Vibrational level population, excited

Fig. 4. A comparison of resonance fluorescence from the excited vibrational level 6 1 (top spectrum) reached by excitation in the absorption band 6 1 with resonance fluorescence from the several excited vibrational levels populated by absorption of light from the 2536 A Hg line. The exciting lines (structure at far right) have been placed above one another to facilitate comparison of the fluorescence structure. Fluorescence is in each case to lower energy from excitation.

Discussion of 2536 A experiments ends with a note concerning the excited vibrational levels populated by that radiation. The perversity of nature demands that this convenient exciting line must coincide with a complex region of absorption in benzene, and this is borne out by inspection of the spectrum shown in Fig. 10. The rotational structure of at least five absorption bands overlaps the exciting line. Only one of these had been correctly assigned prior to 1971. 

In contrast to classical overbarrier reactions, QMT can occur from the lowest vibrational quantum levels without thermal activation. Under these circumstances at the lowest temperatures, the degree of tunneling, and hence the reaction rate, is independent of temperature. At some point as the temperature is raised, higher vibrational levels become populated. As illustrated in Figure 10.1, the effective barrier is narrower for excited vibrational levels, and hence tunneling becomes more facile, leading to an increase in rate. Finally, as temperatures are raised further, classical reaction begins to compete, and usually dominates at room temperature (but, not always). 

Since the CO2 laser line corresponds to a transition between two excited vibrational levels, only those CO2 molecules can be excited by absorption of the laser line which are in the (OOl)-level, populated at 300 ° K with about 1 % of the total number of molecules. In spite of this low population density, the laser-excited fluorescence method is easily achieved because of the large exciting laser intensity. 

Considering first the case where the population of excited vibrational levels is negligible, we have for the rotational frequencies... 

Now consider the case with appreciable population of excited vibrational levels. The set of molecules with vibrational quantum number v will have its own value of Bv and will give rise to its own pure-rotation spectrum. Thus each line in Fig. 4.5 will have a series of vibrational satellites. Bv is given by (4.75), where ae is small compared to Be, so that the vibrational satellites lie near the main line. These satellites are shown for the transition in Fig. 4.6. Note the rapid decrease in intensity... 

As previously mentioned, for most diatomic molecules at room temperature, the population of excited vibrational levels is negligible. We therefore first consider transitions for which the initial vibrational level is u = 0. The selection rules (4.108) allow the transitions v = 0- l, 0— 2,... 

Figure 3. Field-matter interactions for a pair of electronic states. The zero and first excited vibrational levels are shown for each state (A). The fields are resonant with the electronic transitions. A horizontal bar represents an eigenstate, and a solid (dashed) vertical arrow represents a single field-matter interaction on a ket (bra) state. (See Refs. 1 and 54 for more details.) A single field-matter interaction creates an electronic superposition (coherence) state (B) that decays by electronic dephasing. Two interactions with positive and negative frequencies create electronic populations (C) or vibrational coherences either in the excited (D) or in the ground ( ) electronic states. In the latter cases (D and E) the evolution of coherence is decoupled from electronic dephasing, and the coherences decay by the vibrational dephasing process.

Estimation of population of the ground and excited vibrational levels for ring out-of-plane-vibrations demonstrate that even in the case of unsubstituted pyrimidine ring, 18% of molecules possess considerably nonplanar geometry of ring... 

The complexity of analysis depends on the relative values of collisional relaxation rates and the degree to which excited vibrational levels become populated thermally or under excitation conditions. For OH it is advantageous to pump into the electronic level to either the ground or first excited vibrational level. 

For molecular species measurement the exciting laser pulse (with a spectral energy density Uv) is tuned on a rotational line of an electronic transition. If Nj is the population of the lower vibrational level, the population N2 of the excited vibrational level increases according to... 

For triatomic molecules, the contribution of hot bands cannot be expressed as a function of energy alone (see (5)) and therefore cannot be expressed in a compact analytic formula like Formula (C.3). However, for rigid triatomic molecules like CO2, NO2, SO2, O3 and N2O, the contribution of hot bands is weak at room temperature (and below) because hco kT for all normal mode frequencies. Note that the width of the contribution to the Abs. XS associated with each excited vibrational level (hot bands) is proportional to the slope of the upper FES along the normal mode of the ground electronic corresponding to each excited (thermally populated) vibrational level. This fact explains why numerical models (e.g. using ground state normal coordinates) are able to calculate the Abs. XS. These calculations are of Frank-Condon type. 

Van Bentham and Davis ° demonstrated the presence of vibrationally excited I2 in a flowing I2/02(a) system using LIF detection. Population of the 33 < u < 44 levels was observed, and a comparison of the time dependent profiles for I2 and I indicated that I2 could be the intermediate from which I waa produced. Van Bentham and Davis ° briefly discussed the origin of the 4 detected in their experiment. Conditions were such that dissociation was probably initiated by reactions (8) and (9), but in the region where spectra for were recorded the concentration of I was high enough for reaction (10) to be the dominant local source of I2. Van Bentham and Davis ° examined the qualitative effect of the He carrier gas on the I2 vibrational level population distribution. As expected, vibrational relaxation was observed as the He pressure increased. 

Although I2 vibrational levels in the range 10 < u < Uth cannot be dissociated by 02(a) they may still play a role in the overall process. Evidence that transfer from 2(0) excites u > 10 levels more rapidly than u < 10 levels was obtained by Barnault et It has been suggeted that excitation from the mid range vibrational levels populates metastable electronically excited states ... 

To determine the nascent distribution, we examined 4 produced by reaction (10) under low pressure conditions. Pulsed photolysis of I2 at 496 nm was used to generate I. As only a fraction of the I2 was dissociated, 4 then appeared due to I + I2 collisions. The excited vibrational levels were probed using LIF of the D X transition with full rotational resolution. The nascent vibrational population distribution extracted from this spectrum is shown in Fig. 6, which reveals a strong preference for near resonant E-V transfer. 

A demonstration of the efficacy of MBER spectroscopy is the recent experiments on HF carried out by Bass, DeLeon, and Muenter [14]. In an effort to obtain Stark, Zeeman, and hyperfine properties, measurements were made that gave accurate values for both the ground and first excited vibrational levels of HF. Conventional resonance experiments can be done if the D = 1 state can be sufficiently populated. Using a color center IR laser to excite HF to u = 1, J = 1 levels, all the properties measured for the u = 0 and V = 1 states had essentially identical precision. The results included dipole moments, magnetic shielding anisotropies, rotational magnetic moments, magnetic susceptibilities, transition moments, and first and second derivatives with respect to internuclear separation of the properties. 

Because the population of the first excited vibrational level is much less than that of the ground state, the intensity of the anti-Stokes lines is less than that of the... 

This type of distribution, which presents an inversion at a vibrational quantum number given by dj = Tg/25 81 + 0.5 predicts a high population of excited vibrational levels for i/Tg > 1. [In Eq. (4) E10 is the energy of level 1 and 5 is the anharmoni-city of the molecule]. 

An elegant way to study the dynamics from excited vibrational levels of the electronic ground state is to make use of the femtosecond pump dump probe scheme in transient absorption experiments. The molecular system is initially excited to the Si state and, using a second pulse of longer wavelength (the dump pulse), excited vibrational levels of the So state are populated via stimulated emission.197... 

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