To illustrate how badly things can go awry when orbital invariance is sacrificed, we begin with an example of the low-lying excited states of a dipeptide that has been used in previous tests of Λ and Γ. 9,11 Guido et al. noted that the CMO and NTO representations afford different values of ∆r and Γ for these systems, but did not pursue this observation in detail. We computed excited states at the TD-CAM-B3LYP/6-31(n+,n+)G* level, meaning that n sets of diffuse functions are added to all atoms, starting from 6-31G*. 101,102 Beyond 6-31++G* (n = 1), diffuse functions are added in geometric progression, scaling the exponents by successive factors of (3.32) -1 . 101 Due to the ultra-diffuse nature of these basis sets, tighter thresholds and denser quadrature grids are used for these calculations, as described in Section 3 .1.