Resonance scheme

As illustrated in Fig. 3.41, several laser schemes can be used to ionize elements and molecules. Scheme (a) in this figure stands for non-resonant ionization. Because the ionization cross-section is very low, a very high laser intensity is required to saturate the ionization process. Scheme (b) shows a simple single-resonance scheme. This is the simplest but not necessarily the most desirable scheme for resonant post-ionization. Cross-... 

Regitz noted the importance of the resonance (Scheme 9) in pentacoordinated phosphirenes for the short C-P bonds and the long C=C bond [39] as compared to the corresponding bonds in 1/f-phosphirene. 

FIGURE 9. Resonance scheme for dimeric trans nitrosomethane... 

Other stable carbocations are those with an adjacent heteroatom, e.g. oxygen, which can stabilize the cation through resonance (Scheme 5.8). 

Fig. 1 b shows the 2D-IR spectrum of the rhenium complex (4 mM in DMSO) in the electronic ground state. The 2D-IR spectrum is measured according to our double-resonance scheme [2,14], employing a spectrally narrow IR pump pulse and a broadband IR probe pulse... 

The initial step in the double-resonance scheme is the excitation of a local mode hydrogen stretch vibration localized in a hydrogen halide moiety. In principle, this can be done either at the fundamental or one of the overtones. With presently available Ti sapphire lasers and parametric oscillators (OPOs), it is possible to saturate fundamentals and first overtones, thus ensuring maximum population transfer. Second overtones cannot be pumped as efficiently, but offer enormous discrimination against background and can be used to shift frequencies out of the vacuum ultraviolet and into a more user-friendly part of the ultraviolet. Thus, first and second overtones are very attractive. 

We can elaborate this VB formulation for the cycloaddition by replacing the nearest-neighbour active-space AOs in VB structures 50 and 51 with Coulson-Fischer orbitals [34(b)]. Thus if a and b are now the singly-occupied carbon and oxygen AOs of HCNO, and c and d are the singly-occupied carbon AOs of HCCH, the c and d AOs in structure 50 can be replaced by the Coulson-Fischer MOs c + k d and d + k"c. In structure 51, a + Ad, b + Ac, c + K b and d + K"a can replace the a, b c and d AOs. Use of these orbitals permits additional canonical Lewis VB structures to be included in the equivalent Lewis structure resonance scheme. The mechanism can then accommodate some charge transfer between the HCNO and HCCH reactants. The more-flexible wavefunction of Eq.(13),... 

Alternative VB representations for the cycloaddition process are displayed and discussed in Refs. [2,10,19,34], Some of them also include the less-important increased-valence structures, such as 8-10 here, in the resonance schemes. Recent MO [35] and spin-coupled VB [36] studies for this process do not give consideration to the concerted diradical formulation. The VB studies of Ref. [37] correspond to the concerted diradical mechanism discussed in Ref. [34]. 

Neither of these wavefunctions generates the uncontaminated spectroscopic ground-states of the separated reactants. These states are obtained via the linear combination P = /i - V2/2 which ensures that each of the the three degenerate Ms = 1 components of both 02 and R contributes to the ground-state resonance scheme for the reactants. This linear combination is orthogonal to /2, which generates 5 = 0 excited states for the reactants. 

The simplest chemical process is the breaking of a bond between two atoms involving two electrons. In this dissociation there is a competition between the homolytic fission, in which each atom maintains one electron, and the heterolytic fission, in which one of the atoms retains the electrons. This competition is very sensitive to the polarization of the environment because in the heterolytic dissociation there is a separation of charges. In order to focus the problem let us take two atoms, A and B, initially bonded through a classical resonance scheme involving three structures written in terms of two hybrids, xa and xb, located on different atoms. Denoting all electrons not involved in the bond as core the wavefunction... 

The transition from 2-nitrobenzothiazole to 2-nitrothiazole is reported [780] to involve a 6 ppm upfield shift of the carbon atoms resonance (Scheme 3.14). 

Because of the inclusion of Dewar-type as well as the Kekul6-type structures in the Lewis structure resonance scheme, the increased-valence structures are more stable than are the familiar Kekule-type Lewis structures from which they are derived, provided that the one-electron bond polarity parameters, are chosen variationally. Therefore as discussed already in Section 8, a better (i.e. lower energy) VB description of the bonding may be obtained when increased-valence structures rather than only the component Kekul6-type structures, are used to provide VB representions of electronic structure. 

