Molecules, rotational and vibrational

In principal one can calculate the electronic energy as a function of the Cartesian coordinates of the three atomic nuclei of the ground state of this system using the methods of quantum mechanics (see Chapter 2). (In subsequent discussion, the terms coordinates of nuclei and coordinates of atoms will be used interchangeably.) By analogy with the discussion in Chapter 2, this function, within the Born-Oppenheimer approximation, is not only the potential energy surface on which the reactant and product molecules rotate and vibrate, but is also the potential... 

In the case of isolated atoms purely electronic transitions can be obtained, while, in the more general case of molecules, rotational and vibrational motions... 

When a molecule rotates and vibrates simultaneously, two forces can appear. One is the apparent centrifugal force present whenever a mass is rotated the second is the Coriolis force. The coupling which has been observed between a rotation and a vibration has been related to this Coriolis force. 

In an ideal molecular gas, each molecule typically has translational, rotational and vibrational degrees of freedom. The example of one free particle in a box is appropriate for the translational motion. The next example of oscillators can be used for the vibrational motion of molecules. 

These results do not agree with experimental results. At room temperature, while the translational motion of diatomic molecules may be treated classically, the rotation and vibration have quantum attributes. In addition, quantum mechanically one should also consider the electronic degrees of freedom. However, typical electronic excitation energies are very large compared to k T (they are of the order of a few electronvolts, and 1 eV corresponds to 10 000 K). Such internal degrees of freedom are considered frozen, and an electronic cloud in a diatomic molecule is assumed to be in its ground state f with degeneracy g. The two nuclei A and... 

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... 

For a RRKM calculation without any approximations, the complete vibrational/rotational Flamiltonian for the imimolecular system is used to calculate the reactant density and transition state s sum of states. No approximations are made regarding the coupling between vibration and rotation. Flowever, for many molecules the exact nature of the coupling between vibration and rotation is uncertain, particularly at high energies, and a model in which rotation and vibration are assumed separable is widely used to calculate the quantum RRKM k(E,J) [4,16]. To illustrate this model, first consider a linear polyatomic molecule which decomposes via a linear transition state. The rotational energy for tire reactant is assumed to be that for a rigid rotor, i.e. 

Faubel M and Toennies J P 1977 Scattering studies of rotational and vibrational excitation of molecules Adv. Atom. Mol. Phys. 13 229... 

Some other extremely iisellil spectroscopic teclmiques will only be mentioned here. Probably the most important one is spectroscopy in free jet expansions. Small molecules have often been studied by gas-phase spectroscopy where sharp rotational and vibrational structure gives detailed iufonnation about molecular... 

The close-coupling equations are also applicable to electron-molecule collision but severe computational difficulties arise due to the large number of rotational and vibrational channels that must be retained in the expansion for the system wavefiinction. In the fixed nuclei approximation, the Bom-Oppenlieimer separation of electronic and nuclear motion pennits electronic motion and scattering amplitudes f, (R) to be detemiined at fixed intemuclear separations R. Then in the adiabatic nuclear approximation the scattering amplitude for ... 

Parker G A and Pack R T 1978 Rotationally and vibrationally inelastic scattering in the rotational lOS approximation. Ultra-simple calculation of total (differential, integral and transport) cross sections for nonspherical molecules J. Chem. Phys. 68 1585... 

The molecular mechanics or quantum mechanics energy at an energy minimum corresponds to a hypothetical, motionless state at OK. Experimental measurements are made on molecules at a finite temperature when the molecules undergo translational, rotational and vibration motion. To compare the theoretical and experimental results it is... 

This completes our introduction to the subject of rotational and vibrational motions of molecules (which applies equally well to ions and radicals). The information contained in this Section is used again in Section 5 where photon-induced transitions between pairs of molecular electronic, vibrational, and rotational eigenstates are examined. More advanced treatments of the subject matter of this Section can be found in the text by Wilson, Decius, and Cross, as well as in Zare s text on angular momentum. 

For molecules and ions having more than one atom, the extra energy can make the component bonds rotate and vibrate faster (rovibrational energy). Isolated atoms, having no bonds, cannot be excited in this way. 

As excited atoms, molecules, or ions come to equilibrium with their surroundings at normal temperatures and pressures, the extra energy is dissipated to the surroundings. This dissipation causes the particles to slow as translational energy is lost, to rotate and vibrate more slowly as rovibrational energy is lost, and to emit light or x-rays as electronic energy is lost. 

As for diatomic molecules, there are stacks of rotational energy levels associated with all vibrational levels of a polyatomic molecule. The resulting term values S are given by the sum of the rotational and vibrational term values... 

On the high-pressure side of the nozzle molecules may be seeded into the jet of helium or argon and are also cooled by the many collisions that take place. However, in discussing temperature in molecules, we must distinguish between translational, rotational and vibrational temperatures. The translational temperature is the same as that of the helium or argon carrier gas and may be less than 1 K. 

At low energies, the rotational and vibrational motions of molecules can be considered separately. The simplest model for rotational energy levels is the rigid dumbbell with quantized angular momentum. It has a series of rotational levels having energy... 

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