3.2 Obtaining good initial orbitals for multireference wave function calculations.
A closed shell is needed to make sure all initial orbitals show full Oh symmetry in D2h calculations. This is important to avoid symmetry breakings from the beginning.
Programs to be used: SCF and RASSCF. Integrals should have been calculated.
Calculating all the electrons at once tends to lead to symmetry breakings. An alternative follows.
3.2.1 Procedure of increasing occupancy by defining successive closed shells.
A bit tedious, but extremely clean. The orbitals obtained will be used extensively: it pays.
Look at the printouts and note how the unoccupied orbitals rearrange in the expected order as more electrons (interactions) are included from calc. 1 to 5 below. (Number of electrons = 2 × closed shell orbitals).
* Ce at 0,0,0; F at xF,xF,xF. xF = 2.700 bohr in this case.
*
* calc. init. vectors closed shell used program iter conv(1) symmetry (2)
* 0. core-Ham 5 2 2 1 2 1 1 0 scf 5 no ok
* Ce: 1-3s,2-3p,3d
* 1. from 0 5 2 2 1 2 1 1 0 rasscf 20 yes ok
* 2. from 1 9 3 3 3 3 3 3 1 rasscf 20 yes ok
* Ce: 1-4s,2-3p,3-4d
* F: 1s
* 3. from 2 14 4 4 3 4 3 3 1 rasscf 20 no ok
* Ce: 1-5s,2-4p,3-4d
* F: 1s,2s2p(some)
* 4. from 3 14 6 6 4 6 4 4 2 rasscf 20 no ok
* Ce: 1-5s,2-5p,3-4d
* F: 1s,2s2p(some)
* 5. from 4 14 9 9 7 9 7 7 5 rasscf 200 yes ok
* Ce: 1-5s,2-5p,3-4d
* F: 1s,2s2p
* this is it: 4f(0)-1A1g ground state of (CeF8Ba12)20+ embedded in BaF2.........
Convergence does not matter along the procedure. It matters only at the end.
Check symmetry of MOs in the printouts:
Oh degeneracies: eg (block 1), t1u,t2u (blocks 2,3,5), t1g,t2g (blocks 4,6,7), eu (block 8).
Use the lanthanide basis set ”to see” the symmetry of MOs:
Ce s functions 6= 0 a1g; =0 other or negligible contribution;
Ce p functions 6= 0 t1u; =0 other or negligible contribution;
Ce d functions
3.2.2 Produce “supersymmetry” input data.
MOs of different Oh irreps appear in each D2h block and we should prevent they mix because mixing could result in symmetry breakings. This is the purpose of using “supersymmetry” (supsym keyword in program RASSCF).
MOs (with correct symmetry) and their corresponding supersymmetry data should in general be used as input for wavefunction calculations in other geometries and/or other states and serve to make sure that the symmetry is kept so that the new output MOs symmetry is ok.
Supersymmetry classifies the MOs so that only those in the same class (irrep) are allowed to mix along the MO optimizations.
Use the printout of the last calculation in 3.2.1 to define supersymmetry data as ex- plained in file ../vectors/Supersymmetry data/Supsym.data.
Note that the content of Supsym.data should be included in rasscf.input file to be used.
This data will be useful for all wavefunction calculations in Ce3+/Ce4+ and Pr3+/Pr4+ (or other Ln with the same type and size of basis set). So, even if it seems to be tedious, it is done only once.
Note that supersymmetry classification is usually maintained by output MOs, which is good when restart is needed due to non-convergence.