Mulliken charges are mathematical constructions that have no relation to physical charges. They depend extremely on the basis set, you can easily obtain nonsense charges with imbalanced basis sets with diffuse functions. With small basis sets it gives some credible charges. CHELPG and other charges have more connection to physics. Please use those. But I prefer the electrostatic potential mapped on the molecular surface.

Mulliken charges are mathematical constructions that have no relation to physical charges. They depend extremely on the basis set, you can easily obtain nonsense charges with imbalanced basis sets with diffuse functions. With small basis sets it gives some credible charges. CHELPG and other charges have more connection to physics. Please use those. But I prefer the electrostatic potential mapped on the molecular surface.

Dear Gabor

Thanks for your answer. It seems that your opinion is very close to mine.

Mulliken is just  partitioning of density matrix and basis set dependent. It is too old and has lots of deficiency. It does not have any physical meaning.

Dear Sirous,

Thanks for your answer. I wonder why Mulliken analysis is still part of the Gaussian 09 output?

Mulliken charges do not represent a physical observable. The fact that they are basis set dependent is not the worse defect, given that many properties (including the geometry) are basis set and method dependent. Anyway, it is important to properly define what you mean by "experimental ionic character of the atoms". Written like that it is lacking of a proper physical ground. Which physical observable you refer to? Last but not least, atoms in a molecule or in a solid must be defined otherwise also the physical observable cannot be directly related to a given atomic property. One such way is Bader's partitioning of the electron density (a physical observable that can be in fact measured). Charges fitting the electrostatic potential are also sound, because they do refer to a physical observable. Anyway it is obvious that Bader's charges and electrostatic potential fitting do not have to coincide: they are two different definitions, both based on observables.

I think it is just the author's decision because when you have density matrix , you can have mulliken population analysis with no cost, also there are lots of researchers who still use it. Also, the definition of  atomic charge  is arbitrary. You can not rely on them. The concept of atomic charge is misleading. I prefer to work with charge density which can be obtained by experiment. Unfortunately different definitions (mulliken, Lowdin and Lowdin based partitioning schemes, nbo , aim provide us with different atomic charge.  In addition, for instance 0.005e dose not have any meaning, it means you have chopped electrons!!!!...

Piero Macchi, in solids I found close agreement between Bader's charges and Born's charges derived when doing IR intensity evaluations. Anyway,  Bader's partitioning of the electron density is not just one way to define basins... it is the unique way to partition the space which is physically meaningful: atomic properties derived by integrating the appropriate operator over the atomic basin defined according to the Bader's criteria,  have definite values and are,  in principle,  real observables.

Mauro, thanks for your comment. Of course Bader's partitioning provide definite values for atomic properties. It however provides them also for non-nuclear attractors, which are a bit difficult to include within the frame of chemistry. Moreover, your concept of "physically meaningful" requires some explanation, otherwise it could be arbitrary. For me it could be physically meaningful to use the atomic charges fitting the electrostatic potential (incidentally an observable), if my aim is that of producing a simplified description of the electrostatics of a molecule. It is known, instead, that Bader's partitioning is not so efficient in terms of electrostatics, because you need high order poles to represent the electrostatic potential. Moreover, one should distinguish observable and measurable. Bader's atoms are observable, but you need to measure X-ray or gamma-ray or TEM diffraction images and do a reconstruction of the electron density with a particular model before computing them. So can we really say they are measurable? What I really measure (the scattering of a radiation) does not depend at all from the partitioning of atoms in a molecule (whatsoever partitioning). It depends on the total electron distribution of a crystal (or maybe a single molecule using in the future X-FEL). On the other hand, if you want to determine a crystal structure, an atomic partitioning is quite useful to fit a reasonable model, but then much simpler schemes than Bader's are normally used and in fact more efficient.

