Vibrational 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... 

Haarhoff P C 1963 The density of vibrational energy levels of polyatomic molecules Mol. Phys. 7 101-17... 

The model Hamiltonian of Section II captures some of the essential features of the electronic and vibrational structure of polyatomic molecules, like benzene and 5ym-triazine, that have both nondegenerate and degenerate, Jahn-Teller active, electronic levels. In this section interference experiments are described which will be sensitive to the geometric phase development accompanying adiabatic nuclear motion on either of the electronic potential energy surfaces in the Jahn-Teller pair. 

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,... 

This kinetic approximation assumes a single vibrational temperature 77 for CO2 molecules and, therefore, is sometimes referred to as quasi equilibrium of vibrational modes. As one can see from (5-20), most of the vibrationally excited molecules can be considered as being in quasi continuum in this case. Vibrational kinetics of polyatomic molecules in quasi continuum was discussed in Chapter 3. The CO2 dissociation rate is limited not by elementary dissociation itself, but via energy transfer from a low to high vibrational excitation level of the molecule in the W-relaxation processes. Such a kinetic situation was referred to in Chapter 3 as the fast reaction limit. The population of highly excited states with vibrational energy E depends in this case on the number of vibrational degrees of freedom 5 and is proportional to the density of the vibrational states p E) a. The... 

Optical-microwave double resonance (OMDR) can considerably improve the situation and extends the advantages of microwave spectroscopy to excited vibrational or electronic states, because selected levels in these states can be populated by optical pumping. Generally dye lasers or tunable diode lasers are used for optical pumping. However, even fixed frequency lasers can often be used. Many lines of intense infrared lasers (for example, CO2, N2O, CO, HF, and DF lasers) coincide with rotational-vibrational transitions of polyatomic molecules. Even for lines that are only close to molecular transitions the molecular lines may be tuned into resonance by external magnetic or electric fields (Sect. 1.6). The advantages of this OMDR may be summarized as follows ... 

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 vibrational energy levels of polyatomic molecules are the sum of harmonic oscillator energy level expressions, as in Eq. (22.4-19). 

Diatomic Molecules (Spin Neglected), 258. Symmetry Properties of the Wave Functions, 261. Selection Rules for Optical Transitions in Diatomic Molecules, 262. The Influence of Nuclear Spin, 265. The Vibrational and Rotational Energy Levels of Diatomic Molecules, 268. The Vibrational Spectra of Polyatomic Molecules, 273. 

The selection rule for vibronic states is then straightforward. It is obtained by exactly the same procedure as described above for the electronic selection rules. In particular, the lowest vibrational level of the ground electronic state of most stable polyatomic molecules will be totally synnnetric. Transitions originating in that vibronic level must go to an excited state vibronic level whose synnnetry is the same as one of the coordinates, v, y, or z. 

Infrared Spectra for Molecules and Polyatomic Ions The energy of infrared radiation is sufficient to produce a change in the vibrational energy of a molecule or polyatomic ion (see Table 10.1). As shown in Figure 10.14, vibrational energy levels are quantized that is, a molecule may have only certain, discrete vibrational energies. The energy for allowed vibrational modes, Ey, is... 

As for diatomic molecules, there are stacks of rotational energy levels associated with all vibrational levels of a polyatomic molecule. The resulting term values S are given by the sum of the rotational and vibrational term values... 

The +, —, e, and/labels attached to the levels in Figure 7.25 have the same meaning as those in Figure 6.24 showing rotational levels associated with and Ig vibrational levels of a linear polyatomic molecule. Flowever, just as in that case, they can be ignored for a Z — I, type of electronic transition. 

In this section, we focus our attention on applications of the CDF protocol to control of population transfer between vibrational levels of a nonrotating polyatomic molecule. The vibrational spectrum of a polyatomic molecule is rich, and if one wishes to transfer population between two states in a subset of selected states that is embedded in the complete manifold of molecular vibrational states, it is... 

These discussions provide an explanation for the fact that fluorescence emission is normally observed from the zero vibrational level of the first excited state of a molecule (Kasha s rule). The photochemical behaviour of polyatomic molecules is almost always decided by the chemical properties of their first excited state. Azulenes and substituted azulenes are some important exceptions to this rule observed so far. The fluorescence from azulene originates from S2 state and is the mirror image of S2 S0 transition in absorption. It appears that in this molecule, S1 - S0 absorption energy is lost in a time less than the fluorescence lifetime, whereas certain restrictions are imposed for S2 -> S0 nonradiative transitions. In azulene, the energy gap AE, between S2 and St is large compared with that between S2 and S0. The small value of AE facilitates radiationless conversion from 5, but that from S2 cannot compete with fluorescence emission. Recently, more sensitive measurement techniques such as picosecond flash fluorimetry have led to the observation of S - - S0 fluorescence also. The emission is extremely weak. Higher energy states of some other molecules have been observed to emit very weak fluorescence. The effect is controlled by the relative rate constants of the photophysical processes. 

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... 

F ERMI RESONANCE. In polyatomic molecules. Hvo vibrational levels belonging to different vibrations lor combinations of vibrations) may happen lo have nearly die same energy, and therefore be accidentally degenerate. As was recognized hy Fermi in the case of CO such a "resonance" leads to a perturbation of the energy levels that is very similar to the vibrational perturbations of diatomic molecules. 

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. 

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