Artigo quimica

I n the Classroom

Screening Percentages Based on Slater Effective Nuclear
Charge as a Versatile Tool for Teaching Periodic Trends
Kimberley A. Waldron,* Erin M. Fehringer, Amy E. Streeb, Jennifer E. Trosky, and Joshua J. Pearson
Department of Chemistry, Regis University, Denver, CO 80221; *[e-mail]

Background
The solutions to the Schrödinger equation allow us to understand the hydrogen atom in terms of its electron density at radial distances from the nucleus. Consideration of the helium atom brings new complications. Each of helium’s two electrons does not each “feel” two full units of nuclear charge owing to the presence of the other electron. The interelectronic interaction between its two electrons must be estimated. One of the most common ways to approach this problem is to assume that each electron in a given atom is hydrogen-like and that it experiences interactions due to the presence of other electrons. This can be accomplished using the
“variational method” in which an energy is arbitrarily set for the system and that energy is minimized by the manipulation of several parameters incorporated in the orbital wave functions.
J. C. Slater adopted this type of approach by developing
“Slater-type orbitals” (STOs), which approximate hydrogenlike orbitals. These (nodeless) orbitals are expressed by Slater in terms of a wave function with polar coordinates (1, 2): ψ (r,θ, φ) = Nnl r n 1e ξr Yml (θ, φ)

(1)

where Y are the spherical harmonics and ξ = Z */n *. Using the variational method, the “effective” principal quantum number n * and the “effective” atomic number Z * are varied by Slater in a way that minimizes the energy of the system.
In order to obtain the best value of ξ , Slater developed a set of rules that allows quantification of shielding by partitioning the electrons into groups: electrons within the same group or occupying “inner” groups all contribute to the shielding
(3). For example, rule four provides that an electron in a shell