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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.