rnThe application of the frozen-core approximation to the calculation of the shielding tensor of nuclear magnetic resonance (NMR) spectroscopy is discussed and an implementation is presented. A complete formulation of the shielding calculation within the frozen-core approximation is given, both in general t e r m and for the special case of density functional theory (DFT) and "gauge including atomic orbitals" (GIAOs). The practical implementation is validated by a detailed discussion of the consequences of the approximation. The general conclusion is drawn that the frozen-core approximation is a useful tool for shielding calculations-if the valence space is increased to contain at least the ns, np, ( n -l)p, ( n -l ) d (fourth period and higher) shells, where n is the number of the given period in the periodic table of elements. The new method is applied to nSe shieldings and chemical shifts for a small number of compounds. The agreement between theory and experiment is good for relative shifts, whereas calculated absolute shieldings are generally too small by about 300-400 ppm. This difference is attributed to the relativistic contraction of the core density at the selenium atom that had been explicitly incorporated into the experimental absolute shielding scale. 0 1996 John Wiley & Sons, Inc.of chemistry and beyond. The range of nuclei that can be studied by NMR is steadily increasing. Thus, the area of multinuclear NMR, i.e., the study of nuclei other than--say-',*H, I3C, l4,I5N, I9F, 31 P, or 33S, is rapidly gaining importance [ll.The theoretical prediction of shielding tensors has a long and successful history. These calculations are carefully reviewed annually [21. A good