Aromaticity in 'benzene-like' D6h rings

Whereas it may be most convenient for many purposes to use CASSCF canonical orbitals, which transform as irreducible representations of the molecular point group, for others it may be more instructive to examine representations of the same CASSCF wavefunction that are based instead on relatively localized orbitals, resembling those envisaged in classical valence bond theory. Ultimately, none of these representations of precisely the same CASSCF wavefunction is any more 'correct' than any other. On the other hand, if a representation based on orthogonal orbitals appears (at first sight) to give a conflicting assessment of the various VB-like characteristics of that wavefunction, then it could be important to remember that valence bond theory is traditionally based on notions of nonorthogonal localized orbitals. Our own strong preference is to consider representations in which a very compact VB-like component based on nonorthogonal relatively localized orbitals is overwhelmingly dominant.

Starting from CASSCF(6,6)/6-31G(d,p) wave functions, we considered different interpretations of the pi electron systems for various (constrained) 'benzene-like' D6h rings, using the CASVB code to exploit the invariance of the total CASSCF wavefunction to arbitrary nonsingular transformations of the active orbitals. Various quantities that are obtained rather directly from the calculations provide a fairly consistent ordering of the degree of aromaticity: C6H6 ~ B6 > N6 > Al6 ~ Si6H6. Subsequent fully-variational optimization of the VB-like description, again using the CASVB code, leads only to rather modest further changes to the shapes of the orbitals, to the weights of the different modes of spin coupling, and to energy differences such as the vertical resonance energy.

Reference: "Modern VB-like representations of selected D6h "aromatic" rings." J.G. Hill, D.L. Cooper and P.B. Karadakov, J. Phys. Chem. A 110, 7913-7917 (2006).