Approaches Pathways to the Grail

The computational approaches to interpreting the wavefunction have split along two basic approaches. The earliest procedures were based on distributing the elearons between the atoms in a molecule based on the occupancy of the atomic orbitals. Thus, the Hilbert space is subdivided on the basis of where the orbitals are centered. We term this approach the orbital-based method, and discuss three major procedures for dissecting the orbitals. 

The major alternative approach is to subdivide physical space into regions that define the volume occupied by each atom in a molecule. Then, all electrons that are found in this volume are assigned to that atom. One simply integrates p within an atomic basin. The problem is to define the extent of the atomic basin. We term this approach the spatially based method. Two major variants are discussed below. 

Recently, two other methods for determining atomic charge have been developed, neither of which makes reference either to orbitals or to the space associated with a given atom. Instead, one method involves the calculation of the atomic polar tensor, and the second fits the elearostatic potential to an expansion of charges at the atomic nuclei. 

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