Bond angle constraint

Introduce bond and bond angle constraints as required. 

Both synthetic and natural polymers have superstructures that influence or dictate the properties of the material. Many of these primary, secondary, tertiary, and quaternary structures are influenced in a similar manner. Thus, the primary structure is a driving force for the secondary structure. Allowed and preferred primary and secondary bondings influence structure. For most natural and synthetic polymers, hydrophobic and hydrophilic domains tend to cluster. Thus, most helical structures will have either a hydrophobic or hydrophilic inner core with the opposite outer core resulting from a balance between secondary and primary bonding factors and steric and bond angle constraints. Nature has used these differences in domain character to create the world around us. 

We finally note that is possible to use Gauss principle to obtain equations of motion when the system is subject to holonomic constraints such as bond length or bond angle constraints. In this case one obtains the same equations of motion as one would obtain by applying the Lagrange equation. 

Bond angle constraint aided by solvophobic effect Fig. 15.1. Examples of polymers with conformational restriction due to steric and bond angle constraints. 

Bond angle constraint aided by electrostatic interactions... 

Figure 26. Nearest-neighbor H-bonds observed in ( peptides synthesized from l-(aminomethyl)cyclopropanecarboxylic acids.226 This S(8) pattern is an example of residue-induced turn formation, resulting from the dihedral and bond angle constraints introduced into the ft2-2 backbone by the cyclopropyl substituents. The crystal structures show a dipeptide and tripeptide in which the S(8) H-bond segments are rendered in thick cylinders. For the dipeptide, Newman projections are shown looking down the Ca—Cp bond and the C(O)—Ca bond.

Again, consider the system of N particles and / general holonomic constraints, and assume that bond-angle constraints (/ < /) are present. For bond-angle constraints, the general holonomic constraint, Eq. [1], takes the special form... 

Table 1. Comparison of Angle-Constraint and Triangulation Procedures for Bond-Angle Constraints Using the SHAKE Algorithm on 13,824 SPC/E Rigid Water Molecules"...

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