The natural charge (also known as NPA charge) and "NBO charge" are the same thing, the latter is incorrect name of the former. The formulism of Mulliken charge and NPA charge are essentially identical, the key difference is that the Mulliken charge is calculated under original basis functions, while NPA charge is derived based on natural atomic orbitals (NAOs).

If your purpose is studying electrostatic interaction between metal and gas molecule based on atomic charges, both Mulliken and NPA charges are not good choice, because their reproducibility of electrostatic potential around molecular van der Waals surface are relatively unsatisfactory. ESP fitting charges (e.g. CHELPG, MK, HLY...) and ADCH charge (DOI: 10.1142/S0219633612500113, which can be computed by Multiwfn program) are generally better choice.

thank you Tian Lu .this is really helpfull to me in my study.

Adding on top of Tian Lu's answer. You might be interested in Martin & Zipse's benchmark (J. Comput. Chem., 2005, 26, 97-105), as well as my own study on different types of effective atomic charge describing the charge distribution in Transitiom metal, specifically Mn(salen), complexes (Int. J. Quantum Chem., 2014, 114, 525-533).

In general, both Mulliken and Lowedin charges are highly dependent on the basis set and may lead to some population inversions when handling metal atoms (i.e. the metal gets negative and the ligand becomes positive). As Mentioned above, CHelpG charges and other ESP fitting schemes are good for developing molecular mechanics forcefields, but may give irrealistic results for atoms inside dense coordination spheres (for example hexavalent atoms). NBO/NPA is usually a sensible approach when trying to attain some physical insight or descriptors for reactivity, as the use of natural orbitals makes it less prone to errors due to the basis set. Finally, Bader's AIM/QTAIM (which is my main speciality) trends to overemphatize charge separation, and forces you to also consider effective atomic dipole moments to get an accurate representation of the charge distribution.

I hope this helps.

Atom, as a spherically symmetric system, has no dipole moment, Filipe.

Dear Eugene,

QTAIM atomic basins are not spherical.

If they are not spherical, then they are not atomic, Filipe.