Isotropic magnetic shielding in the classification of aromaticities for low-lying electronic states of benzene and cyclobutadiene with an additional investigation into non-orthogonal Boys localization.

Quantum chemical calculations are performed to analyse the isotropic shielding over a fine grid through benzene and cyclobutadiene in various electronic states in order to analyse aromaticity. The use of both two-dimensional contour plots and three-dimensional isovalue plots allows unambiguous classification of aromaticity and antiaromaticity. The S0 and S2 states of benzene and the S1 and T1 states of cyclobutadiene are found to be aromatic whilst the S1 and T1 states of benzene and the S0 and S2 states of cyclobutadiene are found to be antiaromatic. This was found to be in agreement with previous predictions based on NICSs and magnetic susceptibility exaltations, but the current method was able to provide a far clearer distinction between the aromatic and antiaromatic states. Furthermore a study was performed to investigate the possibility of a non-orthogonal Boys localization procedure. Taking the molecular orbitals of water as an example, an algorithm was implemented which scanned a vast number of transformation matrices in an attempt to minimize the Boys functional with no constraint on orthogonality. It was found that the value of the Boys functional could be increased by removal of the orthogonality constraint but that critical problems arose concerning orbitals becoming linearly dependent. Methods of solving the self-convergence problem for non-orthogonal localized orbitals are suggested including the use of an alternative localization functional.