THE ASSOCIATION CONSTANT OF A FLEXIBLE MOLECULE AND A SINGLE ATOM - THEORY AND SIMULATION

In the calculation of a complexation constant by molecular simulation, an arbitrary range of coordinates is usually introduced that defines when two molecules are to be considered as "associated," and when they are to be considered as "free " The arbitrariness of this definition leads to an ill-defined association constant. In practice, this does not lead to a less-accurate prediction of the association constant, as long as the complexation is strong. However, when the association constant is so small that the complex has a finite probability to dissociate during the simulation, the arbitrariness in the definition of the complex leads to a large error in the predicted pK. To solve these (conceptual) problems, the statistical thermodynamics of the complexation of a single atom by a larger molecule are reanalyzed. From this analysis a rigorous definition of the complexation constant emerges, based on a thermodynamic argument. The connection between potential of mean force measurements and the free-energy perturbation method (based on a thermodynamic cycle) is illucidated. It is concluded that the former method is the most natural way to obtain the complexation constant. To calculate the potential of mean force, the use of an umbrella sampling technique for the radial distribution function at infinite dilution is crucial. This sampling technique can also be used when a solvent is present explicitly, which requires the use of a well-chosen coupling-constant integration path. Some example calculations are given for simple linear and cyclic chain molecules.