Changes in Symmetry

Finally, it is to be remarked that the molecular symmetry in itself may be sufficient to modify radiation resistance. This is suggested by the well-known fact that a change in symmetry may transform a forbidden transition into an allowed one.31 This case is realized for n-n transitions in benzene and its less symmetrical halogen derivatives. The phenomenon might occur on condition that the transitions considered play a sufficient relative part in radiation resistance. 

Hisatsune and co-workers [290—299] have made extensive kinetic studies of the decomposition of various ions in alkali halide discs. Widths and frequencies of IR absorption bands are an indication of the extent to which a reactant ion forms a solid solution with the matrix halide. Sodium acetate was much less soluble in KBr than in KI but the activation energy for acetate breakdown in the latter matrix was the larger [297]. Shifts in frequency, indicating changes in symmetry, have been reported for oxalate [294] and formate [300] ions dispersed in KBr. 

Surface reconstmction and relaxation can be understood as a deviation from the bulk-truncated stmcture on the atomic level, by which the surface minimizes its free energy [Kolb, 1996]. In particular, surface reconstruction usually involves a change in the periodicity of the surface and in some cases a change in symmetry as well, whereas surface relaxation is a (small) rearrangement of surface layers. 

Figure 9 shows the effect of deprotonation of adsorbed formic acid which occurs on warming the surface to above 270 K. Spectrum (a) can be assigned by comparison with the photoelectron spectrum of the free molecule. The formate species also gives rise to four spectral bands and, since the number of expected orbitals is the same, it is tempting to assume a one-to-one correspondence, allowing of course for the change in symmetry from Cs to C2v- The application of selection rules proves, however, that such an... 

Every phase transition is associated with a change in symmetry as well as in order. To facilitate quantitative analysis, Landau introduced the concept of an order parameter, and expressed the free energy, 0, as follows ... 

Exchange of Eu3+ for Na+ was demonstrated by the phosphorescence spectra obtained for these systems, which also showed that the spectrum did not change during induction this suggests that no change in symmetry occurred at the cation sites during this time. 

SrTiOs undergoes a structural change from cubic to tetragonal symmetry at —110° K. Additional lines appear [619] in the fluorescence spectrum of Eu3+ doped SrTiOs, as expected due to this change in symmetry. 

Azulene has weak absorption in the visible region (near 7000 A) and more intense band systems in the ultraviolet. The first ultraviolet system, which commences at about 3500 A, has been examined in substitutional solid solution in naphthalene (Sidman and McClure, 1956) and in the vapour state (Hunt and Ross, 1962), and can be observed in fluorescence from the vapour (Hunt and Ross, 1956). Theory predicts that the transition is 1Al<-lAl(C2K), i.e. allowed by the electronic selection rules with polarization parallel to the twofold symmetry axis (see, e.g., Ham, 1960 Mofifitt, 1954 Pariser, 1956b). The vibrational analysis shows that the transition is allowed but does not establish the axis of polarization. The intensity distribution among the vibrational bands indicates a small increase in CC bond distance without change in symmetry. 

The change in symmetry from copper to silver is related to rather subtle structural differences. If only the four short M—F bonds are considered, then both structures consist of puckered layers formed by joining the square, [MF4] units through corners. These puckered layers lie directly over one another, related by a translation in copper difluoride, but are displaced alternately, related by a glide plane, in silver difluoride (27), (see Fig. 1). In both structures, the fluorine atoms are arranged in considerably distorted hexagonal close-packed arrays, the distortion being more marked for silver. 

Another type of symmetry forbidden reaction has been defined by Woodward and Hoffmann 8> and involves a change in symmetry of the occupied molecular orbitals during the reaction. Certain materials may act as a catalyst in this case, if they can form a reaction intermediate which either circumvents the symmetry rule 9> or lowers the energy of activation, 0>. 

For many years, pericyclic reactions were poorly understood and unpredictable. Around 1965, Robert B. Woodward and Roald Hoffmann developed a theory for predicting the results of pericyclic reactions by considering the symmetry of the molecular orbitals of the reactants and products. Their theory, called conservation of orbital symmetry, says that the molecular orbitals of the reactants must flow smoothly into the MOs of the products without any drastic changes in symmetry. In that case, there will be bonding interactions to help stabilize the transition state. Without these bonding interactions in the transition state, the activation energy is much higher, and the concerted... 

A theory of pericyclic reactions stating that the MOs of the reactants must flow smoothly into the MOs of the products without any drastic changes in symmetry. That is, there must be bonding interactions to help stabilize the transition state, (p. 692)... 

The local symmetry in pentahapto cyclopentadienyl complexes is D5h while in monohapto species it is Cs. Due to this large change in symmetry, vibrational spectroscopy has been a useful tool in distinguishing between the [Pg.124]

In the first instance however, symmetry will be treated in what follows as precisely described by the formalism of group theory and any change in symmetry of a system will be viewed as a transition between perfect symmetry types. 

The temporary anions associated with low-lyin unfilled orbitals generally have lifetimes in the range of 10 - 10 s in the gas phase. This paper discusses the use of electron transmission spectroscopy (ETS) to provide information on these short-lived anions. The sensitivity of the lifetimes to changes in symmetry is illustrated by comparing the electron transmission of benzene and various alkyl substituted benzenes. 

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