Converging atoms

DIRAC presently does not perform an open-shell Hartree–Fock in a strict sense, rather an average-of-configuration calculation, which amounts to the optimization of the average energy of a set of configurations (or determinants) generated from the specification of a given number of open shells and their electron occupations. In the case of atoms, a convergence problem can occur when the inner open-shell orbitals are more stable than outer “closed” shell. From DIRAC21 onwards, we have atomic supersymmetry and can specify the occupation number of each $\kappa$ value. by using the keyword .KPSELE.

As examples of such calculations, we consider the Nb and Np atoms.

Example 1: Nb [Kr]4d⁴5s¹

**DIRAC
.WAVE FUNCTION
.ANALYZE
**HAMILTONIAN
.X2C
**INTEGRALS
*READIN
.UNCONTRACT
**WAVE FUNCTION
.SCF
*SCF
.CLOSED SHELL
 18 18
.OPEN SHELL
 2
 4/10,0
 1/2,0
.KPSELE
 5
 -1  1 -2  2 -3
  8  6 12  4  6
  0  0  0  4  6
  2  0  0  0  0
**ANALYZE
.MULPOP
*MULPOP
.VECPOP
 1..oo
 1..oo
*END OF

Example 2: Np [Rn]5f⁴6d¹7s²

**DIRAC
.WAVE FUNCTION
.ANALYZE
**HAMILTONIAN
.X2C
**INTEGRALS
*READIN
.UNCONTRACT
**WAVE FUNCTION
.SCF
*SCF
.CLOSED SHELL
 44 44
.OPEN SHELL
2
4/0,14
1/10,0
.KPSELE
7
-1  1  -2  2 -3  3 -4
14 10  20 12 18  6  8
 0  0   0  0  0  6  8
 0  0   0  4  6  0  0
**ANALYZE
.MULPOP
*MULPOP
.VECPOP
 1..oo
 1..oo
*END OF