Well, Piero, you are right. "Physically meaningful" should be explained.  I referred to the fact that the energy of an atom has a unique and definite value only if it is calculated over an atomic basin as defined by Bader himself.  Otherwise,  on different partitionings,  formally equivalent operators give different values of energy.  This has nothing to do with the practical measurability of a quantity... and other quantities not directly derivable by the Bader's analysis could be very useful... Anyway,  as I said,  Born's charges which express the response of an ion to an applied electric field, 

... continued... are identical to the Bader's charges,  so that a physical interpretation of the latter quantities is available. 

"I wonder why Mulliken analysis is still part of the Gaussian 09 output?"

Partial charges on the atoms itself have no physical meaning. However, this does not mean that we should not use it.

If what your looking for are charges on atoms, I usually opt for Hirshfield charges instead of Mulliken charges. 

http://www.gaussian.com/g_tech/g_ur/k_population.htm

Dear researchers

Thank you for suggesting alternative partial charge analysis instead of Mullikan analysis such as Bader and Hirshfeld charges. I must try them to check their reliability in my case.

We have used the ESP(MK) and NBO options to the Population keywork in G09 to generate more meaningful charges. This site explains the fitting:

http://www.cup.uni-muenchen.de/ch/compchem/pop/mk.html

Thanks Philippe I have to try your suggested method to check its reliability in my case.

No mulliken is a local observable its can't be measured in a lab the only thing that you can mesure is the total charge for that reason you can't use mulliken as a indicator or ionic character, additionally mulliken depends of the method and basic set that you are using because is a local observable that had a different functional form in each level of theory..

Dear Rumero, 

if it is the case, then what other charges calculation you suggest to find charges on atoms?

thanks....

Dear Ragavendran

Alternative partial charge analysis instead of Mullikan analysis such as Bader and Hirshfeld charges can be suggested.

What basis set  is best for atomic charges?

dear friends please suggest me how to draw the structure of coordination compounds in gaussian software.....bcoz i have draw them several time but not succeed ...while allowed to run in gaussian software it shows link died quickly.......please help me in this regard.

although no compilations in simple molecules while running in gaussan

with regards

rayees ahmad

Net atomic charges, also called partial charges or partial atomic charges, are commonly used for two different purposes: (1) to quantify the transfer of electrons between atoms in a material as computed by quantum chemistry and (2) to construct force-fields (for classical molecular dynamics or Monte Carlo simulations) that approximately reproduce the electrostatic potential surrounding the material. While quantum chemical topology (QCT), also called quantum theory of atoms in molecules (QTAIM), often describes electron transfer in buried atoms with reasonable accuracy, the QCT atomic charges are not suitable to construct point-charge models for classical force-fields, because the QCT atomic multipoles are large in magnitude. (The QCT method can be used to construct accurate force-fields using multi-centered polyatomic multipole expansions, but these are more complicated than the simple point-charge based force-fields often used.) On the other hand, electrostatic potential derived point charges (e.g., CHELP, CHELPG, ESP, Merz-Singh-Kollman, REPEAT) have reasonable accuracy for reproducing the electrostatic potential surrounding the material, but these do not accurately describe electron transfer for buried atoms.

The density –derived electrostatic and chemical (DDEC) methods solve this problem by partitioning the electron density to simultaneously reproduce atomic chemical states and the electrostatic potential surrounding the material with excellent accuracy. The latest generation (called DDEC6) is described in these papers: (a) T. A. Manz and N. Gabaldon Limas, “Introducing DDEC6 atomic population analysis: part 1. Charge partitioning theory and methodology,” RSC Advances, 6 (2016) 47771-47801 (http://dx.doi.org/10.1039/C6RA04656H) and (b) N. Gabaldon Limas and T. A. Manz, “Introducing DDEC6 atomic population analysis: part 2. Computed results for a wide range of periodic and nonperiodic materials,” RSC Advances, 6 (2016) 45727-45747 (http://dx.doi.org/10.1039/C6RA05507A). It gives net atomic charges that are closely correlated to many experimental properties as described in those articles. The DDEC6 method is implemented in the free Chargemol program (http://ddec.sourceforge.net) which can analyze results of GAUSSIAN, VASP, and other quantum chemistry programs.