Bond angle multiplicity

According to the namre of the empirical potential energy function, described in Chapter 2, different motions can take place on different time scales, e.g., bond stretching and bond angle bending vs. dihedral angle librations and non-bond interactions. Multiple time step (MTS) methods [38-40,42] allow one to use different integration time steps in the same simulation so as to treat the time development of the slow and fast movements most effectively. 

Notice that the zinc atom is associated with only four valence electrons. Although this is less than an octet, the adjacent carbon atoms have no lone pairs available to form multiple bonds. In addition, the formal charge on the zinc atom is zero. Thus, Zn has only four electrons in the optimal Lewis structure of dimethyizinc. This Lewis stmcture shows two pairs of bonding electrons and no lone pairs on the inner atom, so Zn has a steric number of 2. Two pairs of electrons are kept farthest apart when they are arranged along a line. Thus, the C—Zn—C bond angle is 180°, and linear geometry exists around the zinc atom. 

Multiple bonds can be treated as ring structures with bent bonds. The distortions dealt with in the preceding paragraph must be taken into account. For example, in ethylene every C atom is surrounded tetrahedrally by four electron pairs two pairs mediate the double bond between the C atoms via two bent bonds. The tension in the bent bonds reduces the angle between them and decreases their repulsion toward the C-H bonds, and the HCH bond angle is therefore bigger than 109.5°. 

Table 8.2 Bond angles in degrees for some molecules having multiple bonds. X = singly, Z = double bonded ligand atom...

Note how the bond angles show the repulsive action of the multiple bonds and of the lone electron pair. 

Table 16.1 Bond angles at the bridging atoms and distances between the central atoms M of linked tetrahedra and octahedra (disregarding possible distortions). The distances are given as multiples of the polyhedron edge length...

Bond angles in molecules containing multiple bonds deviate from the ideal values because a double-bond domain is larger than a single-bond domain, and a triple-bond domain is even larger. Thus... 

Figure 4.24 also shows that multiple bonds distort the bond angles in the same way as a lone... 

The chemical and physical properties of DMFL contrast most sharply with those of FL. The geometrical features, in particular the carbene-carbon bond angle, of these two carbenes are expected to be identical. The most important difference between DMFL and FL is that the spin multiplicities of the lowest electronic states appear to have been inverted. The experiments indicate that the ground-state of DMFL is the singlet. This conclusion is outlined in the reactions shown in Scheme 4. 

One of the basic mles of the VSEPR model states that multiple bonds have larger space requirement and exercise stronger repulsion than single bonds ( the multiple bond rule )- The relationship of the bond angles in XSO2Y sulphones... 

Ball-and-stick models (A2) are used to illustrate the spatial structure of molecules. Atoms are represented as colored balls (for the color coding, see the inside front cover) and bonds (including multiple bonds) as gray cylinders. Although the relative bond lengths and angles correspond to actual conditions, the size at which the atoms are represented is too small to make the model more comprehensible. 

Another classical measure of the molecular geometry of substituents is the Verloop steric parameter. This is calculated from bond angles and atomic dimensions— primarily the lengths of substituent groups and several measures of their width. Trivial as this may sound, the consideration of molecular bulk is an important and often neglected factor in making multiple quantitative correlations of structure and pharmacological activity. Balaban et al. (1980) devised several related methods that are still in use today. 

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