Vibrational modes of molecules

The vibrational modes of molecules adsorbed on a surface provide one with direct information on the nature of the chemical bonds between a molecule and its... 

The partial solution of Eq.(27) for the configurational space can be conceived as a stepwise process. The fluctuations around the transient configuration X(n) = (Rs(n), Rm (n)) contain—pell-mell— vibrations driven by the intramolecular force field, librations and cage vibration modes of molecules as a whole. The transient configuration evolving in a different time scale contains diffusion terms for liquid environments. 

The interaction of photons with electrons in the porous structure, which is the topic of this section, provides information about the PS band structure, while the excitation of vibrational modes of molecules present in the porous structure by photons gives information about its chemical composition, as discussed in Section 6.6. 

While the internal vibrational modes of molecules can display sharp spectral features, the vibrational spectra of modes of bulk matter are broad and relatively featureless. Nonetheless, Raman and infrared methods can be used to study the bulk, the intermolecular degrees of freedom of condensed matter systems. A great deal of information on bulk degrees of freedom has been extracted from electronic spectroscopy, particularly at low temperatures. Such experiments, however, rely on the influence of the medium on an electronic transition. Using ultrafast Raman techniques, including multidimensional methods, and emerging far-IR methods, it is possible to examine the bulk properties of matter directly. 

It should be noted that the laser pump pulses create sets of intermolecular rovibrational coherence. For example, quantum beats appear in time profile of the CARS spectrum from a molecular mixture. - The beat frequency created is equal to the difference between frequencies of vibrational modes of molecules in the mixture. When many sets of inteimolecular... 

The descriptions of the structure, energy, and dynamics of H-bonds continue to be a formidable task for both experimental and theoretical investigations. IR and nuclear magnetic resonance (NMR) techniques have become routine tools to analyze H-bonding interactions in various systems [1-4, 150]. The vibrational modes of molecules in the H-bonded state are affected in several ways. The proton involved in H-bonding interaction exhibits down field shift. Spectroscopic information obtained from these techniques has been used to probe H-bonding interactions. 

In order to introduce the theory of vibrational spectroscopy in inelastic neutron scattering, we make some simplifications that will help us to understand the concepts. First we shall deal with the vibrational modes of molecules in a vacuum or in a dilute gas phase. Note, however, that in INS experiments the sample is cooled to ca 20 K, therefore the molecules are part of an extended solid. However, because the forces that keep the atoms in the molecule are often larger than the forces that molecules experience from other molecules in the condensed phase, isolated molecule calculations can be good models. 

For systems presenting discrete inelastic features due to internal vibrational modes of molecules or ions, a quantum-mechanical formalism is convenient... 

Now that we see that we can combine partition functions for all the quantized energy systems into a total partition function, we can think of other ways to use the quantized energy formulas. There is a curious history for this approach. We can see above that gvib is an important part of the total partition function and yet for many years low-resolution infrared spectra blurred many of the 3N — 6 vibrational modes of molecules typically larger than benzene. Thus the equations for quantum thermodynamics were known before 1940 but could only be applied to cases of small molecules in the gas phase using experimental vibrational frequencies. Since about 1985, quantum chemistry programs have included the calculation of vibrational frequencies with some correction factors that now make it possible to write down the full partition function by including theoretical... 

Transitions between vibrational levels correspond to certain normal vibration modes of molecules or groups of atoms, which are, in turn, related to the degree of freedom presented by molecules. 

The interaction of radiation with matter can take many forms. The photoelectric effect, the Compton effect, and pair generation-armihilation are processes that occur at wavelengths shorter than those encountered in the infrared. Infrared photons can excite rotational and vibrational modes of molecules, but they are insufficiently energetic to excite electronic transitions in atoms, which occur mostly in the visible and ultraviolet. Therefore, a discussion of the interaction of infrared radiation with matter in the gaseous phase needs to consider only rotational and vibrational transitions, while in the solid phase lattice vibrations in crystals must be included. 

Okumura, K., Tanimura, Y. (1997). Femtosecond two-dimensional spectroscopy from anharmonic vibrational modes of molecules in the condensed phase. J. Chem. Phys. 107 2267-2283. 

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