Electronic allowedness

This means that the total emission intensity depends only on the purely electronic transition dipole moment. Thus, the electronic allowedness represents the source of intensity which is distributed according to the Franck-Condon factor to the different vibrational satelHtes. With respect to the symmetry of the Franck-Condon active vibrations, it is remarked that this factor can only be nonzero for totally symmetric modes (if it is referred to fundamentals), since the vibrational ground state n(v = 0) is totally symmetric (e.g.see [154,p. 113]). 

The symmetries of the initial and the final wave functions and of the electromagnetic radiation operator determine the allowedness or forbiddenness of an electronic transition. The transition moment integrand must be totally symmetric for an allowed transition such that Mmn V0. 

As chemists we can pose a simple, focussed question how do the Woodward-Hoffmann rules (WHR) [18] arise from a purely electron density formulation of chemistry The WHR for pericyclic reactions were expressed in terms of orbital symmetries particularly transparent is their expression in terms of the symmetries of frontier orbitals. Since the electron density function lacks the symmetry properties arising from nodes (it lacks phases), it appears at first sight to be incapable of accounting for the stereochemistry and allowedness of pericyclic reactions. In fact, however, Ayers et al. [19] have outlined how the WHR can be reformulated in terms of a mathematical function they call the dual descriptor , which encapsulates the fact that nucleophilic and electrophile regions of molecules are mutually friendly. They do concede that with DFT some processes are harder to describe than others and reassure us that Orbitals certainly have a role to play in the conceptual analysis of molecules . The wavefunction formulation of the WHR can be pictorial and simple, while DFT requires the definition of and calculations with some nonintuitive ( ) density function concepts. But we are still left uncertain whether the successes of wavefunctions arises from their physical reality (do they exist out there ) or whether this successes is merely because their mathematical form reflects an underlying reality - are they merely the shadows in Plato s cave [20]. 

With temperature increase to 4.2 K, a completely different situation develops. Now, the emission stems dominantly from the substates n/ni, which carry much higher allowedness with respect to the purely electronic transition to the ground state at 21,461 cm As consequence, the vibrational modes, which are active in the emission process, are different from those found in the emission of substate I at T=1.2 K. In particular, for several fundamentals such as the 1,056 and 1,497 cm-1 modes, one can also observe weak second members of progressions (not displayed in Fig. 6). Therefore, it can be concluded that these modes represent totally symmetric Franck-Condon (FC) active modes [63, 90, 94-97], The assignment concerning FC activity is in accordance with the observation that many of the FC modes (e.g., 530, 743,1,056 cm-1) are also built upon the false origins and occur as combinations in the 1.2 K spectrum. Using the equation (see for example [49, 63, 95-98])... 

According to Zimmermann [101] and Dewar [102], the allowedness of a concerted pericyclic reaction can be predicted in the following way A cyclic array of orbitals belongs to the Hiickel system if it has zero or an even-number phase inversions. For such a system, a transition state with An+ 2 electrons will be thermally allowed due to aromaticity, while the transition state with An electrons will be thermally forbidden due to antiaromaticity. 

An important consequence of the pseudopericyclic mechanism is that the planar (or nearly planar) transition states preclude orbital overlap between the a- and Jt-orbitals. This implies that all pseudopericyclic reactions are allowed. Therefore, Jt-electron count, which dictates whether a pericyclic reaction will be allowed or forbidden, disrotatory, or conrotatory, is inconsequential when it comes to pseudopericyclic reactions. Bimey demonstrated this allowedness for all pseudopericyclic reactions in the study of the electrocyclic reactions 4.11-4.14. 

In addition to symmetry restrictions on electronic transitions, there are restrictions caused by the necessity of overlap in space of molecular orbitals for the electron in its initial and final states. Where this overiap is small, for example in n -> jt transitions in carbonyl compounds, the electronic integral in Eq. (1) is diminished. The allowedness of a transition F expressed as an oscillator strength can be summarised as in (4) by a series of factors, f, which relate in turn to spin, (s), overlap (o), p (parity), sy (symmetry), and which have the following approximate values fg = 10 , fo = 10 , fp = 10 , fgy = 10 -10 , where F is the oscillator strength of a fully allowed transition. For fluorescence then (fg = 1), values of Icr extend from 10 s for a fully allowed transition, typical say of dyestuffs, through lO s for... 

