Populated rotational states

Although the formation of products in different states is often analysed almost completely, only very few experiments yield state to state photodissociation cross sections. Usually photodissociation experiments are done with a gas at room temperature, where many rotational states are populated in the parent molecule. In this case product formation originates from many different initially populated rotational states of the parent molecule. Even in experiments, in which jet cooling is used to prepare low rotational states, usually more than one state is populated, in particular, if nuclear spins are important, like in H2 or H2O. 

Spacing for rotational levels, gives a spread of populated rotational states, generally peaking, depending upon energy spacing, around J 5-50. 

Figure A3.9.5. Population of rotational states versus rotational energy for NO moleeules seattered from an Ag (111) surfaee at two different ineidenee energies and at = 520 K [25] (a) E = 0.85 eV, 0. = 15° and b) E = 0.09 eV, 9. = 15°. Results at = 0.85 eV show a pronoimeed rotational rainbow.

RRKM theory assumes a microcanonical ensemble of A vibrational/rotational states within the energy interval E E + dE, so that each of these states is populated statistically with an equal probability [4]. This assumption of a microcanonical distribution means that the unimolecular rate constant for A only depends on energy, and not on the maimer in which A is energized. If N(0) is the number of A molecules excited at / =... 

NO prodnet from tire H + NO2 reaetion [43]. Individnal lines in the various rotational branehes are denoted by the total angidar momentum J of the lower state, (b) Simnlated speetnim with the NO rotational state populations adjusted to reprodnee the speetnim in (a). (By permission from AIP.)... 

This book presents a detailed exposition of angular momentum theory in quantum mechanics, with numerous applications and problems in chemical physics. Of particular relevance to the present section is an elegant and clear discussion of molecular wavefiinctions and the detennination of populations and moments of the rotational state distributions from polarized laser fluorescence excitation experiments. 

C3.3.4 DEDUCING ENERGY TRANSFER MECHANISMS FROM POPULATION AND VELOCITY DISTRIBUTIONS OF THE SCATTERED BATH MOLECULES ROTATIONAL STATE POPULATION DISTRIBUTIONS FOR VIBRATIONAL EXCITATION OF THE BATH... 

These results provide so-called "selection rules" because they limit the L and M values of the final rotational state, given the L, M values of the initial rotational state. In the figure shown below, the L = L + 1 absorption spectrum of NO at 120 °K is given. The intensities of the various peaks are related to the populations of the lower-energy rotational states which are, in turn, proportional to (2 L + 1) exp(- L (L +1) h /STi IkT). Also included in the intensities are so-called line strength factors that are proportional to the squares of the quantities ... 

In this particular case, the equilibrium average is taken over the initial rotational states whose probabilities are denoted pir, any initial vibrational states that may be populated, with probabilities piv, and any populated electronic states, with probabilities pig. 

The cancellation of gas phase spectral features using the "half plate design Is far superior to methods Involving a second gas cell placed In the reference beam. This Is because the gas density and Its rotational state population will differ In the two cells for different sample (and therefore gas) temperatures. For high sensitivity measurements, these effects can be difficult to handle using two cells. 

A technique which is not a laser method but which is most useful when combined with laser spectroscopy (LA/LIF) is that of supersonic molecular beams (27). If a molecule can be coaxed into the gas phase, it can be expanded through a supersonic nozzle at fairly high flux into a supersonic beam. The apparatus for this is fairly simple, in molecular beam terms. The result of the supersonic expansion is to cool the molecules rotationally to a few degrees Kelvin and vibrationally to a few tens of degrees, eliminating almost all thermal population of vibrational and rotational states and enormously simplifying the LA/LIF spectra that are observed. It is then possible, even for complex molecules, to make reliable vibronic assignments and infer structural parameters of the unperturbed molecule therefrom. Molecules as complex as metal phthalocyanines have been examined by this technique. 

Proceeding in the spirit above it seems reasonable to inquire why s is equal to the number of equivalent rotations, rather than to the total number of symmetry operations for the molecule of interest. Rotational partition functions of the diatomic molecule were discussed immediately above. It was pointed out that symmetry requirements mandate that homonuclear diatomics occupy rotational states with either even or odd values of the rotational quantum number J depending on the nuclear spin quantum number I. Heteronuclear diatomics populate both even and odd J states. Similar behaviors are expected for polyatomic molecules but the analysis of polyatomic rotational wave functions is far more complex than it is for diatomics. Moreover the spacing between polyatomic rotational energy levels is small compared to kT and classical analysis is appropriate. These factors appreciated there is little motivation to study the quantum rules applying to individual rotational states of polyatomic molecules. 

If only a few rotational states are populated, assumes a few discrete values, and if the exit aperture is small enough, the hexapole field will transmit individual JJCM states depending on the voltage selected (see below). 

The Boltzmann expression can be used to calculate the relative populations of molecules in any rotational state 7 compared to the lowest rotational state 7 = 0 at temperature T (K) ... 

Figure 3.15. Rotational state distributions of NO produced in direct scattering from Ag(lll) at Ts 600 as a function of incident normal energy En. Rotational populations Nj are plotted in such a way that a Boltzmann distribution characterized by a temperature T is a straight line. The different symbols correspond to rotational populations derived from the different rotational transitions as listed. From Ref. [160].

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