Sums in the Energy Equation Modes of Motion

The four steric energy sums in Eq. (4-13) corresponding to sketching, bending, and torsional modes of motion and van der Waals inhamolecultu interaction appear to be about the smallest number one can use in an accurate MM geomehy minimization. 

If we cany out a Taylor s expansion of the potential energy about the equilibrium length of an isolated chemical bond, we get 

The potential energy is never known in an absolute sense but is always measured relative to some arbihary benchmark. Let us set the potential energy to zero at the equilibrium bond length, Vq = 0, which is the bottom of the potential energy well. 

first derivative at the rniniiriurn (or other extremum) of a Ciiiietioii is /ero, dV/dr] 0. The first nonzero term in Eq. (4-15) eoiitains l.d V/dr ] whieh is 

One can start building up a list of MM3 parameters by use of the TINKER analyze command. Don t expect to build up the entire set, which occupies about 100 pages in the MM3 user s manual, but do obtain a few representative examples to get an idea of how a parameter set is constr ucted. From previous exercises and projects, you should have input and output geometries for an alkene, an alkane, and water. From these, the object is to determine the stretching and bending parameters for the C—C, C=C, C—H, and O—H bonds. The C—H bond parameters are not the same 

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