Relativistic theory of nuclear shielding in one-electron atoms 2. Analytical and numerical results

Abstract

Non-decomposition theory (Pyper, N. C., 1983, Chem. Phys. Lett., 96, 204; 1999, Molec. Phys., 97, 381) based on the Dirac equation is used to derive fully relativistic analytical expressions for the nuclear shieldings of the 1s, 2[pbar] and 2p states of any one-electron ion having a point charge—point magnetic dipole nucleus. The physically transparent decomposition description of the 1s shieldings is completed by deriving analytical expressions for the two contributions to the relativistic paramagnetic shielding (σ(MPA)). Addition of the relativistic (σ(MD)) and purely relativistic (σ(MPE)) terms in Pyper (1999) yields the total shielding. Further shieldings are computed using the decomposition method with the nuclear charge distributed uniformly throughout a sphere with the nuclear magnetization residing on its surface. Relativity modifies the shieldings by fractions larger than those for the hyperfine structure, enhancing that of a state for which no other has the same m j , large component orbital angular momentum (l A) and principal quantum number (n A). The increases of factors of 3 to 4 for high Z 1s states, originating mainly from σ(MPA), decrease with reduction in Z or increase in l A or n A. The large magnitudes of the shieldings of orbitals in a pair having the same n A, l A and mj but different jA decrease with increasing Z, being positive for j A = l A −1/2 and negative for j A = l A + 1/2. The point nucleus analytical results for the 1s and 2p m = 3/2 shieldings are approximated as the sum of the non-relativistic result plus the lowest order relativistic correction. This perturbation approach fails for high Z 1s levels. The spatial extension of the nuclear charge and magnetization reduces the shieldings of high Zs states by about 20%, those of high Zσ levels by about 1.5%, leaving those of all other states affected only minimally. Even though σ(MPA) is more sensitive to nuclear spatial extension than the hyperfine structure to which σ(MPE) is proportional, the insensitivity of σ(MD) causes the fractional shielding reductions to be slightly less than for the hyperfine interaction.