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
