6.4 Evaluation of Simulation Experiments

In addition to basic thermodynamic observables such as internal energy (eq. 6.1) and pressure (equ. 6.2) many more details about the structure and the dynamics of statistical-mechanical systems may be accessed. Let us consider two such quantities, the pair correlation function $g(r)$ and the velocity autocorrelation function $C(t)$.


PROJECT MD/MC (LENNARD-JONES): In your Lennard-Jones MD and MC programs, include a procedure to calculate averages of the total potential energy and the virial as defined by

$$W\equiv\sum_{i}\vec{K}_{i}\cdot \vec{r}_{i} = -\frac{1}{2}\sum_{i}\sum_{j} \vec{K}_{ij}\cdot \vec{r}_{ij}$$

From these compute the internal energy and the pressure. Compare with results from literature, e.g. [MCDONALD 74,VERLET 67]. Allow for deviations in the $5-10\,\%$ range, as we have omitted a correction for the finite sample size (`cutoff correction').