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This work introduces a local form for the source function, from each atom, for the electron-density value at a given point. The source function enables one to equate the value of the electron density at any point within a molecule to a sum of atomic contributions and thus to view properties of the density at representative points, such as the bond critical points, from a new perspective. The local form of the function introduces further detail. When plotted along a bond path and with reference to the bond critical point (b.c.p.), the source function shows which regions of the atoms involved in the bonding are accumulating or removing electronic charge at the b.c.p. The local form of the source function therefore represents an interesting fingerprint of a given bonding interaction. The local source may be expressed as a sum of two contributions, related to the kinetic energy density and electronic potential energy density, respectively. This approach gives further physical insight into why an atomic region is accumulating or removing charge at the b.c.p. The local form of the source function is applied to the study of the second-row diatomic hydride series and of a number of prototypical hydrogen-bonded systems. Differences in the local source contributions to the density at bond critical points due to chemical bonding (deformation density) and crystallization (interaction density) are also explored and found to be more informative and experimentally detectable than are the corresponding changes for the bond-critical-point properties of weak intermolecular interactions. This result might be of potential interest when judging the data quality of a charge-density experimental determination. Although the present paper deals with electron densities derived from theoretical computations only, both the source function and its local form should also be easily obtainable from a charge-density quality X-ray diffraction experiment.
