Definition of a topological atom and its properties

With the atomic basins defined in this way, we can now calculate the volume of each atom and other properties such as charges, from which dipole moments can be inferred, and so on. This is done simply by integrating the electron density over space within a defined atomic basin (denoted 12), and truncating the calculation at atoms on the surface of a molecule at a chosen level of electron density. The volume is then defined as the integral over all volume elements t of an atomic basin 12. 

Integration of the electron density over the volume of an atomic basin then provides us with the total electron population N(12) belonging to this atomic basin 12. 

3D representations of the N and H atoms in HN=NH defined by their interatomic surfaces (IAS) and one surface of constant electron density, p — 0.001 au. Two different perspectives are shown for better visibility. 

Taking into account the positive charge of the nucleus Zq, we are able to calculate the atomic charge q Si). 

The atomic dipole moment M(52), a further fundamental property of an atom in a moleeule, is defined for an atomic basin SI as the integral of the charges over aU volume elements within S2, with the origin being set to the nuclear position. This quantity therefore measures the shift of the charge cloud relative to the nucleus. 

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