Overlapping transitions

A major limitation of CW double resonance methods is the sensitivity of the intensities of the transitions to the relative rates of spin relaxation processes. For that reason the peak intensities often convey little quantitative information about the numbers of spins involved and, in extreme cases, may be undetectable. This limitation can be especially severe for liquid samples where several relaxation pathways may have about the same rates. The situation is somewhat better in solids, especially at low temperatures, where some pathways are effectively frozen out. Fortunately, fewer limitations occur when pulsed radio and microwave fields are employed. In that case one can better adapt the excitation and detection timing to the rates of relaxation that are intrinsic to the sample.50 There are now several versions of pulsed ENDOR and other double resonance methods. Some of these methods also make it possible to separate in the time domain overlapping transitions that have different relaxation behavior, thereby improving the resolution of the spectrum. 

The LDr correlates with the orientation of the transition moment of the dye relative to the reference axis, as quantified by the angle a. LDr is also proportional to an orientation factor S (S = 1 denotes perfect alignment of the dye, S = 0 random orientation). For an isolated, non-overlapping transition, Eq. (7) establishes the correlation between LDr, a and S. These definitions lead to the qualitative rule that with an angle a > 55°, a negative LD signal is observed, whereas with a < 55°, a positive signal appears in the spectrum. Thus, with an appropriate set-up the orientation of a chromophore relative to a reference axis can be determined. 

Fig. 1. Schematic free energy-reaction coordinate profiles for a single-electron electroreduction involving solution reactant O and product R at a given electrode potential E, occurring via three different reaction pathways, PAS, P A S, and P A S". Pathway PAS involves energetically favorable precursor and successor states (P and S) but with a weak-overlap transition state. Pathways P A S and P A"S involve energetically similar precursor and successor states, but with the latter involving strong overlap in the transiton state.

Ability to differentiate overlapping transitions Increased resolution without loss of sensitivity... 

For higher J levels we have the problem of overlapping transitions—the MEs cannot be picked apart and only a more qualitative analysis of the behavior of the lifetime and the quantum yield is possible. In the next section we will make such an effort. 

More intense transitions appear at shorter wavelengths but are not of interest in the present study. For the diazoketone 2, the first peak at 385 nm clearly corresponds to the first calculated transition at 372 nm. The much weaker second peak at 330 nm is assigned to the weak calculated transition near 320 nm, and the intense peak at shorter wavelength is assigned to two intense overlapping transitions. 

Spectra of proteins and nucleic acids. Most proteins have a strong light absorption band at 280 nm (35,700 cm ) which arises from the aromatic amino acids tryptophan, tyrosine, and phenylalanine (Fig. 3-14). The spectrum of phenylalanine resembles that of toluene (Fig. 23-7)whose 0-0 band comes at 37.32 x 10 cm. The vibrational structure of phenylalanine can be seen readily in the spectra of many proteins (e.g., see Fig. 23-llA). The spectrum of tyrosine is also similar (Fig. 3-13), but the 0-0 peak is shifted to a lower energy of 35,500 cm (in water). Progressions with spacings of 1200 and 800 cm are prominent. The low-energy band of tryptophan consists of two overlapping transitions and The Lb transition has well-resolved vibrational subbands, whereas those of the La transition are more diffuse. Tryptophan derivatives in hydrocarbon solvents show 0-0 bands for both of these transitions at approximately... 

Three important conclusions emerge from this analysis. First of all, all INDOR responses induced by this particular mechanism will be in the negative direction, as they eifectively correspond to the trace of the valley between a pair of spin-tickled transitions. The second, and more important, conclusion is that INDOR responses will only be induced at frequencies corresponding to transitions that are spin-coupled to the transition that is being monitored no other transitions can induce INDOR responses. Thus, as the third conclusion, the INDOR experiment can be used to detect transitions that are entirely obscured by other overlapping transitions. ... 

The same t3q)e of analysis can be applied to (m- j ) transitions. Again examination of Fig. 4 shows that the (m->0) transition possesses the greatest vibrational overlap. Transitions of type (m->j ) with j > 0 possess vibrational overlaps which decrease as j increases. In cases where i approaches n, 9i 9i oscillates rapidly and (i j ) 0. 

The expression above must be summed over all possible transitions between states m and n to obtain a total absorption coefficient. In rotational spectroscopy, every transition originating in state J consists of 27 + 1 overlapping transitions whose magnetic quantum number M ranges from -7 to +7, but whose frequencies are identical. For plane polarised MMW interacting with all molecules, the relative strength of each M component works out as — and, after... 

Data Analysis. PeakFit version 2.0 from AISN software, Jandel Scientific (Corte Madera, California) was used to separate overlapping transitions in tan(S) and e" versus temperature plots. TA Instruments model 2000 thermal analyzer was used with version 4.1 time-temperature superposition software to analyze the stress data. 

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