:orphan:
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
.. math::
\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 :cite:`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 :ref:`*SCF` and :ref:`*MP2CAL` subsections.