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["Nuno A. G. Bandeira" <nuno.bandeira@ist.utl.pt>]

Anglade Pierre-Matthieu wrote:

> >     (2) Can the Abinit perform the calculation of the electronic Mulliken
> > population analysis ?
>
> Sorry I don't know.

Say you have an MO with 2 AOs:

PHI=c1.chi1+c2.chi2

When you square it:

PHI^2=c1^2.chi1^2 + c2^2.chi2^2 + 2c1c2.chi1.chi2

when you integrate over all space you have:

1= c1^2 + c2^2 + 2c1c2.S12

2c1c2.S12 is called the "(Mulliken) overlap population" (S12 being the 
overlap integral) and it is in a way a measure of the bond strength. 
There's a problem here with the cross term 2c1c2.chi1.chi2 because you 
can't assign the overlap charge density to any one AO. So what Mulliken 
did was to democratically assign the charge density equally between the 
2 AOs thus:

chi1.chi2 ~ (chi1^2+chi2^2)/2

so this way you have "Mulliken gross atomic population" in atoms 1 and 2

PHI^2 = (c1^2+c1c2)chi1^2 + (c2^2+c1c2)chi2^2

N1 = c1^2+c1c2
N2 = c2^2+c1c2

With these values you can obviously define a Mulliken charge. With big 
basis sets some values may become chemically counterintuitive, for 
instance with diffuse gaussian basis functions, but they are nonetheless 
widely used as the main method of population analysis.

The Mulliken population has been extended to solids by Hoffmann with the 
creation of COOP (crystal orbital overlap population). You can read his 
seminal article in JACS,1983,105,3528 and in his book (Solids and 
Surfaces: A Chemist's view of bonding in extended structures, Wiley-VCH)


Regards,
--
Nuno A. G. Bandeira, AMRSC
Graduate researcher and molecular sculptor
Inorganic and Theoretical Chemistry Group,
Faculty of Science
University of Lisbon - C8 building, Campo Grande,
1749-016 Lisbon,Portugal
http://cqb.fc.ul.pt/intheochem/nuno.html
Doctoral student @ IST,Lisbon
--