Separation of core and valence regions in atoms

It is proposed that the minimum in the radial density function R (r) = 4πr2ρ (r) defines a physically meaningful boundary surface separating core and valence regions of first-row atoms. The point rm at which this minimum occurs has been found to fall within the interval in which the linear lnρ (r) vs r plots of these atoms undergo a significant change in slope. When the valence region is defined in the proposed manner, a valid estimate of its electronic energy can be obtained with the formula E=−12π/7 (Z−−i−i) ℱ∞rmρ (r) r dr, in which Ni is the number of electrons in the core region of an atom with nuclear charge Z. This equation is a modified form of an expression previously found to be accurate for atoms. For Be, C, O, F, and Ne, Ni ranges from 2.05 to 2.20 electrons. The core-valence separation in larger atoms may be treated in a similar manner; rm is then the outermost minimum in the radial density function.