Mutual exclusion principle

One should note that, in CO2, the vibration that is symmetric with respect to the center of symmetry (vi) is Raman-active but not IR-active, whereas those that are antisymmetric with respect to the center of symmetry (v2 and v3) are IR-active but not Raman-active. This condition is called the mutual exclusion principle and holds for any molecules having a center of symmetry. ... 

In contrast, the dipole moment of carbon dioxide fluctuates in phase with the asymmetric vibrational mode. Thus, an IR absorption band arises from this mode. On the other hand, as the polarizability of one of the bonds increases as it lengthens, the polarizability of the other decreases, resulting in no net change in the molecular polarizability. Thas, the asymmetric stretching vibration is Raman inactive, f-or molecules with a center of symmetry, such as CO, no IR active iraasi-lions arc in common with Raman aclive transitions. This is often called the mutual exclusion principle. 

Chains may exist with irregular conformations which have lost the inversion symmetry and cause breakdowns of the mutual exclusion principle. 

When IR and Raman spectroscopic techniques are used in combination, the resuits are much greater than with the use of either technique individually. The combined use of IR and Raman spectroscopy extracts most of the obtainable information (silent, or optically inactive, modes and extremely weak modes are not detected). The complementary nature of the IR and Raman data has important practical applications. This complementary nature arises from the differences in selection rules governing the vibrational energy levels. For molecules with a center of symmetry (there are identical atoms on either side of the center of symmetry), no vibrational frequencies are common to the IR and Raman spectra. This principle is called the mutual exclusion principle. Although symmetry might be considered important for low-molecular-weight substances like ethylene and benzene (both of which have a center of symmetry), polymers are not usually expected to have a center of symmetry. Polyethylene has a center of symmetry, and the observed IR and Raman lines do not coincide in frequency (see Fig. 5.1). Theory predicts that eight modes for polyethylene are active in the Raman while only five in the infrared. 

The Exclusion Principle is quantum mechanical in nature, and outside the realm of everyday, classical experience. Think of it as the inherent tendency of electrons to stay away from one another to be mutually excluded. Exclusion is due to the antisymmetry of the wave function and not to electrostatic coulomb repulsion between two electrons. Exclusion exists even in the absence of electrostatic repulsions. 

The example of COj discussed previously, which has no vibrations which are active in both the Raman and infrared spectra, is an illustration of the Principle of Mutual Exclusion For a centrosymmetric molecule every Raman active vibration is inactive in the infrared and any infrared active vibration is inactive in the Raman spectrum. A centrosymmetric molecule is one which possesses a center of symmetry. A center of symmetry is a point in a molecule about which the atoms are arranged in conjugate pairs. That is, taking the center of inversion as the origin (0, 0, 0), for every atom positioned at (au, yi, z ) there will be an identical atom at (-a ,-, —y%, —z,). A square planar molecule XY4 has a center of symmetry at atom X, whereas a trigonal planar molecule XYS does not possess a center of symmetry. 

Similarly, the first-order expansion of the p° and a of Eq. (5.1) is, respectively, responsible for IR absorption and Raman scattering. According to the parity, one can easily understand that selection mles for hyper-Raman scattering are rather similar to those for IR [17,18]. Moreover, some of the silent modes, which are IR- and Raman-inactive vibrational modes, can be allowed in hyper-Raman scattering because of the nonlinearity. Incidentally, hyper-Raman-active modes and Raman-active modes are mutually exclusive in centrosymmetric molecules. Similar to Raman spectroscopy, hyper-Raman spectroscopy is feasible by visible excitation. Therefore, hyper-Raman spectroscopy can, in principle, be used as an alternative for IR spectroscopy, especially in IR-opaque media such as an aqueous solution [103]. Moreover, its spatial resolution, caused by the diffraction limit, is expected to be much better than IR microscopy. 

Figure 9. (a) Schematic representation of the five-module format of a photoactive triad which is switchable only by the simultaneous presence of a pair of ions. This design involves the multiple application of the ideas in Figure 1. The four distinct situations are shown. Note that the presence of each guest ion in its selective receptor only suppresses that particular electron transfer path. The mutually exclusive selectivity of each receptor is symbolized by the different hole sizes. All electron transfer activity ceases when both guest ions have been received by the appropriate receptors. The case is an AND logic gate at the molecular scale. While this uses only two ionic inputs, the principle established here should be extensible to accommodate three inputs or more, (b) An example illustrating the principles of part (a) from an extension of the aminomethyl aromatic family. The case shown applies to the situation (iv) in part (a) where both receptors are occupied. It is only then that luminescence is switched "on". Protons and sodium ions are the relevant ionic inputs.

The general principles outlined above can be illustrated by a variety of recognized catalytic mechanisms. These mechanisms are not mutually exclusive, and a given enzyme might incorporate several types in its overall mechanism of action. For most enzymes, it is difficult to quantify the contribution of any one catalytic mechanism to the rate and/or specificity of a particular enzyme-catalyzed reaction. 

Exotic atomic nuclei may be described as structures than do not occur in nature, but are produced in collisions. These nuclei have abundances of neurons and protons that are quite different from the natural nuclei. In 1949, M.G, Mayer (Argonne National Laboratory) and J.H.D. Jensen (University of Heidelberg) introduced a sphencal-shell model of die nucleus. The model, however, did not meet the requirements and restrains imposed by quantum mechanics and the Pauli exclusion principle, Hamilton (Vanderbilt University) and Maruhn (University of Frankfurt) reported on additional research of exotic atomic nuclei in a paper published in mid-1986 (see reference listedi. In addition to the aforementioned spherical model, there are several other fundamental shapes, including other geometric shapes with three mutually peipendicular axes—prolate spheroid (football shape), oblate spheroid (discus shape), and triaxial nucleus (all axes unequal). 

The sharing of three pairs of elections between two atoms can be accomplished by extrapolation of die above considerations. That is, since there can only be one o bond connecting the atoms, then die othei two pairs of shared electrons must be in two diffeient tc bonds, each of which is formed by the parallel overlap of a p orbital. Furthermore die n bonds must be mutually orthogonal so as not to violate the Pauli exclusion principle. Hybridization of one s orbital and one p oibital gives two equivalent sp hybiid AOs which are linearly opposite to one anodier. 

So far, we have never observed, by n.m.r. spectroscopy, oligosaccharides or glycopeptides bearing Fuc and NeuAc both linked to the same N-acetyllactosamine branch this is in agreement with the biosynthetic principle of mutual exclusion existing in transferring (1— 3)-1 inked a-fucosyl and (2— 6)-linked a-sialyl groups to the same N-acetyl lactosamine branch, as formulated by Hill and coworkers.88... 

This aspect of precaution is taken as the working definition in the EU. Although three identifiable interpretations of precaution exist, they are not mutually exclusive (see Appendix 2.3). It is therefore more appropriate to consider various interpretations as aspects rather than versions of the application of the precautionary principle (Appendix 2.3). 

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