# Long-range WFT/short-range DFT¶

Long-range wave function theory (lrWFT) combined with short-range density functional theory (srDFT) is based on a separation of the two-electron interaction

$\frac{1}{r_{12}}=\frac{erf\left(\mu r_{12}\right)}{r_{12}} - \frac{1-erf\left(\mu r_{12}\right)}{r_{12}}$

here using the error function (erf). The first term, the long-range interaction, is assigned to wave function theory, whereas the second term, the short-range interaction, is assigned to DFT. Contrary to conventional DFT the fictitious reference (Kohn-Sham) system is no longer non-interacting and can not be solved exactly, so that the hierarchy of approximate wave function methods must be invoked. MP2-srDFT has been implemented in DIRAC by Ossama Kullie and Trond Saue [Kullie2011].

## Specification of functionals¶

### srLDA¶

Short-range LDA is specified as:

**HAMILTONIAN
.DFT
CAM p:alpha=0.0 p:beta=1.0 p:mu=0.4 x:slater=1.0 c:srvwn5=1.0

### srGGA¶

Two flavours of short-range PBE has been implemented in DIRAC. The short-range PBE of Hirao and co-workers is specified as:

**HAMILTONIAN
.DFT
CAM p:alpha=0.0 p:beta=1.0 p:mu=1.0 x:PBEX=1.0 c:srPBEC=1.0

The short-range PBE of Scuseria and co-workers is specified as:

**HAMILTONIAN
.HFXATT
1.0D0
.HFXMU
1.0D0
.DFT
GGAKEY HJSX=1.0 srPBEC=1.0

## MP2-srDFT¶

MP2-srDFT is activated by specifying the short-range DFT functional as above and complementing with:

**WAVE FUNCTIONS
.SCF
.MP2

Further specifications can be given in the *SCF and *MP2CAL subsections.