Developing paradigms of chemical bonding: adaptive natural density partitioning

A method of description of the chemical bonding combining the compactness and intuitive simplicity of Lewis theory with the flexibility and generality of canonical molecular orbital theory is presented, which is called adaptive natural density partitioning. The objects of chemical bonding in this method are n-center 2-electron bonds, where n goes from one (lone-pair) to the maximum number of atoms in the system (completely delocalized bonding). The algorithm is a generalization of the natural bonding orbital analysis and is based on the diagonalization of the blocks of the first-order density matrix in the basis of natural atomic orbitals. The results obtained by the application of the algorithm to the systems with non-classical bonding can be readily interpreted from the point of view of aromaticity/antiaromaticity concepts. The considered examples include Li-4 cluster and a family of planar boron clusters observed in molecular beams.