Vibronics

This means diat half the rotational levels of every vibronic state are missing in this molecule. Missing levels arise in other molecules and can also involve nuclei with nonzero spin they arise for the aimnonia molecule NH3. 

This last transition moment integral, if plugged into equation (B 1.1.2). will give the integrated intensity of a vibronic band, i.e. of a transition starting from vibrational state a of electronic state 1 and ending on vibrational level b of electronic state u. 

Equation (B 1.1.8) gives the intensity of one vibronic band in an absorption spectrum. It is also of interest to consider... 

For molecules we can use Bom-Oppenlieimer wavefimctions and talk about emission from one vibronic level to another. Equation (B1.1.5T equation tb 1.1.6) and equation tb 1.1.7) can be used just as they were for absorption. If we have an emission from vibronic state iih to the lower state a, the rate constant for emission would be given by... 

Often it is possible to resolve vibrational structure of electronic transitions. In this section we will briefly review the symmetry selection rules and other factors controlling the intensity of individual vibronic bands. 

In the Bom-Oppenlieimer approxunation the vibronic wavefrmction is a product of an electronic wavefimction and a vibrational wavefunction, and its syimnetry is the direct product of the synuuetries of the two components. We have just discussed the synuuetries of the electronic states. We now consider the syimnetry of a vibrational state. In the hanuonic approximation vibrations are described as independent motions along nonual modes Q- and the total vibrational wavefrmction is a product of frmctions, one wavefunction for each nonual mode ... 

The selection rule for vibronic states is then straightforward. It is obtained by exactly the same procedure as described above for the electronic selection rules. In particular, the lowest vibrational level of the ground electronic state of most stable polyatomic molecules will be totally synnnetric. Transitions originating in that vibronic level must go to an excited state vibronic level whose synnnetry is the same as one of the coordinates, v, y, or z. 

The synnnetry selection rules discussed above tell us whether a particular vibronic transition is allowed or forbidden, but they give no mfonnation about the intensity of allowed bands. That is detennined by equation (Bl.1.9) for absorption or (Bl.1.13) for emission. That usually means by the Franck-Condon principle if only the zero-order tenn in equation (B 1.1.7) is needed. So we take note of some general principles for Franck-Condon factors (FCFs). 

Figure Bl.1.2. Spectrum of fonnaldehyde with vibrational resolution. Several vibronic origins are marked. One progression m starting from the origin is indicated on the line along the top. A similar progression is built on each vibronic origin. Reprinted with pennission from [20]. Copyright 1982, American Chemical Society.

Several other vibronic origins are also marked in this spectrum. The second major peak is the 4j band, with... 

At 321 mn there is a vibronic origin marked This has one quantum of v, the antisynnnetric C-H stretching mode, in the upper state. Its intensity is induced by a distortion along This state has B2 vibrational symmetry. The direct product of B2 and A2 is B, so it has B vibronic syimnetry and absorbs x-polarized light. One can also see a 4 6,, vibronic origin which has the same syimnetry and intensity induced by... 

A very weak peak at 348 mn is the 4 origin. Since the upper state here has two quanta of v, its vibrational syimnetry is A and the vibronic syimnetry is so it is forbidden by electric dipole selection rules. It is actually observed here due to a magnetic dipole transition [21]. By magnetic dipole selection rules the A2- A, electronic transition is allowed for light with its magnetic field polarized in the z direction. It is seen here as having about 1 % of the intensity of the syimnetry-forbidden electric dipole transition made allowed by... 

If the experunental technique has sufficient resolution, and if the molecule is fairly light, the vibronic bands discussed above will be found to have a fine structure due to transitions among rotational levels in the two states. Even when the individual rotational lines caimot be resolved, the overall shape of the vibronic band will be related to the rotational structure and its analysis may help in identifying the vibronic symmetry. The analysis of the band appearance depends on calculation of the rotational energy levels and on the selection rules and relative intensity of different rotational transitions. These both come from the fonn of the rotational wavefunctions and are treated by angnlar momentum theory. It is not possible to do more than mention a simple example here. 

A good example is the spectnun of naphthalene. The two lowest excited states have 62 and synnnetries and are allowed for one-photon transitions. A weak transition to one of these is observable in die two-photon spectnun [33], presumably made allowed by vibronic effects. Much stronger two-photon transitions are observable at somewhat higher energies to a and an A state lying quite close to the energies predicted by theory many years earlier [34]. 

