Force field parameter definition

Like many other chemical concepts the concept of strain is only semi-quantitative and lacks precise definition. Molecules are considered strained if they contain internal coordinates (interatomic distances (bond lengths, distances between non-bonded atoms), bond angles, torsion angles) which deviate from values regarded as normal and strain-free . For instance, the normal bond angle at the tetra-coordinated carbon atom is close to the tetrahedral value of 109.47°. In the course of force field calculations these normal values are defined more satisfactorily, though in a somewhat different way, as force field parameters. 

The results for thrombin show that our previous parametrization of the LIE coefficients holds rather well in this case, provided that a constant term of -2.9 kcal/mol is added. At present it is not clear to us why thrombin would require such a constant term while, e.g., trypsin does not, but this issue is currently under investigation (see also Ref. 47 for a discussion of thrombin versus trypsin). Furthermore, one should note that with our computational procedures and the Gromos87 force field the results for thrombin inhibitors differ from those of Ref. 35 as well as Ref. 43. That is to say, three independent studies involving thrombin inhibitors have arrived at significantly different parametrizations of the LIE equation, that in all cases reproduce the experimental data well. It therefore seems clear that the differences in the computational procedures have a definite effect on the parameters of the binding energy approximation. 

A more basic difficulty and one not yet adequately resolved is that encountered in the use of artificial models to represent molecules. From a rigorous point of view the entire behavior of a molecular encounter is determined by the force field surrounding each molecule. By representing molecular force fields by artificial models we avoid the impossible mathematical problem involved in the rigorous approach. The result, however, is to introduce an entirely new set of molecular parameters which remain as yet unpredictable from simpler molecular properties. In the case of the hard sphere model we have introduced the molecular diameter additional parameters which were somewhat concealed in the discussion, namely, the two accommodation coefficients, one for velocity transfers between molecules in collision and the other for collision between molecules and surfaces. 

For the more complicated molecular models such as, for example, those that assume central forces, we replace the above set of parameters by a new set involved in defining the force field. If we add to this the problem of complex molecules (i.c., those with internal structure), then there is the additional set of parameters needed to define the interactions between the internal molecular motions and the external force fields. From the point of view of the hard sphere model this would involve the definition of still more accommodation coefficients to describe the efficiency of transfer of internal energy between colliding molecules. 

Figure 1 Definition of basic parameters in force fields. Bond lengths (/), angles (d), torsion angles (co), and nonbonded distances (r) are exemplified in //-propanol.

The versions of MM potentials (generally called force fields) for solvent molecules may be simpler, and in fact limited libraries of MM parameters are used to describe internal geometry change effects in liquid systems. We report in Table 8.4 the definitions of the basic, and simpler, expressions used for liquids. 

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