Electronic broadening

P. Bunt, M. Sprik, and R. Vuilleumier (2003) Thermal versus electronic broadening in the density of states of liquid water. Chem. Phys. Lett. 376, p. 68 R. Iftimie, J. W. Thomas, and M. E. Tuckerman (2004) On-the-fly localization of electronic orbitals in Car-Parrinello molecular dynamics. J. Chem. Phys. 120, p. 2169... 

The clearest results in electrochemical in situ STM of redox molecules and biomolecules are obtained when the bias voltage and the electronic broadenings are small, that is... 

High-resolution spectroscopy used to observe hyperfme structure in the spectra of atoms or rotational stnicture in electronic spectra of gaseous molecules connnonly must contend with the widths of the spectral lines and how that compares with the separations between lines. Tln-ee contributions to the linewidth will be mentioned here tlie natural line width due to tlie finite lifetime of the excited state, collisional broadening of lines, and the Doppler effect. 

Figure Bl.6.6 The Bethe surface. The sharp ridge corresponds to scattering from a single stationary target electron the broadened ridge to scattering from the electrons in an atom or molecule.

In electron-spin-echo-detected EPR spectroscopy, spectral infomiation may, in principle, be obtained from a Fourier transfomiation of the second half of the echo shape, since it represents the FID of the refocused magnetizations, however, now recorded with much reduced deadtime problems. For the inhomogeneously broadened EPR lines considered here, however, the FID and therefore also the spin echo, show little structure. For this reason, the amplitude of tire echo is used as the main source of infomiation in ESE experiments. Recording the intensity of the two-pulse or tliree-pulse echo amplitude as a function of the external magnetic field defines electron-spm-echo- (ESE-)... 

Figure Cl.5.2. Fluorescence excitation spectra (cps = counts per second) of pentacene in /i-teriDhenyl at 1.5 K. (A) Broad scan of the inhomogeneously broadened electronic origin. The spikes are repeatable features each due to a different single molecule. The laser detuning is relative to the line centre at 592.321 nm. (B) Expansion of a 2 GHz region of this scan showing several single molecules. (C) Low-power scan of a single molecule at 592.407 nm showing the lifetime-limited width of 7.8 MHz and a Lorentzian fit. Reprinted with pennission from Moemer [198]. Copyright 1994 American Association for the Advancement of Science.

Each vibrational peak within an electronic transition can also display rotational structure (depending on the spacing of the rotational lines, the resolution of the spectrometer, and the presence or absence of substantial line broadening effects such as... 

Experimental confirmation of the metal-nitrogen coordination of thiazole complexes was recently given by Pannell et al. (472), who studied the Cr(0), Mo(0), and W(0) pentacarbonyl complexes of thiazole (Th)M(CO)5. The infrared spectra are quite similar to those of the pyridine analogs the H-NMR resonance associated with 2- and 4-protons are sharper and possess fine structure, in contrast to the broad, featureless resonances of free thiazole ligands. This is expected since removal of electron density from nitrogen upon coordination reduces the N quad-rupole coupling constant that is responsible for the line broadening of the a protons. 

The concept of a chromophore is analogous to that of a group vibration, discussed in Section 6.2.1. Just as the wavenumber of a group vibration is treated as transferable from one molecule to another so is the wavenumber, or wavelength, at which an electronic transition occurs in a particular group. Such a group is called a chromophore since it results in a characteristic colour of the compound due to absorption of visible or, broadening the use of the word colour , ultraviolet radiation. 

The third band system, involving the removal of an electron from the 1 2 orbital, is vibrationally complex, consistent with the orbital being strongly bonding and favouring a linear molecule. Presumably both Vj and V2 are excited but the bands in this system are considerably broadened, making analysis unreliable. 

In atoms in which electrons in M or A shells take part to some extent in molecular orbital formation some transitions in the L spectmm may be broadened. Similarly, in an M emission spectmm, in which the initial vacancy has been created in the M shell, there is a greater tendency towards broadening due to molecular orbital involvement. 

Figure 9.18 shows a typical energy level diagram of a dye molecule including the lowest electronic states Sq, and S2 in the singlet manifold and and T2 in the triplet manifold. Associated with each of these states are vibrational and rotational sub-levels broadened to such an extent in the liquid that they form a continuum. As a result the absorption spectrum, such as that in Figure 9.17, is typical of a liquid phase spectrum showing almost no structure within the band system. 

Consider Figure la, which shows the electronic energy states of a solid having broadened valence and conduction bands as well as sharp core-level states X, Y, and Z. An incoming electron with energy Eq may excite an electron ftom any occupied state to any unoccupied state, where the Fermi energy Ap separates the two... 

The phenomena of beam broadening as a function of specimen thickness are illustrated in Fig. 4.20 each figure represents 200 electron trajectories in silicon calculated by Monte Carlo simulations [4.91, 4.95-4.97] for 100-keV primary energy, where an infinitesimally small electron probe is assumed to enter the surface. In massive Si the electrons suffer a large number of elastic and inelastic interactions during their paths through the material, until they are finally completely stopped. The resulting penetration depth of the electrons is approximately 50 pm and in the... 

Fig. 4.20. Comparison of beam broadening in Si as a function of thickness for 100 keV primary electron energy (A) bulk specimen, (B) 200 nm, (C) 50 nm thickness.

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