Aromatic Ring Current - Relative Aromaticity

Relative Aromaticity

Numerous attempts have been made to quantify aromaticity with respect to the observed ring current. One method is called diamagnetic susceptibility exaltation Λ defined as the difference between the measured magnetic susceptibility of a compound and a calculated value based on group additivity tables. Benzene is clearly aromatic (Λ = −13.4), borazine (Λ = −1.7) and cyclohexane (Λ = 1.1) are not aromatic and cyclobutadiene (Λ = +18) is antiaromatic.

Another measurable quantity is the chemical shift of lithium ions Li+ in complexes of lithium with aromats because lithium tends to coordinate to the face of the aromatic rings. Thus the lithium atom in cyclopentadienyl lithium (CpLi) has a chemical shift of −8.6 ppm (aromatic) and its Cp₂Li− complex a shift of −13.1.

Both methods suffer from the disadvantage that values depend on ring size. The nucleus-independent chemical shift (NICS) is a computational method that calculates the absolute magnetic shieldings at the center of the ring taken with reversed sign. In this method negative NICS values indicate aromaticity and positive values antiaromaticity.

Yet another method called the harmonic oscillator model of aromaticity (HOMA) is defined as a normalized sum of squared deviations of bond lengths from the optimal value, which is assumed to be realized for a fully aromatic system. An aromat has HOMA value 1 whereas a non-aromatic compound has value 0. For all-carbon systems, a HOMA value is obtained making use of this equation:

with the value of 257.7 the normalization value, n-number of CC bonds, d_opt the optimized bond length (1.388 angstrom) and d_i the experimental or computed bond length.