Magnetization harmonics, solid systems

In addition to the above prescriptions, many other quantities such as solution phase ionization potentials (IPs) [15], nuclear magnetic resonance (NMR) chemical shifts and IR absorption frequencies [16-18], charge decompositions [19], lowest unoccupied molecular orbital (LUMO) energies [20-23], IPs [24], redox potentials [25], high-performance liquid chromatography (HPLC) [26], solid-state syntheses [27], Ke values [28], isoelectrophilic windows [29], and the harmonic oscillator models of the aromaticity (HOMA) index [30], have been proposed in the literature to understand the electrophilic and nucleophilic characteristics of chemical systems. 

To relate Dff to the anisotropic motion of a molecule in a liquid crystalline solvent, we employ the function P(d, < ), defined as the probability per unit solid angle of a molecular orientation specified by the angles 6 and <3>, the polar coordinates of the applied magnetic field direction relative to a molecule-fixed Cartesian coordinate system. We expand P(0, ) in real spherical harmonics ... 

In nmr spectroscopy the solute orientation is often described by an orientational probability function P(0,0) [45]. TO,0) is a measure for the probability (per unit solid angle) that the applied magnetic field (or the optic axis of the liquid crystal) assumes the spherical coordinates (dy 0) in the molecule-fixed coordinate system (x, y, z). P(0, 0) can be expressed in terms of spherical harmonics of second order as follows [45] ... 

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