Functional groups expressed as graphs extracted from the Laplacian of the electron density

The valence charge concentration shell, as determined by the Laplacian of the electron density, is used as a source of quantum topological graphs, called L-graphs. A considerable number of such graphs are extracted from the ab initio wave functions of 31 molecules calculated at the B3LYP/6-311+G(2d,p)//B3LYP/6-311+G(2d,p) level, covering common functional groups in organic chemistry. We show how L-graphs can be constructed from a largely transferable subgraph called atomic L-graph. We investigate the topological stability of the L-graphs as a function of the basis set. Reliable and consistent atomic L-graphs are only obtained with basis sets of triple-zeta quality or higher. The recurrence of invariant motifs or subgraphs in the L-graphs enables the isolation of 16 atomic L-graphs.