An approach very closely related to that of Woodward and Hoffmann is the so-called Hiickel-Mobius approach 35> based on the rule An +2 electron systems prefer Hiickel geometries and An electron systems prefer Mobius geometries 36>. When no symmetry exists and there is no cyclic orbital array the allowedness or forbiddenness of a reaction can be determined by following the form of the MO s during the reaction 37>. A detailed quantum mechanical study of the stereochemistry of thermal and photo cyclo-addition reactions has been reported38), and a quantum mechanical discussion of the applicability of the Woodward-Hoffmann rules can be found in a paper by George and Ross 39>. 

Between 1965 and 1969 Woodward and Hoffmann presented rules for each of the different classes of pericyclic reaction.677 They showed that the allowedness or otherwise of reactions depended critically upon the number of electrons involved and on the stereochemistry of the reaction. We shall go through the rules twice first the rules class by class, and then again using the single generalised mle that they presented in 1969 that applies to all classes of pericyclic reactions. 

Other symmetry perturbations of the 7t-electron cloud increasing the allowedness of the bands (higher absorptivities) result from substitution in the benzene ring. The bands akin to unsubstituted benzene at 185,210 and 260 nm are usually referred to as the (two) primary bands (or B and LJ and the secondary band (or L ) respectively (Murrell, 1963). Steric repulsions among the substituents and fusion of the benzene system with small rings cause static molecular distortions, and so enhance absorptivity. In some cases this hyperchromic effect is significant, even dramatic. For... 

The electron configuration, of a particular state is a list of its occupied orbitals, a superscript 2 indicating occupancy by two electrons of opposite spin. The two ground-state configurations correlate because each has three doubly occupied orbitals, two of them symmetric and one antisymmetric with respect to m. The correlation or non-correlation of the states of reactant and product does not depend on the energetic ordering of their occupied orbitals, but simply on whether the number of doubly-occupied orbitals with each symmetry label is the same in both. It follows that the initial slope of the HOMO is irrelevant to this criterion of allowedness . 

Unlike Figs. 5.1 and 5.2, the correspondence diagrams in Fig. 5.11 are not rudimentary , because they incorporate all of the information necessary to deduce the allowedness of the thermal isomerizations. The six combinations of the (Tec-bonding orbitals of benzene retain their C2V labels in prismane and Dewarbenzene as do its six CH-bonding combinations. The analysis of the reaction is thus reduced to a six-electron problem the occupied orbitals involved are the three Hiickel-MOs of benzene - labelled as in Fig. 1.2, the long a-bonding orbital ((725) in its two valence isomers, and the symmetric (-I-) and antisymmetric (—) combinations of (Ti3 and <74 in prismane or of TTie and 34 in Dewarbenzene. 

We saw earlier that the probability of electric dipole absorption is related to the transition dipole moment. However, there are a variety of terms commonly used to describe the strength or probability of absorption. The allowedness or forbiddenness of the transition, and oscillator strength, /, are useful ideas where the relative, rather than absolute value, of the strength of coupling is required. These terms are factors used to describe how likely absorption is by reference to the ideal oscillator of a free electron where the transition is fully allowed and both the allowedness and oscillator strength are unity. 

The choice of phase indication in the molecular orbital is arbitrary and it is equally valid to choose to rotate together the unshaded orbitals in Equation 5.14, that is, 90° clockwise rotation at C-2 paired with 90° counterclockwise rotationatC-6. Both choices are equally valid for consideration of allowedness and both indicate disrotatory motion, but each may lead to different stereoisomeric products. Two allowed motions should be considered in all pericyclic reactions. Which of the two disrotatory motions occurs will be determined in most cases by steric or electronic effects among the substituents, or both may occur. Conrotation, in which both orbitals rotate in the same direction, is forbidden for this reaction because it leads to antibonding overlap at one end. 

Fig. 27. By applying a magnetic field the wavefunctions of the states 11) and II > mix. The matrix element shown symbolizes this mechanism, which provides allowedness to the transition from the perturbed state Ig) to the ground state 10). Using this process it is possible to continuously tune the vibrational satellite structure in emission. At B = 0 T the spectrum is dominated by Herzberg-Teller (HT) induced satellites, while with increasing field strength the electronic origin and Franck-Condon (f C) satellites strongly grow in. This is seen in the spectra reproduced in Fig. 24...

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