The mechanism involves the loss of water molecule from a protonated diol, followed by 1,2-nucleophilic shift of a group. Since the diol is symmetrical, protonation and loss of water take place with equal probability at either hydroxyl group. The resulting 3°-carbocation is relatively stable but 1,2-methyl shift generates an even more stable carbocation in which the charge is delocalized by heteroatom resonance (Scheme 2.11). 

Fig. 7.3 (a) 2D Brillouin zone of graphene showing characteristic points K and T and Dirac cones located at the six comers (K points), (b) Second-order double resonance scheme for the D peak (close to F) (c) Raman spectral process for the D peak (involving two neighboring K points of the Brillouin zone K and K ). El is the incident laser energy. (After Ref. [46, 48])... 

It is only when the interactions expressed by Eq. (8.27) are neglected that orbital hybridization seems to have an effect and, thus, seems to explain some molecular properties. This is so, both in m.o. theory and in v.b. theory. Ironically, it is more difficult to take these interactions into account in v.b. theory where the concept of hybrid orbital was first introduced. For example, it is more difficult to do a complete v.b. treatment of CH4, with inclusion of the less traditional formulae in the resonance scheme (and which accounts for the non-independence of bonds), than to do a fully delocalized treatment by m.o. theory, at the same degree of approximation. But if the complete treatment is carried out, the v.b. result is the same irrespective of the hybridization considered, just as any m.o. result is the same whether pure, hybrid orbitals or a mixture of both are taken as the basis for the linear combinations. 

In general, the effects of alkyl and alkoxyl (e.g. CH3—O) groups are well known and understood. For example, ortho and para alkyls (at positions 2,4,6) stabilize the phenoxyl radical by inductive and hyperconjugative effects and, in addition, ortho groups provide steric hindrance to minimize undesirable wasting reactions such as pro-oxidation (equation 21). In addition, the conjugative effect of a heteroatom, for example at the para-position, provides stabilization through resonance (Scheme 4). 

If the crystal is close to, but not exactly at, the phase matching orientation relative to k(u> 1), then a weak 2aq beam will be generated propagating at a small angle relative to k(u 1). Minimization of this deviation angle provides a basis for servo-correction of the crystal orientation to maximize SHG. It also ensures that, as uq is scanned, the 2u>i beam pointing direction is constant, which is good news for multiple resonance schemes that require careful superposition of several beams of laser radiation. 

When the electronic transition is between a known rotational level (N", e/f determined in a double resonance scheme) of a case (b) initial state and an unknown rotational level of a case (d) final state, the existence of pattern-forming rotational quantum numbers [[B"N"(N" + 1) for case (b) and B+N+ (N+ +1) for case (d)] provides a basis for N+ — N" rotational assignments. 

An inter-ring 77 -77 -haptotropic shift of an MnjCOjs fragment in an anionic dibenzopentalene has also been observed in the interconversion of 7 and 8 using line-shape analysis of the methyl resonances (Scheme 6). " Reference to the review of Oprunenko " is recommended for a comprehensive treatment of intra-ring haptotropic rearrangements. 

For some spectroscopic problems it is necessary to use three lasers in order to populate molecular or atomic states that cannot be reached by two-step excitation. One example is the investigation of high-lying vibrational levels in excited electronic states, which give information about the interaction potential between excited atoms at large internuclear separations. This potential V R) may exhibit a barrier or hump, and the molecules in levels above the true dissociation energy V(R = 00) may tunnel through the potential barrier. Such a triple resonance scheme is illustrated in Fig. 5.42a for the Na2 molecule. A dye laser Li excites the selected level (v J )... 

The double bond-no-bond resonance scheme invoked in Fig. 2 implies geometrical changes beyond those noted above in bond lengths. The delocalization of the nitrogen lone pair into the C-X cr is expected to also involve a... 

The combination of laser-spectroscopic techniques with molecular beams and RF spectroscopy has considerably enlarged the application range of optical-RF double-resonance schemes. This optical-RF double-resonance method has now become a very powerful technique for high-precision measurements of electric or magnetic dipole moments, of Lande factors, and of fine or hyper-fine splitting in atoms and molecules. It is therefore used in many laboratories. 

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