Vibrational spectra symmetry force constants

For this case, the primary change that is observable in the IR spectrum is due to changes in the vibrahonal frequencies of the probe molecule due to modificahons in bond energies. This can lead to changes in bond force constants and the normal mode frequencies of the probe molecule. In some cases, where the symmetry of the molecule is perturbed, un-allowed vibrational modes in the unperturbed molecule can be come allowed and therefore observed. A good example of this effect is with the adsorption of homonuclear diatomic molecules, such as N2 and H2 (see Section 4.5.6.8). 

Eight combination vibrations and overtones, respectively, have been observed in the rR spectrum of Se42+ in 25% oleum, and these have been used to calculate the harmonic wave number coi = 321.8 0.5 cm-1 and the anharmonicity constants Xu = -0.55 andx42 = -1.3 cm-1 (76). Because of the high molecular symmetry, the spectroscopic data are insufficient to calculate accurate force constants, but when most of the interaction constants are neglected (i.e., set equal to zero) the following force constants for Se42+ can be deduced (in N/cm) (70, 76) ... 

Infrared spectroscopy has broad appHcations for sensitive molecular speciation. Infrared frequencies depend on the masses of the atoms involved in the various vibrational motions, and on the force constants and geometry of the bonds connecting them band shapes are determined by the rotational stmcture and hence by the molecular symmetry and moments of inertia. The rovibrational spectmm of a gas thus provides direct molecular stmctural information, resulting in very high specificity. The vibrational spectrum of any molecule is unique, except for those of optical isomers. Every molecule, except homonudear diatomics such as O2, N2, and the halogens, has at least one vibrational absorption in the infrared. Several texts treat infrared instrumentation and techniques (22,36—38) and their appHcations (39—42). 

In molecules with a high degree of symmetry, many of the vibrations may occur between groups of atoms with the same reduced mass and same force constant. These vibrations will have the same frequency and will he superimposed on the spectrum. When this occurs, the vibrations are said to be degenerate. In symmetrical molecules several modes of vibration may occur at identical fi-equencies, such as the two identical frequencies such as the CH2 vibrations in linear polyethylene. In cases like these, symmetry does not require the fi-equencies to coincide however, due to chemical considerations the absorption bands overlap. Thus, a highly symmetrical molecule of many atoms, such as benzene, will give a simple... 

That is, transitions are normally between states of the same spin. Other selection rules may relate to the geometrical symmetry of the molecule. The molecular transitions seen in the visible and ultraviolet regions of the spectrum must be transitions from one rotational-vibrational-electronic state to another. We shall consider this in detail for a hypothetical diatomic molecule for which the ground state and excited state potential curves are those shown in Figure 10.8. For both electronic state potential energy curves there are sets of vibrational states and rotational sublevels. Notice that the equilibrium distance is not the same for both curves and that the curvature (i.e., the force constant) is not the same either. Thus, there are a different vibrational frequency and a different rotational constant for each electronic state. This has to be taken into account in working out the transition frequencies. 

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