Rotational and vibrational energy

Midey A J and Viggiano A A 1998 Rate constants for the reaction of Ar" with O2 and CO as a function of temperature from 300 to 1400 K derivation of rotational and vibrational energy effects J. Chem. Phys. at press... 

Viggiano A A and Morris R A 1996 Rotational and vibrational energy effects on ion-molecule reactivity as studied by the VT-SIFDT technique J. Phys. Chem. 100 19 227-40... 

Kreutz T G and Flynn G W 1990 Analysis of translational, rotational, and vibrational energy transfer in collisions between COj and hot hydrogen atoms the three dimensional breathing ellipse model J. Chem. Phys. 93 452-65... 

Molecules possess discrete levels of rotational and vibrational energy. Transitions between vibrational levels occur by absorption of photons with frequencies v in the infrared range (wavelength 1-1000 p,m, wavenumbers 10,000-10 cm , energy differences 1240-1.24 meV). The C-0 stretch vibration, for example, is at 2143 cm . For small deviations of the atoms in a vibrating diatomic molecule from their equilibrium positions, the potential energy V(r) can be approximated by that of the harmonic oscillator ... 

Molecules possess discrete levels of rotational and vibrational energy, and transitions between vibrational levels occur by absorption of photons with frequencies in the mid-infrared range. There are four types of vibration ... 

Molecular spectroscopy. This spectroscopy deals with the interaction of electromagnetic radiation with molecules. This results in transition between rotational and vibrational energy levels besides electronic transitions. 

Vibrational spectroscopy can help us escape from this predicament due to the exquisite sensitivity of vibrational frequencies, particularly of the OH stretch, to local molecular environments. Thus, very roughly, one can think of the infrared or Raman spectrum of liquid water as reflecting the distribution of vibrational frequencies sampled by the ensemble of molecules, which reflects the distribution of local molecular environments. This picture is oversimplified, in part as a result of the phenomenon of motional narrowing The vibrational frequencies fluctuate in time (as local molecular environments rearrange), which causes the line shape to be narrower than the distribution of frequencies [3]. Thus in principle, in addition to information about liquid structure, one can obtain information about molecular dynamics from vibrational line shapes. In practice, however, it is often hard to extract this information. Recent and important advances in ultrafast vibrational spectroscopy provide much more useful methods for probing dynamic frequency fluctuations, a process often referred to as spectral diffusion. Ultrafast vibrational spectroscopy of water has also been used to probe molecular rotation and vibrational energy relaxation. The latter process, while fundamental and important, will not be discussed in this chapter, but instead will be covered in a separate review [4],... 

A chemical reaction can be viewed as occurring via the formation of an excited state that can be any one of the degrees of freedom of the collection of N atoms. That is, translational, rotational, vibrational, and electronic excitation can lead to a chemical reaction. We often do not need to consider explicitly the quantized nature of rotational and vibrational energies in practical applications because of time scale considerations. For example, when a chemical reaction proceeds via a vibrationally excited state, in which the average lifetime typically is about 3 x 10" where T is in Kelvins... 

Figure 10.7—Representation of the rotational and vibrational energy levels and conversion into the vibrational rotational spectrum (at bottom). The fundamental vibration corresponds to V = +1 and J ll-The vibrational rotational band corresponds to all the allowed quantum leaps. If the scale of the diagram is in cm-1 the arrows correspond to the wavenumbers of absorption. The R branch corresponds to A J = +1 and the P branch to A J = -1. They are located on each side of the Q band, which is absent in the spectrum (AJ = 0 corresponds, here, to a forbidden transition).

There is another optical method which studies these energy modifications and produces a spectrum that contains almost the same information as that obtained in the mid IR Raman. In this technique, a solution of the sample in a solvent such as water is irradiated by intense, monochromatic laser light in the visible region. The composition of the beam diffused by species present in the sample is analysed at 90c to the incident beam. In this process, bands called Stokes fines are observed beside the incident beam, at greater wavelengths. If the differences between these bands and the wavelength of the incident beam are expressed as wavenumbers, the values obtained correspond to the difference in rotational and vibrational energy levels obtained by absorption spectroscopy (Fig. 10.24). 

Thermal energy, the energy contained in the heat of a chemical substance, is essentially the translational energy of molecules. There are two forms of kinetic energy which play an important role in photophysics the rotational and vibrational energies of molecules. 

Infrared (ir) 100 to 10,000 Rotational-vibrational excitation Rotational and vibrational energy levels of molecules (Section 9-7)... 

This is in accord with the spectroscopic selection rules, derived from theoretical arguments, that predict which transitions between rotational and vibrational energy levels are allowed and which are forbidden. ... 

The Cl2 molecule has not only translational energy but also rotational and vibrational energy. The disordering due to this energy contributes to the overall energy disorder. The molecule also has twice as many atoms. However, matter is more organized in the molecule, so the molar entropy of the molecule is not twice that of the atom. 

The energy of a molecule includes translational, rotational, and vibrational energy, as well as electronic... 

However, the small rotation inhibition heuristic for si and sll may be flawed for guests at the upper size boundary of the large cavity. For guest molecules of intermediate sizes, such as cyclopropane and trimethlylene oxide, small changes in size caused by thermal stimulation of rotational and vibrational energies may be sufficient to determine the occupied cavity as discussed in the following section. 

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