Homogeneous broadening mechanisms

The width of a velocity-selective excitation resonance is determined by the homogeneous width 2F. Table 3.1 provides a quantitative understanding of the various mechanisms contributing to the homogeneous width. 

The first and the most fundamental effect is the radiative broadening due to the spontaneous decay of an excited state (the half-width of the spectral line is r = 7rad = 7). A spectral line due to spontaneous decay has a Lorentzian shape (eqn 2.5). The lifetime of an excited atomic or molecular state depends on the oscillator strength of the transition and the radiation wavelength. For electronic transitions of atoms and molecules in the visible region of the spectrum, l/7rad — s. For metastable atomic and vibrational molecular levels, the radiative lifetime may be much longer, namely 

Type Origin Line width, Au Range of values 

Natural broadening Spontaneous decay of an excited state 1 2irr r = natural lifetime Atoms lO -lO Hz Molecules lO-lO Hz 

Lorentz (collision) broadening Interparticle collisions (TrTcoii)- Tcoii = mean time between collisions 3 X 10 -3 X 10 Hz (at 1 mTorr pressure) 

---

This Lorentzian line-shape function has been sketched in Figure 1.4(b). The natural broadening is a type of homogeneous broadening, in which all the absorbing atoms are assumed to be identical and then to contribute with identical line-shape functions to the spectrum. There are other homogeneous broadening mechanisms, such as that due to the dynamic distortions of the crystalline environment associated with lattice vibrations, which are partially discussed in Chapter 5. 

I.r. laser spectroscopy and quadrupole mass spectrometry were used by Fischer et al. to study vibrational predissociation of clusters of C2H4, and CsHg, but-l-ene, cis- and trans-but-2-ene, and isobutene. They obtained spectra in the range 2900—3200 cm and for C2H4 clusters predissociation was observed to result from excitation near the v-i, and vg fundamentals and the i 2 + V12 combination band. The vibrational bands were observed to have Lorentzian lineshapes with IWHM of ca. 5 cm. A homogeneous broadening mechanism was assumed and the widths were used to calculate excited-state lifetimes. Valentini and co-workers studied the predissociation of C2H4 clusters at 950 cm in a crossed laser/molecular beam apparatus. 

Table 3.1 Homogeneous broadening mechanisms of spectral lines...

Energy transfer in solution occurs through a dipole-dipole interaction of the emission dipole of an excited molecule (donor) and the absorptive moment of a unexcited molecule (acceptor). Forster<40) treated the interaction quantum mechanically and derived and expression for the rate of transfer between isolated stationary, homogeneously broadened donors and acceptors. Dexter(41) formulated the transfer rate using the Fermi golden rule and extended it to include quadrupole and higher transition moments in either the donor or the acceptor. Following the scheme of Dexter, the transfer rate for a specific transition is... 

The dimerization of 28 has also been studied by Prasad, who used Raman spectroscopy to monitor both changes in intermolecular vibrations and lattice phonon modes [73]. The Raman spectrum shows the disappearance of alkene stretches at 997, 1180, 1593, and 1625 cm-1 as expected, and the appearance of cyclobutane modes at 878,979, and 1001 cm-1. Phonon modes broadened as the reaction progressed, and bands around 15-40 cm-1 showed a shift in frequency. Between about 50 and 66% conversion it was difficult to define distinct bands, but after that point product bands grew in distinctly. This amalgamation behavior is good evidence for a homogeneous reaction mechanism. 

The ethylene cluster experiments and interpretation are discussed below as follows. Section II summarizes important aspects of the experiment. Section III gives details on the spectral analysis with respect to inhomogeneous versus homogenous broadening as well as saturation effects. Section IV discusses structural information obtained from the spectra. Section V discusses the vibrational predissociation mechanism for these complexes and compares the results to other systems. 

It has been shown that spontaneous or even coherent Raman scattering cannot be used to distinguish between the fast homogeneous and the slow inhomogeneous broadening mechanisms in vibrational transitions [18. 

---