Excitation, mode

For some systems qiiasiperiodic (or nearly qiiasiperiodic) motion exists above the unimoleciilar tlireshold, and intrinsic non-RRKM lifetime distributions result. This type of behaviour has been found for Hamiltonians with low uninioleciilar tliresholds, widely separated frequencies and/or disparate masses [12,, ]. Thus, classical trajectory simulations perfomied for realistic Hamiltonians predict that, for some molecules, the uninioleciilar rate constant may be strongly sensitive to the modes excited in the molecule, in agreement with the Slater theory. This property is called mode specificity and is discussed in the next section. 

As discussed in section A3.12.2. intrinsic non-RRKM behaviour occurs when there is at least one bottleneck for transitions between the reactant molecule s vibrational states, so drat IVR is slow and a microcanonical ensemble over the reactant s phase space is not maintained during the unimolecular reaction. The above discussion of mode-specific decomposition illustrates that there are unimolecular reactions which are intrinsically non-RRKM. Many van der Waals molecules behave in this maimer [4,82]. For example, in an initial microcanonical ensemble for the ( 211 )2 van der Waals molecule both the C2H4—C2H4 intennolecular modes and C2H4 intramolecular modes are excited with equal probabilities. However, this microcanonical ensemble is not maintained as the dimer dissociates. States with energy in the intermolecular modes react more rapidly than do those with the C2H4 intramolecular modes excited [85]. 

It is also possible to measure microwave spectra of some more strongly bound Van der Waals complexes in a gas cell ratlier tlian a molecular beam. Indeed, tire first microwave studies on molecular clusters were of this type, on carboxylic acid dimers [jd]. The resolution tliat can be achieved is not as high as in a molecular beam, but bulk gas studies have tire advantage tliat vibrational satellites, due to pure rotational transitions in complexes witli intennolecular bending and stretching modes excited, can often be identified. The frequencies of tire vibrational satellites contain infonnation on how the vibrationally averaged stmcture changes in tire excited states, while their intensities allow tire vibrational frequencies to be estimated. 

As illustrated by the spectra of P. furiosus 3Fe Fd shown in Fig. 8, the relative intensities of the Raman bands for [Fe3S4l clusters vary considerably with excitation wavelength. However, because of the extensive mixing of Fe-S and Fe-S modes, excitation profiles in the region 400-650 nm appear to be of little use in effecting electronic... 

As evidenced by the correlation of the BH model with the experimental data, Figure 2.4, the model is only in qualitative accord with the experiment. Clearly, the BH model cannot account for the breadth in the correlation of the rate constants for porton transfer with driving force. The origin of the discrepancy may lie in the single-mode nature of the BH model, which allows only for vibrational excitation in the low-frequency promoting mode. Excitation in the reactant and product modes of the vibration associated with the transferring proton is not taken into account in the BH model. Therefore, the discrepancy between experiment... 

The second transition shows in most cases clearly resolved vibrational structure. The mode excited seems to be the same as in the first transition, its frequency being usually in the range 1200—1400 cm . The geometry changes due to transi tion II are smaller than those due to transition I, as in transition II the first vibrational component is the most intense (and not the second as in transition I ) and the third component in II is much smaller than the first. This vibrational component intensity pattern is one reason why the half height width of transition II is much smaller than that of transition I (e.g., A 1/2 - 2300 cm in 1). Another reason is that transition II seems not to excite combinations with lower frequency modes. 

At infrared wavelengths extinction by the MgO particles of Fig. 11.2, including those with radius 1 jam, which can be made by grinding, is dominated by absorption. This is why the KBr pellet technique is commonly used for infrared absorption spectroscopy of powders. A small amount of the sample dispersed in KBr powder is pressed into a pellet, the transmission spectrum of which is readily obtained. Because extinction is dominated by absorption, this transmission spectrum should follow the undulations of the intrinsic absorption spectrum—but not always. Comparison of Figs. 10.1 and 11.2 reveals an interesting discrepancy calculated peak extinction occurs at 0.075 eV, whereas absorption in bulk MgO peaks at the transverse optic mode frequency, which is about 0.05 eV. This is a large discrepancy in light of the precision of modern infrared spectroscopy and could cause serious error if the extinction peak were assumed to lie at the position of a bulk absorption band. This is the first instance we have encountered where the properties of small particles deviate appreciably from those of the bulk solid. It is the result of surface mode excitation, which is such a dominant effect in small particles of some solids that we have devoted Chapter 12 to its fuller discussion. 

