Splitting factor group

The resonance splitting of intramolecular modes in the crystalline state is often called Davydov splitting or factor group splitting . In contrast to the static field effects of the crystal, this splitting is due to the dynamical interaction of the constituents in the primitive cell... 

Six comments are appropriate at this point. Firstly, it is the experience of the reviewer that chemically-similar compounds with very similar infrared and Raman spectra in factor-group split regions are isomorphous. This method is probably at least as reliable as X-ray powder methods when there is a significant change in scattering factors between the two compounds studied (e.g. bromo-derivatives of... 

The tetrahedral structures XHj are still extensively investigated, and the factor-group splittings reported, although the attention is now also focussed on the single-crystal spectra. 

In the infrared spectrum of polyethylene (Fig. 4.1-2A) this band is split into a doublet at 720 and 731 cm This factor group splitting (Fig. 2.6-1 and Sec. 2.7.6.4) is a result of the interaction between the molecules in crystalline lattice areas. It may be used to investigate the crystallinity of polymers (Drushel and Iddings, 1963 Luongo, 1964). Polyethylene has a unit cell of the factor group Dih (compare Secs. 2.7.5 and 2.7.6.3) which contains a -CH2-CH2- section of two neighboring chains. Each of these sections has a center of inversion in the middle of the C-C bond (Fig. 4.1-3). Therefore the rule of mutual exclusion (Sec. 2.7.3.4) becomes effective The vibrations of the C-C bonds cannot be infrared active and further there are no coincidences of vibrational frequencies in the infrared and Raman spectrum of linear polyethylene. 

Figure 7 illustrates the temperature-dependent IR factor group splitting of the alkyl chain CH2 scissoring mode of human SC as a function of... 

Figure 7 (a) Temperature-dependent factor group splitting of the infrared-active, CH2 scissoring mode of human stratum comeum as a function of different hydration (open circle, 0% closed square, 17% open triangle, 33% closed triangle, 70% open square, 300%). (b) The same data plotted on an expanded scale. (From Ref. 40.)... 

Berkowitz and Wahl9 have reviewed the experimental and theoretical estimates of the dissociation energy of molecular fluorine. The Raman and far-i.r. spectra of crystalline F2 show that in this state the element resembles 02 more closely than it does the other halogens.10 The intermolecular forces, in particular, are extremely weak, as exemplified by the small shifts of the internal frequencies from their gas-phase values, the absence of observable factor-group splitting of the fundamental and overtones, and the low value of the external (lattice) vibrations. 

The Neutral Exciton Model for Triplet Factor-Group Splittings in Aromatic Crystals. 

Some peaks in the INS spectrum are not seen in the infrared or Raman spectra for example the factor group splitting of all the modes in the INS is readily apparent because of the absence of selection rules. In the infrared and Raman spectra, some of the factor group components are either forbidden or have zero intensity. 

In Davydov (or factor group) splitting vibrational phase relationships between molecules in the same xmit cell give rise to an in-phase and an out-of-phase splitting. Each positive (or negative) component of the split pair falls on its own respective positive (negative) dispersion curve, the two curves are of similar shape but distinct. 

In Table 6.12 we list the compounds studied and some of their properties [76,78,79,82,83,84,85,86,87,88]. In most cases, the INS spectra show little or no evidence for dispersion, although this is not always the case. Fig. 6.26 shows the INS spectra of Li[AlH4] and Na[AlH4], which contain tetrahedral [AlHi] ions. The spectra are complex indicating that both factor group splitting and dispersion are large in these systems and to obtain a complete analysis both of these factors will need to be explicitly included. 

Zeise s salt, K[Pt(C2H4)Cl3]H20, is the best known and most-studied ethene-metal complex. The structure is related to the structure of the square planar [PtCU] ion, ethene replacing one Cl with its C=C axis perpendicular to the PtC plane. It is regarded as a model of ethene binding to a transition metal centre. The INS spectrum of the anhydrous complex is shown in Fig. 7.18 [77].The spectrum was assigned with the aid of a Wilson GF method calculation, see Table 7.11. However, a more recent spectrum. Fig. 1.1, shows that the factor group splitting of the... 

The analysis so far has all been based on the isolated molecule approximation. For maleic anhydride this is valid as the agreement between the gas phase calculation and the solid state spectrum shows. However, it does not account for some of the most intense bands in the spectrum, those below 200 cm in the lattice mode region. It is possible to assign the bands, if it is assumed that the librational modes are more intense and occur at higher fi equency than the translational modes. It also requires the assumption that the factor group splitting is small (there... 

This means that each state which is transformed according to the irreducible representation Au of the site group is split in the crystal into two exciton states of symmetry corresponding to the factor group irreducible representations Au and Bu, respectively. Sometimes such splitting is named a factor group splitting. 

The asterisk indicates that from these data, factor group splittings may be determined (Davydov). The following values of AD result PcH2 1750, 1450 PcCo 458 PcNi 399 PcCu 166 cm-1. 

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