:orphan:

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Properties at the MCSCF level of theory
=======================================

In this tutorial we will look at a simple example of computing one-electron properties using a Kramers-restricted MCSCF
(KRMC) and Hartree-Fock (HF) wave function in DIRAC.
For more details on the implementation and the method, see :cite:`Jensen1996`, :cite:`Thyssen2004` , :cite:`Thyssen2008` and
:cite:`Knecht2009`, respectively.

We consider the Be atom using :math:`\mbox{C}_{2v}` symmetry::

  INTGRL
  Be atom in uncontracted Pierloot basis set, MOLCAS 5, ANO-S
  Generated small component via RKB
  C   1    2XY Y         .10D-15
          4.    1
  Be 1           .00000000           .00000000           .00000000
  LARGE    3    2    1    1
  H   7    0    3
        2732.3281
         410.31981
          93.672648
          26.587957
           8.6295600
           3.0562640
           1.1324240
  H   3    0    3
            .18173200
            .05917000
            .02071000
  H   4    0    3
           1.1677000
            .36500000
            .11410000
            .03570000
  H   3    0    3
            .54680000
            .14650000
            .03930000
  FINISH

and generate the following menu file::

	**DIRAC
	.TITLE
	 Testing KRMC and KR-CI for Be in Pierloot basis
	.ANALYZE
	.WAVE FUNCTION
	.PROPERTIES
	**PROPERTIES
	.RHONUC
	.EFFDEN
	.WAVE F
	2
	 DHF
	 KRMC
	**HAMILTONIAN
	.X2C
	**WAVE FUNCTION
	.SCF
	.KRMCSCF
	*SCF
	.CLOSED SHELL
	 4
	*KRMCSCF
	.CI PROGRAM
	LUCIAREL
	.INACTIVE
	 1
	.GAS SHELL
	 2
	 0 2 / 1
	 2 2 / 3
	.SYMMETRY
	 1
	.PRINT
	 5
	*OPTIMI
	.ANALYZ
	**END OF

Here we ask for the contact density :math:`\rho(0)` (.RHONUC) as well as effective density :math:`\bar{\rho}` (.EFFDEN) at the Be nucleus
calculated at the HF and MCSCF level of theory using the exact two-component Hamiltonian. In the MCSCF step we define a
CAS(2,4) space correlating 2 electrons in 4 Kramers pairs (2s2p shell of Be). 

The results read as follows::

    HF:
    Rho at nuc Be 01 :     33.94937443146 a.u.
    EFFD:Be 01       :     33.94934902177 a.u.

    KRMC:
    Rho at nuc Be 01 :     33.89686536890 a.u.
    EFFD:Be 01       :     33.89683999776 a.u.

From this we can conclude that non-dynamical (and partially dynamical) correlation included in our CAS wave function
seems to reduce both, :math:`\rho(0)` and :math:`\bar{\rho}` at the Be nucleus compared to the uncorrelated Hartree-Fock values.