Fig. 4. Results of classical and PIMD simulations.

The recently developed estimators based on perturbation theory were used to evaluate structural and electronic observables (30). (A) Comparison of the interatomic distance distributions, $\mathit{h}(\mathit{r})={\langle \frac{2}{\mathit{N}(\mathit{N}-1)}{\displaystyle {\sum }_{\mathit{i}<\mathit{j}}^{\mathit{N}}}\mathrm{\delta }(\mathit{r}-||\overrightarrow{{\mathit{r}}_{\mathit{i}}}-\overrightarrow{{\mathit{r}}_{\mathit{j}}}||)\rangle }_{\mathit{P},\mathit{t}}$, obtained from GDML (blue line) and DFT (dashed red line) with classical MD (main frame), and PIMD (inset). a.u., arbitrary units. (B) Probability distribution of the dihedral angles (corresponding to carboxylic acid and ester functional groups) using a 20 ps time interval from a total PIMD trajectory of 200 ps.