CCL: negative values in Mulliken spin distribution

[Marcel Swart <marcel.swart##icrea.cat>]

Susi,

we’re saying the same thing, *but* with one big difference.

The probability density you talk about leads to a Mulliken

population analysis, be it the total or separated for spin-up

and spin-down. Like I said, this population analysis is a 

representation of the charge density, which are (usually)

being assigned to atoms. Whether you take the total charge,

or the difference between alfa- and beta-populations is to

get “spin-density charges” is irrelevant for the concept of

how you get from the density to the atomic populations.

There are many different ways how to get from a charge

density to an atomic population analysis, of which Mulliken

is one choice. But these atomic populations (and hence

the Mulliken (spin) charges) DO directly give a representation

of the charge density; how well it represents it is another issue.

That was my (maybe too subtle) point.

Marcel

On 23 Jan 2014, at 19:27 , Susi Lehtola susi.lehtola_._alumni.helsinki.fi <owner-chemistry ~~ ccl.net> wrote:

First of all, to set things straight, it is a simplification of the
charge density, which are being assigned to atoms. Hence,
yes, it is not a real density.

No, it is not. You're mixing concepts. Mulliken charges and Mulliken
spin charges are not the same thing. The first deals with
electric charge, while the second deals with spin. (Also, I was
talking about a probability density, which is always non-negative.)

In the former you substract electronic charge from the nuclear
charge to get the net atomic charge. For instance, O in H2O has a
negative charge due to a relative surplus of electrons. (Here,
different methods give a variety of different answers, for example
Löwdin can assign O to be positive!)

In the latter you substract the amount of spin down electrons from the
amount of spin up electrons. The value 0 will mean that there are an
equal amount of spin up and down electrons for the atom. A positive
value will mean that spin up electrons are in surplus for the atom,
while a negative value will mean that spin down electrons are in
surplus.

If you calculate a spin polarized system, e.g. the oxygen molecule with
spin multiplicity M=3, you'll have a net positive spin charge in the
system, since you'll have two more spin up electrons than spin down
electrons. Here, both oxygen atoms will have spin charge +1, although
the electric charge is 0.

On the other hand, even spin neutral systems may have atoms with large
negative and large positive charges, e.g. in the case of
antiferromagnetic couplings between atoms.

===================================
Prof. Dr. Marcel Swart

ICREA Research Professor at
Institut de Química Computacional i Catàlisi
Universitat de Girona

Facultat de Ciències
Campus Montilivi

17071 Girona

Catalunya (Spain)

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