Molecular resonant states spectra

The spectra presented in Figures 1-3 demonstrate that high quality, transient resonance Raman spectra can be obtained for Ni(OEP) and Ni(PP) solutions using Soret excitation. These spectra can be interpreted on a molecular level by comparison with the extensive theoretical and experimental data base that exists for ground state nickel porphyrin species (8-16 and refs, therein). The coordination state of nickel porphyrins can easily be detetmined from the resonance Raman spectrum of the sample (10.12). Several modes in the Raman spectrum of porphyrins are quite sensitive to the state of axial ligation (10.12). In particular, the marker lines V4, 11 2> 3 10 (porphyrin skeletal mode designations follow those of Abe et al., (I2a). The designation... 

Although theoretical techniques for the characterization of resonance states advanced, the experimental search for reactive resonances has proven to be a much more difficult task [32-34], The extremely short lifetime of reactive resonances makes the direct observation of these species very challenging. In some reactions, transition state spectroscopy can be employed to study resonances through "half-collision experiments," where even very short-lived resonances may be detected as peaks in a Franck-Condon spectrum [35-38]. Neumark and coworkers [39] were able to assign peaks in the [IHI] photodetachment spectrum to resonance states for the neutral I+HI reaction. Unfortunately, transition state spectroscopy is not always feasible due to the absence of an appropriate Franck-Condon transition or due to practical limitations in the required level of energetic resolution. The direct study of reactive resonances in a full collision experiment, such as with a molecular beam apparatus, is the traditional and more usual environment to work. Unfortunately, observing resonance behavior in such experiments has proven to be exceedingly difficult. The heart of the problem is not a... 

At the end of this section, one should note, that the quantum mechanical system in a potential cavity of large size may also be described as a system of discrete spectrum states with energies being almost constant and a system of decreasing stationary states for an enlarged "potential box". It is well known that the system of typical "ladder" structures in the spectrum gives rise to resonant states of molecular systems (see e.g. [92,93] and references therein), but the resonant states (the poles of continuation in a complex plane for the resolvent matrix elements) are a special field of Quantum Science and we shall not consider them here (see [5], Sect. XII.6 for discussions, or [55], Sect. 3). 

FlG. 10.5. The dispersion curves of the coherent polaritonic states (solid lines) and of uncoupled cavity photons and the molecular excitation (dashed lines). The crosses show the end-points of the part of the spectrum with well-defined wavevector. On the right, the broadened line of the molecular resonance is shown. The inset shows the excitonic weights (10.26) for upper ( cix ) 2) and lower ( cix ) 2) polaritonic branches. Reprinted with permission from Agranovich et al. (15). Copyright 2003, American Physical Society. 

A bound resonance at the threshold of a XANES spectrum can be determined by a resonance in the atomic cross section or by a molecular bound state, like the white line at threshold of the K-edge of tetrahedral clusters, shown in Fig. 14 and 15. Multiple... 

Figure 1 shows a 50 MHz CP/MAS C NMR spectrum of ramie cellulose and a stick-type nmr spectrum of low molecular weight cellulose( DP <10) In deuterated dimethyl sulfoxide solution(DMSO) (8 ) (The broken and solid lines In the CP/MAS spectrum will be explained below.). As already reported(9,10), the assignments for the Cl, C4 and C6 carbons are relatively easy, based on analogies with the solution state spectrum. However, It should be noted that these resonance lines shift downfleld by 2.3-9.6 ppm In the solid state compared to the solution state. The cause of such large downfleld shlfts(to be explained In the next section) Is attributed to the different conformations about the P-l,4-glycosldlc linkage and the exo-cyclic C5-C6 bond in which these carbons are Involved. 

The peptide cvclo(Glv-Pro-GlvK presents a quite different situation. The analysis of its NMR spectrum leads to the conclusion that it adopts a Cp-symmetric conformation in solution, at least on NMR timescales. The solution NMR spectrum (Figure 2B) shows the minimum number of resonances expected (one per carbon in the repeating trlpeptlde unit). By contrast, in the solid-state spectrum there Is clear indication of asymmetry since there are two Pro Cg resonances in Figure 2A, X-ray diffraction analysis has revealed an asymmetric molecular conformation for the crystalline peptide (17), with two different types of 3-turns, only one of which is intramolecularly hydrogen-bonded. Analysis of the solid state isotropic chemical shifts in terms of local conformation yields a picture of the molecule which is consistent with the X-ray data,... 

The large amplitude of the continuum resonance states is a direct result of the non Hermitian properties of Hamiltonian (i.e. the resonance eigenfunctions which are associated with complex eigenvalues are not in the Hermitian domain of the molecular Hamiltonian). Let us explain this point in some more detail. As was mentioned above Moiseyev and Priedland [7] have proved that if two N x N real symmetric matrices H and H2 do not commute, there exists at least one value of parameter A = such that matrix H + XH2 possesses incomplete spectrum. That is at A A there are at least two specific eigenstates i and j for which ]imx j ei — ej) =0 and also lim ( i j) — 0- Since and ipj are orthogonal (within the general inner product definition i.e., i/ il i/ j) = = 0 not in the... 

The resonance Raman spectrum of the class III ascorbate peroxidase isoenzyme II from tea leaves was consistent with an unusual five-coordinate quantum mechanically mixed-spin haem. Porphyrin-ring oxidation state marker bands were assigned for a range of Ru (Por)L2 complexes, where Por = TPP and substituted derivatives, L = PhNO. IR spectroscopy was used to probe the coupling of ground state molecular vibrations with low-energy electronic transitions of Ru(III, II) porphyrin dimer species. ... 

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