Appendix 1

Exchange and correlation functionals and potentials

(a) Dirac-Slater exchange energy functional and potential

 

 

 

 

 

 

 

 

(b) von Barth-Hedin exchange energy functional and potential 

 

 

 

 

 

 

 

 

 

 

 

 

(c) Becke exchange energy functional and potential 

 

 

 

 

 

 

 

(d) Perdew-Wang 91 exchange energy functional and potential 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

(e) Perdew-Zunger LSD correlation energy functional and potential

 

 

 

 

 

where sgn(s ) is 1 for and 1 for  

low density limit

 

 

high density limit

 

 

Parameter

i=0

i=1

     

g

0.1423

0.0843

b 1

1.0529

1.3981

b 2

0.3334

0.2611

A

0.0311

0.0155

B

0.0480

0.0269

C

0.0020

0.0007

D

0.0116

0.0048

     

 Table A1 - Constants used in the Perdew-Zunger parametrization of the Ceperley-Alder quantum Monte-Carlo results for a homogeneous electron gas

 

(f) Vosko-Wilk-Nusair correlation energy functional

 

 

 

 

 

 

 

 

 

Parameter

I

II

III

       

Ai

0.0621841

0.0310907

0.033774

bi

3.72744

7.06042

1.131071

ci

12.9352

18.0578

13.0045

x0i

0.10498

0.32500

0.0047584

       

 Table A2 - Constants for the Vosko-Wilk-Nusair parametrization

 

(g) von Barth-Hedin correlation energy functional and potential

 

 

 

 

 

 

 

 

 

 

 

 

 

(h) Perdew 86 correlation energy functional and potential

 

 

 

 

 

 

 

 

 

 

  

(i) Perdew 91 correlation energy functional and potential

 

 

 

 

 

 

 

 

 

 

 

 

(j) Lee, Yang and Parr correlation energy functional and potential