[Wien] The correlation and exchange formulas of potential and energy for PBE functional

[Gavin Abo]

 From what I see at that link, the exchange-correlation energy is given by:

Exc = Ex + Ec (1)

The exchange-correlation potential [ 
http://susi.theochem.tuwien.ac.at/events/ws2015/Tran-talk_xc.pdf (slide 
5) ] is:

Vxc = d(Exc)/d(rho) (2)

Plugging (1) into (2):

Vxc = d(Ex + Ec)/d(rho) (3)

 From the sum-rule [ 
https://en.wikipedia.org/wiki/Sum_rule_in_differentiation ]:

Vxc = d(Ex)/d(rho) + d(Ec)/d(rho) (4)

Let (4) take the form:

Vxc = Vx + Vc (5)

where

Exchange potential: Vx = d(Ex)/d(rho) (6)

Correlation potential: Vc = d(Ec)/d(rho) (7)

Page 112 of the WEIN2k 16.1 usersguide has:

individual keywords : EX_PBE EC_PBE VX_PBE VC_PBE

In some form, those are probably the potential equations that the PBE 
code is based on.
If not, at least the variable names Vx and Vc in equation (6) and (7) 
match quite nicely with the keywords VX_PBE and VC_PBE, respectively.

On 1/16/2017 11:39 AM, Fecher, Gerhard wrote:
> Did you read and understand https://en.wikipedia.org/wiki/Local-density_approximation ?
>
> Ciao
> Gerhard
>
> DEEP THOUGHT in D. Adams; Hitchhikers Guide to the Galaxy:
> "I think the problem, to be quite honest with you,
> is that you have never actually known what the question is."
>
> ====================================
> Dr. Gerhard H. Fecher
> Institut of Inorganic and Analytical Chemistry
> Johannes Gutenberg - University
> 55099 Mainz
> and
> Max Planck Institute for Chemical Physics of Solids
> 01187 Dresden
> ________________________________________
> Von: Wien [wien-bounces at zeus.theochem.tuwien.ac.at] im Auftrag von Abderrahmane Reggad [jazairdz at gmail.com]
> Gesendet: Montag, 16. Januar 2017 13:27
> An: wien at zeus.theochem.tuwien.ac.at
> Betreff: Re: [Wien] The correlation and exchange formulas of potential and energy for PBE functional
>
> Thank you Dr Gavin for your ansswer
>
> It's what I am looking for .
>
> What about the formulas of the potentials Pc and Px?
>
> Best regards
>
> --
> Mr: A.Reggad
> Laboratoire de Génie Physique
> Université Ibn Khaldoun - Tiaret
> Adresse: BP 144 AL ATTAF AIN DEFLA
> Tel: +213(0)561861963
> Algerie