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The potential of mean force () is usually applied in the Boltzmann inversion method as a first guess for the effective pair interaction potential that ought to reproduce the correct radial distribution function in a mesoscopic simulation. [5]
However, the physical meaning of these statistical PMFs has been widely disputed, since their introduction. [4] [5] [8] [9] The main issues are: The wrong interpretation of this "potential" as a true, physically valid potential of mean force; The nature of the so-called reference state and its optimal formulation;
An alternative to free-energy perturbation for computing potentials of mean force in chemical space is thermodynamic integration. Another alternative, which is probably more efficient, is the Bennett acceptance ratio method. Adaptations to FEP exist which attempt to apportion free-energy changes to subsections of the chemical structure. [5]
Forces derivable from a potential are also called conservative forces. The work done by a conservative force is = where is the change in the potential energy associated with the force. The negative sign provides the convention that work done against a force field increases potential energy, while work done by the force field decreases potential ...
The potential functions representing the non-bonded energy are formulated as a sum over interactions between the particles of the system. The simplest choice, employed in many popular force fields, is the "pair potential", in which the total potential energy can be calculated from the sum of energy contributions between pairs of atoms ...
If the force is not conservative, then defining a scalar potential is not possible, because taking different paths would lead to conflicting potential differences between the start and end points. Gravitational force is an example of a conservative force, while frictional force is an example of a non-conservative force.
Alternatives to umbrella sampling for computing potentials of mean force or reaction rates are free-energy perturbation and transition interface sampling. A further alternative, which functions in full non-equilibrium, is S-PRES.
The radial distribution function is an important measure because several key thermodynamic properties, such as potential energy and pressure can be calculated from it. For a 3-D system where particles interact via pairwise potentials, the potential energy of the system can be calculated as follows: [6]