Constant Valence Angle

The maximum possible chain length l is assigned to a constant valence angle chain in diW-trans conformation. It can be calculated from simple geometric principles to be given by... 

Constant Valence Angle Chains with Hindered Rotation... 

Since the conformational energies also lie in this range, the assumption of a constant valence angle can lead to problems. 

Valency of an ion effective number of electrons per ion Angle on a crystal surface numerical constant an angle Contact angle at the edge of a solid Surface tension of a liquid Critical surface tension"... 

Figure 2. A contour diagram of the conformational energy of p-cellobiose computed from eqn. (6) holfing constant all variables except < ), v see ref. 5 for details. The rigid glucose residue geometry was taken from ref. 23, and the valence angle p at 04 was chosen as 116 in accordance with the results of pertinent crystal structure determinations. Contours are drawn at 2,4, 6, 8,10,25, and 50 kcal/mol above the absolute minimum located near ( ), v = -20 , -30 higher energy contours are omitted.

Y, and Z are connected by bonds of fixed length joined at fixed valence angles, that atoms W, X, and Y are confined to fixed positions in the plane of the paper, and that torsional rotation 0 occurs about the X-Y bond which allows Z to move on the circular path depicted. If the rotation 0 is "free such that the potential energy is constant for all values of 0, then all points on the circular locus are equally probable, and the mean position of Z, i.e., the terminus of , lies at point z. The mean vector would terminate at z for any potential function symmetric in 0 for any potential function at all, except one that allows absolutely no rotational motion, the vector will terminate at a point that is not on the circle. Thus, the mean position of Z as seen from W is not any one of the positions that Z can actually adopt, and, while the magnitude ll may correspond to some separation that W and Z can in fact achieve, it is incorrect to attribute the separation to any real conformation of the entity W-X-Y-Z. Mean conformations tiiat would place Z at a position z relative to the fixed positions of W, X, and Y have been called "virtual" conformations.i9,20it is clear that such conformations can never be identified with any conformation that the molecule can actually adopt... 

In the CFF context, Kb is not a force constant of any bond in any molecule, and 6 is not the equilibrium value of any valence angle. They are energy function parameters with units of force constant and angle. In the actual case, kJmol A" and rad. 

In some cases (such as torsional barrier terms) it is possible to do this definitively, while in others (such as valence angle deformation force constants and ideal distances and angles) it is not. However, useful starting points for the empirical refinement can be derived from experiment. 

The units for the force constants are usually given in mdyn A-1 (bond length), mdyn A rad"2 (valence angle bending and out-of-plane distortion) and mdyn A (torsion angle deformation). 

Now we consider the valence angle bending force field as it appears from the DMM picture. For this end the geometry variation given by the vectors eq. (3.139) must be inserted in eq. (3.72) and the required elasticity constant can be obtained by extracting the second order contribution in vectors 6[Pg.260]

Typically, in the MM framework, the increment from the bending is considered a quadratic function of valence angles. The formula for bending eq. (3.151) can be rewritten in this form. This is obtained by substituting eq. (3.140) to the second order expansion eq. (3.151) and significant simplifications based on vector algebra. After that we see that the bending force field constant can be written as ... 

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