Vibrational energy theory

The existence of the polyad number as a bottleneck to energy flow on short time scales is potentially important for efforts to control molecnlar reactivity rising advanced laser techniqnes, discussed below in section Al.2.20. Efforts at control seek to intervene in the molecnlar dynamics to prevent the effects of widespread vibrational energy flow, the presence of which is one of the key assumptions of Rice-Ramsperger-Kassel-Marcns (RRKM) and other theories of reaction dynamics [6]. 

Uzer T 1991 Theories of intramolecular vibrational energy transfer Rhys. Rep. 199 73-146... 

Bigwood R, Gruebele M, Leitner D M and Wolynes P G 1998 The vibrational energy flow transition in organic molecules theory meets experiment Proc. Nati Acad. Sc/. 95 5960... 

Examining transition state theory, one notes that the assumptions of Maxwell-Boltzmann statistics are not completely correct because some of the molecules reaching the activation energy will react, lose excess vibrational energy, and not be able to go back to reactants. Also, some molecules that have reacted may go back to reactants again. 

Vibrational energy, which is associated with the alternate extension and compression of die chemical bonds. For small displacements from the low-temperature equilibrium distance, the vibrational properties are those of simple harmonic motion, but at higher levels of vibrational energy, an anharmonic effect appears which plays an important role in the way in which atoms separate from tire molecule. The vibrational energy of a molecule is described in tire quantum theory by the equation... 

This rule conforms with the principle of equipartition of energy, first enunciated by Maxwell, that the heat capacity of an elemental solid, which reflected the vibrational energy of a tliree-dimensional solid, should be equal to 3f JK moH The anomaly that the free electron dreory of metals described a metal as having a tliree-dimensional sUmcture of ion-cores with a three-dimensional gas of free electrons required that the electron gas should add anodier (3/2)7 to the heat capacity if the electrons behaved like a normal gas as described in Maxwell s kinetic theory, whereas die quanmtii theory of free electrons shows that diese quantum particles do not contribute to the heat capacity to the classical extent, and only add a very small component to the heat capacity. 

A solid body, the molecules of which are monatomic, and all vibrating with a constant frequency, v, is called an Einstein s solid, since it formed the subject of Einstein s application of the theory of ergonic distribution considered in 222—24. The equation for the vibrational energy... 

Table 9-10. Experimental binding energies D0 [kcal/mol] for the cationic methyl complexes of the 3d elements and deviations from these data obtained at various levels of theory. Calculated values include a uniform zero point vibrational energy correction of 2.6 kcal/mol. 

Another approach to relating the hardness to atomic parameters is that of Grimvall and Thiessen (1986) in which hardness is related to vibrational energies. Their theory is slightly modified here by using vibrational energy densities instead of the energies themselves. Specific heat data measure the excitation... 

Internal conversion refers to radiationless transition between states of the same multiplicity, whereas intersystem crossing refers to such transitions between states of different multiplicities. The difference between the electronic energies is vested as the vibrational energy of the lower state. In the liquid phase, the vibrational energy may be quickly degraded into heat by collision, and in any phase, the differential energy is shared in a polyatomic molecule among various modes of vibration. The theory of radiationless transitions developed by Robinson and Frosch (1963) stresses the Franck-Condon factor. Jortner et al. (1969) have extensively reviewed the situation from the photochemical viewpoint. 

The presence of the electron acceptor site adjacent to the donor site creates an electronic perturbation. Application of time dependent perturbation theory to the system in Figure 1 gives a general result for the transition rate between the states D,A and D+,A. The rate constant is the product of three terms 1) 27rv2/fi where V is the electronic resonance energy arising from the perturbation. 2) The vibrational overlap term. 3) The density of states in the product vibrational energy manifold. 

Finally, it can be shown from the quantum theory of vibrational energy in the solid state that, at temperatures above the Debye temperature 6D, the density of phonons, np, is inversely related to 0D according to the equation... 

T. Uzer, Phys. Rep., 199, 73 (1991). Theories of Intramolecular Vibrational Energy Transfer. 

W2 Weizmann-2 theory ZPVE zero point vibrational energy... 

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