Vibrational excitation inelastic case

The theoretical model developed to explain these experiments is based on inelastic tunneling of electrons from the tip into the 2ir adsorbate resonance that induces vibrational excitation in a manner similar to that of the DIMET model (Figure 3.44(b)). Of course, in this case, the chemistry is induced by specific and variable energy hot electrons rather than a thermal distribution at Te. Another significant difference is that STM induced currents are low so that vibrational excitation rates are smaller than vibrational de-excitation rates via e-h pair damping. Therefore, coherent vibrational ladder climbing dominates over incoherent ladder climbing,... 

The energy analysis of these inelastically scattered electrons is carried out by a cylindrical sector identical to the monochromator. The electrons are finally detected by a channeltron electron multiplier and the signal is amplified, counted and recorded outside of the vacuum chamber. A typical specularly reflected beam has an intensity of 10 to 10 electrons per second in the elastic channel and a full width at half maximum between 7 and 10 meV (60-80 cm l 1 meV = 8.065 cm-- -). Scattering into inelastic channels is between 10 and 1000 electrons per second. In our case the spectrometer is rotatable so that possible angular effects can also be studied. This becomes important for the study of vibrational excitation by short range "impact" scattering (8, 9, 10). 

When the bias voltage corresponds to chemical potential shifts smaller than the quantum of vibration the electron cannot yield its energy to the vibration because there is no final state at the surface electrode available (Fig. 1(a)). At T = 0, the excitation happens suddenly when the bias voltage energy is larger than the quantum of vibration. The inelastic electron can continue its propagation into an empty electronic state now available above the sample Fermi level. In this case, a new channel for electronic transport has been open this is called the inelastic channel (Fig. 1(b)). 

Hence the outcome of the vibration excitation on the conductance is too complicated to predict. This is particularly true when there is a strong mixing of molecular states with metallic states. In this case, the interplay between the elastic contribution (exchange effects) and the purely inelastic one (increase of tunneling probability) is difficult to assess except after complete electronic structure calculations. 

Thus, in the Stokes case, the molecule is initially in its lowest-lying vibrational levels. The incident photon, at an energy much lower than necessary to reach the lowest-lying excited electronic state (i.e. the sample is transparent at this wavelength), excites the molecule to a virtual state (dashed line in Figure 9-4A) from which it immediately scatters inelastically. The scattered photon is at lower energy than the exciting photon and the molecule is vibrationally excited in one or more vibrational modes. 

The interaction of an electron with a molecule is described as a collision or impact, although the electron is so small that there is no collision in the usual sense of the word. The collision process may be termed elastic (the electron is merely deflected), inelastic (energy is transferred from the electron to the molecule), and superelastic (energy is transferred from the molecule to the electron). Electron-impact ionization is an example of an inelastic collision. The energy imparted to a molecule during an inelastic collision can lead to rotational, electronic, and vibrational excitation with or separate from ionization. Further, multiple-electron excitation can occur followed by autoionization, and the latter process has been shown to lead to a substantial fraction of total ionized species in many cases (S. Meyerson et al., 1963). Thus, an electron of energy 20 eV may lead to any of the above excitations of a molecule. The gas pressures used in a mass spectrometer and the density of electrons in the electron-beam are such that multiple electron-molecule interactions leading to ionization are improbable. 

Similar problems are encountered in a description of elastic or rotationally inelastic collisions of the electrons with molecules that have permanent dipole moment. However in this case K is never zero because k0 and ki have different norms due to an energy transfer to the vibrational excitation. 

In the e + M case, a very sensitive Indicator of shape resonance behavior Is the vibrational excitation channel. Vibrational excitation Is enhanced by shape resonances (3,17), and Is typically very weak for non-resonant scattering. Hence, a shape resonance, particularly at Intermediate energy (10-40 eV) (41,50), may be barely visible In the vlbratlonally and electronically elastic scattering cross section, and yet be displayed prominently In the vlbratlonally Inelastic, electronically elastic cross section. 

Because they lend themselves to studies using both photochemical and chemical activation, bimolecular reactions of vibrationally excited hydrogen halides have been more throughly investigated than any other family of reactions. The rate constants in Table 1.3 have been obtained by the laser-induced vibrational fluorescence technique and correspond to the sum of rate constants for reactive and inelastic processes. The main problem is to establish the atomic concentrations accurately. This is usually accomplished by gas-phase titration in a discharge-flow system, although photolysis methods have also been employed. To find the ratio of reaction to non-reactlve relaxation, product concentrations have to be observed. This has been done in relatively few cases. Some systems have also been studied using the infrared chemiluminescence depletion technique (see Section 1.5.1). These experiments supply relative rate data for removal from several vibrational levels, and, in favorable cases, also provide some information about the rotational-state dependence of these rates. 

In either case, the information on the vibrational transition is contained in the energy difference between the excitation radiation and the inelastically scattered Raman photons. Consequently, the parameters of interest are the intensities of the lines and their position relative to the Rayleigh line, usually expressed in wavenumbers (cm 1). As the actually recorded emissions all are in the spectral range determined by the excitation radiation, Raman spectroscopy facilitates the acquisition of vibrational spectra through standard VIS and/or NIR spectroscopy. 

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