Counterclockwise rotation

As viewed m the drawing a 120° counterclockwise rotation of C 4 places its hydroxyl group m the proper position At the same time this rotation moves the CH2OH group to a position such that it will become a substituent that is up on the five membered ring The hydrogen at C 4 then will be down m the furanose form... 

A consistent direction of twist is maintained clockwise or counterclockwise rotations are equally probable. 

The equations of Table 2-5 are all scalar equations representing discrete components of motions along orthogonal axes. The axis along which the component to or a acts is defined in the same fashion as for a couple. That is, the direction of to is outwardly perpendicular to the plane of counterclockwise rotation (Figure 2-7). 

Ga ), (Ca t), counterclockwise rotations through 180° about the x axis (y axis) followed by the translation t ... 

C4 t) 6, counterclockwise rotation about the z axis through 90°, followed by the translation t, followed by time reversal ... 

FIGURE 1.40 The two spin states of an electron can be represented as clockwise or counterclockwise rotation around an axis passing through the electron. The... 

In contrast to Southwest Japan, opening of northeastern part of the Japan Sea is unclear, compared with the southwestern part of Japan. Tosha and Hamano (1988) made a paleomagnetic study of Tertiary rocks of Oga Peninsula (northern Honshu) and considered that a counterclockwise rotation of Northeast Japan with respect to eastern Asia took place between about 22 Ma and 15 Ma and the before the rotation. Northeast Japan was situated along the east coast of the Asian continent. 

This operation corresponds to a counterclockwise rotation of the vector r. Since cosf = cos(—9) and sin0 = — sin(—9), the matrix for clockwise rotation is... 

Figure 1 .Graphical decomposition of the plane wave icos9 into clockwise and counterclockwise rotating components. Construction and projection of only the left circulating component i cos 8 + j sin 9 is shown.

The eclipsed conformation A of the intact aztreonam molecule becomes relaxed, through the counterclockwise rotation about the C3 - C4 bond to the... 

That is, the transformation is represented as successive rotations of y, P, a about the e3, e2, and axes. A positive rotation is a counterclockwise rotation.1 Since R is unitary, it follows that the Cartesian coordinates transform as... 

Figure 6.57 Ten connectivity patterns for a diphasic solid. Each phase has zero-, one-, two-, or three-dimensional connectivity to itself. In the 3-1 composite, for example, the shaded phase is three-dimensionally connected and the unshaded phase is one-dimensionally connected. Arrows are used to indicate the connected directions. Two views of the 3-3 and 3-2 patterns are given because the two interpenetrating networks are difficult to visualize on paper. The views are related by 90° counterclockwise rotation about Z. (After Newnham Cross, 1981.)...

Femtosecond pulse trains offer another control knob to rotational excitation of molecules, namely, the control of its directionality. By applying a series of laser pulses, linearly polarized at an angle with respect to one another, either clockwise or counterclockwise rotation can be initiated in a molecular ensemble [27]. The effect has been experimentally demonstrated with a sequence of only two pulses [28], and longer pulse trains [29, 30]. The latter were dubbed chiral because of the directional rotation of light polarization from pulse to pulse shown in Figure 10.3a. Chiral pulse trains enable control of the sense of molecular rotation... 

Figure 2.4. Counterclockwise rotation by jt/2 around the origin. The two vectors really are the same length.

Similarly, counterclockwise rotation (or C in a clockwise direction) is described by... 

In the transition state of the enantio-determining cyclometalation step, F - G, the Rh, nitrogen, C(l), and one of the hydrogens would be roughly coplanar, which requires either clockwise or counterclockwise rotation about the N—C(l) axis (see the Newman projection formula F in Scheme 16). The transition state models la and lb explain the prevailing clockwise rotation of the conformer Fa with respect to the coun-... 

Consider first a Cartesian coordinate system with unit basis vectors ei, e2, e3. We define the effect of a positive rotation about the z axis through an angle 0, corresponding to a symmetry operation G, say, as a counterclockwise rotation since... 

The classification of molecular symmetry operations that we shall follow here is the conventional one (see, e.g., Tinkham [2]), involving rotations about a specified axis, denoted Cn for a counterclockwise rotation through reflections in a plane, de-... 

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