CASSCF

4.3 Performing CASSCF calculations.

4.3.1 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 dPr−F distances (totally symmetric mode of the PrF8 cube). External lattice is frozen beyond PrF8. 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.

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

In Pr4+ we have the same blocks and Oh irreps than in Ce3+. In Pr3+ the blocks and irreps are:

          block          irreps                            block          irreps

                                                 4f2 manifold

          3Ag                       3A2g    3Eg            1Ag            1A1g    1A2g    1Eg

          3Tg4          3T1g     3T2g                         1Tg4          1T1g     1T2g

          3Tg6          3T1g     3T2g                         1Tg6          1T1g     1T2g

          3Tg7          3T1g     3T2g                         1Tg7          1T1g     1T2g

               4f15d1 and 4f16s1 manifolds

            3Au            3A1u    3A2u    3Eu               1Au            1A1u    1A2u    1Eu

          3Tu2          3T1u    3T2u                         1Tu2          1T1u    1T2u

          3Tu3          3T1u    3T2u                         1Tu3          1T1u    1T2u

          3Tu5          3T1u    3T2u                         1Tu5          1T1u    1T2u

• 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 Pr4+ and Pr3+ have the same set of inactive orbitals derived from: Pr 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):

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

(atomic) (Oh)

Pr4+

4f1-2Fu 2A2u                     2     8         1      1       0 2 2 0 2 0 0 1 (1)

        2T1u                     2     2,3,5     2      1             "

        2T2u

5d -2D is very high in energy (lowest atomic level: 115052 cm-1)

we will not calculate these terms nor those derived from 6s-2S.

Pr3+

         A1g A2g Eg T1g T2g

        --------------------

        |    2S+1=3         |

 4f2-3Hg|         1   2   1 |    3     1         3      2       3 2 2 1 2 1 1 1 (1)

     3Fg|     1       1   1 |    3     4,6,7     6      2             "

     3Pg|             1     | =>

  Total | 0   1   1   4   2 |

        |    2S+1=1         |

     1Gg| 1       1   1   1 |    1     1        10      2             "

     1Dg|         1       1 |    1     4,6,7     6      2             "

     1Ig| 1   1   1   1   2 |    1

     1S | 1                 |

Total   | 3   1   3   2   4 |

          2S+1= 1,3

         A1u A2u Eu T1u T2u

        --------------------

        |   5deg-2Eg        |

4f1-2A2u|         1         | => 3     8         9      2       3 2 2 1 2 1 1 1 (1)

    2T1u|             1   1 |    3     2,3,5    11      2             "

    2T2u|             1   1 |

        |   5dt2g-2T2g      |

4f1-2A2u|             1     |    1     8         9      2       3 2 2 1 2 1 1 1 (1)

    2T1u|     1   1   1   1 |    1     2,3,5    11      2             "

    2T2u| 1       1   1   1 |

        |   6s -2A1g        |

4f1-2A2u|     1             |

    2T1u|             1     |

    2T2u|                 1 |

        |                   |

  Total | 1   2   3   6   5 |

1. Note that the same active space must be used in all states that will be mixed by Spin Orbit. This is a requisite of program RASSI.

• • 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.

4.3.2 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.

      • Edit the inputs/CASPT2/head.ms-caspt2.input file so that the RASSCF ana- lyzer can prepare irrep and geometry dependent inputs for MS-CASPT2 calcula- tions with the program CASPT2 (see below ** in Sec. 4.4.1). 

        • Update and invoke do.analyze.rasscf.  This script shell calls the analyzer shells/pre-post/analyze.rasscf.subblocks.ksh, which uses the files:

• • • *.rasscf.output

    • $Block.key configurations

    • inputs/CASPT2/head.ms-caspt2.input

and produces the files:

• • • *.rasscf.assignments, which must be checked.

    • *.rasscf.summary, which are useful to detect errors if something goes wrong. 

    • *.rasscf.efit.dat, which will be used in the next step.

    • inputs/CASPT2/$Irrep.$GeomLab.ms-caspt2.input, which are input files for subsequent MS-CASPT2 calculations on the selected roots of a block that belong to the same irrep. 

• • 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 Pr.RAS.PT2.SO.agr, and import rasscf.curves.txt in the window of the CASSCF results as suggested in README.agr.

    • Use colors to identify states and label them trying to find out: (1) in the case of states of the f 2 manifold, their parent atomic term: 3 H , 3 F , 3 P (increasing energy) 1G, 1D, 1I, 1S (increasing energy); (2) in the other states, their 4f5deg, 4f5dt2g, 4fφa1gITE, ... configurational character. For this, use the tables of atomic-to-Oh correspondence of Sec. 4.3.1. You can also check the printouts to observe the occupations of natural orbitals to make sure, for instance, whether 5d is 5deg or 5dt2g. Note also that the bond length of states follows these trends, which also helps to label states:

4f5deg     <   4f2   <   4f5dt2g

Pr4+   <   Pr3+ 4fφITE    < other states of Pr3+.

And, of course, you need to check the shape of the curves, which can be either regular (and common to all states of the same dominant configuration) or cor- respond to avoided crossings, which indicate that states of different dominant configurations and same symmetry avoid crossings and change configurational character from one side to the other of the crossing. 

• 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.