CASSCF

3.3 Performing CASSCF calculations.

3.3.1 Prepare and submit all the CASSCF calculations using the program RASSCF.

• Goal: to calculate wave functions and energies of relevant states to produce the energy curves in the chosen grid of dCe−F distances (totally symmetric mode of the CeF8 cube). External lattice is frozen beyond CeF8. The CASSCF wave functions are multi- configurational SCF wave functions. So:

  • The MOs calculated are variational for an average state energy. They are expanded in a variational linear combination of symmetry adapted orbitals (the symmetry adapted orbitals are constructed from the atomic basis sets using symmetry couplings only by SEWARD).

  • The CI expansion associated with the complete active space (see below) is also variational.

Note, however, that in the simple Ce3+/Ce4+ cases, the wavefunctions are single ref- erence (one-configuration wf), like Hartree-Fock wf, but for open-shells, which might demand the mixing of one or several determinants to obtain the particular single- configuration wf.

• In the inputs directory, check $Block.rasscf.input files.

In Ce4+ we only have 1Ag, which contains the 1A1g irrep. In Ce3+ we have the following blocks and Oh irreps:

          block          irreps

               4f1 manifold

          2Au            2A2u

          2Tu2          2T1u    2T2u

          2Tu3          2T1u    2T2u

          2Tu5          2T1u    2T2u

               5d1 and 6s1 manifolds

          2Ag            2A1g    2Eg

          2Tg4          2T2g

          2Tg6          2T2g

          2Tg7          2T2g

The subspecies of degenerate states (E, both in block 1; T, in blocks 2,3,5 or 4,6,7) must be calculated as they can mix through spin-orbit coupling.

• Defining the multielectronic wave functions in RASSCF:

  • The total number of electrons of the wavefunctions to be calculated is:

2×(No. inactive orbitals) + No. of active electrons.

• • Inactive orbital space (= doubly occupied):

Both Ce4+ and Ce3+ have the same set of inactive orbitals derived from: Ce 1-5s2, 2-5p6, 3-4d10, plus 8F 1-2s2, 2p6 (cf. AOs transformation table in Sec. 3.1.3); total 134 electrons:

          Inactive 14 9 9 7 9 7 7 5

• • Active orbital space:

Any occupation (0/1/2) of the active orbitals in the RAS2 space, compatible with the number of active electrons and Spin&Symmetry restrictions will be allowed to expand the multielectronic wf (this defines a full CI within the active orbital space):

Ln    config. Terms 2S+1 D2h sym block roots active e- Active orbitals (RAS2)

      (atomic)(Oh)

Ce4+  4f0-1S  1A1g   1     1             1      2      1 0 0 0 0 0 0 0   (1)

Ce3+  4f1-2F  2A2u   2     8             1      1      3 2 2 1 2 1 1 1   (2)

              2T1u   2     2,3,5         2      1          "

              2T2u

      5d-2D   2Eg    2     1             3      1          "

              2T2g   2     4,6,7         1      1          "

      6s-2S   2A1g   2     1

1. CASPT2 fails if there are 0 electrons and 0 active orbitals. For this reason the a1g active orbital is moved from the Inactive to the RAS2 active space:

Inactive  13 9 9 7 9 7 7 5;  RAS2 1 0 0 0 0 0 0 0 

Of course, the total energies obtained this way are the same as those obtained in the last calculation in 3.2.1 described above.

2. Note that the same active space must be used in all states that will be mixed by spin-orbit coupling. This is a requisite of RASSI program that will be later used for RASSI-SO calculations. Actually, many of the active orbital will not be occupied because of the wave function Spin&Symmetry requisites (note the warnings in the printout of RASSCF). Active orbitals in 4f1-2A2u, for example, could be: 0 0 0 0 0 0 0 1; so, 3 2 2 1 2 1 1 1 is a waste, but does not harm!

• • Printout of the wave functions.

  • Prwf should be 0.00 to allow for symmetry analyses of the wf (see below).

  • Initial orbitals.

  • In the vectors directory, check $Block.input.RasOrb files. All of them contain the set of vectors produced in Sec. 3.2.1; their corresponding Supsym data is given in the $Block.rasscf.input files. Note $Restart Rasscf=0 in run.rasscf.sh (in shells directory) indicates this is not a restart calculation, hence $Block.input.RasOrb vectors will be used.

  • Submit the RASSCF calculations.

    • • Go to the shells directory.

      • Edit j.calculation and uncomment only the “ksh run.rasscf.sh $Block” lines of the target blocks.

      • Invoke prepare.jobs to prepare all the job files, update do.submit, and invoke it to submit all the jobs.

3.3.2 Analyze and plot the results of RASSCF.

It is very important to check that everything is correct before moving to the next step (MS-CASPT2 calculations).

• • Go to the printouts directory.

  • Grep the rc= value in all printouts. It should be 0. Check some printouts (symmetry and degeneracies) and move all of them to some meaningful subdirectory to process them, like ./RASSCF.

  • The printout files are $Cluster.$GeomLab.$Block.rasscf.output.

  • Use the RASSCF analyzers to assign the D2h states to Oh irreps and to partially prepare input for EFIT program (which is not a part of MOLCAS, but one of the tools for the present procedures).

    • • Go to ./RASSCF.

      • Check $Block.key configurations files.

      • Key configurations are used by the RASSCF analyzer to find out the irrep of states. They are chosen and copied from the list of configurations in the ”Wave function printout” section of RASSCF printout. The analyzer produces assignment files to be used by the analyzer of CASPT2 and, eventually, to prepare input for MS-CASPT2 calculations.

        • • • Update and invoke do.analyze.rasscf.

            • This script shell calls the analyzer shells/pre-post/analyze.rasscf.ksh.

      • Check the assignments made in the $Block.rasscf.assignments files. Note that *.summary and *.efit.dat files have also been created; the former are useful to detect errors if something goes wrong and the latter will be used in the next step.

• Use EFIT to fit the CASSCF energy curves and to prepare input to plot them. Fitting the energy curves to a polynomial (using only points close to the minimum) allows to obtain bond lengths, totally symmetric vibrational energies, and minimum-to-minimum energy differences. XMGRACE is a good alternative to plotting the energy curves.

  • • Go to the results directory.

    • Update rasscf.efit.inp.head and prep.rasscf.efit, and run the latter. Check file rasscf.efit.out.

    • To plot the CASSCF energy curves, run XMGRACE, open Ce.RAS.PT2.SO.agr, and import rasscf.curves.txt in the window of the CASSCF results.

    • Edit rasscf.efit.inp and run “efit.ksh rasscf” until the fitting of the energy curves has a good quality. The data in rasscf.efit.out immediately after the keyword SUMMARY will be later read to make a LATEX table in a report.