Torsional bond angles

Fij ure4-8 The TI C C II Torsional Bond Angle in Deformed Ethylene. I he normal torsional angle is fj) — (E. 

Atomistically detailed models account for all atoms. The force field contains additive contributions specified in tenns of bond lengtlis, bond angles, torsional angles and possible crosstenns. It also includes non-bonded contributions as tire sum of van der Waals interactions, often described by Lennard-Jones potentials, and Coulomb interactions. Atomistic simulations are successfully used to predict tire transport properties of small molecules in glassy polymers, to calculate elastic moduli and to study plastic defonnation and local motion in quasi-static simulations [fy7, ( ]. The atomistic models are also useful to interiDret scattering data [fyl] and NMR measurements [70] in tenns of local order. 

The second method for representing a molecule in 3D space is to use internal coordinates such as bond lengths, bond angles, and torsion angles. Internal coordinates describe the spatial arrangement of the atoms relative to each other. Figure 2-91 illustratc.s thi.s for 1,2-dichlorocthanc. 

Figure 2-91. Internal coordinates of 1,2-dichloroethane bond lengths and r2, bond angle a, and torsion angle r.

Spanned by tbc atoms 4, 2, and 1, and 2, 1, and 3 (tlic ry-planc), Except of the first three atoms, each atom is described by a set of three internal coordinates a distance from a previously defined atom, the bond angle formed by the atom with two previous atoms, and the torsion angle of the atom with three previous atoms. A total of 3/V - 6 internal coordinates, where N is the number of atoms in the molecule, is required to represent a chemical structure properly in 3D space. The number (,3N - 6) of internal coordinates also corresponds to the number of degrees of freedom of the molecule. 

The PEF is a sum of many individual contributions, Tt can be divided into bonded (bonds, angles, and torsions) and non-bonded (electrostatic and van der Waals) contributions V, responsible for intramolecular and, in tlic case of more than one molecule, also intermoleculai interactions. Figure 7-8 shows schematically these types of interactions between atoms, which arc included in almost all force field implementations. 

You can include geometric restraints—for interatomic distances, bond angles, and torsion angles—in any molecular dynamics calculation or geometry optim i/.ation. Here are some applications of restrain ts ... 

Any length, bond angle, or torsion defined in a named selection (see the lype.Kfhe.m Reference Manual)... 

The computational effort is significantly increased if three-body terms are included in the model. Even with a simple pairwise model, the non-bonded interactions usually require by far the greatest amount of computational effort. The number of bond, angle and torsional terms increases approximately with the number of atoms (N) in the system, but the number of non-bonded interactions increases with N. There are N(N —l)/2 distinct pairs of... 

At Its most basic level separating the total strain of a structure into its components is a qualita tive exercise For example a computer drawn model of the eclipsed conformation of butane using ideal bond angles and bond distances (Figure 3 8) reveals that two pairs of hydrogens are separated by a distance of only 175 pm a value considerably smaller than the sum of their van der Waals radii (2 X 120 pm = 240 pm) Thus this conformation is destabilized not only by the torsional strain associ ated with its eclipsed bonds but also by van der Waals strain... 

A second but much less stable nonplanar conformation called the boat is shown in Eigure 3 14 Like the chair the boat conformation has bond angles that are approximately tetrahedral and is relatively free of angle strain It is however destabi hzed by the torsional strain associated with eclipsed bonds on four of its carbons The... 

Steric strain (Section 3 2) Destabilization of a molecule as a result of van der Waals repulsion distorted bond distances bond angles or torsion angles... 

Step 12. FinaHy, the crystaHographer analy2es the results, tabulates some critical information (eg, bond distances, bond angles, torsion angles, planarity of groups of atoms, etc), and prepares a report on the stmcture deterrnination. The time for stmcture solution and refinement as outlined here is normally 2 to 8 h depending on the complexity of the stmcture. 

---