MOLPRO

17 THE DENSITY FUNCTIONAL PROGRAM 114
17.4 Density Functionals
In the following, ρ α and ρ β are the α and β spin densities; the total spin density is ρ;
The gradients of the density enter through
σ αα = ∇ρ α · ∇ρ α ,σ ββ = ∇ρ β · ∇ρ β ,σ αβ = σ βα = ∇ρ α · ∇ρ β ,σ = σ αα + σ ββ + 2σ αβ (5).
χ α =
√
σαα
ρ 4/3 α
, χ β =
√ σββ
ρ 4/3
β
. (6)
υ α = ∇ 2 ρ α ,υ β = ∇ 2 ρ β ,υ = υ α + υ β . (7)
Additionally, the kinetic energy density for a set of (Kohn-Sham) orbitals generating the density
can be introduced through
τ α =
α
∑
i
|∇φ i | 2 ,τ β =
β
∑
i
|∇φ i | 2 ,τ = τ α + τ β . (8)
All of the available functionals are of the general form
F [ρ s ,ρ ¯s ,σ ss ,σ ¯s ¯s ,σ s ¯s ,τ s ,τ ¯s ,υ s ,υ ¯s ] =
∫
d 3 rK (ρ s ,ρ ¯s ,σ ss ,σ ¯s ¯s ,σ s ¯s ,τ s ,τ ¯s ,υ s ,υ ¯s ) (9)
where ¯s is the conjugate spin to s.
Below is a list of keywords for the functionals supported by MOLPRO. Additionally there are
a list of alias keywords deatailed in the next section for various combinations of the primary
functionals listed below.
PBEC
PW86
B95
TH4
TH2
ECERF
PBE Correlation Functional
doi:10.1103/PhysRevLett.77.3865
.. GGA Exchange Functional.
doi:10.1103/PhysRevB.33.8800
Becke 1995 Correlation Functional.
tau dependent Dynamical correlation functional.
doi:10.1063/1.470829
.. Density an gradient dependent first and second row exchangecorrelation
functional.
doi:TH3/4
.. Density and gradient dependent first row exchange-correlation
functional.
doi:10.1021/jp980259s
Short-range LDA correlation functional. Local-density approximation
of correlation energy
for short-range interelectronic interaction erf(µr 21 )/r 12 ,
S. Paziani, S. Moroni, P. Gori-Giorgi, and G. B. Bachelet, Phys.
Rev. B 73, 155111 (2006).
(
[φ 2 (ζ )] 3 √ ) µ rs
Q
εc
SR (r s ,ζ , µ) = εc PW92
φ 2
+ a
(ζ ) 1 µ 3 + a 2 µ 4 + a 3 µ 5 + a 4 µ
(r s ,ζ )−
(1 + b 2 0 µ2 ) 4