Group dipole derivatives

The IETS intensities for the methyl group vibrations of this species are shown in Fig. 9. The theoretical predictions of Kirtley and Hall (34) using KSH, and taking methyl group dipole derivatives from infrared measurements of ethane, assuming the C-S bond normal vs parallel to the interface, are also shown in Fig. 9. Note that for an orientation with the C-S bond normal, the symmetric C-H modes ( 2 and 9 ), which have net dipoles parallel to the C-S bond, are favored over the anti-symmetric modes ( 4,7, and 11), which have net dipole moments perpendicular to the C-S bond, but that for the C-S bond parallel to the surface the situation is reversed. The better, although by no means perfect, agreement between theory and experiment for the C-S bond normal tends to support the proposed orientation of Hall and Hansma. 

D. Group Dipole Derivatives as Infrared Intensity Parameters.72... 

Figure 9. Experimental and theoretical (KSH) IETS intensities for the methyl group vibrations of methyl sulfonate ions on alumina. The theoretical curves assume dipole derivatives from IR measurements of C2He, and compares the predictions for the C—S bond normal vs. parallel to the interface. The relatively better fit for C-S normal supports the proposed orientation of Hall and Hansma.

It has been stated that, when specific hydrogen-bonding effects are excluded, and differential polarizability effects are similar or minimized, the solvent polarity scales derived from UV/Vis absorption spectra Z,S,Ei 2Qi),n, Xk E- ), fluorescence speetra Py), infrared spectra (G), ESR spectra [a( " N)], NMR spectra (P), and NMR spectra AN) are linear with each other for a set of select solvents, i.e. non-HBD aliphatic solvents with a single dominant group dipole [263]. This result can be taken as confirmation that all these solvent scales do in fact describe intrinsic solvent properties and that they are to a great extent independent of the experimental methods and indicators used in their measurement [263], That these empirical solvent parameters correlate linearly with solvent dipole moments and functions of the relative permittivities (either alone or in combination with refractive index functions) indicates that they are a measure of the solvent dipolarity and polarizability, provided that specific solute/ solvent interactions are excluded. 

As a further extension of the method, the interbond angle of the carbonyl groups of derivatives of the type CpFe(CO)2X have been calculated by extending the method of oscillating dipoles to the second derivative of the carbonyl bond dipole moment 91). The results obtained are in remarkable agreement with those calculated using the absolute intensities of the fundamental carbonyl stretching vibrations (52). 

In Section II,D,4 we mentioned that recent ab initio calculations of dipole derivatives for the peptide group in NMA have been used to calculate intensities of IR bands in (Gly) I (Cheam and Krimm, 1985). Such calculated intensities are shown in Fig. 7, and it can be seen that they reproduce the observed intensities quite well. This kind of agreement indicates that the force field is a very satisfactory one, since intensities are a sensitive function of the eigenvectors. While (Gly) I is the only polypeptide so far for which intensities have been calculated, it can be expected that this technique will be used in the future to provide additional information on polypeptide chain conformation. 

With a little group theory, we can determine whether or not the vibration has a dipole derivative. The same symmetry selection rules apply to vibrations as to electronic transitions for a transition to be allowed, the direct product of the representations for the initial and final states must be one of the representations for the transition moment. The transition moments for electric dipole or infrared selection rules correspond to the functions x, y, and z. For Raman transitions, the transition moments correspond to any of the second-order functions of x, y, and z, such as xz or -I- y. The representation of the ground vibrational state is always the totally symmetric representation, so F, F is equal to Fy for fundamental transitions. Therefore, the selection rule for fundamental transitions is F, (x) Fy = F = F. For example, the group theory predicts that for CO2 the transitions V2 = 0 1 and V3 = 0 1 are infrared-allowed, because those vibrational modes have TTu (x,y) and (z) symmetry, respectively. On the other hand, the symmetric stretch transition Vj = 0 1 is forbidden by infrared selection rules but allowed by Raman selection rules, because that vibrational mode has (x + y, z ) symmetry. Here are the relevant rows from the character table in Table 6.4 ... 

