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A New Straightforward Method for Lipophilicity logP Measurement using 19F NMR Spectroscopy
Published on: January 30, 2019
Definition and properties of logopoles of all degrees and orders
1The MacDiarmid Institute for Advanced Materials and Nanotechnology, School of Chemical and Physical Sciences, Victoria University of Wellington, P.O. Box 600, Wellington 6140, New Zealand.
Abstract:
Logopoles are a recently proposed class of solutions to Laplace's equation with intriguing links to both solid spheroidal and solid spherical harmonics. They share the same finite-line singularity as the former and provide a generalization of the latter as multipoles of negative order. In a previous paper [Majic and Le Ru, Phys. Rev. Res. 1, 033213 (2019)2643-156410.1103/PhysRevResearch.1.033213], we introduced and discussed the properties and applications of these new functions in the special case of axisymmetric problems (with azimuthal index m=0). This allowed us to focus on the physical properties without the added mathematical complications. Here we expand these concepts to the general case m≠0. The chosen definitions are motivated to conserve some of the most interesting properties of the m=0 case. This requires the inclusion of Legendre functions of the second kind with degree -m≤n
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