Orbital selection rules

The first two parts of the expression vanish exactly because of Laporte s rule, while the last two survive both parity and orbital selection rules to the extent that the mixing coefficients c and c are non-zero in noncentric complexes. 

Therefore, it follows that in a backside trajectory, we obtain both the lowest crossing point as well as the largest TS resonance energy. Computationally, the backside barrier is smaller by 10—20 kcal/mol compared with a front side attack (42). Equation 6.18 defines an orbital selection rule for an Sn2 reaction. Working out this rather trivial prediction is nevertheless necessary since it constitutes a prototypical example for deriving orbital selection rules in other reactions, using FO—VB configurations. Thus, a simple rule may be stated as follows ... 

Because of the spin-orbit selection rules, only triplet zeroth-order states contribute to the first-order perturbation correction of a singlet wave function. In Rayleigh-Schro dinger perturbation theory, the expansion coefficient a of a triplet zeroth-order state (3spin-orbit matrix element with the electronic ground state (in the numerator) and its energy difference with respect to the latter (in the denominator). 

Table 1 gives the orbital and spin-orbital selection rules appropriate for a D41, copper(II) ion in a compressed and elongated environment. Here the Mulliken... 

Since no advanced calculations on the square-pyramidal closed-shell complexes are available, it is difficult to understand the low transition probability in the emission. As a matter of fact we have the spin selection rule prohibiting fast decay from the excited triplet level. A simple m.o. approachshows that it is hard to see where an orbital selection rule would originate from. The long decay time is then ascribed to orbital overlap restriction, but a more quantitative approach is necessary. 

The e (KE) peaks in the PES (fixed hu) provide information about the relative energies of electronic states of the AB neutral molecule (for example AsO-, Lippa et al., 1998) that, owing to spin or orbital selection rules, are not easily observed by direct study of the neutral molecule spectrum. An anion photodetachment spectrum is recorded by detecting the low-energy electrons ejected as the photon energy is scanned through the successive photodetachment thresholds associated with the energies of each neutral molecule rovibronic state. 

The exact spatial-spin eigenfunctions of a system should belong to representations of the direct product group of spatial and spin symmetry operators. The Hamiltonian including spin is invariant under all the spatial-spin symmetry transformations. Thus the spin-orbit operator (unspecified) is invariant under all space-spin symmetry transformations. The total symmetry of the eigenfunctions is the direct product of the symmetries of the spatial and spin parts of the function. Thus, if we can obtain the irreducible representations of the spin functions, the spin-orbit selection rules will be known from... 

Deduce the first der spin-orbit selection rules for a heteronuclear diatomic molecule with ground state and excited states Z , 11. 

Table 9.8. Second-Order Spin-Orbit Selection Rules for the Appearance of Ungerade Vibrations in Singlet-Triplet Spectra...

The fourth integral governs the electronic orbital selection rule. It has to do with the symmetries of the electronic wave functions in the electronic GS and ES. In order for the electronic transition to be orbitally allowed, the triple direct product must contain the totally symmetric IRR for the point group of the... 

The orbital selection rules for transitions between individual crystal field levels are displayed in terms of the point group irreps of the initial and final state wavefunctiOTis, and for a forced ED transition between 4 Fj 41 F[. 

The fact that orbital selection rules appear to be operative in these reactions may be an indication that the Uoodward-Hoffmann approach can be quite fruitful, not only in the theory of organic reactions, but also in the study of transition metal complexes. 

The orbital selection rule can be stated in different ways. It applies most strictly to species with a center of inversion. For them it can be stated in the following terms. 

By using this approach, it is possible to derive orbital selection rules for cases that are ambiguous in qualitative MO theory. For example, for radical cleavage of ct bonds, using the R with a triplet configuration on the... 

The spin of the photon imposes an additional orbital selection rule on absorption. To conserve angular momentum when a photon is absorbed, a change in electronic orbital angular momentum must balance the angular momenrnm provided by the photon. In atomic absorption, this means that the azimuthal quanmm number / must change by either 1 or +1, depending on whether the photon has left nis = +1) or... 

Utilizing VBCM to Derive Orbital Selection Rules for Reactivity... 

An important conclusion from the VB mixing patterns of the configurations in Scheme 5 is that the nucelophilic substitution and the corresponding electron transfer process follow different orbital selection rules which can be manifested as different stereochemical structures of the corresponding TSs. This prediction was recently vindicated by a theoretical study of ketyl anion radicals and alkyl halides, where the electron transfer and substitution transition states were found to possess different regioselectivity and orientational selectivity which obey the orbital selection rules predicted by the VBCM model. ... 

The above examples illustrate the insight of the VBCM model to problems which range from reaction mechanisms to predictions of TS structure based on orbital selection rules. Much of our current effort is concerned with the application of the VBCM to a variety of chemical problems, especially in odd electron systems, and in organometallic chemistry. 

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