Vibrations diatomic molecule rotational excitation

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... 

The electronic contributions to the g factors arise in second-order perturbation theory from the perturbation of the electronic motion by the vibrational or rotational motion of the nuclei [19,26]. This non-adiabatic coupling of nuclear and electronic motion, which exemplifies a breakdown of the Born-Oppenheimer approximation, leads to a mixing of the electronic ground state with excited electronic states of appropriate symmetry. The electronic contribution to the vibrational g factor of a diatomic molecule is then given as a sum-over-excited-states expression... 

Aside from vibration and rotation constants, an important piece of information available from electronic spectra is the dissociation energies of the states involved. In electronic absorption spectroscopy, most of the diatomic molecules will originate from the c"=0 level of the ground electronic state. The vibrational structure of the transition to a given excited electronic state will consist of a series of bands (called a progression) representing changes of 0—>0, 0—>1, 0- 2,..., 0— t nax, where... 

Absorption and Emission Spectra of Small Molecules. In diatomic molecules the number of vibrational and rotational levels is small, so that their energy spacing remains relatively large. Their absorption spectra are therefore line spectra which correspond to transitions to stable , associative excited states, but if a dissociative excited state is reached then the absorption spectrum becomes a continuum since such states have no vibrational levels. 

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... 

In chemiluminescence experiments such as those described previously in the experimental section, emission spectra characteristic of the excited products of ion-neutral collisions are obtained, that is, intensities of the emitted radiation as a function of wavelength. This permits identification of the electronically excited states produced in the reaction as well as determination of the relative populations of these states. In addition if the luminescence measurements are made using beam techniques, excitation functions (intensity of a given transition as a function of the translational energy of the reactants) can be measured for certain transitions. As is discussed later, some of the observed transitions exhibit translational-energy thresholds. In the emission spectra from diatomic or polyatomic product molecules, band systems are sometimes observed from which the relative importance of vibrational and rotational excitation accompanying electronic excitation may be assessed. 

Charge-transfer and dissociative-charge-transfer reactions of diatomic ions with various molecules that yield luminescence spectra are summarized in Table IV.B, part 3. In some of these, for example, the H2+ —N2 reaction, vibrational and rotational excitation have again been observed to accompany electronic excitation.155, 426 Molecular-ion reactions are generally accompanied by more extensive rotational excitation of the products than occurs with atomic-ion reactions.439... 

The photochemist is little interested in rotational energy, mainly because it is an unimportant fraction of the total energy possessed by an electronically excited molecule under most experimental conditions. The vibrational energy is quite another matter, and we must now examine the possibilities which may arise after the electronic energy of a diatomic molecule is increased. 

The principal reaction discussed above forms oxygen molecules in high vibrational levels of the ground state. This is chemi-excitation but is not chemiluminescence vibration-rotation transitions of homonuclear molecules are forbidden. For such cases electronic absorption spectroscopy is the required technique. For reactions in which a heteronuclear diatomic (or a polyatomic) molecule is excited these transitions are allowed. They are overtones of the molecular transitions that occur in the near infrared. These excited products emit spontaneously. The reactions are chemiluminescent, their emission spectra may be obtained and analyzed in order to deduce the detailed course of the reaction. 

Figure 16.13. Energy-level scheme for a diatomic molecule, showing the rotational energy transition (r), the vibrational energy transition (v) in the ground state (No), and electronic energy transition (e) from S0 to the excited state (,S i).

A molecule can only absorb infrared radiation if the vibration changes the dipole moment. Homonuclear diatomic molecules (such as N2) have no dipole moment no matter how much the atoms are separated, so they have no infrared spectra, just as they had no microwave spectra. They still have rotational and vibrational energy levels it is just that absorption of one infrared or microwave photon will not excite transitions between those levels. Heteronuclear diatomics (such as CO or HC1) absorb infrared radiation. All polyatomic molecules (three or more atoms) also absorb infrared radiation, because there are always some vibrations which create a dipole moment. For example, the bending modes of carbon dioxide make the molecule nonlinear and create a dipole moment, hence CO2 can absorb infrared radiation. 

The second type of predissociation observed for diatomic molecules is known as electronic predissociation the principles are illustrated in figure 6.28. A vibrational level v of a bound state E lies below the dissociation asymptote of that state, but above the dissociation asymptote of a second state E2. This second state, E2, is a repulsive state which crosses the bound state E as shown. The two states are mixed, and the level v can predissociate via the unbound state. It is not, in fact, necessary for the potential curves of the two states to actually cross. It is, however, necessary that they be mixed and there are a number of different interaction terms which can be responsible for the mixing. We do not go into the details here because electronic predissociation, though an important phenomenon in electronic spectroscopy, seldom plays a role in rotational spectroscopy. Since it involves excited electronic states it could certainly be involved in some double resonance cases. 

In this section we study more closely the molecular matrix element [Eq. (13)]. The P decay in a molecule may lead to the excitation of all the degrees of freedom—electronic, vibrational, and rotational. Let us first show that the recoil of the radioactive nucleus does not excite the electronic degrees of freedom. To this end we introduce the relative coordinates using the Jakobi transformation and, in order to simplify the calculations, consider a diatomic molecule with N electrons. 

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