Spectrum stick

Figure Al.6.13. (a) Potential energy curves for two electronic states. The vibrational wavefunctions of the excited electronic state and for the lowest level of the ground electronic state are shown superimposed, (b) Stick spectrum representing the Franck-Condon factors (the square of overlap integral) between the vibrational wavefiinction of the ground electronic state and the vibrational wavefiinctions of the excited electronic state (adapted from [3]).

Figure Bl.15.12. ESEEM spectroscopy. (A) Top energy level diagram and the corresponding stick spectrum for the two allowed (a) and two forbidden (f) transitions. Bottom time behaviour of the magnetization of an allowed (a) spin packet and a forbidden (f) spin packet during a two-pulse ESE sequence (see figure Bl.15.11 (A)). (B) The HYSCORE pulse sequence.

Figure 3.3 Stick spectrum showing hyperfine pattern for coupling to three equivalent 59Co nuclei (1=1/2) computed to (a) first-order and (b) second-order in perturbation theory. (Adapted from ref. 7.) (c) Isotropic ESR spectrum of [PhCCo3(CO)9r in THF solution at 40°C.

In Fig. 3 we present the stick spectrum [corresponding to infinite resolution see eq. (12)] generated from a Gaussian wave packet of the form... 

Fig. 27a-c. Electron spin echo envelope modulation of Co(acacen), temperature 4K. a) Nuclear modulation pattern of Co(acacen) diluted into a Ni(acacen) 1/2 H20 single crystal. Crystal setting rotation axis I,

Fourier transform of the nuclear modulation pattern (From R. de Beer1 4)) c) Stick spectrum ENDOR frequencies (AmN = 1, 2) calculated from the hfs and quadruple tensors in Ref. 59 dashed lines ms = - 1/2, full lines ms = 1/2... 

Figure 6.9 Observed opto-thermal spectrum of the Avcw = 3 overtone of benzene (points with error bars) and a stick spectrum calculated by means of the algebraic theory. Labels indicate the most important states involved in borrowing intensity from the CH overtone. Adapted from Bassi et al. (1993).

Figure 0.1 Stimulated emission pumping (SEP, Hamilton et al., 1986 Northrup and Sears, 1992) is a new experimental technique for accessing higher-lying vibrational levels of molecules in their ground electronic states. Shown is the SEP vibrational spectrum of S02, where a pair of dips represent one vibrational level. (Adapted from Yamanouchi, Takeuchi, and Tsuchiya, 1990.) The stick spectrum at the bottom represents the position of the vibrational levels given by Equation (0.1) with the constants given in Table 0.1. The bright levels are represented by longer sticks.

Fig. 1.1. Induced rotovibrational absorption of O2 pairs. The heavy curve represents the measurement the light curve is a theoretical envelope ( stick spectrum ) of the Raman 0 and S branches. The envelope of the Q branch is shown as a broken line after [128].

Fig. 3.23. Rototranslational spectrum of CO2-CO2 at 296 K [186, 34]. The dashed curve is the profile of the stick spectrum. The dotted curve describes an average through the three-body profile (x) (intensity scale in arbitrary units) peak absorption of that component amounts to 2.2 x 10 7 cm 1amagat-3.

Fig. 3.38. Absorption of N2-Ar in the fundamental band of N2 [111]. Nitrogen and argon densities were both 19 amagat room temperature measurement ( ) the solid line represents a fit based on the stick spectrum and a J-independent quadrupole transition moment. In pure nitrogen, an almost identical spectrum was obtained.

O branch). The measurement is given by the dots. The curve drawn was constructed from the envelopes of the stick spectrum of N2 (which is well known from Raman studies). The curve approximates the measurement quite closely. In order to fit the experimental line shape one had to take the dependence of the quadrupole transition moments on the rotational quantum number into account. 

B Monomer radical and polymer radical spectra overlapping at [VAc] = 3.2 X 10 1M. The stick spectrum shows the hyperfine lines assigned to the polymer radicals... 

Energy levels and spectral line pattern (stick spectrum) for an unpaired electron interacting widi two nonequivalent protons whose spin orientations are indicated at the right. The dashed levels and dashed transition arrow indicate die case for an uncoupled free electron. 

Figure 2. ESR spectrum of pseudorotating Ks in an Ar matrix at 34.2 K. The stick spectrum shows the predicted intensity distribution for three equivalent nuclei. Also indicated are K atom resonances for several matrix sites. He = 3312.3 G is the resonance field of a free electron...

The resulting energy levels are depicted in Fig. la,b, where the energy is plotted against magnetic field. The resonance frequencies depend, of course, on the field. For experimental reasons, in EPR spectroscopy one keeps the frequency of the microwave field constant (usually close to 9 GHz, X-band, or to 35 GHz, Q-band), and varies the field Bq. The resulting transitions (corresponding to A = hv (microwaves)) are indicated with arrows, and displayed in a so-called stick spectrum (Fig. Ic). 

The information of an EPR spectrum is contained in (i) the resonance frequency (in practice the g value), (ii) the line shape or spectral structure, and (iii) the relaxation behaviour. Comparison of the characteristic parameters with those of known species often leads to identification of the paramagnetic entity under investigation. More fundamentally, they give insight into the magnetic interactions to which the unpaired electron is subjected, and thus into the structure of its environment. In actuality, the stick spectrum of Fig. Ic will consist of resonances with Lorentzian line shape in the case of individual transitions as in Fig. 1, or with Gaussian line shape when many different unresolved hyperfine interactions are... 

Fig. 1. Energy level diagram of a -spm- and spin-1 quadrupolar nuclei. In the bottom are shown the stick spectrum of a single crystal...

Because the Fourier transform of a delta comb is a delta comb again, 5((w) corresponds to a stick spectrum similar to a MAS spectrum with rotational sidebands (cf. Fig. 3.3.7(c)). 

Fig. 11,7. C CP/MAS spectra of i-PP at various temperature. This sample is crystallized isothermally at 140°C. The stick spectrum indicates the chemical shifts in solution NMR spectrum.

The chemical shifts of the new broad peaks are similar to those of peaks in the solution NMR spectrum, which is shown as a stick spectrum in Fig. 

Fig. 11.16. The NMR stick spectra of s-PP predicted for the chains with preferred conformations. The chemical shift difference on the basis of the -y-effect is noted in the stick spectrum...

Figure 17.4 shows the Si nuclear shielding of the model compounds with various conformations for the main chain of PMPS calculated by the FPT CNDO/2 MO theory (a), together with the observed Si chemical shifts of PMPS (b) at 393, 333 and 153 K. For convenience, they are schematically represented by the stick spectrum. The relative peak intensity is indicated by the stick height. As shown in Fig. 17.4, the calculated Si nuclear shielding is converted with respect to that of the trans-TT conformation. The chemical shifts for the conformers of TT, GT (TG) and GG were ca. 0-0.7, 4.0-4.9 and 9.1-10.1 ppm, respectively. The calculated Si chemical shifts for all the... 

Figure 1. Computed13 discrete stick spectrum (a) and the fit by (2.17) (solid line) to the distribution of fluctuations in that spectrum, (b). The initial state is at an energy (indicated by an arrow in (a)) above the onset of large-scale chaos in the classical dynamics of the Hamiltonian. The accessed final states span a wide range of energies about , and there are no very strong or many very weak transitions.

A discrete stick spectrum, normalized to a total strength of unity, is given by... 

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