Parallel transition

Although taking place over a somewhat wider range of c[ij], this transition parallels the variation of JeR from Zimm-like to Rouse-like behavior at low concentrations (15). It also supports the contention (Section 5) that coil overlap is the principal structural variable affecting viscoelastic behavior at low to moderate concentrations. 

Similar curves are obtained with other synthetic polypeptides, and in most cases they are reasonably independent of the nature of the amino acid side chains. In synthetic polypeptides and proteins the observed Cotton effects do not arise from isolated chromophores but are composite curves resulting from several transitions assigned to the amide bonds in the 200-m/x region. The a-helical curve, for example, results from three optically active absorption bands. One around 222 m/ arises from an n — 7T transition of nonbonding electrons, and the other two at 208 and 191 m/ji are attributed to w — tt transitions parallel and perpendicular to the axis of the helix. These transitions of the a-helix and the resulting Cotton effects characteristic of the a-helix are at present of great interest in interpreting ORD curves of membranes. 

The allowed changes in the rotational quantum number J are AJ = 1 for parallel (2 ) transitions and A7= 0, 1 for perpendicular (II ) transitions. Parallel transitions such as for acetylene thus have P i J= 1) and R(AJ = +1) branches with a characteristic minimum between them, as shown for diatomic molecules such as HCl in Fig. 37-3 and for the HCN mode in Fig. 2. However, perpendicular transitions such as Vs for acetylene and V2 for HCN (Fig. 2) have a strong central Q branch (AJ = 0) along with P and R branches. This characteristic PQR-Yersus-PR band shape is quite obvious in the spectrum and is a useful aid in assigning the symmetries of the vibrational levels involved in the infrared transitions of a hnear molecule. 

Usha and Wittebort (1989) studied the NMR of crystalline cram-bin. At 140 K the protein hydrate is stationary, with t = 1 msec. Above 200 K changes in the signal with temperature are consistent with a glass transition or melting of the hydration water. This broad transition parallels closely the changes with temperature found for the heat capacity, Mossbauer spectroscopic, and other properties of hydrated protein crystals. At room temperature no more than 12 water molecules are orien-tationally ordered. The average rotational correlation time of the hydration water is about 40 times longer than that for bulk water. 

The intra-unit HCN electronic transitions parallel those of isoelectronic N2 with the lowest energy excited states arising from excitations to the and g n multiplet... 

The isotactic polymer is somewhat more disruptive (A Tx/2 = 0.48 C, cooperative unit = 180 molecules), but it is the stereoirregular polymer — Sample 2, curve D — which causes the most severe broadening of the melting endotherm. The trcuisition half-width is increased to I.IO C, which corresponds to a cooperative unit of 80 molecules (i.e., a symmetrical transition with equivalent AHu, uid T would have a cooperative unit of 80 molecules). In each case, the effect of the polymer on the pre-transition parallels the effect on the main transition. 

Many of the ideas that are essential to understanding polyatomic electronic spectra have already been developed in the three preceding chapters. As in diatomics, the Born-Oppenheimer separation between electronic and nuclear motions is a useful organizing principle for treating electronic transitions in polyatomics. Vibrational band intensities in polyatomic electronic spectra are frequently (but not always) governed by Franck-Condon factors in the vibrational modes. The rotational fine structure in gas-phase electronic transitions parallels that in polyatomic vibration-rotation spectra (Section 6.6), except that the rotational selection rules in symmetric and asymmetric tops now depend on the relative orientations of the electronic transition moment and the principal axes. Analyses of rotational contours in polyatomic band spectra thus provide valuable clues about the symmetry and assignment of the electronic states involved. 

