Group moment derivatives

Snyder [27] then allows particular group moment derivatives M, to have the same values in different molecules... 

Aj (obs) jjjg observed intensity of the k vibration in molecule p and and Sp ° are initial values for the group moment derivatives and the scaling factor. These give an initial estimated value for the intensity A](p(. Using Eq. (3.78) the following expression for y](p is obtained... 

Aside from the refinement procedure the significance of group moment derivatives depends gready on the validity of the basic assumptions implicit in the formulation. Neverdieless, the method appears to be quite convenient for calculations in systems where to ly non-rqiproximate theories is not possible for symmetry reasons or the size of the molecule. It is, therefore, not surprising that die method of Snyder has been lied in calculadons of intensities of various molecules [112-114] including proteins [115],... 

The reduction of the C— Br and C—1 group moments from 1.10 and 0.90 in bromo- and iodo-benzene to about 0.80 and 0.50 in 2-bromo- and 2-iodo-thiophene has been ascribed to the larger weight of resonance forms such as (8) and (9) in the thiophene series. The chlorine, nuclear, quadrupole, resonance frequencies of chloro-substituted thiophenes are much higher than those of the corresponding benzene derivatives. This has been ascribed to a relayed inductive effect originating in the polarity of the C—S o-bond in thiophenes. The refractive indices, densities, and surface tension of thiophene, alkyl- and halo-thiophenes, and of some other derivatives have been... 

The upper limit for / follows from the hydrogen distribution and aliphatic group distribution derived from proton spin resonance measurements at the temperature of liquid nitrogen (3). Table III shows all structural parameters obtained directly from the second moment H2 (in gauss2) together with H.i/H. 

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. 

Rule III chiefly applies to multi-substituted benzene derivatives. If we assume that the six carbon atoms in benzene are arranged so as to form a regular hexagon, the angle between the directions of the substituents is 6o° in the or Ao-position, 120° in the mp -position, and 180° in the /> m-position. If the two substituents have the group moments fx and /xg he moment of the di-substituted molecule is given by... 

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). 

The dipole moments of substituted phenyl azides were calculated by vector addition of the group moments, assuming that the substituted groups are colinear and lie in the plane of the ring . Significant discrepancies from experimental values are displayed by ortho derivatives, where mutual induction between the close polar groups should occur ortho effect). In nitro derivatives a more extended type of interaction was postulated to account for the discrepancy shown by the para compound . ... 

Other than H2, the most accurate calculations are on the dipole moment derivatives and transition probabilities in small molecules, mostly diatomics. There are two groups of calculations of particular note. First, there is the work based on theTableCI program ofBuenkerand Peyerimhoff. These are... 

In the case of polarizability derivatives, however, the sparsity of results is not due to lack of interest, as this is a property that is just as important as the dipole moment derivative. Here the problem is that the calculations are more difficult, though not so much more difficult as to justify the comparatively small number of calculations in this area. There was a brief period of activity some five or six years ago in which various MC-SCF and Cl methods were tried on small molecules. ° Some earlier calculations are listed elsewhere.As with the quadrupole moment results, most of these could easily be improved upon with the aid of a large-scale multi-reference Cl calculation, which would be well within current capabilities. Some more recent polarizability derivative calculations, mostly SCF, may be found in Refs. 220 and 246-257. The most detailed of these is an M BPT calculation by Diercksen and Sadlej on CO. Another interesting group of calculations has considered the derivatives of the frequency-dependent polarizability. This shows some expected effects, for example that the frequency dependence in CI2 is noticeable, and some unexpected results, for example that the intensity of the V4 Raman-active mode of CH has a very marked frequency dependence. Dacre has provided some calculations on the polarizability of rare-gas dimers, which is of interest to the collision-induced Raman spectrum of such systems. Calculations of hyperpolarizabilities are confined to small systems. A recent example is for LiH. An example of the use of hyperpolarizability derivatives can be found where some fairly crude calculations were nevertheless useful in distinguishing two possible mechanisms in the collision-induced Raman spectrum of CO2. 

If the solvent is polar, this situation is exacerbated because the bands associated with vibrations of polar groups tend to be stronger than those associated with nonpolar groups since the dipole moment derivative, 0p/02 (see Section 1.2), is usually high. For example, a greater proportion of the spectrum of 2-hexanone held in a 100-pm cell is lost by absorption than for -hexane, even though these molecules both have approximately the same number of atoms. The worst case of all is when water is the solvent. For the smdy of aqueous solutions, the cell has to be no thicker than about 10 pm if the transmittance at all wavenumbers below 2000 cm is to exceed 10%. 

A detailed discussion of how to derive the orientation of adsorbates from reflection spectra of adsorbates on dielectric substrates is beyond the scope of this book, as the direction of the dipole moment derivative for each of the vibrational modes of the adsorbate must be known. To obtain the spectra on the right-hand column of Figure 13.19, Brunner et al. [12] calculated the spectra after varying the angles subtended by each functional group until the spectra calculated for p- and j-polariza-tion matched the corresponding measured spectra at all incidence angles. Because the reflection spectra of thin films on dielectric surfaces may be measured with both p- and s-polarization, the orientation of adsorbates on dielectric substrates can be estimated more accurately in practice than on metallic substrates. 

A. The carbonyl group has a large dipole moment derivative, which gives rise to very intense absorption bands. 

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