where the matrices A ± B are orbital Hessians, i.e., stability matrices. Solution of this equation for excitation energies ω will fail if the triplet instability matrix A + B exhibits any negative eigenvalues. Such instabilities are found to be widespread once one an excited-state trajectory moves away from the Franck-Condon excitation point and begins to explore bond-breaking regions of the potential energy surface, leading to the suggestion that the TDA is effectively mandatory for photochemical applications.