The observed darkening of the indium slides results from a shift of the absorption peak because of the coating on the particles. Because of the cumbersomeness of the expressions for coated ellipsoids (Section 5.4) this shift can be understood most easily by appealing to (12.15), the condition for surface mode excitation in a coated sphere. For a small metallic sphere with dielectric function given by the Drude formula (9.26) and coated with a nonabsorbing material with dielectric function c2, the wavelength of maximum absorption is approximately... 

M. Shmilovits-Ofir, R. B. Gerber. Proton transfer and dissociation of GlyLysH(- -) following O-H and N-H stretching mode excitations dynamics simulations, J. Am. Chem, Soc., 133 ... 

We, however, are interested in the extremely non-Markovian timescales, much shorter than on which all bath modes excitations oscillate in unison and the... 

There are two modes excited by the AC field, longitudinal and transverse. For crystals in the 100-300 pm thickness range, only the transverse standing wave needs to be considered (Janshoff et al 2000). The actual lateral displacement of a point on the crystal surface (and therefore the mass sensitivity) is the Gaussian function of the radial distance from the center of the electrode (Fig. 4.5). It also depends on the amplitude of the applied electric field and ranges from few nm/V in water to tens of nm/V in air or in vacuum. 

Figure 4. Comparison of a theoretical magnitude-mode excitation spectrum (top) with those detected (on one pair of cell transverse plates) during transmission (on the other pair of cell transverse plates) of a frequency-sweep (middle) or SWIFT (bottom) waveform. The time-domain signals were zero-filled once before Fourier transformation to reveal the full shape of the excitation magnitude spectrum. Note the much improved uniformity and selectivity for SWIFT compared to frequency-sweep excitation.

Figure 6. Simultaneous FT/ICR excitation/ejection of two ions of very similar mass-to-charge ratio, produced via electron ionization of toluene. In each plot, the heavy line represents the experimental FT/ICR mass spectrum, and the light line represents the magnitude-mode excitation spectrum used to produce that ICR signal. Top and 13c 2CgH7+ are excited with uniformly...

Possible Solutions Because z-mode excitations degrade the performance of FTMS, methods to minimize z-mode excitations are necessary. Theoretical (Equation 1) and experimental results suggest several possible strategies. 

The observations that there is an "optimum" orbit size and that peaks split for orbits not too much larger than the optimum orbit suggest that the optimum orbit occurs because of special circumstances. One possible circumstance is a coincidence of frequencies for ions with low and high z-mode amplitudes so that if there are mass discriminating differences in the way the ions populate the trap or in the way ions are excited, then systematic mass measurement errors can be expected. Excitation of the cyclotron mode does produce a spread in cyclotron radii, and mass discriminating z-mode excitation is discussed elsewhere in this chapter. Thus, frequency variations that cause systematic mass errors are due in part to trap field inhomogeneities. These effects are evident at low ion populations and may be due in part to excitation induced ion cloud deformation which increases with ion number. 

Z-Mode Excitation Excitation of ions at their trapping... 

The value of the exchange modes of the magnetic resonance has the same order of a magnitude as triplet excitations in the dimerized state [5], These modes exist in both U- and D-AFM states. Furthermore, these modes excite by a high frequency magnetic field polarized perpendicular to easy axis. Their intensities define by the DM interactions. The spin oscillations in these modes respect to a violation of 3D AFM order along chains as well as between chains. Therefore, one can expect an amplification of their intensities under motion of boundaries between coexisting SP- and AFM states. The next experiments are necessary to make situation clear. 

Recent neutron scattering measurements [25] have revealed a well-defined fe (TO) soft mode in pmn at high temperatures that becomes overdamped by the polar nanoregions below the Burns temperature, Td. Thus, while the soft mode below Td is not a well-defined excitation in the spectrum, the large value of e and its strong temperature and pressure dependences between Td and Tm clearly implicate low-lying optic mode excitations. 

We wish to add that there exists a wide variety of literature that considers the opposite case of monochromatic excitation by an infinitely narrow line causing velocity selection, such as [261, 268, 269, 320, 362] and the sources quoted therein. This description has been developed basically in connection with laser theory it refers most often to stabilized single-mode excitation. The intermediate case between monochromatic and broad line excitation is the most complex one, requiring integration over the modal structure of the laser inside the bounds of the absorption contour [28, 231, 243]. 

---