Rotation, internal Rotational energy

A linear molecule, such as any diatomic molecule, carbon dioxide, and ethyne (acetylene, HC=CH), can rotate about two axes perpendicular to the line of atoms, and so it has two rotational modes of motion. Its average rotational energy is therefore 2 X jkT = kT, and the contribution to the molar internal energy is NA times this value ... 

A nonlinear molecule, such as water, methane, or benzene, can rotate about any of three perpendicular axes, and so it has three rotational modes of motion. The average rotational energy of such a molecule is therefore 3 X jkT = ]kT. The contribution of rotation to the molar internal energy of a gas of nonlinear molecules is therefore... 

The inversion barrier for syn/anti isomerization of H2Si=NH is only 5.6 kcal mol-1, whereas the internal rotation energy is 37.9 kcal mor1 (SOCI level of calculation). The rotation barrier can be equated to the ir-bond strength. The inversion transition state has an even shorter SiN bond length of 153.2 pm. The symmetry is C2V.9,10... 

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. 

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... 

Thus, a molecule may exist in many states of different energy. The internal energy in a certain state may be considered to be made up of contributions from rotational energy, E ou vibrational energy, E vib and electronic energy, E i as described by equation (5.2) ... 

It appears that there are two processes that contribute to this O( D) production. The first is so-called hot-band absorption by 03 in which the additional energy comes from internal vibrational and rotational energy (Michelsen et al., 1994), a phenomenon that is well established in the case of N02 photodissociation (see later). This is believed to be responsible for O( D)... 

Energy barriers for internal rotation have been derived, especially during the 1950s, by analyzing (68M12 68M13) microwave spectra of molecules. The method works with molecules with a permanent dipole moment and in the gas phase. Limitations are dictated by the molecular size. The barriers are obtained from rotational energy levels of the molecule as a whole, perturbed by the internal rotor. When different conformers are present in the sample and their interconversion is slower than microwave absorption (barriers smaller than 20 kJ mol can be measured), the spectrum is just a superposition of the lines of the separate species which can be qualitatively and quantitatively determined. 

NMR Determination of Internal Rotation Rates and Rotational Energy Barriers 59... 

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. 

In evaluating the viability of a new experimental technique for studying ion-molecule reactions, a number of factors must be considered. Ultimately our aims are to measure relative cross sections for reactions as a function of both the internal energy of the ion and the collision energy. It is important that the collision energy can be varied down to = 10 meV where the rotational energy may be comparable with the translational energy. 

The falloff curve of the quantum yield is explained by the contribution of the internal (mostly rotational) energy to supplement the incident photon energy (550,810), (see Section 1-4.3 for details). Above 4358 A a small ( 0.01) but significant yield of NO was observed, which is attributed to reactions of electronically excited N02 (NO ) by Jones and Bayes (550). 

The rotational energies represent the spinning motions of a molecule, when the entire molecule rotates around one of its inertial axes. This should not be confused with internal rotation which is the rotational motion of one part of a molecule with respect to some other part of the same molecule. 

In the calculation of the thermodynamic properties of the ideal gas, the approximation is made that the energies can be separated into independent contributions from the various degrees of freedom. Translational and electronic energy levels are present in the ideal monatomic gas.ww For the molecular gas, rotational and vibrational energy levels are added. For some molecules, internal rotational energy levels are also present. The equations that relate these energy levels to the mass, moments of inertia, and vibrational frequencies are summarized in Appendix 6. 

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