Minus states

Moreover, there are two diradical states of symmetry Cs constructed on the basis of 1-electron base states. To help visualizing the analysis we use the planes associated to the CH2 groups. At n/4 the planes defining each CH2 sigma base states at opposite sites have normal vectors making a nil angle. The local 7i-axis serve to identify new 1-e-base states Yj+ and y. The + state has two local NPs the minus (-) state increases the number of nodes by one unit. The... 

Within the PPP approximation the singlet and triplet Cl matrices for an alternant hydrocarbon each factor into two separate matrices for the plus states and the minus states corresponding to the linear combinations... 

The ground state behaves like a minus state since it interacts only with minus states excited configurations of the type however, behave like plus states. In this approximation the transition moments between two plus states or two minus states vanish, and such transitions are forbidden. Electric dipole transitions are allowed only between plus and minus states (Pariser, 1956). 

When first-order configuration interaction is taken into account, the contributions from these two transitions add in-phase for excitation into the plus state and out-of-phase for excitation into the minus state cf. Equation (1.26). From the coordinates and or and depicted in Figure 1.9, it is easy to see that for. T-rronx-butadiene Af, = A/, = 0. Accordingly = 0, the transition probability is zero and the transitions into the plus and the minus states are both forbidden. For. y-ds-butadiene, which does not possess a center of symmetry, M, = 0, but M. 0. The transition moment differs from zero and is oriented perpendicular to the long axis of the molecule. The transition into the plus state is therefore allowed. For excitation into the minus state the two contributions cancel each other and this transition is forbidden irrespective of the molecular geometry. (Cf. also Example 1.9.)... 

First-order Cl, which for alternant hydrocarbons gives rise to the distinction between plus and minus states (cf. Section 1.2.4). 

As depicted in Fig. 1.4, the difference between the initial and final Gibbs energy levels (state D minus state A) AGs dictates the solubility of the drug in the solvent. The difference between the initial energy levels and the intermediate RTM state energy level (state C minus state A) represents the energy required to bring the system... 

The energies associated with and different states are obtained, designated by Pariser (65) as plus and minus states. 

The experimental spectrum of alternant aromatic hydrocarbons will generally display a strong absorption band due to the transition to the plus state, a medium weak one due to the transition n+1 <- , and a very weak one. since the transition to the minus state is formally forbidden. It should be noted that Clar 40) has introduced for the transition n + l- w the symbol p and for the plus and minus states the notation jS" " and a. 

If the excited states 1) would simply be given by Eq. (9) and fjL is restricted to the first two terms in Eq. (11), then we obtain the well known result that the transitions to the minus-states in Eq. (9) are forbidden and those to the plus-states are allowed with equal intensities. This yields the characteristic spectrum " with one peak at position Wo + A and another peak at position Wq — 2A, and an intensity ratio of 2 1, that is obtained when only the electrostatic dipole-dipole interactions are included (wq = = b)- In general, the excited states 1 from Eq. (8) are more complex, however. For arbitrary orientations of the monomers all dimer transitions become allowed, in principle, and their intensities become orientation-dependent, just as their frequencies. 

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