Anharmonic coupling molecules

In the Heitler-London approximation, with allowance made only for biquadratic anharmonic coupling between collectivized high-frequency and low-frequency modes of a lattice of adsorbed molecules (admolecular lattice), the total Hamiltonian (4.3.1) can be written as a sum of harmonic and anharmonic contributions ... 

Rather strong temperature variation has been seen in the infrared spectra of CO/Ni(l 11) . Figure 7 shows the peak width and position as a function of substrate temperature for the c(4 x 2) structure, where all molecules are chemisorbed in the bridge position. As seen in the figure the peak width increases strongly with increasing temperature and there is also a small upward shift of the peak position. We observe that both the peak width and position reaches a constant value for very low temperatures, so it could be possible that the behaviour can be explained in terms of an anharmonic coupling. Persson et developed a new theory for this problem, partly... 

The important conclusion is that we get a very good fit to the experimental data assuming an anharmonic coupling to one specific low frequency mode. The normal mode calculation of CO bridgebond on Ni by Richardson and Bradshaw estimates for the frustrated translation to = 76 cm and for the frustrated rotation m = 184 cm " while it is known from EELS data that the metal-molecule stretch is found at 400 cm The calculated values should... 

Fig. 8. The position and width of the infiraied absorption peak as function of substrate temperature for the ( 3 X 3)R30° structure of CO on Ru(001). All molecules are chemisorbed in the ontop position and the solid lines are calculated within the theory describing the anharmonic coupling to a low frequency mode.

Comparing with the normal mode calculation and the experimentally determined value for CO/Pt(lll) below, it seems likely that for the ontop bonded molecules the anharmonic coupling is to the frustrated translation. As expected, d(o is then negative as the C—O stretch vibration frequency decreases when going away from the ontop position. 

J. Manz Prof. H. J. Neusser has presented to us beautiful high-resolution spectra of medium-size molecules and clusters such as benzene and C6H6 At (see current chapter). The individual lines have been assigned to individual rovibronic eigenstates of the systems, and their widths have been interpreted in terms of various intramolecular processes between zero-order states (e.g., Coriolis coupling, anharmonic couplings between bright and dark states, and so on). 

For the amines they found NH3 < MeNH2 < Me2NH < Me3N. For the chloroform-amine complexes the Av are 12,26,45 and 53 cm-1 in this order. No subbands were resolved. This is, no doubt, due to the low frequency of the bridge stretching vibration v for these very weakly H-bonded systems and to the weakness of the anharmonic coupling between them. The existence of the molecules in more than one conformation broadens the bands and makes the observation of the subbands even more difficult. 

An alternative approach widely used in polyatomic molecule studies is based on the Golden Rule and a perturbative treatment of the anharmonic coupling (57,62). This approach is not much used for diatomic molecules. In the liquid O2 example cited above, the Hamiltonian must be expanded to 30th order or so to calculate the multiphonon emission rate. But for vibrations of polyatomic molecules, which can always find relatively low-order VER pathways for each VER step, perturbation theory is very useful. In the perturbation approach, the molecule s entire ladder of vibrational excitations is the system and the phonons are the bath. Only lower-order processes are ordinarily needed (57) because polyatomic molecules have many vibrations ranging from higher to lower frequencies and only a small number of phonons, usually one or two, are excited in each VER step. The usual practice is to expand the interaction Hamiltonian (qn, Q) in Equation (2) in powers of normal coordinates (57,62) ... 

Since the combination band anharmonicity (<10 cm 1) (84) is less than our spectral resolution ( 60 cm-1 in this measurement), excitation of the combination C-C stretch and C=N stretch is seen as excitation of both fundamentals (44). Pumping the combination band causes an instantaneous jump in the populations of the C-H stretch, C-C stretch, and C=N stretch. The directly pumped C=N stretch excitation rises to a level about 20 times greater than when it is indirectly populated with C-H stretch pumping. A C=N stretch and a C-C stretch on the same molecule can annihilate each other via cubic anharmonic coupling to create C-H stretch excitations (47). 

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