Diatomic molecules, spectra

G. Herzberg, Molecular Spectra and Molecular Structure. I Spectra Diatomic Molecules, D. Van Nostrand, Princeton, 1950. 

Figure 6.7 Rotational transitions accompanying a vibrational transition in (a) an infrared spectrum and (b) a Raman spectrum of a diatomic molecule...

The solar spectrum is, of course, as well studied as our planetary atmosphere will permit. More information will be forthcoming as spectra from man-made satellites are recorded above the atmosphere. At this time, the spectra of many diatomic molecules have been detected. These are not the familiar, chemically stable molecules we find on the stockroom shelf. These are the molecules that are stable on a solar stockroom shelf. Figure 25-3 shows some of these and the location in the periodic table of the elements represented. 

The spectrum calculated in the secular non-adiabatic approximation reproduces some special peculiarities of the spectra observed. In following papers (see Table 7.1) for diatomic molecules the dependence of the resolved spectra components on the rotational quantum number was described. As an example, the experimental dependence %(j) = Tj+1. /r is shown in Fig. 7.5. 

Except in simple cases, it is very difficult to predict the infrared absorption spectrum of a polyatomic molecule, because each of the modes has its characteristic absorption frequency rather than just the single frequency of a diatomic molecule. However, certain groups, such as a benzene ring or a carbonyl group, have characteristic frequencies, and their presence can often be detected in a spectrum. Thus, an infrared spectrum can be used to identify the species present in a sample by looking for the characteristic absorption bands associated with various groups. An example and its analysis is shown in Fig. 3. 

The rotational microwave spectrum of a diatomic molecule has absorption lines (expressed as reciprocal wavenumbers cm ) at 20, 40, 60, 80 and 100 cm . Calculate the rotational partition function at 100 K from its fundamental definition, using kT/h= 69.5 cm" at 100 K. 

These and other values [381,406] allow us to depict the dielectric spectrum of a bilayer, shown in Fig. 5.2. Given this view, one can think of the phospholipid bilayer as a dielectric microlamellar structure as a solute molecule positions itself closer to the center of the hydrocarbon region, it experiences lower dielectric field (Fig. 5.2). At the very core, the value is near that of vacuum. A diatomic molecule of Na+Cl- in vacuum would require more energy to separate into two distinct ions than that required to break a single carbon-carbon bond ... 

For this case, the primary change that is observable in the IR spectrum is due to changes in the vibrahonal frequencies of the probe molecule due to modificahons in bond energies. This can lead to changes in bond force constants and the normal mode frequencies of the probe molecule. In some cases, where the symmetry of the molecule is perturbed, un-allowed vibrational modes in the unperturbed molecule can be come allowed and therefore observed. A good example of this effect is with the adsorption of homonuclear diatomic molecules, such as N2 and H2 (see Section 4.5.6.8). 

The excited molecules normally release their energy by spontaneous emission of fluorescence, terminating not only in the initial ground state but on all vibronic levels of lower electronic states to which transitions are allowed. This causes a fluorescence spectrum which consists, for instance, in the case of an excited singlet state in a diatomic molecule, of a progression of either single lines (A/ = 0 named Q-lines) or of doublets (A7 = 1 P- and i -lines) ... 

Until recently, only estimates of the Hartree-Fock limit were available for molecular systems. Now, finite difference [16-24] and finite element [25-28] calculations can yield Hartree-Fock energies for diatomic molecules to at least the 1 ghartree level of accuracy and, furthermore, the ubiquitous finite basis set approach can be developed so as to approach this level of accuracy [29,30] whilst also supporting a representation of the whole one-electron spectrum which is an essential ingredient of subsequent correlation treatments. 

Within this "rigid rotor" model, the absorption spectrum of a rigid diatomic molecule should display a series of peaks, each of which corresponds to a specific J ==> J+l transition. The energies at which these peaks occur should grow linearally with J. An example of such a progression of rotational lines is shown in the figure below. 

This chapter consists of the application of the symmetry concepts of Chapter 2 to the construction of molecular orbitals for a range of diatomic molecules. The principles of molecular orbital theory are developed in the discussion of the bonding of the simplest molecular species, the one-electron dihydrogen molecule-ion, H2+, and the simplest molecule, the two-electron dihydrogen molecule. Valence bond theory is introduced and compared with molecular orbital theory. The photo-electron spectrum of the dihydrogen molecule is described and interpreted. 

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