Rotational Levels of Polyatomic Molecules

I 3.1 Rotational Levels of Polyatomic Molecules, 14 I 3.2 Vibrational Levels of Polyatomic Molecules, 15 I 3.3 Electronic Stales of Polyatomic Molecules, 16 1-4 Thermal Contribution to Photodissociation, 18... 

Very little is known about the nature of rotational energy transfer in a collision between an electronically excited molecule and a ground-state atom or molecule. In the few reported studies the experimental method is fundamentally the same as that described at the beginning of Section III.A. An initial rotational distribution is established by narrow-band excitation. The fluorescence emission contour is recorded twice, under collision-free and thermal equilibrium conditions, and then again under conditions such that there is one collision during the lifetime of the excited state. The differences in the rotational contours of the three emission spectra are then used to infer the pathway of rotational energy transfer, and the rate of that transfer. Some examples of the emission spectra recorded under these conditions are shown in Fig. 22. Because of the small spacings between the rotational levels of polyatomic molecules most excitation sources prepare nonthermal superpositions of rotational states rather than pure rotational states, and this complicates interpretation of the observations. 

Systematic studies into resonant transitions between the low-lying (u = 0,1,2,3) vibrational-rotational levels of polyatomic molecules were undertaken precisely because of the need to explain the spectra of resonant multiple-photon excitation (MPE) and multiple-photon dissociation (MPD) of polyatomic molecules by IR laser radiation. Despite the large amount of experimental and theoretical work, up to now no comprehensive qualitative description of the MPE process for the lower levels of polyatomic molecules has been achieved, which is probably explained by the lack of data on the complex structure of the vibrational levels u = 2,3,4 of such molecules. Nevertheless, the qualitative picture seems quite clear. 

The states of polyatomic molecules are governed by the same Boltzmann probability distribution as those of atoms and diatomic molecules. The rotational levels of polyatomic molecules are generally large enough that many rotational states are occupied. The rotation of a linear polyatomic molecule such as acetylene or cyanogen is just... 

Proceeding in the spirit above it seems reasonable to inquire why s is equal to the number of equivalent rotations, rather than to the total number of symmetry operations for the molecule of interest. Rotational partition functions of the diatomic molecule were discussed immediately above. It was pointed out that symmetry requirements mandate that homonuclear diatomics occupy rotational states with either even or odd values of the rotational quantum number J depending on the nuclear spin quantum number I. Heteronuclear diatomics populate both even and odd J states. Similar behaviors are expected for polyatomic molecules but the analysis of polyatomic rotational wave functions is far more complex than it is for diatomics. Moreover the spacing between polyatomic rotational energy levels is small compared to kT and classical analysis is appropriate. These factors appreciated there is little motivation to study the quantum rules applying to individual rotational states of polyatomic molecules. 

EBK) semiclassical quantization condition given by Eq. (2.72). In contrast to the RKR method for diatomics, a direct method has not been developed for determining potential energy surfaces from experimental anharmonic vibrational/rotational energy levels of polyatomic molecules. Methods which have been used are based on an analytic representation of the potential energy surface (Bowman and Gazdy, 1991). At low levels of excitation the surface may be represented as a sum of quadratic, cubic, and quartic normal mode coordinates (or internal coordinate) terms, that is,... 

The H+ molecular ion is the simplest polyatomic molecule, and was discovered by J.J. Thompson in 1911 (1). Although its chemistry has been studied extensively using mass spectrometric methods, its spectrum has only recently been observed. The first spectroscopic studies were described by Oka (2) for H+, and by Shy, Farley, Lamb and Wing (3) for D+ and H2D+. These studies were confined to the first few vibration-rotation levels of the molecules and confirmed the essential correctness of the theoretical descriptions of the molecule in these low energy states. 

I 2.1 Rotational Energy Levels of Diatomic Molecules, K I 2.2 Vibrational Energy Levels of Diatomic Molecules, 10 I 2.3 Electronic Stales of Diatomic Molecules, 11 I 2.4 Coupling of Rotation and Electronic Motion in Diatomic Molecules Hund s Coupling Cases, 12 1-3 Quantum States of Polyatomic Molecules, 14... 

McKean 182> considered the matrix shifts and lattice contributions from a classical electrostatic point of view, using a multipole expansion of the electrostatic energy to represent the vibrating molecule and applied this to the XY4 molecules trapped in noble-gas matrices. Mann and Horrocks 183) discussed the environmental effects on the IR frequencies of polyatomic molecules, using the Buckingham potential 184>, and applied it to HCN in various liquid solvents. Decius, 8S) analyzed the problem of dipolar vibrational coupling in crystals composed of molecules or molecular ions, and applied the derived theory to anisotropic Bravais lattices the case of calcite (which introduces extra complications) is treated separately. Freedman, Shalom and Kimel, 86) discussed the problem of the rotation-translation levels of a tetrahedral molecule in an octahedral cell. 

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. 

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. 

Her Herzberg, G. Molecular Spectra and Molecular Structure III. Electronic Spectra and Electronic Structure of Polyatomic Molecules, New York Van Nostrand Reinhold Company, 1966. 7OH0U Hougen, J.T. The Calculation of Rotational Energy Levels and Rotational Line Intensities in Diatomic Molecules, Natl. Bur. Stand. Monogr. 115 (1970). 

The importance of the Raman spectrum lies especially in the fact that it also occurs for homonuclear molecules, which, according to sections 22 and 23, have no rotation and vibration-rotation spectra. Hence, it may be used to supplement the evidence derived from electronic bands, regarding the energy of vibrational and rotational levels in the ground state, and for a confirmation of the values of and thus obtained. Researches of this sort have actually been carried out on HCl by Wood and on Hg, Ng, Og, CO by Rasetti (for literature see G) and (lO)) and, more recently, on CO by Amaldi(is). Really essential, however, is the Raman effect in analysing the possible vibrations of polyatomic molecules, as we shall see in the next chapter. For such molecules very rarely have sharply defined electronic bands, while the rotation and vibration-rotation data usually are insufficient to arrive at a unique description of the molecular behaviour. 

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