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

Non-decomposition theory (Pyper, N. C., 1983, Chem. Phys. Lett., 96, 204; 1 999, Molec. Phys., 97, 381) based on the Dirac equation is used to derive f ully relativistic analytical expressions for the nuclear shieldings of the 1s, 2p and 2p states of any one-electron ion having a point charge-point ma gnetic dipole nucleus. The physically transparent decomposition description of the Is shieldings is completed by deriving analytical expressions for t he two contributions to the relativistic paramagnetic shielding (sigma((MPA ))). Addition of the relativistic (sigma((MD))) and purely relativistic (si gma((MPE))) terms in Pyper (1999) yields the total shielding. Further shiel dings are computed using the decomposition method with the nuclear charge d istributed uniformly throughout a sphere with the nuclear magnetization res iding on its surface. Relativity modifies the shieldings by fractions large r than those for the hyperfine structure. enhancing that of a state for whi ch 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 sigma((MPA)), decrease nith reduction in Z or increase in l(A) or n(A). The large magnitudes of the shi eldings of orbitals in a pair having the same n(A), l(A) and m(j) but diffe rent 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 fo r the 1s and 2p m = 3/2 shieldings are approximated as the sum of the non-r elativistic result plus the lowest order relativistic correction. This pert urbation approach fails for high Z Is levels. The spatial extension of the nuclear charge and magnetization reduces the shieldings of high Z s states by about 20%, those of high Z (p) over bar levels by about 1.5%, leaving th ose of all other states affected only minimally. Even though sigma((MPA)) i s more sensitive to nuclear spatial extension than the hyperfine structure to which sigma((MPE)) is proportional. the insensitivity of sigma((MD)) cau ses the fractional shielding reductions to be slightly less than for the hy perfine interaction.