Translation components

These values predict a value of -34.0 kcal moT for AH . This value is in excellent agreement with experiment (-34.0 2.0 kcal mol). Note that we didn t need to run a frequency job on Li, but rather computed the enthalpy correction as 2 RT (just a translational component). 

In Point Groups, one point of the lattice remains invarient under symmetry operations, i.e.- there is no translation involved. Space Groups are so-named because in each group all three- dimensional space remains invarient under operations of the group. That is, they contain translation components as well as the three symmetiy operations. We will not dwell upon the 231 Space Groups since these relate to determining the exact structure of the solid. However, we will show how the 32 Point Groups relate to crystal structure of solids. 

The glide operations are indicated by a,c, or n, depending on the direction of the translation component. 

If a rotation axis is correctly oriented, but incorrectly positioned, an additional translation component, perpendicular to the rotation axes, is introduced. The... 

A symmetry operation can have both rotational and translational components, and is described in the Seitz notation as R s. The terms R and s are the rotational and translational parts of the 3d symmetry element, respectively, such that... 

The effect of the translational component of the element R s can be considered in an analogous manner... 

Crystal symmetries that entail centering translations and/or those symmetry operations that have translational components (screw rotations and glides) cause certain sets of X-ray reflections to be absent from the diffraction pattern. Such absences are called systematic absences. A general explanation of why this happens would take more space and require use of more diffraction theory than is possible here. Thus, after giving only one heuristic demonstration of how a systematic absence can arise, we shall go directly to a discussion of how such absences enable us to take a giant step toward specifying the space group. 

The combination of reflection and translation gives a glide plane. If the gliding direction is parallel to the a axis, the symbol for the axial glide plane is a and the operation is reflection in the plane followed by translation parallel to the a axis by a/2 . Similar axial glide planes b and c have translation components of b/2 and c/2, respectively. 

Laue symmetry is 2/m (disregarding the translational components of the 21-axis and the c glide), so the space group belongs to the monoclinic system. The simplified symbol P2 /c normally replaces the full symbol P 2 /c, and the old Schonflies symbol C A (the fifth space group derived from the point group C2h) is seldom used. 

Figure 8 An example for which the classical dynamics is a poor approximation to the quantum dissociation at off-normal incidence on W(1 00) [65]. For high initial parallel momentum, K, the wavepacket propagates in an set of adiabatic librational states which have strong couplings between rotational and translational components. These show large, non-classical avoided crossings.

The space group symmetry regulates the mutual arrangement of the structural units, not only by means of operations of inversion, reflection, and rotation, but also by translations and by symmetry operations with a translational component. 

Translation component is one-half of the true translation along the face diagonal of a centered plane lattice. 

Discrete Rotational Symmetry This is a subset of continuous rotations and reflections in three-dimensional space. Since rotation has no translational components their symmetry groups are known as point groups. Point groups are used to specify the symmetry of isolated objects such as molecules. 

Presumably, the incubation at 80 C acts by ultimately shaping the assembly product formed at 65°C into a spatial design capable of efficiently interacting with the other translational components. This conformational adjustment, in fact a fine tuning of the particle shape, is absolutely dependent on spermine. This observation, and the evidence that spermine is essential to activate the peptidyltransferase center of crenarchaeal ribosomes (see section 3.4), suggest that spermine-like polyamines (notably thermine) are an integral and essential constituent of the large subunits of crenarchaeal ribosomes. 

Interchangeability of translational components 5.1. Interchangeability of ribosomal subunits... 

In the case of molecular solids the translational component, for instance, refers to displacements of the scattering atom by virtue of whole body translational vibrations of the molecule and provides... 

Table 2.5 The factor group, G/T, of the space group of the diamond lattice (Fd3m Oj). The operations are identified in the form R(x,y )/r with R a rotation about the axis (x,y ) and r a translation. The translational components of the factor group operations are listed in fractional unit cell coordinates, t equal to l/2,l/2,l/2 in, for example, C2(0,l,l) l/2,l/2,l/2. Note, that the first 24 operations listed identify the point group Tj.

The symmetry of the crystal is indicated in its diffraction pattern. Systematic absences in the diffraction pattern show that there are translational symmetry elements relating components in the unit cell. The translational component of the symmetry elements causes selective and predictable destructive interference to occur when the specific translation in the arrangement of atoms are simple fractions of the normal lattice... 

Glide plane A glide plane involves reflection across a plane combined with a translation. For an axial glide plane, denoted a, b or c, the translational component is or f, respectively. For a c-glide plane, if the mirror plane is perpendicular... 

Systematically absent Bragg reflections Bragg reflections that have no intensity, because of translational components of any symmetry in the unit-cell contents and which have h, k, and I values that are systematic in terms of oddness or evenness. These absences depend only upon symmetry in the atomic arrangement in the crystal, and they can be used to derive the space group. For example, all reflections for which h + k is odd may be absent, showing that the unit cell is C-face centered. 

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