Molecule electronic transition

A great variety of problems can be studied in the far-infrared by means of Fourier transform spectroscopy vibrations of molecules and crystal lattices, rotation of molecules, electronic transitions in paramagnetic ions and semicon-... 

Spin coupling of unpaired electrons with an applied magnetic field Rotation of molecules Vibration of molecules Rotation/vibration of molecules Electronic transitions (some large molecules only) Electronic energy... 

For polyatomic molecules, electronic transitions involve molecular orbitals such transitions require energy in the ultraviolet region and are of vital importance in ultraviolet spectroscopy. 

In a perfect molecule, electronic transitions would go like this Absorption of a photon excites a molecule from initial (usually ground) state to excited state excited state emits a photon having the same energy/frequency/wavelength and molecule goes from excited state to previous initial ground state. The first process, excitation, would be followed by the exact opposite process, called deexcitation or decay. Such processes would follow quantum-mechanical selection rules strictly. 

Franck-Condon principle According to this principle the time required for an electronic transition in a molecule is very much less than the period of vibration of the constituent nuclei of the molecule. Consequently, it may be assumed that during the electronic transition the nuclei do not change their positions or momenta. This principle is of great importance in discussing the energy changes and spectra of molecules. 

In absorption spectroscopy, the attenuation of light as it passes tln-ough a sample is measured as a function of wavelength. The attenuation is due to rovibrational or electronic transitions occurring in the sample. Mapping out the attenuation versus photon frequency gives a description of the molecule or molecules responsible for the absorption. The attenuation at a particular frequency follows the Beer-Lambert law,... 

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. 

Here each < ) (0 is a vibrational wavefiinction, a fiinction of the nuclear coordinates Q, in first approximation usually a product of hamionic oscillator wavefimctions for the various nomial coordinates. Each j (x,Q) is the electronic wavefimctioii describing how the electrons are distributed in the molecule. However, it has the nuclear coordinates within it as parameters because the electrons are always distributed around the nuclei and follow those nuclei whatever their position during a vibration. The integration of equation (Bl.1.1) can be carried out in two steps—first an integration over the electronic coordinates v, and then integration over the nuclear coordinates 0. We define an electronic transition moment integral which is a fimctioii of nuclear position ... 

If one of the components of this electronic transition moment is non-zero, the electronic transition is said to be allowed if all components are zero it is said to be forbidden. In the case of diatomic molecules, if the transition is forbidden it is usually not observed unless as a very weak band occurring by magnetic dipole or electric quadnipole interactions. In polyatomic molecules forbidden electronic transitions are still often observed, but they are usually weak in comparison with allowed transitions. 

One of the consequences of this selection rule concerns forbidden electronic transitions. They caimot occur unless accompanied by a change in vibrational quantum number for some antisynnnetric vibration. Forbidden electronic transitions are not observed in diatomic molecules (unless by magnetic dipole or other interactions) because their only vibration is totally synnnetric they have no antisymmetric vibrations to make the transitions allowed. 

Condon E U 1928 Nuclear motion associated with electron transitions in diatomic molecules Phys. Rev. 32 858-72... 

Herzberg G, Lagerquist A and Malmberg C 1969 New electronic transitions of the C2 molecule absorption in the vacuum ultraviolet region Can. J. Phys. 47 2735-43... 

The SHG/SFG technique is not restricted to interface spectroscopy of the delocalized electronic states of solids. It is also a powerful tool for spectroscopy of electronic transitions in molecules. Figure Bl.5.13 presents such an example for a monolayer of the R-enantiomer of the molecule 2,2 -dihydroxyl-l,l -binaphthyl, (R)-BN, at the air/water interface [ ]. The spectra reveal two-photon resonance features near wavelengths of 332 and 340 mu that are assigned to the two lowest exciton-split transitions in the naphtli-2-ol... 

Optical metiiods, in both bulb and beam expermrents, have been employed to detemiine tlie relative populations of individual internal quantum states of products of chemical reactions. Most connnonly, such methods employ a transition to an excited electronic, rather than vibrational, level of tlie molecule. Molecular electronic transitions occur in the visible and ultraviolet, and detection of emission in these spectral regions can be accomplished much more sensitively than in the infrared, where vibrational transitions occur. In addition to their use in the study of collisional reaction dynamics, laser spectroscopic methods have been widely applied for the measurement of temperature and species concentrations in many different kinds of reaction media, including combustion media [31] and atmospheric chemistry [32]. 

This teclnhque can be used both to pennit the spectroscopic detection of molecules, such as H2 and HCl, whose first electronic transition lies in the vacuum ultraviolet spectral region, for which laser excitation is possible but inconvenient [ ], or molecules such as CH that do not fluoresce. With 2-photon excitation, the required wavelengdis are in the ultraviolet, conveniently generated by frequency-doubled dye lasers, rather than 1-photon excitation in the vacuum ultraviolet. Figure B2.3.17 displays 2 + 1 REMPI spectra of the HCl and DCl products, both in their v = 0 vibrational levels, from the Cl + (CHg) CD reaction [ ]. For some electronic states of HCl/DCl, both parent and fragment ions are produced, and the spectrum in figure B2.3.17 for the DCl product was recorded by monitoring mass 2 (D ions. In this case, both isotopomers (D Cl and D Cl) are detected. 

The easiest method for creating many vibrational excitations is to use convenient pulsed visible or near-UV lasers to pump electronic transitions of molecules which undergo fast nonradiative processes such as internal conversion (e.g. porjDhyrin [64, 65] or near-IR dyes [66, 62, 68 and 62]), photoisomerization (e.g. stilbene [12] or photodissociation (e.g. Hgl2 [8]). Creating a specific vibrational excitation D in a controlled way requires more finesse. The easiest method is to use visible or near-UV pulses to resonantly pump a vibronic transition (e.g. 

The electronic transitions which produce spectra in the visible and ultraviolet are accompanied by vibrational and rotational transitions. In the condensed state, however, rotation is hindered by solvent molecules, and stray electrical fields affect the vibrational frequencies. For these reasons, electronic bands are very broad. An electronic band is characterised by the wave length and moleculai extinction coefficient at the position of maximum intensity (Xma,. and emai.). 

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). 

In 1925, before the development of the Schrodinger equation, Franck put forward qualitative arguments to explain the various types of intensity distributions found in vibronic transitions. His conclusions were based on an appreciation of the fact that an electronic transition in a molecule takes place much more rapidly than a vibrational transition so that, in a vibronic transition, the nuclei have very nearly the same position and velocity before and after the transition. 

Section 6.13.2 and illustrated in Figure 6.5. The possible inaccuracies of the method were made clear and it was stressed that these are reduced by obtaining term values near to the dissociation limit. Whether this can be done depends very much on the relative dispositions of the various potential curves in a particular molecule and whether electronic transitions between them are allowed. How many ground state vibrational term values can be obtained from an emission spectrum is determined by the Franck-Condon principle. If r c r" then progressions in emission are very short and few term values result but if r is very different from r", as in the A U — system of carbon monoxide discussed in Section 7.2.5.4, long progressions are observed in emission and a more accurate value of Dq can be obtained. 

The +, —, e, and/labels attached to the levels in Figure 7.25 have the same meaning as those in Figure 6.24 showing rotational levels associated with and Ig vibrational levels of a linear polyatomic molecule. Flowever, just as in that case, they can be ignored for a Z — I, type of electronic transition. 

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