Polyatomic molecules rotational spectroscopy

Electrons, protons and neutrons and all other particles that have s = are known as fennions. Other particles are restricted to s = 0 or 1 and are known as bosons. There are thus profound differences in the quantum-mechanical properties of fennions and bosons, which have important implications in fields ranging from statistical mechanics to spectroscopic selection mles. It can be shown that the spin quantum number S associated with an even number of fennions must be integral, while that for an odd number of them must be half-integral. The resulting composite particles behave collectively like bosons and fennions, respectively, so the wavefunction synnnetry properties associated with bosons can be relevant in chemical physics. One prominent example is the treatment of nuclei, which are typically considered as composite particles rather than interacting protons and neutrons. Nuclei with even atomic number tlierefore behave like individual bosons and those with odd atomic number as fennions, a distinction that plays an important role in rotational spectroscopy of polyatomic molecules. 

I. N. Levine (1975) Molecular Spectroscopy (John Wiley Sons, New York). A survey of the theory of rotational, vibrational, and electronic spectroscopy of diatomic and polyatomic molecules and of nuclear magnetic resonance spectroscopy. 

Approaches to Vibration-Rotation Spectroscopy for Polyatomic Molecules. 

Equation (9.38), if restricted to two particles, is identical in form to the radial component of the electronic Schrodinger equation for the hydrogen atom expressed in polar coordinates about the system s center of mass. In the case of the hydrogen atom, solution of the equation is facilitated by the simplicity of the two-particle system. In rotational spectroscopy of polyatomic molecules, the kinetic energy operator is considerably more complex in its construction. For purposes of discussion, we will confine ourselves to two examples that are relatively simple, presented without derivation, and then offer some generalizations therefrom. More advanced treatises on rotational spectroscopy are available to readers hungering for more. 

The pure-rotational Raman spectrum of a polyatomic molecule provides information on the moments of inertia, hence allowing a structural determination. For a molecule to exhibit a pure-rotational Raman spectrum, the polarizability must be anisotropic that is, the polarizability ellipsoid must not be a sphere. As noted in Section 5.2, a spherical top has a spherical polarizability ellipsoid, and so gives no pure-rotational Raman spectrum. Symmetric and asymmetric tops have asymmetric polarizabilities. The structures of several nonpolar molecules (which cannot be studied by microwave spectroscopy) have been determined from their pure-rotational Raman spectra these include F2, C2H4, and C6H6. 

Microwave spectroscopy often gives more definite and precise information on the structure of polyatomic molecules than vibration-rotation and electronic spectra. For example, consider the simplest oxime formald-oxime, CH2=NOH. There are two likely structural configurations for this... 

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. 

Polyatomic molecules have more complex microwave spectra, but the basic principle is the same any molecule with a dipole moment can absorb microwave radiation. This means, for example, that the only important absorber of microwaves in the air is water (as scientists discovered while developing radar systems during World War II). In fact, microwave spectroscopy became a major field of research after that war, because military requirements had dramatically improved the available technology for microwave generation and detection. A more prosaic use of microwave absorption of water is the microwave oven it works by exciting water rotations, and the tumbling then heats all other components of food. 

The first successful application of molecular beam electric resonance to the study of a short-lived free radical was achieved by Meerts and Dymanus [142] in their study of OH. They were also able to report spectra of OD, SH and SD. Their electric resonance instrument was conventional except for a specially designed free radical source, in which OH radicals were produced by mixing H atoms, formed from a microwave discharge in H2, with N02 (or H2S in the case of SH radicals). In table 8.24 we present a complete A-doublet data set for OH, including the sets determined by Meerts and Dymanus, with J = 3/2 to 11/2 for the 2n3/2 state, and 1/2 to 9/2 for the 2ni/2 state. Notice that, for the lowest rotational level (7 = 3/2 in 2n3/2), the accuracy of the data is higher. These transitions were observed by ter Meulen and Dymanus [143], not by electric resonance methods, but by beam maser spectroscopy, with the intention of providing particularly accurate data for astronomical purposes. This is the moment for a small diversion into the world of beam maser spectroscopy. It has been applied to a large number of polyatomic molecules, but apparently OH is the only diatomic molecule to be studied by this method. 

Most fundamental rotation-vibration bands are located in the mid-infrared region from 4000 - 400 cm". A few vibrational bands appear in the far infrared where purely rotational spectra of light molecules with two or three atoms are also observed. This is in contrast to heavier polyatomic molecules the study of their rotational spectra is the domain of the microwave spectroscopist who employs different equipment, particularly, monochromatic tunable radiation sources. Rotational constants determined from IR-work are therefore usually less accurate than those obtained by microwave spectroscopy. 

G. D. Carney, L. L. Sprandel, and C. W. Kern, Variational approaches to vibration-rotation spectroscopy for polyatomic molecules. Adv. Chem. Phys. 37, 305-379 (1978). 

New experimental teehniques have increased the capacity of rotationally resolved spectroscopy tremendously. They are generating experimental data at an unprecedented rate and with excellent precision. As a result of all these developments, we know a lot more with much greater precision and accuracy about many more molecules. This includes equilibrium structures of polyatomic molecules. 

The Broida oven is a nearly ideal source for the spectroscopy of diatomic molecules and small polyatomic molecules such as CaOH. For larger species, however, the spectral congestion is too severe and the collisional relaxation rates are too high to record resonant, rotationally resolved spectra. The solution to this problem is to lower the temperature to eliminate the spectral congestion and to lower the pressure to eliminate the... 

For more discussion of nuclear motion in diatomic molecules, see Section 13.2. For the rotational energies of polyatomic molecules, see Levine, Molecular Spectroscopy, Chapter 5. 

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