Samples were drawn from up to 14.4 million “observations” of the dihedral angles of the R,S stereoisomer of tartaric acid, a molecule with 7 internal-rotation degrees of freedom, obtained from molecular-dynamics trajectories of this molecule by Hnizdo et al.4 (link) The simulations used a box of 72 molecules in the NVT ensemble at 485 K; the details are given in ref. 4 (link). The resulting marginal distributions of the seven dihedral angles of R,S-tartaric acid are displayed in Figure 2 as smoothed histograms. Correlations among some pairs of dihedral angles are illustrated in Figure 3 by two-dimensional contour plots.
To minimize correlations between different “observations,” the molecular-dynamics trajectory was 20 ns long, and only snapshots separated by 100 fs were utilized, each snapshot being that of 72 independent molecules. The time ordering of the full 14.4 million set of the seven dihedral angles of tartaric acid obtained in this way was then randomly shu²ed, so that the convergence behavior of entropy estimates as a function of (pseudo-)random-sample size n, as opposed to the trajectory length in time, could be investigated.
To minimize correlations between different “observations,” the molecular-dynamics trajectory was 20 ns long, and only snapshots separated by 100 fs were utilized, each snapshot being that of 72 independent molecules. The time ordering of the full 14.4 million set of the seven dihedral angles of tartaric acid obtained in this way was then randomly shu²ed, so that the convergence behavior of entropy estimates as a function of (pseudo-)random-sample size n, as opposed to the trajectory length in time, could be investigated.
