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

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Title: Relativistic theory of nuclear shielding in one-electron atoms 2. Analytical and numerical results.
Authors: Pyper, N. C., Zhang, Z. C.
Source: Molecular Physics. 08/10/99, Vol. 97 Issue 3, p391-413. 23p. 17 Charts.
Subjects: Relativistic particles, Radiation shielding, Electrons, Atomic orbitals
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, 2p 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 (sigma(MPA)). Addition of the relativistic (sigma(MD)) and purely relativistic (sigma(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 , large component orbital angular momentum (lA) and principal quantum number (nA). The increases of factors of 3 to 4 for high Z 1s states, originating mainly from sigma(MPA), decrease with reduction in Z or increase in lA or nA. The large magnitudes of the shieldings of orbitals in a pair having the same nA, lA and mj but different jA decrease with increasing Z, being positive for jA = lA - 1/2 and negative for jA = lA + 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 Z s states by about 20% , those of high Z p levels by about 1.5% , leaving those of all other states affected only minimally. Even though sigma(MPA) is more sensitive to nuclear spatial extension than the hyperfine structure to which sigma(MPE) is proportional, the insensitivity of sigma(MD) causes the fractional shielding reductions to be slightly less than for the hyperfine interaction. [ABSTRACT FROM AUTHOR]
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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, 2p 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 (sigma(MPA)). Addition of the relativistic (sigma(MD)) and purely relativistic (sigma(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 , large component orbital angular momentum (lA) and principal quantum number (nA). The increases of factors of 3 to 4 for high Z 1s states, originating mainly from sigma(MPA), decrease with reduction in Z or increase in lA or nA. The large magnitudes of the shieldings of orbitals in a pair having the same nA, lA and mj but different jA decrease with increasing Z, being positive for jA = lA - 1/2 and negative for jA = lA + 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 Z s states by about 20% , those of high Z p levels by about 1.5% , leaving those of all other states affected only minimally. Even though sigma(MPA) is more sensitive to nuclear spatial extension than the hyperfine structure to which sigma(MPE) is proportional, the insensitivity of sigma(MD) causes the fractional shielding reductions to be slightly less than for the hyperfine interaction. [ABSTRACT FROM AUTHOR]
ISSN:00268976
DOI:10.1080/002689799163785