Rotation, internal diatomic molecule

Figure Al.2.2. Internal nuclear motions of a diatomic molecule. Top the molecule in its equilibrium configuration. Middle vibration of the molecule. Bottom rotation of the molecule.

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... 

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 ... 

Figure 1. Translation, rotation, and vibration of a diatomic molecule. Every molecule has three translational degrees of freedom corresponding to motion of the center of mass of the molecule in the three Cartesian directions (left side). Diatomic and linear molecules also have two rotational degrees of freedom, about rotational axes perpendicular to the bond (center). Non-linear molecules have three rotational degrees of freedom. Vibrations involve no net momentum or angular momentum, instead corresponding to distortions of the internal structure of the molecule (right side). Diatomic molecules have one vibration, polyatomic linear molecules have 3V-5 vibrations, and nonlinear molecules have 3V-6 vibrations. Equilibrium stable isotope fractionations are driven mainly by the effects of isotopic substitution on vibrational frequencies.

In addition to the processes just discussed that yield vibrationally and rotationally excited diatomic ions in the ground electronic state, vibrational and rotational excitations also accompany direct electronic excitation (see Section II.B.2.a) of diatomic ions as well as charge-transfer excitation of these species (see Section IV.A.l). Furthermore, direct vibrational excitation of ions and molecules can take place via charge transfer in symmetric ion molecule collisions, as the translational-to-internal-energy conversion is a sensitive function of energy defects and vibrational overlaps of the individual reactant systems.312-314... 

Rotational energy contributes to the internal energy of a diatomic molecule, and classically any rotational speed is possible. We will return to rotational properties in Chapter 8, when we discuss quantum mechanics, which imposes restrictions on the rotational energy we will find that transitions between allowed rotational states let us measure bond lengths or cook food in microwave ovens. 

The maximum hardness principle also demands that hardness will be minimum at the transition state. This has been found to be true for different processes including inversion of NH3 [147] and PH3 [148], intramolecular proton transfer [147], internal rotations [149], dissociation reactions for diatomics [150,151], and hydrogen-bonded complexes [152]. In all these processes, chemical potential remains either constant or passes through an extremum at the transition state. The maximum hardness principle has also been found to be true (a local maximum in hardness profile) for stable intermediate, which shows a local minimum on the potential energy surface [150]. The energy change in the dissociation reaction of diatomic molecules does not pass through a... 

Energy in diatomic molecules is distributed among three kinds of internal excitations rotational, vibrational, and electronic. The rotational energy is described empirically by a truncated (denoted by. .. ) series in J( J + 1),... 

Even for molecules in the ground electronic state, our knowledge about cross sections is largely limited to the room-temperature condition, in which vibrational and rotational states are populated in a thermal distribution. Then, for a diatomic molecule, the ground vibrational state is predominantly populated. However, for a polyatomic molecule, normal modes with small quanta must be appreciably excited. For the full understanding of kinetics in plasma chemistry, it is important to assess the role of the internal energy of reactant molecules. 

Equation (28-71) indicates that the rotational motion of diatomic molecules yields rotation,classical = T/B, where B is a characteristic rotational temperature that is, at most, a few tens of Kelvin (see Table 28-2). The rotational contribution to the internal energy is... 

The internal motion of a diatomic molecule consists of vibration, corresponding to a change in the distance R between the two nuclei, and rotation, corresponding to a... 

The energy disposal and effective upper state lifetimes have been reproduced using classical trajectory calculations a quasi-diatomic assumption was made to determine the slope of the section through the upper potential energy surface along the N—a bond from the shape of the u.v. absorption profile. The only adjustable parameter was the assumption of a parallel transition in the quasi-diatomic molecule. In contrast, a statistical adiabatic channel model which assumed dissociation via unimolecular decomposition out of vibrationally and rotationally excited level in the ground electronic state (following internal con-... 

Regarding the motions of atomic nuclei, those that remain are the rotational motions. In this section, rotational motion is explained in somewhat more detail, because it is concerned with the nature of chemistry. What is important to consider is that the energies associated with the rotational motions of molecules are part of the kinetic energies, and therefore overlap with the translational motion energies without operation. That is, a variable separation is required for the translational motions, which are the motions of entire systems, and the rotational motions, which are internal motions (Gasiorowicz 1996). In the case of diatomic molecules, the Hamiltonian operator is given as... 

The use of the master equation to describe the relaxation of internal energy in molecules is, in fact, nothing more than the writing of a set of kinetic rate equations, one equation for each individual rotation-vibration state of the molecule. The simplest case we can consider is that of an assembly of diatomic molecules highly diluted in a monatomic gas under these conditions, we only need to consider the set of processes... 

Photodissociation of a diatomic molecule is a simpler process than the photolysis of a polyatomic molecule because the two fragments formed in the photolysis of a diatomic cannot possess internal vibrational or rotational energy. Thus, a photolysis experiment for a diatomic molecule has been selected as an example to present the recording of ion images conceptually, and to highlight what information can be extracted from them. 

---