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).