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

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-boun...@zeus.theochem.tuwien.ac.at] im Auftrag von Abderrahmane
Gesendet: Montag, 16. Januar 2017 13:27
An: wien@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

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