After the alignment of all 3 million snapshots with the medoid structure, we obtain an estimate of the electron density by performing a 3D KDE based on the sampled electron positions. A visualization of the obtained density compared with one obtained within the BOA is shown in Figure . Although there are some artifacts from the random sampling in the non-BO density, and although the BO density is not vibrationally averaged, the agreement between the two treatments is striking. In conclusion, we introduced a new definition of molecular structure that is based on the probabilistic interpretation of quantum mechanics, and suggested a practical method for obtaining the structure(s) using MCMC sampling and clustering analysis. We applied our approach to the homonuclear D + 3 molecule, and demonstrated that our analysis unambiguously yields an equilateral triangular structure very similar to the one obtained within the BOA. Furthermore, we demonstrated that our approach allows a glimpse into the electronic structure of molecules by extracting vibrationally averaged electron densities. With this powerful new paradigm, we are looking forward to the emergence of future methods that can treat larger molecules in a fully quantum-mechanical fashion and investigate systems such as small chiral molecules, where it is known that both enantiomeric structures must be present with equal probability. In contrast to our interpretation of molecular structure in terms of statistical correlations, understanding the emergence of a purely classical structure-e.g., the fact that chiral molecules exist in unique enantiomers showing optical activity-is still an open problem that remains to be solved.