Coupling stretching vibrations

Very recently, SC-SCF in hyperspherical coordinates was tested for the coupled stretching vibrations of H20 and C02.25 The hyperspherical coordinates are highly collective and are thus expected to be very suitable for SCF. Also, for the states considered here the hyperspherical system provides a good frequency separation between the coordinates involved. For a linear, nonbending molecule A-B-C, the Hamiltonian of the stretching vibrations can be written as follows in hyperspherical coordinates (which are just plane polar coordinates in this case) ... 

If the Hamiltonian now contains the Casimir operators of both G, and G[, which do not commute, then the labels of neither provide good quantum numbers. Of course, in general such a Hamiltonian has to be diagonalized numerically. In this way one can proceed to break the dynamical symmetries in a progressive fashion. In (61) all the quantum numbers of G, up to G remain good. If we add another subalgebra beside Gz only those quantum numbers provided by G, on will be conserved, etc. In applications, the different chains are found to correspond to different limiting cases such as the normal versus the local mode limits for coupled stretch vibrations (99). 

B2.5.351 after multiphoton excitation via the CF stretching vibration at 1070 cm. More than 17 photons are needed to break the C-I bond, a typical value in IR laser chemistry. Contributions from direct absorption (i) are insignificant, so that the process almost exclusively follows the quasi-resonant mechanism (iii), which can be treated by generalized first-order kinetics. As an example, figure B2.5.15 illustrates the fonnation of I atoms (upper trace) during excitation with the pulse sequence of a mode-coupled CO2 laser (lower trace). In addition to the mtensity, /, the fluence, F, of radiation is a very important parameter in IR laser chemistry (and more generally in nuiltiphoton excitation) ... 

Explicit forms of the coefficients Tt and A depend on the coordinate system employed, the level of approximation applied, and so on. They can be chosen, for example, such that a part of the coupling with other degrees of freedom (typically stretching vibrations) is accounted for. In the space-fixed coordinate system at the infinitesimal bending vibrations, Tt + 7 reduces to the kinetic energy operator of a two-dimensional (2D) isotropic haiinonic oscillator. 

Other general circumstances in which normal vibrations tend to be localized in a particular group of atoms arise when there is a chain of atoms in which the force constant between two of them is very different from those between other atoms in the chain. For example, in the molecule HC=C—CH=CH2 the force constants in the C—C, C=C and C=C bonds are quite dissimilar. It follows that the stretchings of the bonds are not strongly coupled and that each stretching vibration wavenumber is typical of the C—C, C=C or C=C group. 

The IR spectra of several enaminoketones have been reported, and a study of these spectra has shown strong coupling between the C=0 and C=C stretching vibrations and band splitting due to rotational isomerism (7SciJJb). 

Harmonic IR spectra of C3H2 calculated at the RHF/6-311++G(d,p), MP2/6-31 1++G(d,p) and MP4/6-31 1++G(d,p) levels are reported in Table 3. The results are nicely converging as electronic correlation is progressively included in the wave function. Excellent agreement between theory and experiment is thus obtained at the MP4 level, which allows for a correct treatment of simultaneous correlation effects in coupled vibrations. The only discrepancies which could show up, would proceed from anharmonicity, as illustrated by the CH stretching vibrations which are found shifted to higher frequencies than anticipated. 

The v, i(b2) vibration featuring the asymmetric CC stretching vibration, which is strongly coupled with the asymmetric CH in-plane bending vibration (at 1061 cm- experimentally) is shifted by 20-25 cm towards lower frequencies, each time deuterium is incorporated in the molecule. The intensity ratio of V3 between the vs (ba) and the V4(a,) dominant feature is almost unchanged with deuteration. 

Even more complex experiments have been performed on matrix isolated Fe(C0)4, generated by UV photolysis of Fe(C0)5. Isotopic labelling coupled with CW-CO laser pumping (65) of the CO stretching vibrations ( 1900 cnrl) showed that the rearrangement mode of Fe(C0)4 follows an inverse Berry pseudo-rotation as shown in Figure 8. 

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