Point atoms

In most common chiral molecules, chirality arises from chiral tetravalent atoms. A conformation-independent chirality code (CICC) was developed that encodes the molecular chirality originating from a chiral tetravalent atom [42], For more generality, a conformation-dependent chirality code (CDCC) is used [43]. CDCC ti cats a molecule as a rigid set of points (atoms) linked by bonds, and it accounts for chirality generated by chirality centers, chirality axes, or chirality planes. 

The key idea of the fast torsion angle dynamics algorithm in Dyana is to exploit the fact that a chain molecule such as a protein or nucleic acid can be represented in a natural way as a tree structure consisting of n+1 rigid bodies that are connected by n rotatable bonds (Fig. 2.1) [74, 83]. Each rigid body is made up of one or several mass points (atoms) with invariable relative positions. The tree structure starts from a base, typically... 

This is the highest multiplicity Mmax of the given space group and corresponds to the lowest site symmetry (each point is mapped onto itself only by the identity operation ). In this general position the coordinate triplets of the Mmax sites include the reference triplet indicated as x, y, z (having three variable parameters, to be experimentally determined). In a given space group, moreover, it is possible to have several special positions. In this case, points (atoms) are considered which... 

We begin with the way chemists perceive similarity between two molecules. This process involves, consciously or unconsciously, comparing several types of structural features present in the molecules. For example, considering the five aliphatic alcohols (represented by their H-suppressed molecular graphs) in Figure 1, we note both similarities and differences they are all four-carbon alcohols a, b, c and d are acyclic, whereas e has a ring a and b are primary alcohols, c and e are secondary alcohols and d is a tertiary alcohol b and c have the same skeleton, but for the labeling of points (atoms), while the other skeletons are distinct etc. 

There are only discrete, non-overlapping point atoms in the structure (this requires diffraction data with resolution of about 1 A)... 

Fig. 6. Gaussian curves as a function of increasing width. As the degree of softness increases, the curves represent fuzzy atoms, and as the degree of softness deceases, the Gaussian converges to a point atom model.

In order to reduce the number of variables, the location of the end point atoms A and C is fixed and only atom B is allowed to move. A condensed phase environment is represented by adding a harmonic oscillator degree of lieedom coupled to atom B. This can be interpreted as a fourth atom which is coupled in a harmonic way to atom B... 

The simplest chiral objects (stereomodels) are composed of four nonplanar points (atoms). Connection of four points requires at least three lines (bonds) that can be arranged in two ways to form a helical or a tripodal unit ... 

Orthorhombic crystals are similar to both tetragonal and cubic crystals because their coordinate axes are still orthogonal, but now all the lattice parameters are unequal. There are four types of orthorhombic space lattices simple orthorhombic, face-centered orthorhombic, body-centered orthorhombic, and a type we have not yet encountered, base-centered orthorhombic. The first three types are similar to those we have seen for the cubic and tetragonal systems. The base-centered orthorhombic space lattice has a lattice point (atom) at each comer, as well as a lattice point only on the top and bottom faces (called basal faces). All four orthorhombic space lattices are shown in Figure 1.20. 

A closer comparison of bond valence and electron density models is not possible because of the different underlying assumptions of the models. The forces in the bond valence model act between structureless point atoms, but the forces in the electron density model are exerted by electrons on nuclei and vice versa. This basic difference makes it difficult to compare the two models in greater detail. They are best seen as complementary, the electron density model providing important information about the nature of the bonding between the atoms, the bond valence model providing a simple tool for predicting structure and properties, particularly in cases where the structure is complex. 

Circle the molecule from each pair that should have a higher boiling point (atomic numbers Cl = 17 O = 8 C = 6 H =1) ... 

To simplify the discussion we will restrict it to the case of point atoms and to one dimension and thus return to Equation (2.4). Suppose that xp has a random error up superimposed on it so that... 

It is worth pointing out that, even without the effects of disorder, there will be a fairly rapid, though not monotonic, decrease of intensity with progressively higher order of diffraction maxima except in the artificial case of point atoms. The extreme case of this effect is illustrated by the argument associated with Equations (2.10) and (2.11). 

Examine the trends for boiling points, atomic radii, and ionization energies using the Interactive Periodic Table (eChapter 20.2). Explain the factors that account for each of these trends. 

Figure 8 Geometrical parameters describing the relative orientation of reactant double bonds. T and T are the tt-orbitals of the double bonds, and A, B, and C are the point atoms. The distance between T and T represents the extent of overlap of T and T. ...

Not all of the minerals Information included is occur in each country. crystal structure, density (in g cm 3), melting point, boilin g point, atomic radius (in pm), and electronegativity, in that order. ... 

M2. Malmstadt, H. V., and Chambers, W. E., Precision null-point atomic absorption spectrochemical analysis. Anal. Chem. 32, 225-235 (1960). 

In the present context, we are dealing with molecular and other structures in which sets of points [atoms] are distributed in fixed positions, which definition includes the structures of regular solids and indeed polymers of defined point symmetry. In cases of high symmetry, such structures exhibit a natural centre and the sets of fixed points lie on spheres about this centre. 

A. D, Buckingham and K. L. Clarke-Hunt. The pair polarizability anisotropy of SF in the point-atom-polarizability approximation. Molec. Phys., 40 643-648 (1980). 

According to conventional texts, forces act between point atoms, spheres, cylinders and planes in a kind of pythagorean and ptolemaic imperative that ignores curvature. There is nowhere an awareness that shape may have a role to play, except to please the eye. Nature ever geometrised, said somebody. Tme. But it has good reasons. 

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