Transition vibrational

Vibrational transitions, usually associated with simultaneous rotational transitions, occur in the i.r. and near i.r., and give rise to bands characteristic of the vibrational and rotational... 

We will explore the effect of three parameters 2 -and < )> that is, the time delay between the pulses, the tuning or detuning of the carrier frequency from resonance with an excited-state vibrational transition and the relative phase of the two pulses. We follow closely the development of [22]. Using equation (Al.6.73). 

Zhu L, Chen W, Hase W L and Kaiser E W 1993 Comparison of models for treating angular momentum in RRKM calculations with vibrator transition states. Pressure and temperature dependence of CI+C2H2 association J. Phys. Chem. 97 311-22... 

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]. 

To compare the relative populations of vibrational levels, the intensities of vibrational transitions out of these levels are compared. Figure B2.3.10 displays typical potential energy curves of the ground and an excited electronic state of a diatomic molecule. The intensity of a (v, v ) vibrational transition can be written as... 

Figure B2.3.10. Potential energy eiirves [42] of the ground X and exeited A eleetronie states of the hydroxyl radieal. Several vibrational levels are explieitly drawn in eaeh eleetronie state. One vibrational transition is explieitly indieated, and the upper and lower vibrational wavefiinetions are plotted. The upper and lower state vibrational quantum numbers are denoted V and v", respeetively. Also shown is one of the three repulsive potential energy eurves whieh eorrelate with the ground 0( P) + H dissoeiation asymptote. These eause predissoeiation of the higher rotational and vibrational levels of the A state.

Recently, the state-selective detection of reaction products tluough infrared absorption on vibrational transitions has been achieved and applied to the study of HF products from the F + H2 reaction by Nesbitt and co-workers (Chapman et al [7]). The relatively low sensitivity for direct absorption has been circumvented by the use of a multi-pass absorption arrangement with a narrow-band tunable infrared laser and dual beam differential detection of the incident and transmission beams on matched detectors. A particular advantage of probing the products tluough absorption is that the absolute concentration of the product molecules in a given vibration-rotation state can be detenuined. 

The result of all of the vibrational modes contributions to la (3 J-/3Ra) is a vector p-trans that is termed the vibrational "transition dipole" moment. This is a vector with components along, in principle, all three of the internal axes of the molecule. For each particular vibrational transition (i.e., each particular X and Xf) its orientation in space depends only on the orientation of the molecule it is thus said to be locked to the molecule s coordinate frame. As such, its orientation relative to the lab-fixed coordinates (which is needed to effect a derivation of rotational selection rules as was done earlier in this Chapter) can be described much as was done above for the vibrationally averaged dipole moment that arises in purely rotational transitions. There are, however, important differences in detail. In particular. 

The derivation of these seleetion rules proeeeds as before, with the following additional eonsiderations. The transition dipole moment s itrans eomponents along the lab-fixed axes must be related to its moleeule-fixed eoordinates (that are determined by the nature of the vibrational transition as diseussed above). This transformation, as given in Zare s text, reads as follows ... 

The selection rules for AK depend on the nature of the vibrational transition, in particular, on the component of itrans along the molecule-fixed axes. For the second 3-j symbol to not vanish, one must have... 

For purely rotational transitions, the initial and final eleetronie and vibrational states are the same. Moreover, the eleetronie and vibrational states are not summed over in the analog of the above development beeause one is interested in obtaining an expression for a partieular Xiv /ie ==> Xfv Vfe eleetronie-vibrational transition s lineshape. As a result, the... 

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 ... 

Each vibrational transition observed in the gas phase gives rise to what is called a band in the spectmm. The word line is reserved for describing a transition between rotational levels associated with the two vibrational levels giving rise to the fine stmcture of a band. However, in the solid or liquid phase, where this fine stmcture is not present, each vibrational transition is sometimes referred to as a line rather than a band. 

We have seen in Section 5.2.1.4 that there is a stack of rotational energy levels associated with all vibrational levels. In rotational spectroscopy we observe transitions between rotational energy levels associated with the same vibrational level (usually v = 0). In vibration-rotation spectroscopy we observe transitions between stacks of rotational energy levels associated with two different vibrational levels. These transitions accompany all vibrational transitions but, whereas vibrational transitions may be observed even when the sample is in the liquid or solid phase, the rotational transitions may be observed only in the gas phase at low pressure and usually in an absorption process. 

Figure 6.7 Rotational transitions accompanying a vibrational transition in (a) an infrared spectrum and (b) a Raman spectrum of a diatomic molecule...

Figure 6.7(a) illustrates the rotational energy levels associated with two vibrational levels u (upper) and il (lower) between which a vibrational transition is allowed by the Au = 1 selection rule. The rotational selection rule governing transitions between the two stacks of levels is... 

As for a diatomic molecule, the general harmonic oscillator selection mle for infrared and Raman vibrational transitions is... 

For vibrational transitions to be allowed in the infrared specttum there is an additional requirement that there must be an accompanying change of dipole moment and, in the... 

Although we have been able to see on inspection which vibrational fundamentals of water and acetylene are infrared active, in general this is not the case. It is also not the case for vibrational overtone and combination tone transitions. To be able to obtain selection mles for all infrared vibrational transitions in any polyatomic molecule we must resort to symmetry arguments. 

The vibrational transition intensity is proportional to R, the square of the vibrational transition moment R where... 

In the most usual cases, where the lower level is the zero-point level, F(i/ ") = A and the requirement for a Raman vibrational transition becomes... 

Raman scattering is normally of such very low intensity that gas phase Raman spectroscopy is one of the more difficult techniques. This is particularly the case for vibration-rotation Raman spectroscopy since scattering involving vibrational transitions is much weaker than that involving rotational transitions, which were described in Sections 5.3.3 and 5.3.5. For this reason we shall consider here only the more easily studied infrared vibration-rotation spectroscopy which must also be investigated in the gas phase (or in a supersonic jet, see Section 9.3.8). 

Figure 6.24 Rotational transitions accompanying a infrared vibrational transition in a...

As we proceed to molecules of higher symmetry the vibrational selection rules become more restrictive. A glance at the character table for the point group (Table A.41 in Appendix A) together with Equation (6.56) shows that, for regular tetrahedral molecules such as CH4, the only type of allowed infrared vibrational transition is... 

In a molecule such as the asymmetric rotor formaldehyde, shown in Figure 5.1(f), the a, b and c inertial axes, of lowest, medium and highest moments of inertia, respectively, are defined by symmetry, the a axis being the C2 axis, the b axis being in the yz plane and the c axis being perpendicular to the yz plane. Vibrational transition moments are confined to the a, b or c axis and the rotational selection mles are characteristic. We call them... 

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