Normal mode tetrahedral molecule

It is well known that the tetrahedral frame of the CH4 molecule is easily distorted. If the tetrahedral frame of CH4 were robust, the purely rotational infrared spectra of CH4 would not exist. However, even at temperatures as low as room temperature, the CH4 molecule features hundreds of very weak, dipole-allowed rotovibrational lines at frequencies from 42 to 208 cm-1, the so-called groundstate to groundstate (gs—>gs) transitions. Moreover, more than 1500 weak, dipole-allowed transitions exist within the polyad system v /v — 1/2/1, at frequencies from 14 to 500 cm-1 [42]. These allowed transitions arise from distortions of the tetrahedral frame by rotation and the internal dynamics of the CH4 molecule, due to the coupling of normal modes of the flexible CH4 frame. Collisional frame distortion should probably be associated with unresolved gs— gs and similar polyad bands. Some evidence of such collision-induced bands of CH4 in CH4-X complexes has been pointed out [39-41]. Besides these collision-induced bands that presumably are due to collisional frame distortion of CH4, fairly significant, unexplained collision-induced bands also exist that are shaped by rotovibrational transitions of the collisional partner X = H2, N2, or CH4, and by double transitions of the bimolecular CH4-X complex [39-41]. 

When XeF4 was first prepared it was thought to be highly symmetrical, but it was not known whether it was a tetrahedral or a square-planar molecule. The infra-red absorption spectrum of XeF4 consists of three fundamental bands and the vibrational Raman spectrum also has three bands. Determine the symmetry of the normal modes of a... 

An isolated n-atom molecule has 3n degrees of freedom and in—6 vibration degrees of freedom. The collective motions of atoms, moving with the same frequency and which in phase with all other atoms, give rise to normal modes of vibration. In principle, the determination of the form of normal modes for any molecule requires the solution of equation of motion appropriate to the n-symmetry. Methods of group theory are important in deriving the symmetry properties of the normal modes. With the aid of the character tables for point groups and the symmetry properties of the normal modes, the selection rules for Raman and IR activity can be derived. For a molecule with a center of symmetry, e.g. AXe, octahedral molecule, a non-Raman active mode is also IR active, whereas for the BX4 tetrahedral molecule, some modes are simultaneously IR and Raman active. 

A tetrahedral M(BHit)tt molecule has 57 normal modes of vibration which are divided into five symmetry types, 4Ai + A2 + 5E + 5Ti + 9T2. The nine T2 modes are infrared active and the 4Ai (polarized), 5E, and 9T2 modes are Raman active. Those vibrations of Ti and A2 symmetry are both infrared and Raman inactive. 

In both liquid water and ice, H2O molecules interact extensively via O— bonds. However, there are marked differences between the two phases. In the latter, H2O molecules are tetrahedrally hydrogen-bonded, and this local structure is repeated throughout the crystal. In liquid water, however, the O—H- O bond distance and angle vary locally, and the bond is sometimes broken. Thus, its vibrations cannot be described simply by using the three normal modes of the isolated H2O molecule. According to Walrafen et al. [444] an isosbestic point exists at 3403 cm in the Raman spectrum of liquid water obtained as a function of temperature, and the bands above and below this frequency are mainly due to non-hydrogen-bonded and hydrogen-bonded species, respectively. In addition, liquid water exhibits librational and restricted translational modes that correspond to rotational and translational motions of the isolated molecule, respectively. The librations yield a broad contour at 1000-330 cm while the restricted translations appear at 170 and 60 cm [445]. For more details, see the review by Walrafen [446]. 

Figure 2.17 illustrates the four normal modes of vibration of a tetrahedral XY4 molecule. All four vibrations are Raman-active, whereas only V3 and V4 are infrared-active. Appendix VII lists the G and F matrix elements for such a molecule. 

In general, each normal mode in a molecule has its own frequency, which is determined in the normal mode analysis [24] However, this is subject to the constraints imposed by molecular symmetry [18, 25,26]. For example, in the methane molecule CH, four of the normal modes can essentially be designated as normal stretch modes, i. e. consisting primarily of collective motions built from the four C-H bond displacements. The molecule has tetrahedral S3Tnmetry, and this constrains the stretch normal mode frequencies. One mode is the totally symmetric stretch, with its own characteristic frequency. The other three stretch normal modes are all constrained by symmetry to have the same frequency, and are referred to as being triply-degenerate. 

Figure II-9 illustrates the four normal modes of vibraiion of a tetrahedral XY4 molecule. All four vibrations are Raman active, whereas only P3 and are infrared active. Fundamental frequencies of XH4-type molecules are listed in Table II-60. The trends p, and v > V4 hold for ihe majority of the compounds. The XH stretching frequencies may be lowered whenever the XH4 ions form hydrogen bonds with counterions. In the same family of the periodic table, the XH stretching frequency decreases as the mass of the X atom increases. Shirk and Shrivef noted, however, that the p, frequency and the corresponding force constant show an unusual trend in Group HI A ...

The five-atom XY4 molecules and ligands commonly adopt tetrahedral and square-planar shapes. The normal modes of tetrahedral and square-planar XY4 are shown in Figure 5.5. Tetrahedral XY4 molecules show two normal modes that are infrared-active , while the square-planar XY4 molecules show three... 

Figure 5.5 Normal modes of vibration of (a) tetrahedral and (b) square-planar XY4 molecules. From Nakamoto, K., Infrared and Raman Spectra of Inorganic and Coordination Compounds , in Handbook of Vibrational Spectroscopy, Vol. 3, Chalmers, J. M. and Griffiths, P. R. (Eds), pp. 1872-1892. Cop)uight 2002. John " Afiley Sons Limited. Reproduced with permission.

Fig. 12.22 Four representative normal modes of a tetrahedral molecule.

The mode of extraction in these oxonium systems may be illustrated by considering the ether extraction of iron(III) from strong hydrochloric acid solution. In the aqueous phase chloride ions replace the water molecules coordinated to the Fe3+ ion, yielding the tetrahedral FeCl ion. It is recognised that the hydrated hydronium ion, H30 + (H20)3 or HgO,, normally pairs with the complex halo-anions, but in the presence of the organic solvent, solvent molecules enter the aqueous phase and compete with water for positions in the solvation shell of the proton. On this basis the primary species extracted into the ether (R20) phase is considered to be [H30(R20)3, FeCl ] although aggregation of this species may occur in solvents of low dielectric constant. 

A test of this possibility came from an analysis of the IETS intensities of methyl sulfonic acid on alumina. Hall and Hansma (33) used the vibrational mode energies of this surface species to show that it was ionically bonded to the alumina and that the SOj group ( with tetrahedral bonding) had oxygen atoms in nearly equivalent chemical positions. They predicted that the molecule, which had a surface geometry of two back to back tripods, was oriented with the C-S bond normal to the oxide surface. 

The methyl group bonded to a metal (M-CH3) exhibits the six normal vibrations expected for tetrahedral ZXY3 molecules. In addition, CMC bending and CH3 torsional modes are expected for M(CH3) (n > 2) compounds. In M(CHs)4 derivatives (M = Si or Sn) the CH3 rocking, MC stretching and CMC... 

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