Electron vibrations

While a laser beam can be used for traditional absorption spectroscopy by measuring / and 7q, the strength of laser spectroscopy lies in more specialized experiments which often do not lend themselves to such measurements. Other techniques are connnonly used to detect the absorption of light from the laser beam. A coimnon one is to observe fluorescence excited by the laser. The total fluorescence produced is nonnally proportional to the amount of light absorbed. It can be used as a measurement of concentration to detect species present in extremely small amounts. Or a measurement of the fluorescence intensity as the laser frequency is scaimed can give an absorption spectrum. This may allow much higher resolution than is easily obtained with a traditional absorption spectrometer. In other experiments the fluorescence may be dispersed and its spectrum detennined with a traditional spectrometer. In suitable cases this could be the emission from a single electronic-vibrational-rotational level of a molecule and the experimenter can study how the spectrum varies with level. 

Electronic spectra are almost always treated within the framework of the Bom-Oppenlieimer approxunation [8] which states that the total wavefiinction of a molecule can be expressed as a product of electronic, vibrational, and rotational wavefiinctions (plus, of course, the translation of the centre of mass which can always be treated separately from the internal coordinates). The physical reason for the separation is that the nuclei are much heavier than the electrons and move much more slowly, so the electron cloud nonnally follows the instantaneous position of the nuclei quite well. The integral of equation (BE 1.1) is over all internal coordinates, both electronic and nuclear. Integration over the rotational wavefiinctions gives rotational selection rules which detemiine the fine structure and band shapes of electronic transitions in gaseous molecules. Rotational selection rules will be discussed below. For molecules in condensed phases the rotational motion is suppressed and replaced by oscillatory and diflfiisional motions. 

A-B relative or external motion undergo free-free transitions (E., E. + dE.) (Ej Ej+ dE within the translational continuum, while the structured particles undergo bound-bound (excitation, de-excitation, excitation transfer) or bound-free (ionization, dissociation) transitions = (a, 3) ->/= (a, (3 ) in their internal electronic, vibrational or rotational structure. The transition frequency (s ) for this collision is... 

Electronic structure theory describes the motions of the electrons and produces energy surfaces and wavefiinctions. The shapes and geometries of molecules, their electronic, vibrational and rotational energy levels, as well as the interactions of these states with electromagnetic fields lie within the realm of quantum stnicture theory. 

Myers A B, Tchenio P and Moerner W E 1994 Vibronic spectroscopy of single molecules exploring electronic-vibrational frequency correlations within an inhomogeneous distribution J. Lumin. 58 161-7... 

This completes our introduction to the subject of rotational and vibrational motions of molecules (which applies equally well to ions and radicals). The information contained in this Section is used again in Section 5 where photon-induced transitions between pairs of molecular electronic, vibrational, and rotational eigenstates are examined. More advanced treatments of the subject matter of this Section can be found in the text by Wilson, Decius, and Cross, as well as in Zare s text on angular momentum. 

The interaction of a molecular species with electromagnetic fields can cause transitions to occur among the available molecular energy levels (electronic, vibrational, rotational, and nuclear spin). Collisions among molecular species likewise can cause transitions to occur. Time-dependent perturbation theory and the methods of molecular dynamics can be employed to treat such transitions. 

These so-called interaction perturbations Hint are what induces transitions among the various electronic/vibrational/rotational states of a molecule. The one-electron additive nature of Hint plays an important role in determining the kind of transitions that Hint can induce. For example, it causes the most intense electronic transitions to involve excitation of a single electron from one orbital to another (recall the Slater-Condon rules). 

The tools of time-dependent perturbation theory can be applied to transitions among electronic, vibrational, and rotational states of molecules. 

For electronic-vibration-rotation transitions, the initial and final electronic states are different as are the initial and final vibrational and rotational states. As a result, the sum... 

This development thus leads to the following definition of C(t) for the electronic, vibration, and rotation case ... 

Here, I(co) is the Fourier transform of the above C(t) and AEq f is the adiabatic electronic energy difference (i.e., the energy difference between the v = 0 level in the final electronic state and the v = 0 level in the initial electronic state) for the electronic transition of interest. The above C(t) clearly contains Franck-Condon factors as well as time dependence exp(icOfvjvt + iAEi ft/h) that produces 5-function spikes at each electronic-vibrational transition frequency and rotational time dependence contained in the time correlation function quantity <5ir Eg ii,f(Re) Eg ii,f(Re,t)... 

All of these time correlation functions contain time dependences that arise from rotational motion of a dipole-related vector (i.e., the vibrationally averaged dipole P-avejv (t), the vibrational transition dipole itrans (t) or the electronic transition dipole ii f(Re,t)) and the latter two also contain oscillatory time dependences (i.e., exp(icofv,ivt) or exp(icOfvjvt + iAEi ft/h)) that arise from vibrational or electronic-vibrational energy level differences. In the treatments of the following sections, consideration is given to the rotational contributions under circumstances that characterize, for example, dilute gaseous samples where the collision frequency is low and liquid-phase samples where rotational motion is better described in terms of diffusional motion. 

If the rotational motion of the molecules is assumed to be entirely unhindered (e.g., by any environment or by collisions with other molecules), it is appropriate to express the time dependence of each of the dipole time correlation functions listed above in terms of a "free rotation" model. For example, when dealing with diatomic molecules, the electronic-vibrational-rotational C(t) appropriate to a specific electronic-vibrational transition becomes ... 

If any atoms have nuclear spin this part of the total wave function can be factorized and the energy treated additively. ft is for these reasons that we can treat electronic, vibrational, rotational and NMR spectroscopy separately. 

In Figure 2.2(a) states m and n of an atom or molecule are stationary states, so-called because they are time-independent. This pair of states may be, for example, electronic, vibrational or rotational. We consider the three processes that may occur when such a... 

Electronic, vibrational and rotational transitions may be involved in Raman scattering but, in this chapter, we consider only rotational transitions. 

Molecules initially in the J = 0 state encounter intense, monochromatic radiation of wavenumber v. Provided the energy hcv does not correspond to the difference in energy between J = 0 and any other state (electronic, vibrational or rotational) of the molecule it is not absorbed but produces an induced dipole in the molecule, as expressed by Equation (5.43). The molecule is said to be in a virtual state which, in the case shown in Figure 5.16, is Vq. When scattering occurs the molecule may return, according to the selection mles, to J = 0 (Rayleigh) or J = 2 (Stokes). Similarly a molecule initially in the J = 2 state goes to... 

The use of molecular and atomic beams is especially useful in studying chemiluminescence because the results of single molecular interactions can be observed without the complications that arise from preceding or subsequent energy-transfer coUisions. Such techniques permit determination of active vibrational states in reactants, the population distributions of electronic, vibrational, and rotational excited products, energy thresholds, reaction probabihties, and scattering angles of the products (181). 

If we deal with N isolated non-interacting entities such as the molecules in a gas at low density, we can further divide up molecular energies with reasonable accuracy into their electronic, vibrational and rotational contributions... 

Teudt considers that the nasal sensory nerves have electron vibrations which are increased by resonance when odoriferous substances having corresponding intramolecular electron vibrations are inspired with air, and he concludes that a chemical element can the more readily induce odour in... 

Initial conditions for the total molecular wavefunction with n = I (including electronic, vibrational and rotational quantum numbers) can be imposed by adding elementary solutions obtained for each set of initial nuclear variables, keeping in mind that the xi and 5 depend parametrically on the initial variables... 

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