Lennard-Jones potential energy function molecular dynamics calculations

The second simulation technique is molecular dynamics. In this technique, which was pioneered by Alder, initial positions of theparticles of a system of several hundred particles are assigned in some way. Displacements of the particles are determined by numerically simulating the classical equations of motion. Periodic boundary conditions are applied as in the Monte Carlo method. The first molecular dynamics calculations were done on systems of hard spheres, but the method has been applied to monatomic systems having intermolecular forces represented by the square-well and Lennard-Jones potential energy functions, as well as on model systems representing molecular substances. Commercial software is now available to carry out molecular dynamics simulations on desktop computers. ... 

Two simulation methods—Monte Carlo and molecular dynamics—allow calculation of the density profile and pressure difference of Eq. III-44 across the vapor-liquid interface [64, 65]. In the former method, the initial system consists of N molecules in assumed positions. An intermolecule potential function is chosen, such as the Lennard-Jones potential, and the positions are randomly varied until the energy of the system is at a minimum. The resulting configuration is taken to be the equilibrium one. In the molecular dynamics approach, the N molecules are given initial positions and velocities and the equations of motion are solved to follow the ensuing collisions until the set shows constant time-average thermodynamic properties. Both methods are computer intensive yet widely used. 

We have developed such a force field, named SPEEDY (Simplified Parameters for Energy Evaluation and DYnamics). SPEEDY uses the QPACK protein model and residue interaction potentials.- The terms of the potential function are analogous to those used in molecular mechanics calculations. Since the backbone virtual dihedral and bond angles are dependent on the complicated geometry of the polypeptide backbone, these terms are not represented independently. Residue interactions are represented by Lennard-Jones type functions scaled by their... 

The success of a molecular mechanics or molecular dynamics simulation depends on the proper choice of expressions for the calculation of the conformational energy. Suppose you distrusted the Lennard-Jones (12,6) potential for assessing a particular polypeptide conformation and replaced the repulsive term by an exponential function of the form e . (a) Sketch the form of the potential energy and locate the distance at which it is a minimum, (b) Identify the distance at which the exponential-6 potential energy is a minimum. 

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