connected with an unstructured electron density. For the atoms from N to Ne, only the unstructured solution is found. Total energies resulting from the structured electron density lie in all cases above the corresponding orbital-based Kohn–Sham (KS) data, obtained from a Slater determinant obeying the fermionic nature of the electrons, while the unstructured solution yields total energies far below the KS data. The proposed ansatz seems to allow for both energetic minima: the first one accounting for the fermionic nature of the electrons, while the second one showing Boson-like characteristics. Thus, the proposed ansatz provides new insight for systematic approaches in orbital-free density functional theory.