It is known that the square root of the electron density satisfies {-(1/2${\nabla }^2$+$v_{\theta }$([n];r) +$v_s$([n];r)}$n^{1/2}$(r) =${\varepsilon }_M$$n^{1/2}$(r), where $v_s$ is the Kohn-Sham potential and ${\varepsilon }_M$ is its highest-occupied orbital energy. The Pauli potential $v_{\theta }$ is defined as the functional derivative of the difference between the noninteracting kinetic energy $T_s$[n] and the full von Weizsäcker kinetic energy. It has already been proven that $v_{\theta }$([n];r)≥0 for all r. By starting primarily with a slightly modified version of an equation of Bartolotti and Acharya, new exact properties of $v_{\theta }$([n];r) are derived for the purpose of approximating it. The gradient expansion for $T_s$[n] gives a $v_{\theta }$([n];r) that is found to violate several of the exact conditions. For instance, $v_{\theta }$≥0 is violated unless the full von Weizsäcker term is employed. A new approximate form for $v_{\theta }$([n];r) is proposed.

• Received 29 February 1988

DOI:https://doi.org/10.1103/PhysRevA.38.625