By die transformation (3.3) a substantial step is made in die transition from experimental intensities into quantities characterizing molecular structure. At die first place, a natural separation between dipole derivatives associated with bond stretchings and angle deformations is achieved. In some cases the dp/dSj derivatives can be associated with vibrations localized within certain atomic groupings. Such distortions may be described by local group symmetry coordinates. Snyder [27] first applied dipole moment derivatives with respect to group symmetry coordinates as basic parameters in infrared intensity analysis on a series of crystalline n-alkanes. The procedure described in his work will be discussed later in this section. 

The index G refers to a molecular-fixed Cartesian system in which die dipole moment derivatives with respect to normal coordinates are obtained. The summation is over the group symmetry coordinates. Eq. (3.70) can be solved if the Cartesian ctmqionents of dpo/dQ are known. Introducing Eq. (3.70) into Eq. (1.50) the following relation between the dipole derivatives dpQ/dSj and the intensity A)( is obtained... 

A second Cartesian reference system, still molecule-fixed, oriented as dictated by the symmetry elements of the group of atoms associated with Sj is introduced. It is designated by gjf (i = 1, 2, 3). The dipole derivatives dpQ/dSj are expressed in the group local Cartesian system as... 

In the case of the AB2 (C2v) molecule A is invariant imder the full point group and the symmetry species associated with non-zero dipole derivatives will be Aj (z), Bi (x) and B2 (y). The character table for C2v point group is shown in Table 4.2. 

Sometimes it is claimed that the biological activity of a series depends on the group dipole moment (p) rather than on cr. Actually it is not possible to make this differentiation for mono-substituted derivatives because the two constants are mathematically related. They can be distinguished, however, in di-substitution, when o will prove simply additive, but p vecto-rially additive, and hence often self-cancelling. For values of p, see Sutton (1955). 

The first empirical and qualitative approach to the electronic structure of thiazole appeared in 1931 in a paper entitled Aspects of the chemistry of the thiazole group (115). In this historical review. Hunter showed the technical importance of the group, especially of the benzothiazole derivatives, and correlated the observed reactivity with the mobility of the electronic system. In 1943, Jensen et al. (116) explained the low value observed for the dipole moment of thiazole (1.64D in benzene) by the small contribution of the polar-limiting structures and thus by an essentially dienic character of the v system of thiazole. The first theoretical calculation of the electronic structure of thiazole. benzothiazole, and their methyl derivatives was performed by Pullman and Metzger using the Huckel method (5, 6, 8). 

Interesting structures can be formed by combinations of ring and side-chain substituents in special relative orientations. As indicated above, structures (28) contain the elements of azomethine or carbonyl ylides, which are 1,3-dipoles. Charge-separated species formed by attachment of an anionic group to an azonia-nitrogen also are 1,3-dipoles pyridine 1-oxide (32) is perhaps the simplest example of these the ylide (33) is another. More complex combinations lead to 1,4-dipoles , for instance the pyrimidine derivative (34), and the cross-conjugated ylide (35). Compounds of this type have been reviewed by Ramsden (80AHCl26)l). 

Figure 4.2. Rotational-energy barriers as a function of substitution. Tbe small barrier ( 2kcal) in ethane (a) is lowered even further ( O.Skcal) if three bonds are tied back by replacing three hydrogen atoms of a methyl group by a triple-bonded carbon, as in methylacetylene (b). The barrier is raised 4.2 kcal) when methyl groups replace the smaller hydrogen atoms, as in neopentane (c). Dipole forces raise the barrier further ( 15 kcal) in methylsuccinic acid (d) (cf. Figure 4.3). Steric hindrance is responsible for the high barrier (> 15 kcal) in the diphenyl derivative (e). (After...

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