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 [Jensen1996], [Thyssen2004] , [Thyssen2008] and [Knecht2009], respectively.

We consider the Be atom using \(\mbox{C}_{2v}\) 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 \(\rho(0)\) (.RHONUC) as well as effective density \(\bar{\rho}\) (.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, \(\rho(0)\) and \(\bar{\rho}\) at the Be nucleus compared to the uncorrelated Hartree-Fock values.