Doublet analysis

Subak-Sharpe H., Elton R.A., Russell G.J. (1974). Evolutionary implications of doublet analysis. Symp. Soc. Gen. Microbiol. 24 131-150. 

Figure 2 Result of doublet analysis (right) and conventional mapping for micorseismicity in the Hijiori HDR field, Japan, by Tezuka arui Niitsuma (2000).

To nnderstand the internal molecnlar motions, we have placed great store in classical mechanics to obtain a picture of the dynamics of the molecnle and to predict associated patterns that can be observed in quantum spectra. Of course, the classical picture is at best an imprecise image, becanse the molecnlar dynamics are intrinsically quantum mechanical. Nonetheless, the classical metaphor mnst surely possess a large kernel of truth. The classical stnichire brought out by the bifiircation analysis has accounted for real patterns seen in wavefimctions and also for patterns observed in spectra, snch as the existence of local mode doublets, and the... 

NMR is the method of choice for determining the ratio of EO units to PO units since the analysis is simple to perform, does not require calibration, and is applicable over a wide range of EO-PO ratios. The spectrum contains only two resonances a doublet due to the methylene groups of the PO units, and a composite band, which is due to the CH2O groups of the PO and EO... 

The first molecule to be studied in this manner, methyl alcohol, is a rather special case because of the very small moment of inertia of the OH group. Consequently, most of the doublets are so widely split that only one member has been observed. Nevertheless a very precise barrier value was obtained from the analysis. 

One possibility for this was demonstrated in Chapter 3. If impact theory is still valid in a moderately dense fluid where non-model stochastic perturbation theory has been already found applicable, then evidently the continuation of the theory to liquid densities is justified. This simplest opportunity of unified description of nitrogen isotropic Q-branch from rarefied gas to liquid is validated due to the small enough frequency scale of rotation-vibration interaction. The frequency scales corresponding to IR and anisotropic Raman spectra are much larger. So the common applicability region for perturbation and impact theories hardly exists. The analysis of numerous experimental data proves that in simple (non-associated) systems there are three different scenarios of linear rotator spectral transformation. The IR spectrum in rarefied gas is a P-R doublet with either resolved or unresolved rotational structure. In the process of condensation the following may happen. 

In order to have a full notion of the spectrum, it is enough now to complete the analysis by consideration of spectral doublets. The doublet, corresponding to transitions between levels (j = 1, m = 1 l = 0,1 n = 0), is described by the following block of matrices (7.38) ... 

The Kai/a2 doublet illustrated in Figure 5.2 is most frequently used for analysis, although as the atomic number of the emitting element increases, the energy required... 

A very similar application of the modified Bloch equations was based in the work of Adams and Connelly.4 ESR spectra (Figure 5.8) of [Mo P(0 Me)3 2(MeC = CMc)Cp] show the expected triplet (two equivalent 31P nuclei) at 280 K, but only a doublet at 160 K. At intermediate temperatures, the lines broaden. The interpretation is that the alkyne undergoes a pendulum oscillation, which in the extrema diverts spin density from one or the other phosphite. Interestingly, the diamagnetic cation undergoes a similar motion on the NMR time scale, but then the alkyne undergoes a complete rotation. Thus, analysis of the effect leads to a measure of the rate of the oscillation. The... 

Complexes 41 and 42 were characterized by their IR and H-NMR spectra, and 41 also by elemental analysis. Table III contains the pertinent spectral data. Noteworthy are the very low energy terminal carbonyl bands for 41 and 42 at 1864 cm-1 (hexane). The weak 7r-accepting abilities of PR3 (R = Et, Ph) allow the lone CO ligand to 77-backbond to the Ti(II) center to a much greater degree. The -NMR spectrum of 41 exhibited a doublet (/H-p = 1.5 Hz) at 8 4.75 due to the coupling of the cyclo-pentadienyl protons with the 31P nucleus, while complex 42 exhibited a broad cyclopentadienyl singlet at 8 4.67. 

---