Water molecule vibrational analysis

As the molecule vibrates it can also rotate and each vibrational level has associated rotational levels, each of which can be populated. A well-resolved ro - vibrational spectrum can show transitions between the lower ro-vibrational to the upper vibrational level in the laboratory and this can be performed for small molecules astronomically. The problem occurs as the size of the molecule increases and the increasing moment of inertia allows more and more levels to be present within each vibrational band, 3N — 6 vibrational bands in a nonlinear molecule rapidly becomes a big number for even reasonable size molecules and the vibrational bands become only unresolved profiles. Consider the water molecule where N = 3 so that there are three modes of vibration a rather modest number and superficially a tractable problem. Glycine, however, has 10 atoms and so 24 vibrational modes an altogether more challenging problem. Analysis of vibrational spectra is then reduced to identifying functional groups associated... 

The analysis of vibration spectra proceeds by the use of normal modes. For instance, the vibration of a nonlinear water molecule has three degrees of freedom, which can be represented as three normal modes. The first mode is a symmetric stretch at 3586 cm , where the O atom moves up and the two H atoms move away from the O atom the second is an asymmetric stretch at 3725 cm where one H atom draws closer to the O atom but the other H atom pulls away and the third is a bending moment at 1595 cm , where the O atom moves down and the two H atoms move up and away diagonally. The linear CO2 molecule has four normal modes of vibration. The first is a symmetric stretch, which is inactive in the infrared, where the two O atoms move away from the central C atom the second is an asymmetric stretch at 2335 cm where both O atoms move right while the C atom moves left and the third and fourth together constitute a doubly degenerate bending motion at 663 cm where both O atoms move forward and the C atom moves backward, or both O atoms move upward and the C atom moves downward. 

In Figure 11 we demonstrate the application of the contour CSM analysis on the lone-pair orbital of a distorted water molecule (perhaps a frozen moment of a vibration, or a water molecule in a matrix of amorphous ice, or a water molecule trapped in a micropore). The ratio of length of the two O-H bonds is 0.9 (instead... 

SAPT avoids the subtraction of large energy values that is necessarily part of a supermolecule ab initio calculation. A supermolecule calculation obtains the interaction energy of monomers A and B, AVab, as Tab - Va - Vb. whereas SAPT finds AVab directly. The interaction evaluated in SAPT is defined so as to be free of BSSE however, the other requirements on basis-set quality and for correlation effects still hold. SAPT has yielded highly accurate interaction data, first for rare gas atoms interacting with small molecules [72 74] and more recently with molecule molecule clusters such as the CO2 dimer [75]. Further examples are the very accurate results achieved for Ne HCN [76] and a parr potential for water [77]. Another example study of perturbative treatment of the interaction potential has been a study of rare gas HCN clusters [78] which included vibrational analysis. 

The most common protic solvent is water. It is also one of the most complex from the point of view of vibrational spectroscopy because of its highly structured nature. Since water is a triatomic, non-linear molecule it has three vibrational modes, which are illustrated in fig. 5.13. The Vj mode is the symmetrical stretch V2 is the bending mode and V3 is the asymmetrical stretch. All three vibrational modes for water are active in the infrared because they involve changes in the dipole moment. Activity in the Raman spectrum requires that the polarizability of the molecule changes during vibration. Analysis of this aspect of molecular properties is more difficult but it shows that all three modes are also Raman active. A summary of the frequencies of these vibrations for H2O, and the isotopes D2O, and HOD determined from gas phase spectra are given in table 5.7. 

In addition to measurements of lifetime of these vibrational excited states, time-resolved nonlinear IR could also give precise information on the mechanisms of deexcitation of these states. It could thus be shown that relaxation of the first excited state of modes of water molecules in liquid water was mainly due to resonance interactions of these modes with excited bending modes (65). As a result of the analysis of ID IR spectra shown above, Fermi resonance with bending modes allows the energy of the first excited state of to be transferred to the overtone of the bending band. It offers a fast relaxation path toward vibrational levels of a lower energy. Time-resolved nonlinear IR spectroscopy shows that this process is the main relaxation mechanism of and is at the origin of an unexpected increase of the relaxation time when temperature increases (66, 67). 

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