Other
Scientific paper
Jan 1974
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1974rspsa.336..251s&link_type=abstract
Proceedings of the Royal Society of London. Series A, Mathematical and Physical Sciences, Volume 336, Issue 1605, pp. 251-256
Other
2
Scientific paper
The McConnell-Buckingham-Stiles expansion \underset L=2to{ ∞ to{sum}} \underset M=0to{ Lto{sum}} (ALM cos MΦ + BLM sin MΦ ) PLM(cos θ )/RL+1 describes magnetic shielding at the point P(R,θ,Φ) outside a molecule in terms of anisotropies ALM and BLM in the magnetic multipolar susceptibilities and the associated Legendre polynomials PLM(cos θ ). This expansion is restricted to regions further from an internal origin than the most distant part of the molecular electron-density. It is shown that shieldings in other regions adjoining the molecule are conveniently calculated using the expansion \underset L=0to{ ∞ to{sum}} \underset M=0to{ Lto{sum}} (FLM cos MΦ + GLM sin MΦ ) RL PLM(cos θ ) about an external origin selected to lie closer to field-points of interest than to the molecule. Second-order quantum-mechanical perturbation theory has been used to derive formulae for the observables ALM, BLM, FLM and GLM, each of which is a sum of diamagnetic and paramagnetic components. The orbital component of the dipolar term F00 in the latter expansion is the Lamb-Ramsey expression for magnetic shielding.
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