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