Molecular vibration energy

Straub J E and Berne B J 1986 Energy diffusion in many dimensional Markovian systems the consequences of the competition between inter- and intra-molecular vibrational energy transfer J. Chem. Phys. 85 2999 Straub J E, Borkovec M and Berne B J 1987 Numerical simulation of rate constants for a two degree of freedom system in the weak collision limit J. Chem. Phys. 86 4296... 

Consideration of work by Buchel nikova (4) on the dissociative attachment of electrons to HC1 leads to the conclusion that k4 is given approximately by k4 10-10 e 20 mtRT cm.3 molecule-1 sec.-1 Since K 4 2 X 10-3 el8 miRT at 2000°K., 4 10 13 cm.3 molecule-1 sec.-1 This is considerably smaller than rate constants for other exothermal ion-molecule reactions, which probably reflects the importance of participation of molecular vibrational energy in such reactions. Remember, however, that the uncertainty in 4 is probably at least an order of magnitude. 

Classical mechanics does not apply to the atomic scale and does not take the quantized nature of molecular vibration energies into account. Thus, in contrast to ordinary mechanics where vibrators can assume any potential energy, quantum mechanical vibrators can only take on certain discrete energies. Transitions in vibrational energy levels can be brought about by radiation absorption, provided the energy of the radiation exactly matches the difference in energy levels between the vibrational quantum states and provided also that the vibration causes a fluctuation in dipole. 

Differences in molecular vibration energies correspond to infrared frequencies see Chapter 6. 

A state-of-the-art description of broadband ultrafast infrared pulse generation and multichannel CCD and IR focal plane detection methods has been given in this chapter. A few poignant examples of how these techniques can be used to extract molecular vibrational energy transfer rates, photochemical reaction and electron transfer mechanisms, and to control vibrational excitation in complex systems were also described. The author hopes that more advanced measurements of chemical, material, and biochemical systems will be made with higher time and spectral resolution using multichannel infrared detectors as they become available to the scientific research community. 

Whilst photons have wavelengths similar to interatomic distances for crystallographic work, or energies similar to molecular vibrational energies for spectroscopic work, a neutron has both, i.e. neutrons are suitable for simultaneous elastic and inelastic measurements. 

The quantum-mechanical treatment of molecular vibrations leads to modifications of the harmonic oscillator model. While the Hooke s law treatment presented above would indicate a continuum of vibrational states, the molecular vibrational energy levels are quantised ... 

The equations of ordinary mechanics that we have used thus far do not completely describe the behavior of particles of atomic dimensions. For example, the quantized nature of molecular vibrational energies, and of other atomic and molecular energies as well, docs not appear in these equations. We may, however, invoke the concept of the simple harmonic o.scillator to develop the wave equations of quantum mechanics. Solutions of these equations for potential energies have the form... 

Transitions between inner electron orbitals normally occur in the keV range (X rays) while the energies for transitions between outer orbitals are in the eV region (visible or near UV and IR regions). The fine structure of atoms is of the order of 10" eV (-10cm ) and hyperfine structures are typically about 10" eV (-300MHz), molecular vibrational energies split-... 

Li, H., Jensen, G. H. (2002). Partial Hessian vibrational analysis The localization of the molecular vibrational energy and entropy. Theoretica Chimica Acta, 107, 211. 

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