Molecular vibrations selection rules

The Symmetry of Molecules and Molecular Vibrations Selection Rules... 

Bunker, P. R. The vibrational selection rules and torsional barriere of ferrocene. Molecular Physics 9, 247 (1965). 

Nitro complex ions. X -ray analysis of the hexanitrocobalt complex salts, MgLCofNOj), shows that the crystal structure of the K, Rb and Cs salts is cubic and the molecular symmetry of complex ion is Th (9), No structural analysis has been made for the Na salt. The infrared spectrum of the Na salt is quite different from those of the K, Rb and Cs salts as shown in Fig. 1. Since this difference is too large to be explained by the simple outer ion effect, we may expect the difference in the molecular structure to be caused by complex formation. The vibration selection rule shows that the spectrum of the Na salt is consistent with the deformed structure of the S symmetry in which the NO plane rotates about the Co-N axis. 

The fundamental principles upon which the calculation of selection rules are based have been given in Secs. 3-4, 3-5, and 3-6. In this chapter these principles will be applied to the problem of determining the vibrational selection rules for symmetrical molecules. It will be found that certain transitions are forbidden merely because of the symmetry properties of the molecule. Other transitions are found not to be forbidden by symmetry considerations such transitions may nevertheless be missed experimentally because of low intensity due to other causes. On the other hand, transitions forbidden by symmetry sometimes seem to appear in the spectra of liquids, presumably due to the distortion of the symmetry by the neighboring molecules. However, in spite of the fact that so-called forbidden transitions may occur weakly in liquids and so-called allowed transitions are quite frequently not observed, the selection rules given by symmetry considerations are of very great importance as a guide in the interpretation of molecular spectra. 

The vibrational selection rules are determined by the fact that the interaction requires a dipole moment for the molecule that changes as it vibrates. This result does not mean that the molecule must have a permanent electric dipole moment, because vibrational motions in polyatomic molecules can disrupt the molecular... 

This spectrum is called a Raman spectrum and corresponds to the vibrational or rotational changes in the molecule. The selection rules for Raman activity are different from those for i.r. activity and the two types of spectroscopy are complementary in the study of molecular structure. Modern Raman spectrometers use lasers for excitation. In the resonance Raman effect excitation at a frequency corresponding to electronic absorption causes great enhancement of the Raman spectrum. 

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. 

As before, when pf i(Rg) (or dpfj/dRa) lies along the molecular axis of a linear molecule, the transition is denoted a and k = 0 applies when this vector lies perpendicular to the axis it is called n and k = 1 pertains. The resultant linear-molecule rotational selection rules are the same as in the vibration-rotation case ... 

The ir spectra acquired in this way are extremely sensitive to the orientation of the surface molecules. Molecules must have a significant component of a molecular vibration perpendicular to the surface to be sensed by coupling with the highly directional electric field. Molecules whose dipole moments are perfectly parallel to the surface caimot couple to the existing electric fields, and therefore, are ir transparent by this method. This selectivity of the approach for molecule dipole moments perpendicular as opposed to parallel to the surface is known as the surface selection rule of irras. 

W.G. Fateley, F. R. Dollish, N. T. Devitt, F. F. Bentley, Infrared and Raman Selection Rules for Molecular and Lattice Vibrations The Correlation Method, Wiley, New York, 1972... 

Atomic spectra are much simpler than the corresponding molecular spectra, because there are no vibrational and rotational states. Moreover, spectral transitions in absorption or emission are not possible between all the numerous energy levels of an atom, but only according to selection rules. As a result, emission spectra are rather simple, with up to a few hundred lines. For example, absorption and emission spectra for sodium consist of some 40 peaks for elements with several outer electrons, absorption spectra may be much more complex and consist of hundreds of peaks. 

These selection rules are affected by molecular vibrations, since vibrations distort the symmetry of a molecule in both electronic states. Therefore, an otherwise forbidden transition may be (weakly) allowed. An example is found in the lowest singlet-singlet absorption in benzene at 260 nm. Finally, the Franck-Condon principle restricts the nature of allowed transitions. A large number of calculated Franck-Condon factors are now available for diatomic molecules. 

For a fundamental vibrational mode to be IR-active, a change in the molecular dipole must take place during the molecular vibration. This is described as the IR selection rule. Atoms that possess different electronegativity and are chemically bonded change the net dipole of a molecule during normal molecular vibrations. Typically, antisymmetric vibrational modes and vibrations due to polar groups are more likely to exhibit prominent IR absorption bands. 

The dipole and polarization selection rules of microwave and infrared spectroscopy place a restriction on the utility of these techniques in the study of molecular structure. However, there are complementary techniques that can be used to obtain rotational and vibrational spectrum for many other molecules as well. The most useful is Raman spectroscopy. 

Polymer films were produced by surface catalysis on clean Ni(100) and Ni(lll) single crystals in a standard UHV vacuum system H2.131. The surfaces were atomically clean as determined from low energy electron diffraction (LEED) and Auger electron spectroscopy (AES). Monomer was adsorbed on the nickel surfaces circa 150 K and reaction was induced by raising the temperature. Surface species were characterized by temperature programmed reaction (TPR), reflection infrared spectroscopy, and AES. Molecular orientations were inferred from the surface dipole selection rule of reflection infrared spectroscopy. The selection rule indicates that only molecular vibrations with a dynamic dipole normal to the surface will be infrared active [14.], thus for aromatic molecules the absence of a C=C stretch or a ring vibration mode indicates the ring must be parallel the surface. 

Spectroscopic techniques look at the way photons of light are absorbed quantum mechanically. X-ray photons excite inner-shell electrons, ultra-violet and visible-light photons excite outer-shell (valence) electrons. Infrared photons are less energetic, and induce bond vibrations. Microwaves are less energetic still, and induce molecular rotation. Spectroscopic selection rules are analysed from within the context of optical transitions, including charge-transfer interactions The absorbed photon may be subsequently emitted through one of several different pathways, such as fluorescence or phosphorescence. Other photon emission processes, such as incandescence, are also discussed. 

Fateley, W. G., Dollish, F. R., McDeritt, N. T., Bentley, F. F. Infrared and Raman selection rules for molecular and lattice vibration The correlation method. New York Wiley-Inter-science 1972... 

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