The fundamental assumption underlying the MM method is that the positions of the atoms of a molecule, ion, solvate or crystal lattice are determined by forces between pairs of atoms (bonds, van der Waals interactions, hydrogen bonding and electrostatic interactions), groups of three atoms (valence angles) and groups of four atoms (torsional angles, planes) (Figure 3.1).
The energies E i resulting from these forces are related to the positions of the nuclei in a molecule, and therefore enforce the entire molecular structure. The energy lost by moving atoms away from their ideal positions is related to the strain or steric energy, U total [Eq. (3.1)] as a function of the nuclear geometry.
Minimization of the strain energy U total by rearrangement of the nuclei leads to an optimized structure and a value for the minimized strain energy.
It is important to realize that, for any arrangement of more than two atoms, the strain energy minimized structure does not have ideal (zero strain) distances and angles. This is demonstrated in the case of ethane (Figure 3.2) where, due to the repulsion of the protons, the experimentally determined CรC distance in ethane of 1.532 ร
, which is well reproduced by empirical force-field calculations, is slightly longer than the ideal CรC separation of 1.523 ร
used in the MM2 force field [128, 129]. Further examples are presented in Table 3.1. With increasing substitution of the carbon atoms, the CรC separation increases up to 1.611 ร
in tris-t-butylmethane.
Similar effects are observed in coordination compounds. In Table 3.2, 1) calculated and experimentally determined CoรN distances for various cobalt(III) hexaamines, 1) MOMEC 97 [89] required Hyperchem for molecule display and building. MOMEC 3 [90] is a molecular mechanics program which was designed especially for coordination and inor-ganic compounds. MOMEC 2007 is freely available for academic use for Windows and Unix/Linux platforms [91].