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 m_j but different j_A 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.