Atom-selective vibrational

The low Ti content (up to 3 wt % in Ti02) makes the extraction of vibrational, energetic, and geometric features specific to Ti04 moieties a difficult task as the experimental data are dominated by the features of the siliceous matrix. This is the reason why the structure of the local environment around Ti(IV) species inside TS-1 was only definitively assessed more than 10 years after the discovery of the material, when the atomic selectivity of X-ray absorption spectroscopies (both XANES and EXAFS) were used [58-60]. 

The simplest systems in which the effect of a selective vibrational excitation can be studied are those of reactions of free atoms with vibrationally excited diatomic molecules. The various channels for removal of the vibrationally excited molecules BC (v) may be written as... 

Fig. 2 Screenshot of the window that plots the spectra together with the representation of the atomic displacements of a selected vibrational normal mode...

Atoms have complete spherical synnnetry, and the angidar momentum states can be considered as different synnnetry classes of that spherical symmetry. The nuclear framework of a molecule has a much lower synnnetry. Synnnetry operations for the molecule are transfonnations such as rotations about an axis, reflection in a plane, or inversion tlnough a point at the centre of the molecule, which leave the molecule in an equivalent configuration. Every molecule has one such operation, the identity operation, which just leaves the molecule alone. Many molecules have one or more additional operations. The set of operations for a molecule fonn a mathematical group, and the methods of group theory provide a way to classify electronic and vibrational states according to whatever symmetry does exist. That classification leads to selection rules for transitions between those states. A complete discussion of the methods is beyond the scope of this chapter, but we will consider a few illustrative examples. Additional details will also be found in section A 1.4 on molecular symmetry. 

Iditional importance is that the vibrational modes are dependent upon the reciprocal e vector k. As with calculations of the electronic structure of periodic lattices these cal-ions are usually performed by selecting a suitable set of points from within the Brillouin. For periodic solids it is necessary to take this periodicity into account the effect on the id-derivative matrix is that each element x] needs to be multiplied by the phase factor k-r y). A phonon dispersion curve indicates how the phonon frequencies vary over tlie luin zone, an example being shown in Figure 5.37. The phonon density of states is ariation in the number of frequencies as a function of frequency. A purely transverse ition is one where the displacement of the atoms is perpendicular to the direction of on of the wave in a pmely longitudinal vibration tlie atomic displacements are in the ition of the wave motion. Such motions can be observed in simple systems (e.g. those contain just one or two atoms per unit cell) but for general three-dimensional lattices of the vibrations are a mixture of transverse and longitudinal motions, the exceptions... 

Polyatomic molecules vibrate in a very complicated way, but, expressed in temis of their normal coordinates, atoms or groups of atoms vibrate sinusoidally in phase, with the same frequency. Each mode of motion functions as an independent hamionic oscillator and, provided certain selection rules are satisfied, contributes a band to the vibrational spectr um. There will be at least as many bands as there are degrees of freedom, but the frequencies of the normal coordinates will dominate the vibrational spectrum for simple molecules. An example is water, which has a pair of infrared absorption maxima centered at about 3780 cm and a single peak at about 1580 cm (nist webbook). 

SpartanView models provide information about molecular energy dipole moment atomic charges and vibrational frequencies (these data are accessed from the Properties menu) Energies and charges are available for all quantum mechanical models whereas dipole moments and vibrational frequencies are provided for selected models only... 

Vibrational spectra are often so complicated that assignment of a particular absorption to a given bond is difficult. One way to confirm that an assignment is correct is to carry out selective isotopic substitution. For example, we can replace a hydrogen atom with a deuterium atom. If an iron-hydride (Fe—H) stretch occurs at 1950 cm-1, at what energy will this stretch occur, approximately, for a compound that has deuterium in place of the hydrogen Refer to Major Technique 1, which follows these exercises. 

In summary, NIS provides an excellent tool for the study of the vibrational properties of iron centers in proteins. In spectroscopies like Resonance Raman and IR, the vibrational states of the iron centers are masked by those of the protein backbone. A specific feature of NIS is that it is an isotope-selective technique (e.g., for Fe). Its focus is on the metal-ligand bond stretching and bending vibrations which exhibit the most prominent contributions to the mean square displacement of the metal atom. 

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