Resonance mixing

HB-2) unusually long bond lengths Rab and Rue, corresponding to high populations of <7Ab an(l obc antibonds and strong resonance mixing (3.197) ... 

Finally, Table 3.42(c) summarizes the qualitative NRT results, confirming that (except for terminal obh bonds) the B—B and B—H bond orders all involve strong resonance mixing. 

As described in Section 3.5, any polar M—L bond is susceptible to backside attack by a Lewis base I. to form a linear (or near-linear) 3c/4e /ryperbonded L i- M -i L triad, equivalent to strong resonance mixing of the form... 

Table 15.3. Lowering of the energy from resonant mixing for pure and SCVB 2 orbitals.

Another feature of the resonance mixing, already alluded to, is the sign inversion which is caused by the different nature of the matrix elements that mix the Kekule structures for aromatics and antiaromatics. Thus, in the case of benzene (part a), the ground state is the positive combination of the two Kekule structures, while in cyclobutadiene (part b), the ground state is the negative combination.15116158210 214 Consequently, the twin excited states are the negative and positive linear combin-tions, respectively, for aromatics and antiaromatics.13-15-115-209 212 This relationship of the ground and excited states to the fundamental Kekule structures has been derived early on by the pioneers of VB theory.211-214... 

Special emphasis is placed on (i) the validity of a core/valence separation, with and without freezing of the core orbitals (ii) the quality of a perfect-pairing approximation, where appropriate, and the need for resonance mixing as the geometry changes (iii) the effect of various constraints during the optimization of the orbitals - and the way in which they affect the qualitative picture of the origin of the bonds. 

We have also employed ETS to study the effect of fluorine substitution on the ir orbitals of benzene and ethylene (10). Here we briefly discuss the results for the fluoroethylenes. Fluorine substitution is known to cause only small shifts in tv ionization potentials (IP) of unsaturated hydrocarbons (1 1). For example, the vertical iv IP s of ethylene and perfluoroethylene agree to within 0.1 eV. The reason that has been most often forwarded to explain this is that the electron withdrawing inductive effect, which stabilizes the occupied orbitals, is nearly cancelled by the destabilizing resonance mixing of the fluorine p orbitals with the ir orbitals of the ethylenic double bond. 

The transition at 2320 cm-1 in the (8 OH, 7 OH) plane shows four maxima of intensity specific to the combination 000) —> 011) (this transition is practically invisible in the infrared or Raman). Finally, a superposition of the OH stretching, 000) — 1100), and 5 OH overtone, 000) —> 020), is observed at 2560 cm-1. The observed intensity ratio for fundamental and overtone is close to that given by Eq. (6). There is no evidence for Fermi resonance mixing the wave functions [Novak 1963 Lucazeau 1973],... 

Similar behavior has been observed in CdSe clusters [60], Using laser excitation near the red edge of the absorption band, sharp luminescence with well-defined vibronic structures can be observed. The decay kinetics shows two components—a temperature-insensitive 100-ps component and a microsecond, temperature-sensitive component. The luminescence spectrum develops a 70-cm-1 red shift as the fast component decays. The three-level thermal equilibration model again has to be invoked to explain these kinetic data. Based on the polarization measurement, the authors suggest that it is the hole, instead of the electron, that is shallowly trapped. The trap depth is estimated to be 9 meV. The authors further propose that strong resonant mixing exists between the internal MOs and surface MOs. 

When S and T refer to two mixed vibrational levels of the same electronic state, the zero-pressure splittings of levels of S from those of T can be considerable, for instance tens of wavenumbers. Thus any substantial nonresonant process must have an additional term on the right in (3.22) to account for energetically unfavorable circumstances. Despite the differences, the experimental evidence to date points to very rapid collisional transitions between Fermi resonance-mixed vibrational levels in accord with the above theoretical discussions. 

How can other classical features, e.g. resonances, be seen in quantum systems Perhaps the most direct and familiar consequence of a classical resonance, if it occupies a sufficient amount of phase space, is to lead to resonantly mixed quantum states (or metastable states). Typically, vdW stretching freqencies are 30 cm" and vdW bending frequencies are on the order of 15 cm as seen, for example, in a recent study of Ar-glyoxal complexes by Dai and co-workers. This was the case for our NeQ2 study and led, for example, to the importance of the (l,0,-2) resonance. Such 1 2 stretch-bend resonances, in quantum mechanics, are simply Fermi resonances. Indeed, examples of such Fermi resonances have been noted in quantum studies of the metastable states of NeQ2 and ArCl2. vdW stretch-bend interactions have recently been invoked to explain spectral patterns observed in substituted benzene-Ar complexes. 

The stabilization energy, of the transition state relative to the localized structure at the crossing point in the VB state correlation diagram, due to resonance mixing of the VB curves. VB curve crossing diagrams... 

Because the resonance mixing in (8.23) involves three atomic centers competing for two electron pairs, it is also described as three-center, four-electron (3c/4e) hypervalency. The phenomenon can also be identified as hyperbonding and denoted by a distinctive stroke-symbol (L -A— L ) and m-bond notation that suggests its unique electronic character, namely. 

Much weaker is the secondary pull delocalization (10.19) and associated resonance mixing... 

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