Dimensional scaling and renormalization

Chief features of dimensional scaling methods are exemplified by briefly reviewing prototypical applications and recent developments. The pseudoclassical large-D limit usually can be evaluated exactly regardless of the magnitude, nature, and number of strong, nonseparable dynamical interactions. Often, this limit can be accurately linked to D = 3 by perturbation or interpolation methods. This is because the dimension dependence of many-body effects tends to be smooth and mild when calibrated by appropriate one- or few-body problems. A simple renormalization procedure applied to atoms with up N ∼ 100 electrons yields a major part of the correlation energy. From Hartree-Fock input, a renormalized nuclear charge is determined which renders the dimensionally scaled energy at D → ∞ a good approximation to that for D = 3 with the actual Z. Prospects are discussed for other means to exploit dimensional scaling, including an analogous renormalization procedure for molecules. © 1996 John Wiley & Sons, Inc.