Skewing angle

Number of poles Number of stator slots Number of rotor slots Skew angle (degrees)... 

This method was proposed to study LF parameters of anionic bis(phthalocyan-inato)lanthanides, [TBA][LnPc2] (TBA, tetrabutylammonium). They present an idealized molecular symmetry Did, where the two equivalent Pc rings are placed parallel to each other with a skew angle of 45° (Figure 2.2). For this ideal symmetry, only LF terms with q = 0 do not vanish, and the LF Hamiltonian is... 

Rotation Angles and Skew Angles in LnPc2 in Relation to the Lanthanide Contraction... 

Table 8.1 also shows the skew angles . Obviously there seems to be no relationship between the skew angle and the interplanar distance. This may be due to the fact that the calculated interplanar distances are too small, considering the... 

Thus, the two Pc rings of the LnPc2 complexes have a skew angle of about 45° only in the case of the fairly strong it-it contact between the two Pc rings. When the interplanar distance is greater than the usual van der Waals contacts, the skew angle is decreased dramatically. 

We can collect here two classes of molecules, characterized by very large skew angles, between 40° and 90°. Such a situation is found in the first instance in heteroannular dienes. 

Dienes in quasi-s-fraws conformation are found only in cyclic structures where perfect planarity is hindered. The DR also holds valid for this kind of conformation, as demonstrated by the considerations of Section II.D.l.a and also confirmed by all the reported calculations. Indeed, contrary to what is sometimes found for cisoid systems, the rotational strength evaluated by many types of calculation is invariably found to follow the diene rule for transoid systems. However, very small skew angles are usually found in real molecules and this implies that the main contribution to the observed optical activity cannot come from the weak intrinsic distortion, but is more likely to stem from the dissymmetric perturbations, notably of the allylic axial substituents. 

We consider it rather reasonable to suppose that when the distortion is small the n-electron system is delocalized, justifying the diene-picture whereas in the presence of large skew angles the contribution of localized double bonds can be much more important, supporting the olefin-picture. 

The planar conformations s-cis and s-trans cannot be appreciably populated owing to the repulsive steric interaction between the Cg—H and C5-methyl (in the s-cis) or between the same Cg—II and the methyl group on (Q in the s-trans). This repulsion is minimized by introducing a twist around the Q,—( 7 bond. Limiting conformations, with skew angles of about 40° and 140°, can be assumed, as shown in Scheme 8. In this way, an intrinsically dissymmetric chromophore is created. 

We note that y and zi are functions of the skew angle 0 and of the bend angle /i (see Scheme 4) ... 

Takemura and Shida54 prepared the allene radical ion by /-radiolysis of halocarbon solid solution of allene at low temperatures and showed that the radical cation has a lower D2 structure than the precursor with a skew angle of 30-40°. Kubonzo and coworkers55 56 produced by /-radiolysis in a low-temperature halocarbon matrix several derivatives of the allene radical cation, i.e. the radical cations of 1,2-butadiene, 3-methyl-1,2-butadiene,... 

Jacobi Coordinates The Skew Angle in Three Center Collinear Reactions... 

Fig. 6.3 Skewed coordinate potential surfaces for some hydrogen transfer reactions, (a) Top HH+ H = H + HH. (b, upper) CH + C = C + HC. (b, lower) HF + H = H + FH. (c) C1H + Cl = C1+HC1 (schematic). The mass dependence of the skew angle is apparent. The MEP s are indicated as the line Q(/ in Fig. 6.3a and the heavier lines in Fig. 6.3b. The path in Fig. 6.3a marked PP is discussed later in the text, as is the comer cutting path in Fig. 6.3c shown as the dotted line (Figure 6.3ais from Marcus, R. A. and Coltrin, M. E., J. Chem. Phys. 67, 2609 (1977) Figure 6.3b and c are From Agmon, N., Chem. Phys. 76, 203 (1983))...

Table 6.1 Skew angles for collinear reactions of interest AB+C = ABC = A+BC...

Table 6.1 illustrates the calculation of skew angles for some reactions of interest. Figure 6.3a through c shows V(x,y) plots for several examples of collinear A + BC reactions. 

Yamamuro, Penumadu, and Campbell [5] developed another model with a force R of the same magnitude as A but acting at a skew angle a, which is an adjustable parameter. The form of the analysis is similar to that by Tadmor and Klein [7] and Campbell and Dontula [1] in nature. Fig. A5.6 illustrates forces for the model and the changes made to Fig. A5.3. The following is an extended list of assumptions they made ... 

Fig. 4.12 (a) and (f>) (1 x 1) Pt (001), which initially has a square structure, changes into a skewed square shape after pulsed-laser heating to —350 K. Since the change is gradual, they probably represent a disordered phase, (c) Map of (b) showing the skewness angles with respect to the atomic row directions of the underlying layer. Note that tan 4° = pf and tan 11° = j. 

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