# [Pw_forum] Lowdin Charge- sign

Heather Kulik heatherjkulik at gmail.com
Sat Dec 11 07:59:52 CET 2010

```Dear David,

You are right in that the Lowdin charges here refer to the valence electrons
of your system.

The Lowdin charges are calculated as a sum of the projections of the
extended plane wave valence states onto a pseudo-atomic basis (characterized
by the highest valence s, p, d, f states per your output).

The numbers are positive and not negative, as you pointed out, because they
refer to the *number* of electrons (i.e. s, p, and so on).  In your example,
there appears to be approximately four electrons: 1 s-type and 3 p-type
valence electrons attributed to each atom.

The code should also a 'spilling parameter' at the bottom of your output
that tells you how well the projections are capturing the description of the
valence states.   For instance, the projection is capturing 3.96 electrons
per atom in your example.  So, if you expect in your example to have four
valence electrons per atom, then the pseudo-atomic basis is capturing your
extended valence states pretty well.

Hope that helps!
--
Heather K
Postdoc at Stanford University

On Fri, Dec 10, 2010 at 5:54 PM, David Grifith <david.grifith at gmail.com>wrote:

> Dear QE Users
>
> My calculated "Lowdin Charge" values are "positive" as shown below. I
> thought that they must be the charge of the valence electron ! but the sign
> is positive. Also, I don't know that a pseudopotential package like Quantum
> Espresso considers the "core" charge to be calculated or not ?
>
>
>
>     Atom #   1: total charge =   3.9571, s =  0.9145, p =  3.0426, d =
> 0.0000,
>                  spin up      =   1.9786, s =  0.4573, p =  1.5213, d =
> 0.0000,
>                  spin down    =   1.9786, s =  0.4573, p =  1.5213, d =
> 0.0000,
>                  polarization =   0.0000, s =  0.0000, p =  0.0000, d =
> 0.0000,
>      Atom #   2: total charge =   3.9569, s =  0.9154, p =  3.0415, d =
> 0.0000,
>                  spin up      =   1.9785, s =  0.4577, p =  1.5208, d =
> 0.0000,
>                  spin down    =   1.9785, s =  0.4577, p =  1.5208, d =
> 0.0000,
>                  polarization =   0.0000, s =  0.0000, p =  0.0000, d =
> 0.0000,
>      Atom #   3: total charge =   3.9554, s =  0.9153, p =  3.0402, d =
> 0.0000,
>                  spin up      =   1.9777, s =  0.4576, p =  1.5201, d =
> 0.0000,
>                  spin down    =   1.9777, s =  0.4576, p =  1.5201, d =
> 0.0000,
>                  polarization =   0.0000, s =  0.0000, p =  0.0000, d =
> 0.0000,
>      Atom #   4: total charge =   3.9573, s =  0.9164, p =  3.0408, d =
> 0.0000,
>                  spin up      =   1.9786, s =  0.4582, p =  1.5204, d =
> 0.0000,
>                  spin down    =   1.9786, s =  0.4582, p =  1.5204, d =
> 0.0000,
>                  polarization =   0.0000, s =  0.0000, p =  0.0000, d =
> 0.0000,
>      Atom #   5: total charge =   3.9607, s =  0.9155, p =  3.0452, d =
> 0.0000,
>                  spin up      =   1.9804, s =  0.4578, p =  1.5226, d =
> 0.0000,
>                  spin down    =   1.9804, s =  0.4578, p =  1.5226, d =
> 0.0000,
>                  polarization =  -0.0000, s = -0.0000, p = -0.0000, d =
> 0.0000,
>      Atom #   6: total charge =   3.9599, s =  0.9146, p =  3.0453, d =
> 0.0000,
>                  spin up      =   1.9800, s =  0.4573, p =  1.5227, d =
> 0.0000,
>                  spin down    =   1.9800, s =  0.4573, p =  1.5227, d =
> 0.0000,
>                  polarization =  -0.0000, s = -0.0000, p = -0.0000, d =
> 0.0000,
>      Atom #   7: total charge =   3.9600, s =  0.9148, p =  3.0452, d =
> 0.0000,
>                  spin up      =   1.9800, s =  0.4574, p =  1.5226, d =
> 0.0000,
>                  spin down    =   1.9800, s =  0.4574, p =  1.5226, d =
> 0.0000,
>                  polarization =  -0.0000, s = -0.0000, p = -0.0000, d =
> 0.0000,
>
> --
> Sincerely Yours
> David G.
> JCU
>
>
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>
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