Quadruplet states

These quadruplet states lie from higher to lower energy, as shown in Fig. 11. The hyperfine interaction is effectively expressed by... 

A quite similar effect takes place in the case of electron configuration t. In this case the PIT strong vibronic mixing of two excited states and results in a lower orbitally disproportionate component of the type tx t h Utz t)> while the ground quadruplet state A2 corresponds to the Hund s rule distribution... 

Let us first use Eq. (1) to estimate the resistance to distortion arising from n interactions in the high spin states. The results are displayed in Table 2, and show a remarkable constancy at the three levels of computations used in the case of allyl. Note that when Cl is performed in the n space, the n component A of the distortion energy is not any more given by the three first terms in Eq. (1), but one can still compute it as the difference between the total distortion energy and its a component, calculated from the last three terms of Eq. (1). It turns out that A in the quadruplet allyl is effectively smaller than our higher limit of 0.5 kcal/mol, and does not appear to be sensitive to Cl or basis-set extension. Similar results are also observed in benzene and cyclobutadiene, in which the n systems of the high spin states also prove to be rather insensitive to the distortion. 

Polyradicals 6—8 in Scheme 8.3 further show the utility of the Ovchinnikov rule. For example, 2,4-dimethylenepentadienyl, 6, is immediately seen to have a quadruplet ground state, as well as 1,3,5-trimethylenebenzene, 7, while tripropadienemethyl, 8, is a quintuplet (Scheme 8.3). Many other examples are offered in Exercise 8.1. 

Fig. 2. Laser (/ ), microwave ( hf)> and RF ( shf) transitions in pHe+. Vhf is a transition between the SHF states of same total angular momentum J = L that is suppressed by a factor 1 /L compared to the allowed AL = 1 transitions i f- The right-hand side shows the splitting of the parent state of a laser transition into a quadruplet, while on the left-hand side only the dominant doublet splitting for the daughter state is shown...

In a second similar experiment 1Z2) the benzyl radical, PhCHs could be detected after the photodissociation of PhCHjCl, adsorbed on silica gel, under experimental conditions similar to the previous case. The EPR spectrum of this radical in the adsorbed state is more complicated (Fig. 20b) consisting of a triplet, with components split additionally into quadruplets. The spectrum could be satisfactorily interpreted by a delocalization of the lone electron of the methylene group, which is partly injected into the benzene ring. 

To make further progress the form of 4> must be specified. Generally the potential energy will contain terms involving the coordinates of pairs, triplets, quadruplets, etc., of molecules. A few calculations of the equation of state of a fluid with such a general form for have been made. However, the common practice is to assume pair-wise additivity ... 

As follows from these results, orbital disproportionation in systems with half-closed-shell electronic configurations is necessarily accompanied by lowering the spin of the electronic ground state. For the configuration it means transition from the high-spin (HS) triplet A state to the low-spin (LS) singlet state A, while for t this transition is from the quadruplet (HS = 3/2) to the doublet (LS = 1/2) state. Since this transition is induced by the PJT distortion originating from an excited... 

Fig. 9 Cross-section of the APES of Cgo along the ective mode that takes the system from the undistorted high-spin minimum to the distorted low-spin minimum due to the multimode (H + Hu) hg PJT coupling [26]. The zero-point energies (ZPE) tilong this mode (which are different from the global ZPE) show that the lowest vibronic state associated with the electronic spin-doublet state is lower than that for the spin-quadruplet...

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