Skeleton modes, coupling

We will use the 7D CRS Hamiltonian which has been determined and analyzed in Ref. [10] (DFT/B3LYP, 6-31+G(d,p)). In short, the large-amplitude motion of the H/D atom is restricted to the (x,y) plane of the molecule (cf. Fig. 1). The origin of the molecule-fixed coordinate system is at the center of mass, with the axes pointing along the principal axes of inertia for the enol configuration. The H/D motion couples strongly to 5 in-plane skeleton modes, Q = (Q4, Q, Qu, Q26, Q3o)> which are described in harmonic approximation... 

Figure 1 Left Enol-keto tautomerism in salicylaldimine (SA) and normal mode displacements for skeleton modes 1 4 and 1/30. Middle H/D diabatic potential energy curves Ua(Qu) for mode i/u (lowest states ground state, bolding and stretching fundamental, first bolding overtone arrows indicate laser excitation). Right two-dimensional (Qj4,Q3o) cuts through the adiabatic PES (obtained upon diagonalizing the field-free part of Eq. (1)) which has dominantly H/D stretching character but includes state and mode couplings (contours from 0 to 7400 cm-1).

Here, the diabatic PES for the motion of the skeleton modes are Ea(Q) = Ea — faaQ + 1/2QKqqQ and the coupling between the diabatic states is given by V Q) = — fa0Q + 1/2QKq/3Q. The fo0 and Ko0 are the diabatic state matrix elements of the forces and the Hessian for the skeleton modes, respectively. Exemplary PES are shown in Fig. 1. Note that Eq. (1) is exact within the reaction surface approximation, i.e., no assumption concerning an adiabatic separation of H-atom and skeleton motions has been made. 

Not all vibrations exhibit characteristic frequencies. For instance, vibrational frequencies of the various C—C bonds of the carbon backbone in ahphatic molecules are very much coupled to each other (so-called skeleton modes), and they depend very much on the chemical groups coimected to the aliphatic chain. This behavior can also be used for spectrum interpretation. A short list of group frequencies of some chemical groups is given in Tab. 6.1. A more comprehensive list of characteristic bands can be found in spectral correlation tables and charts, for example in [5,6]. 

Farnesol pyrophosphate is an immediate precursor of squalene, the key intermediate in steroid and triterpenoid biogenesis, which arises from the coupling of two farnesol pyrophosphate molecules or of C,s units derived therefrom. The numerous types of sesquiter-penoid carbon skeletons represent various modes of cyclization of farnesol (sometimes with rearrangement) and it is probable that farnesol pyrophosphate is also the source of these compounds. 

In addition, the frequency cooo, as well as the tunneUng distance can also be extracted from the same empirical data. Thus all the information needed to construct a PES is available. Of course, this PES is a rather crude approximation, since all the skeleton vibrations are replaced by a single mode with effective frequency cooo and coupling parameter C. From the experimental data it is known that the strong hydrogen bond (roo < 2.6 A) is usually typical of intramolecular hydrogen transfer. 

The experimental and calculated IR spectra of unsubstituted 1,2-dithiete as well as substituted dithietes furnished evidence in favor of the cyclic structure. Only two vibrational modes of the ring skeleton seem to be closely related. These are the symmetric C=C stretch and the antisymmetric S-S stretch vibrations. The vibrational modes of C-S bonds are coupled and not in all cases easy to assign <1996IJQ859>. 

Robinson and Gulland (1925) were the first to observe that the formation of aporpine alkaloids was by oxidative coupling of benzylisoquinoline precursors. They also pointed out that by a different mode of coupling, the basic carbon skeleton of the morphine alkaloids thebaine (59), codeine (62) and morphine (58) could arise (Fig. 32.20). ( — )-(/ )-Reticuline serves well as a postulated precursor be-... 

Aerogels have a very low thermal conductivity >ltot (W m K )) [66], resulting from a low solid skeleton conductivity, a low gas conductivity and a low radiative infrared transmission [67]. However, an attempt to come to an overall thermal conductivity by summing all factors may be difficult, because the modes are strongly coupled, for example, a change in the solid skeleton conductivity will also result in a change in the infrared absorbance. 

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