Figure 7. Convergence in KB98 rotameric systems.

For each of the eight idealized rotameric systems, we sampled with replacement from the 5 × 10⁴ configurations representing the system, according to the Boltzmann distribution determined by the relative energies of each configuration. These samples were then used to estimate the marginal entropies of all combinations of 1–4 torsions prior to application of MIST (blue lines) or MIE (red lines) to compute −TS°. This procedure was repeated 50 times for each system, and the deviation of each run from the exact result to the same order approximation are shown (pale lines), as well as the mean and standard deviation across the 50 runs (thick lines). Results for bound (top row) and unbound (bottom row) KB98 are shown here. Results for other molecules were similar and can be seen in Figures S1, S2, and S3.