Bailey C G, Dessent C E FI, Johnson M A and Bowen K FI 1996 Vibronic effects in the photon energy-dependent photoelectron spectra of the CFIjCN dipole-bound anion J. Chem. Phys. 104 6976-83... 

Conventional spontaneous Raman scattering is the oldest and most widely used of the Raman based spectroscopic methods. It has served as a standard teclmique for the study of molecular vibrational and rotational levels in gases, and for both intra- and inter-molecular excitations in liquids and solids. (For example, a high resolution study of the vibrons and phonons at low temperatures in crystalline benzene has just appeared [38].)... 

Pinan J P, Ouillon R, Ranson P, Becucci M and Califano S 1998 High resolution Raman study of phonon and vibron bandwidths in isotropically pure and natural benzene crystal J. Chem. Phys. 109 1-12... 

Albrecht A C, Clark R J H, Oprescu D, Owens S J R and Svensen C 1994 Overtone resonance Raman scattering beyond the Condon approximation transform theory and vibronic properties J. Chem. Phys. 101 1890-903... 

Page J B 1991 Many-body problem to the theory of resonance Raman scattering by vibronic systems Top. Appi. Phys. 116 17-72... 

Ohung Y 0 and Ziegler L D 1988 The vibronic theory of resonance hyper-Raman scattering J. Chem. Phys. 88 7287-94... 

Figure Bl.6.11 Electron transmission spectrum of 1,3-cyclohexadiene presented as the derivative of transmitted electron current as a fiinction of the incident electron energy [17]. The prominent resonances correspond to electron capture into the two unoccupied, antibonding a -orbitals. The negative ion state is sufficiently long lived that discrete vibronic components can be resolved.

Schmidt S C, Schiferl D, Zinn A S, Ragan D D and Moore D S 1991 Calibration of the nitrogen vibron pressure scale for use at high temperatures and pressures J. Appi. Phys. 69 2793... 

Fragnito H L, Bigot J-Y, Becker P C and Shank C V 1989 Evolution of the vibronic absorption spectrum in a molecule following impulsive excitation with a 6 fs optical pulse Chem. Phys. Lett. 160 101 ... 

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... 

Figure C2.3.18. Vibronic peak fluorescence intensity ratio (III/I) as a function of SDS concentration for 0.1 % PEO solutions o, —35 000 Daltons —600 000 Daltons). Open symbols are for aqueous solution without added salt, and filled symbols are for 100 mM aqueous NaCl. Reproduced with pennission from figure 2 of [111].

Chestnoy N, Hull R and Brus L E 1986 Higher excited electronic states In clusters of ZnSe, CdSe, and ZnS spln-orblt, vibronic and relaxation phenomena J. Chem. Phys. 85 2237... 

Much of chemistry occurs in the condensed phase solution phase ET reactions have been a major focus for theory and experiment for the last 50 years. Experiments, and quantitative theories, have probed how reaction-free energy, solvent polarity, donor-acceptor distance, bridging stmctures, solvent relaxation, and vibronic coupling influence ET kinetics. Important connections have also been drawn between optical charge transfer transitions and thennal ET. 

Wang C, Mohney B K, Williams R, Hupp J T and Walker G C 1998 Solvent control of vibronic coupling upon intervalence charge transfer excitation of (NC)gFeCNRu(NH3)g- as revealed by resonance Raman and near-infrared absorption spectroscopies J. Am. Chem. Soc. 120 5848-9... 

Hayashi M, Yang T-S, Yu J, Mebel A, Chang R, Lin S H, Rubtsov I V and Yoshihara K 1998 Vibronic and vibrational coherence and relaxation dynamics in the TCNE-HMB complex J. Phys. Chem. A 102 4256-65... 

Condensed phase vibrational or vibronic lineshapes (vibronic transitions create vibrational excitations of electronic excited states) rarely provide infonnation about VER (see example C3.5.6.4). Experimental measurements of VER need much more than just the vibrational spectmm. The earliest VER measurements in condensed phases were ultrasonic attenuation studies of liquids [15], which provided an overall relaxation time for slowly (>10 ns) relaxing small molecule liquids. 

Other early work, which continues to this day, involved vibronic relaxation [6] of large colored molecules such as chrysene [19], pyrene [20] and perylene [21], due to the relative ease of using visible or near-UV light to pump and probe these systems (see example C3.5.6.5 below). 

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. 

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