The SCGVB approach is a modern form of VB theory based on a wavefunction which usually turns out to be a close approximation to its CASSCF counterpart but can be interpreted in terms of a small number of meaningful VB resonance structures. Aromatic and antiaromatic molecules or electronic states usually exhibit resonance or antiresonance. Examples are provided by the SCGVB descriptions of the S0 and S1 states of benzene, which are very different from those obtained using conventional MO theory. In each state the six π electrons populate a single product of six non-orthogonal active (or, spin-coupled) orbitals, the spins of which are coupled in all five possible ways leading to an overall singlet. The optimal SC orbitals turn out to be well-localized, similar in shape to carbon 2p AOs but with small symmetrical protrusions towards neighboring carbons; the optimal spin-coupling pattern, if expressed in terms of Rumer spin functions, is dominated by two equivalent Kekulé structures and has much smaller contributions from three equivalent Dewar structures. In S0 these two structures are in resonance, Ψ(S0) ≈ Ψ(K1) + Ψ(K2), and in S1 they are in antiresonance, Ψ(S1) ≈ Ψ(K1) - Ψ(K2). The standard SCGVB wavefunction makes use of a “N in N” active space; “N in M” active spaces with different numbers of active electrons and active orbitals can be handled through an extension of SCGVB to “N in M” active spaces. The SCGVB(N,M) wavefunction involves the products of non-orthogonal orbitals corresponding to all distributions of N electrons amongst M orbitals in which the smallest number of orbitals possible, |N – M|, are doubly-occupied (for N &gt; M) or omitted (for N &lt; M), and all other active orbitals are singly-occupied; each of these products is combined with a flexible spin function which allows any mode of coupling of the spins of the active orbitals within the product. The SCGVB and SCGVB(M,N) applications that will be discussed include benzene, cyclobutadiene, C5H5-, the Möbius ring C9H9+, the homotropenylium ion.

Spin-coupled generalized valence bond (SCGVB) treatments of aromaticity and antiaromaticity

ACS Fall 2021

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