Molecules vibrational modes

Na transition Na frequency (cm-1) Molecule Vibrational mode, rotational branch Branch center frequency (cm-1) Branch width (cm-1)... 

Symmetry can be helpful in determining the modes of vibration of molecules. Vibrational modes of water and the stretching modes of CO in carbonyl complexes are examples that can be treated quite simply, as described in the following pages. Other molecules can be studied using the same methods. 

Molecule Vibrational mode Band center in cm trai... 

If vibrations within a molecule were independent of the rest of the molecule, then each mode of vibration would be limited to a definite frequency. As an example, all carbon-carbon stretching vibrations regardless of the molecule would have the same frequency. However, for the real molecules vibrational modes can occur over a range of frequencies. The frequency depends upon the mass of the adjacent atoms, resonance and inductive effects, and... 

However, there is a much more profound prior issue concerning anliannonic nonnal modes. The existence of the nonnal vibrational modes, involving the collective motion of all the atoms in the molecule as illustrated for H2O in figure A1.2.4 was predicated on the basis of the existence of a hannonic potential. But if the potential is not exactly hannonic, as is the case everywhere except right at the equilibrium configuration, are there still collective nonnal modes And if so, since they caimot be hannonic, what is their nature and their relation to the hannonic modes ... 

Variational RRKM theory is particularly important for imimolecular dissociation reactions, in which vibrational modes of the reactant molecule become translations and rotations in the products [22]. For CH —> CHg+H dissociation there are tlnee vibrational modes of this type, i.e. the C—H stretch which is the reaction coordinate and the two degenerate H—CH bends, which first transfomi from high-frequency to low-frequency vibrations and then hindered rotors as the H—C bond ruptures. These latter two degrees of freedom are called transitional modes [24,25]. C2Hg 2CH3 dissociation has five transitional modes, i.e. two pairs of degenerate CH rocking/rotational motions and the CH torsion. 

The chemically activated molecules are fonned by reaction of with the appropriate fliiorinated alkene. In all these cases apparent non-RRKM behaviour was observed. As displayed in figure A3.12.11 the measured imimolecular rate constants are strongly dependent on pressure. The large rate constant at high pressure reflects an mitial excitation of only a fraction of the total number of vibrational modes, i.e. initially the molecule behaves smaller than its total size. However, as the pressure is decreased, there is time for IVR to compete with dissociation and energy is distributed between a larger fraction of the vibrational modes and the rate constant decreases. At low pressures each rate constant approaches the RRKM value. 

Consequently, m order for a vibrational mode to be observed in infrared-visible SFG, the molecule in its adsorbed state has to be both IR [(dp/dg,) 0] and Raman [ AaJAQ ) 0] active. 

Figure Bl.6.10 Energy-loss spectrum of 3.5 eV electrons specularly reflected from benzene absorbed on the rheniiun(l 11) surface [H]. Excitation of C-H vibrational modes appears at 100, 140 and 372 meV. Only modes with a changing electric dipole perpendicular to the surface are allowed for excitation in specular reflection. The great intensity of the out-of-plane C-H bending mode at 100 meV confimis that the plane of the molecule is parallel to the metal surface. Transitions at 43, 68 and 176 meV are associated with Rli-C and C-C vibrations.

Figure Bl.25.12 illustrates the two scattering modes for a hypothetical adsorption system consisting of an atom on a metal [3]. The stretch vibration of the atom perpendicular to the surface is accompanied by a change m dipole moment the bending mode parallel to the surface is not. As explained above, the EELS spectrum of electrons scattered in the specular direction detects only the dipole-active vibration. The more isotropically scattered electrons, however, undergo impact scattering and excite both vibrational modes. Note that the comparison of EELS spectra recorded in specular and off-specular direction yields infomiation about the orientation of an adsorbed molecule.

Figure C3.3.12. The energy-transfer-probability-distribution function P(E, E ) (see figure C3.3.2 and figure C3.3.11) for two molecules, pyrazine and hexafluorobenzene, excited at 248 nm, arising from collisions with carbon dioxide molecules. Both collisions that leave the carbon dioxide bath molecule in its ground vibrationless state, OO O, and those that excite the 00 1 vibrational state (2349 cm ), have been included in computing this probability. The spikes in the distribution arise from excitation of the carbon dioxide bath 00 1 vibrational mode.

Diatomic molecules have only one vibrational mode, but VER mechanisms are paradoxically quite complex (see examples C3.5.6.1 and C3.5.6.2). Consequently there is an enonnous variability in VER lifetimes, which may range from 56 s (liquid N2 [18]) to 1 ps (e.g. XeF in Ar [25]), and a high level of sensitivity to environment. A remarkable feature of simpler systems is spontaneous concentration and localization of vibrational energy due to anhannonicity. Collisional up-pumping processes such as... 

In general, at least three anchors are required as the basis for the loop, since the motion around a point requires two independent coordinates. However, symmetry sometimes requires a greater number of anchors. A well-known case is the Jahn-Teller degeneracy of perfect pentagons, heptagons, and so on, which will be covered in Section V. Another special case arises when the electronic wave function of one of the anchors is an out-of-phase combination of two spin-paired structures. One of the vibrational modes of the stable molecule in this anchor serves as the out-of-phase coordinate, and the loop is constructed of only two anchors (see Fig. 12). 

We find it convenient to reverse the historical ordering and to stait with (neatly) exact nonrelativistic vibration-rotation Hamiltonians for triatomic molecules. From the point of view of molecular spectroscopy, the optimal Hamiltonian is that which maximally decouples from each other vibrational and rotational motions (as well different vibrational modes from one another). It is obtained by employing a molecule-bound frame that takes over the rotations of the complete molecule as much as possible. Ideally, the only remaining motion observable in this system would be displacements of the nuclei with respect to one another, that is, molecular vibrations. It is well known, however, that such a program can be realized only approximately by introducing the Eckart conditions [38]. 

Since the stochastic Langevin force mimics collisions among solvent molecules and the biomolecule (the solute), the characteristic vibrational frequencies of a molecule in vacuum are dampened. In particular, the low-frequency vibrational modes are overdamped, and various correlation functions are smoothed (see Case [35] for a review and further references). The magnitude of such disturbances with respect to Newtonian behavior depends on 7, as can be seen from Fig. 8 showing computed spectral densities of the protein BPTI for three 7 values. Overall, this effect can certainly alter the dynamics of a system, and it remains to study these consequences in connection with biomolecular dynamics. 

Figure 7-13. Cross-terms combining internal vibrational modes such as bond stretch, angle bend, and bond torsion within a molecule.

Caution During a sininlation, solvent temperature may increase wh ile th e so In te cools. This is particii larly true of sm all solven t molecules, such as water, that can acquire high translational and rotational energies. In contrast, a macromolecule, such as a peptide, retains most of its kinetic energy in vibrational modes. This problem rem ains un solved, an d this n ote of cau tion is provided to advise you to give special care to simulations using solvent. 

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). 

Run a MOPAC calculation using the PM3 Hamiltonian to determine the normal vibrational modes of the H2O molecule. 

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