Vibrational energy of molecules

Absorption of electromagnetic radiation in the infrared region of the spectrum resulting in changes in the vibrational energy of molecules. 

Absorption of radiation in the infrared region of the electromagnetic spectrum results in changes in the vibrational energy of molecules. Energy changes are typically 6 x 103 to 42 x 103J mol-1, which corresponds to 250-... 

In order to consider the energy factor, let us consider the energy in ground state. The vibrational energy of molecule in ground state is given as... 

Equilibrium stable isotope fractionation is a quantum-mechanical phenomenon, driven mainly by differences in the vibrational energies of molecules and crystals containing atoms of differing masses (Urey 1947). In fact, a list of vibrational frequencies for two isotopic forms of each substance of interest—along with a few fundamental constants—is sufficient to calculate an equilibrium isotope fractionation with reasonable accuracy. A succinct derivation of Urey s formulation follows. This theory has been reviewed many times in the geochemical... 

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. 

Owing to the electron-vibrational interaction in molecules, there is one more possible decay channel for SES. This is the nonradiative relaxation (internal conversion), in which the electron energy is transferred into vibrational energy of molecules (in the condensed phase, into thermal energy of the medium). If the molecule fluoresces, there may also occur fluorescence from the lowest excited state. (According to the empirical rule of Kasha,64 the molecular fluorescence occurs from the lowest excitation level irrespective of the wavelength of the exciting radiation.)... 

It is very important to remember that this definition of a PES is based on the assumption that the atomic positions can be exactly specified, which is the ultimate condition for the structure or shape of a molecule. This means adoption of the Born-Oppenheimer (B.O.) approximation, in which the nuclei are viewed as stationary point charges, whereas the electrons are described quantum mechanically [5]. This approximation is justified by the fact that the electrons are much lighter than the nuclei and hence are moving faster. The classical nature of the atomic nuclei is usually a valid approximation, but the zero-point vibrational energy of molecules or the tunneling effect, for example, make it evident that it does not always hold. 

The subject of statistical mechanics is a branch of mechanics which has been found very useful in the discussion of the properties of complicated systems, such as a gas. In the following sections we shall give a brief discussion of the fundamental theorem of statistical quantum mechanics (Sec. 49a), its application to a simple system (Sec. 496), the Boltzmann distribution law (Sec. 49c), Fermi-Dirac and Bose-Einstein statistics (Sec. 49d), the rotational and vibrational energy of molecules (Sec. 49e), and the dielectric constant of a diatomic dipole gas (Sec. 49/). The discussion in these sections is mainly descriptive and elementary we have made no effort to carry through the difficult derivations or to enter into the refined arguments needed in a... 

The quantum theory only allows the electronic and vibrational energy of molecules to hold certain values. The energy of a molecule may be looked upon as a ladder of allowed electronic energy levels or states (labelled Eq,Ei...) with sub-lev-els according to the vibrational energy (labelled Vq, Vj, V2. . . ) possessed by the molecule. For example, a molecule in its second electronic energy level and its third vibrational level would be labelled i,V2. 

Raman spectroscopy measures the vibrational energies of molecules and there must be a change in the molecule polarizability to have a Raman active... 

The symbols A, B, and C refer to the reactants and the transition state, respectively, S denotes the symmetry numbers, is the imaginary vibration frequency of the transition state, Ui — hJkT. Eqs. (1.24) and (1.25) describe the change in the rate constants defined by the difference between the entropy terms, Eq. (1.26) characterizes the contribution from the difference between the zero vibration energies of molecules with the light and the heavy isotopes. As regards the monomolecular reactions, only the products and the exponents referring to reactants A remain in the numerators of Eqs. (1.24)-(1.26). 

The molecular partition function for a system includes terms that relate to different forms of energy nuclear, electronic, vibrational energy of molecules, their rotational energy, their translational energy and interaction energies between different molecules. 

The zero-point vibrational energies of molecules are affected by interactions, and these may lead to higher or to lower vibrational frequencies. At very high... 

The internal vibrational energy of molecules is not influenced by the adsorption however, to maintain the adsorbed molecules in a vibrational movement requires energy defined as... 

Figure 5.12. (a) Potential energy diagrams and contour maps for a head-on collision between an atom A and a molecule BC which is initially in the ground state. The trajectory in (b) corresponds to a process in which translational energy of A has been converted to vibrational energy of molecule BC. 

---