That expectation is borne out by plots of (∆r) NTO versus d e-h in Fig. . Deviations (∆r) NTO -d e-h are strictly positive and the average deviation is no larger than 0.06 Å for any of the these excited states. Despite this strong correspondence, (∆r) NTO remains numerically distinct from d e-h . It is clear from from the S 1 data in Fig. that the difference is not some systematic error, despite the fact that λ 2 1 ≥ 0.99 in these cases. The formula for ∆r (eq. 9), which involves squaring the amplitudes κ ia separately from the quantity R ia that is to be averaged, is still not an exact expectation value even in these cases. These calculations were carried out with tight thresholds and dense grids as described in Section 3 .1, to answer any question of whether residual differences between (∆r) NTO and d e-h might be numerical artifacts. In any case, the correlation between (∆r) NTO and d e-h is much better than the correlation between (∆r) CMO and d e-h .