Vibrating rotator, energy

If K is adiabatic, a molecule containing total vibrational-rotational energy E and, in a particular J, K level, has a vibrational density of states p[E - EjiJ,K). Similarly, the transition state s sum of states for the same E,J, and Kis [ -Eq-Ef(J,K)]. The RRKM rate constant for the Kadiabatic model is... 

Each and every electronic energy state, labelled k, has a set, labelled L, of vibration/rotation energy levels k,L and wavefiinctions... 

My own research efforts [4] have, for many years, involved taking into account such non-Bom-Oppen-heimer couplings, especially in cases where vibration/rotation energy transferred to electronic motions causes... 

The homonuclear rare gas pairs are of special interest as models for intennolecular forces, but they are quite difficult to study spectroscopically. They have no microwave or infrared spectmm. However, their vibration-rotation energy levels can be detennined from their electronic absorjDtion spectra, which he in the vacuum ultraviolet (VUV) region of the spectmm. In the most recent work, Hennan et al [24] have measured vibrational and rotational frequencies to great precision. In the case of Ar-Ar, the results have been incoriDorated into a multiproperty analysis by Aziz [25] to develop a highly accurate pair potential. 

Far-infrared and mid-infrared spectroscopy usually provide the most detailed picture of the vibration-rotation energy levels in the ground electronic state. However, they are not always possible and other spectroscopic methods are also important. 

In using symmetry to help simplify moleeular orbital or vibration/rotation energy level ealeulations, the following strategy is followed ... 

Here, ej f are the vibration-rotation energies of the initial (anion) and final (neutral) states, and E denotes the kinetic energy carried away by the ejected electron (e.g., the initial state corresponds to an anion and the final state to a neutral molecule plus an ejected electron). The density of translational energy states of the ejected electron is p(E) = 4 nneL (2meE) /h. We have used the short-hand notation involving P P/p to symbolize the multidimensional derivative operators that arise in the non BO couplings as discussed above ... 

Therefore, the simplest classical treatment in which the propagator exp(it (T+V) ) is approximated in the product form exp(it (T) ) exp(it (V)/fc) and die nuclear kinetic energy T is conserved during the transition produces a nonsensical approximation to the non BO rate. This should not be surprising because (a) In the photon absorption case, the photon induces a transition in the electronic degrees of freedom which subsequently cause changes in the vibration-rotation energy, while (b) in the non BO case, the electronic and vibration-... 

SCHWENKE TRUHLAR Vibrational Rotational Energy Transfer 177... 

Figure 2. Vibrational and vibrational-rotational energy levels for a two-atomic molecule.

And third, energy is possessed by virtue of the potential energy, and the translational, vibrational, rotational energy states of the atoms and bonds within the substance, be it atomic, molecular or ionic. The energy within each of these states is quantized, and will be discussed in greater detail in Chapter 9 within the subject of spectroscopy. These energies are normally much smaller than the energies of chemical bonds. 

Clodius, W. B., and Quade, C. R. (1985), Internal Coordinate Formulation for the Vibration-Rotation Energies of Polyatomic Molecules. III. Tetrahedral and Octahedral Spherical Top Molecules, /. Chem. Phys. 82, 2365. 

Nielsen, H. H. (1959), The Vibration-Rotation Energies of Molecules and their Spectra in the Infra-red, in Handb. Physik, S. Flugge (ed.), Vol. 37, part 1, Springer, Berlin. 

Watson, J. K. G. (1984), Higher-Order Vibration-Rotation Energies of the X3 Molecule, J. Mol. Spectr. 103, 350. 

The short-lived activated particle specified by vibration-rotation energy (EJ) most likely undergoes a series of steps which redistribute its internal and rotational energy... 

That effective hamiltonian according to formula 29, with neglect of W"(R), appears to be the most comprehensive and practical currently available for spectral reduction when one seeks to take into account all three principal extramechanical terms, namely radial functions for rotational and vibrational g factors and adiabatic corrections. The form of this effective hamiltonian differs slightly from that used by van Vleck [9], who failed to recognise a connection between the electronic contribution to the rotational g factor and rotational nonadiabatic terms [150,56]. There exists nevertheless a clear evolution from the advance in van Vleck s [9] elaboration of Dunham s [5] innovative derivation of vibration-rotational energies into the present effective hamiltonian in formula 29 through the work of Herman [60,66]. The notation g for two radial functions pertaining to extra-mechanical effects in formula 29 alludes to that connection between... 

In reaction 9.132, molecules A and B form the excited (energized) reactive intermediate species C. Translational energy of the reactant molecules from their relative motion before collision is converted to internal (vibrational, rotational) energy of C. Reaction 9.132 provides a chemical activation (excitation) of the unstable C, with rate constant ka. Note that 9.132 does not involve a third body M for creation of the excited intermediate species, which differs from the unimolecular initiation event in Eq. 9.100. 

The use of tunable lasers as sources in electronic absorption and emission spectroscopy has made possible a very considerable increase in resolution and precision. Electronic spectra are often difficult to analyze because of the many transitions involved. However, with a tunable laser source, one can tune the laser frequency to a specific absorption frequency of the molecule under study and thus populate a single excited electronic vibration-rotation energy level the resulting fluorescence emission spectrum is then simple, and easy to analyze. 

For H2, accurate theoretical calculations3 of the vibration-rotation energy levels have been done by solving the radial differential equation (4.11) using numerical integration. The potential-energy function used is that found from a 100-term variational electronic wave function. 

The vibration-rotation energy expression (4.67) contains the rotational constant Be, which depends on the equilibrium intemuclear separation Re hence investigation of vibrational and rotational spectra of diatomic molecules allows their structure to be determined. 

IR spectra of the fundamental vibrational band of small gaseous diatomic molecules, such as CO and NO, contain a large number of absorption lines that correspond to these vibrational-rotational energy transitions. Since many different rotational levels can be populated at ambient temperature, many different transitions at different energies may occur (Fig. 1). Vibrational-rotational lines are evident only in gas-phase spectra collected at sufficiently high resolution. These lines are not resolved in condensed-phase spectra because of frequent collisions between molecules hence, condensed-phase spectra are characterized by broad absorption bands occurring at the vibrational transition energies. 

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