Figure Bl.4.9. Top rotation-tunnelling hyperfine structure in one of the flipping inodes of (020)3 near 3 THz. The small splittings seen in the Q-branch transitions are induced by the bound-free hydrogen atom tiiimelling by the water monomers. Bottom the low-frequency torsional mode structure of the water duner spectrum, includmg a detailed comparison of theoretical calculations of the dynamics with those observed experimentally [ ]. The symbols next to the arrows depict the parallel (A k= 0) versus perpendicular (A = 1) nature of the selection rules in the pseudorotation manifold.

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.

If we compare with figure C2.2.I I, we can see that this defonnation involves bend and splay of the director field. This field-induced transition in director orientation is called a Freedericksz transition [9, 106, 1071. We can also define Freedericksz transitions when the director and field are both parallel to the surface, but mutually orthogonal or when the director is nonnal to the surface and the field is parallel to it. It turns out there is a threshold voltage for attaining orientation in the middle of the liquid crystal cell, i.e. a deviation of the angle of the director [9, 107]. For all tliree possible geometries, the threshold voltage takes the fonn [9, 107]... 

Otlier possibilities for observing phase transitions are offered by suspensions of non-spherical particles. Such systems can display liquid crystalline phases, in addition to tire isotropic liquid and crystalline phases (see also section C2.2). First, we consider rod-like particles (see [114, 115], and references tlierein). As shown by Onsager [116, 117], sufficiently elongated particles will display a nematic phase, in which tire particles have a tendency to align parallel to... 

Disc-like particles can also undergo an Onsager transition—here tire particles fonn a discotic nematic, where tire short particle axes tend to be oriented parallel to each other. In practice, clay suspensions tend to display sol-gel transitions, witliout a clear tendency towards nematic ordering (for instance, [22]). Using sterically stabilized platelets, an isotropic-nematic transition could be observed [119]. 

In an ambitious study, the AIMS method was used to calculate the absorption and resonance Raman spectra of ethylene [221]. In this, sets starting with 10 functions were calculated. To cope with the huge resources required for these calculations the code was parallelized. The spectra, obtained from the autocorrelation function, compare well with the experimental ones. It was also found that the non-adiabatic processes described above do not influence the spectra, as their profiles are formed in the time before the packet reaches the intersection, that is, the observed dynamic is dominated by the torsional motion. Calculations using the Condon approximation were also compared to calculations implicitly including the transition dipole, and little difference was seen. 

In principle cis 2 butene and trans 2 butene may be mterconverted by rotation about the C 2=C 3 double bond However unlike rotation about the C 2—C 3 single bond in butane which is quite fast mterconversion of the stereoisomeric 2 butenes does not occur under normal circumstances It is sometimes said that rotation about a carbon-carbon double bond is restricted but this is an understatement Conventional lab oratory sources of heat do not provide enough energy for rotation about the double bond m alkenes As shown m Figure 5 2 rotation about a double bond requires the p orbitals of C 2 and C 3 to be twisted from their stable parallel alignment—m effect the tt com ponent of the double bond must be broken at the transition state... 

Although both stereoisomers yield 4 tert butylcyclohexene as the only alkene they do so at quite different rates The cis isomer reacts over 500 times faster than the trans The difference in reaction rate results from different degrees of rr bond develop ment in the E2 transition state Since rr overlap of p orbitals requires their axes to be parallel rr bond formation is best achieved when the four atoms of the H—C—C—X unit he in the same plane at the transition state The two conformations that permit this are termed syn coplanar and anti coplanar... 

FIGURE 10 6 Confor mations and electron delo calization in 1 3 butadiene The s CIS and the s trans con formations permit the 2p or bitalsto be aligned parallel to one another for maxi mum TT electron delocaliza tion The s trans conformation is more stable than the s CIS Stabilization resulting from tt electron de localization is least in the perpendicular conformation which IS a transition state for rotation about the C 2—C 3 single bond The green and yellow colors are meant to differentiate the orbitals and do not indicate their phases... 

A parallel, A —A, band involves rotational transitions between stacks of levels like those in Figure 5.6(a), associated with both A states, and given by Equation (5.32). The selection mles are... 

---