Transition density topology of the L a and L b states in indoles and purines

Matrix elements may be viewed as the scalar projection of an operator onto the transition density between the states involved (trace of matrix product equivalent to double dot product). This means that the operator and transition density matrices must “look the same” if a matrix element is to be the large. Using CNDO/S‐CI wave functions, we have examined the symmetric part of the first‐order transition density matrices (transition bond orders) for a series of aromatic systems whose π electrons are isoelectrornic with the nine‐membered, ten‐π‐electron cyclononatetraene anion, including indenide, indole, benzimidazole, purine, and adenine. The topology of the parent hydrocarbon matrices is not purely even or odd as with alternant systems, thereby precluding exclusive action by vibronic or inductive perturbations. See P. R. Callis, T. W. Scott, and A. C. Albrecht, J. Chem. Phys. 78 , 16 (1983). Nevertheless, interesting and useful patterns have emerged. For example, the matrices show, at a glance, how the D 9th dictated degeneracy of the so‐called L b and L a bands of the parent is retained as accidental degeneracy in some analogs because the crosslinking and heteroatom perturbations have opposite sign and nearly cancel. The first‐order transition bond orders between L a and L b vanish so that real one‐electron operators cannot couple these states in the parent molecule. This leads to distinctive L a and L b patterns which persist throughout the series, thereby providing a logical and satisfying justification for these intuitively assigned labels which are ambiguous in the Platt scheme: if one keys on the six‐membered ring there is a striking correlation between the L a,b transition densities, as they have been assigned, and those of benzene.