Linear molecules vibrational spectroscopy

Vibrational spectroscopy of molecules depends on quantum mechanics, which requires well-defined frequencies and atomic displacements known as the normal modes of vibrations of the molecules. A linear molecule with N atoms has 3N-5 normal modes, and a nonlinear molecule has 3N-6 normal modes of vibrations. Several types of motions leads to normal modes such as (i) stretching motion between two bonded atoms, (ii) bending motion between three atoms connected by two bonds, and (iii) out-of-plane deformation modes take place with changes from a planar structure to a nonplanar one. 

For comparison, the calculated linear and 2D spectra using ft = 12.3 cm-1 and 6 = 52°, which correspond to an a-helical structure (see the contour plot Fig. 19) for the isotopomer Ala -Ala-Ala are shown in Figure 21. The observed spectra for Ala -Ala-Ala are strikingly different from the calculated spectra for a molecule in an a-helical conformation. We emphasize here an important point In contrast to the NMR results on oligo(Ala), in which averaging of different backbone conformations might be present because measurements are made on a time scale that is slow compared to that of conformational motions, these vibrational spectroscopy results are detected on a very fast time scale (Hamm et al, 1999 Woutersen and Hamm, 2000, 2001). This rules out conformational averaging. 

Vibration spectroscopy is also able to measure the concentration of ion radicals (by estimation of the band intensities). Moreover, the IR intensities of some bands in the fingerprint region for organic ion radicals may be much larger than the intensities of the bands for the neutral parent molecules. The examples are polycyclic aromatic hydrocarbons or linear polyenes and their ion radicals. The vibration patterns of the intensity-carrying modes are closely related to the electronic structure of the ion radicals (Torii et al. 1999 and references therein). 

Vibrational sum-frequency spectroscopy (VSFS) is a second-order non-linear optical technique that can directly measure the vibrational spectrum of molecules at an interface. Under the dipole approximation, this second-order non-linear optical technique is uniquely suited to the study of surfaces because it is forbidden in media possessing inversion symmetry. At the interface between two centrosymmetric media there is no inversion centre and sum-frequency generation is allowed. Thus the asynunetric nature of the interface allows a selectivity for interfacial properties at a molecular level that is not inherent in other, linear, surface vibrational spectroscopies such as infrared or Raman spectroscopy. VSFS is related to the more common but optically simpler second harmonic generation process in which both beams are of the same fixed frequency and is also surface-specific. 

Since the Raman effect involves two spin-one photons, the angular-momentum selection mle becomes A J = 0, 2. This gives rise to three distinct branches in the rotation-vibration spectra of diatomic and linear molecules the 0-branch (A / = —2), the Q-branch (A J = 0) and the S-branch (A J = - -2). All diatomic and linear molecules are Raman active. Raman spectroscopy can determine rotational and vibrational energy levels for homonuclear diatomic molecules, which have no infrared or microwave spectra. 

The bond length was measured by Akslhin and Spiridonov (6), but the diffraction patterns were interpreted as indicating a linear molecule. The vibrational frequencies and bond angle are those reported by Calder (7) using matrix isolation spectroscopy and Isotopically enriched materials. 

Additional support for the existence of non-oxo uranyl analogues may be found in the reactions of uranium atoms with small molecules (N2, NO, CO, etc.) in argon matrices. Although not stable outside of the stabilizing matrix, vibrational spectroscopy is consistent with the formation of other linear triatomic species such as NUN, NUO, and... 

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. 

Now consider SO2 which is a bent molecule ( 2 )- Figure 3.12 shows the three normal modes of vibration all give rise to a change in molecular dipole moment and are therefore IR active. A comparison of these results for CO2 and SO2 illustrates that vibrational spectroscopy can be used to determine whether an X3 or XY2 species is linear or bent. 

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