4.4 Performing multi-state CASPT2 calculations.
4.4.1 Prepare and submit all MS-CASPT2 calculations using the program CASPT2.
Goal: including dynamic electron correlation by a second order perturbation method. Once single state (SS) CASPT2 calculations are done using each individual CASSCF root of a given symmetry block as a reference for second order perturbation, the multi- state section begins. The matrix of a second order effective hamiltonian is calculated on the CAS reference basis. The diagonal elements of this matrix are the single-state (SS) CASPT2 energies already available; the off diagonal elements correspond to the interactions of two CAS states through second order perturbation. The effective Hamil- tonian matrix is then diagonalized to obtain the MS-CASPT2 results: the eigenvalues are the MS-CASPT2 energies and the eigenvectors, the CAS’ wave functions, which are linear combinations of the CAS wave functions, are the new effective zeroth order wave functions.
Only valence electron correlation. Note that Ln 5s5p shells must be considered valence. “Frozen” in this context means: no excitations will be allowed from the frozen shells. Core shells should not be correlated. Hence Pr 1-4s,2-4p,3-4d; F 1s should be frozen. Translate that to symmetry MOs and check: Frozen 9 4 4 3 4 3 3 1.
In Pr4+, as in Ce3+, we will do a MS-CASPT2 calculation over blocks rather than over irreps, because the mixing of irreps is negligible.
(**) In the case of Pr3+ we will do the MS-CASPT2 calculation over the states of each Oh irrep separately. So, for example, at RASSCF level we have calculated 9 roots in D2h block 8, which we call 3Au block. This block contains one 3A1u root, two 3A2u roots, and 3×2=6 3Eu roots. Now, to avoid further symmetry breakings at MS-CASPT2 level, we will calculate separately
3Au.3A1u 1 root
3Au.3A2u 2 roots
3Au.3Eu 6 roots
This is why the RASSCF analyzer must create a geometry-dependent and Irrep-dependent input for MS-CASPT2 calculations. For this reason, the following files must be created in inputs/CASPT2 directory:
caspt2.input
ms-caspt2.input, and
head.ms-caspt2.input (**)
The latter is used by the RASSCF analyzer shells/pre-post/analyze.rasscf.subblocks.ksh to append the info necessary to create $Irrep.$GeomLab.ms-caspt2.input. You should supervise the action is done correctly by the analyzer.
Submit the irrep-dependent MS-CASPT2 calculations for all points in the dPr−F grid. For that, in the shells directory: Edit j.calculation and uncomment only the “ksh run.caspt2-sub.sh $Block $Irrep $ms-roots $Caspt2Dir” lines of the target blocks and irreps. Run prepare.jobs to prepare all the job files, update do.submit, and invoke it to submit all the jobs.
4.4.2 Analyze and plot the results of CASPT2.
Go to directory printouts/CASPT2.
Grep the rc= value in all printouts. It should be 0. Check some printouts (e.g. reference energy should be the rasscf one).
Use the CASPT2 analyzers to assign the D2h states to Oh irreps and to partially prepare input for EFIT program.
Update and invoke do.analyze.ms-caspt2.
This script shell links the $Block.$Irrep.rasscf.assignments files in the RASSCF printouts directory ../RASSCF and calls the analyzer shells/pre-post/analyze.ms-caspt2.ksh,
which uses the files:
- *.$Block.$Irrep.*.caspt2.output
- $Block.$Irrep.rasscf.assignments
and produces the files:
*.summary, which are useful to detect errors if something goes wrong
*.MS.efit.dat files for EFIT
$Block.$Irrep.ms-caspt2.assignments, which must be checked and will be used to prepare the input of subsequent RASSI-SO calculations
*.$Block.$Irrep.*.msin.energies which will be used to prepare the input of subsequent RASSI-SO calculations
some other files that will not be used in the present procedure
Use EFIT to fit the MS-CASPT2 energy curves and to prepare input to plot them.
Go to the results directory.
Update MS.efit.inp.head and prep.MS.efit and run the latter. Check file MS.efit.out.
To plot the MS-CASPT2 energy curves, run XMGRACE, open Pr.RAS.PT2.SO.agr, and import MS.curves.txt in the window of the MS-CASPT2 results.
Use colors to identify states as in the CASSCF step. Check README.agr file.
Edit MS.efit.inp and run “efit.ksh MS” until the fitting of the energy curves has a good quality. It is important to check the shape of numerical energy curves: interaction between states of the same symmetry but different configurational character will produce avoided crossings which may result in very anharmonic (even doble-minimum) curves. This should guide the fitting and should serve to point out its accuracy when very irregular curves are obtained. The data in MS.efit.out immediately after the keyword SUMMARY will be later read to make a LATEX table in a report. Substitute the input data after the keyword IN- PUT DATA in MS.efit.inp by that in eordered.efit.inp if increasing energy order is the choice to prepare the table of CASSCF and MS-CASPT2 results next.
4.4.3 Make a basic report with the CASSCF and MS-CASPT2 results.
Make the body of a LATEX table that combines CASSCF and MS-CASPT2 spectroscopic constants calculated with EFIT.
In the results directory, run do.SF.table. It will combine the spectroscopic constants in rasscf.efit.out and MS.efit.out and produce the core of a useful LATEX table in SF.table.tex.dat.
Make the report.
In the results/latex directory, issue make. It will make the report in report.pdf, which can be visualized.
Conclude on the dynamic electron correlation effects by comparing MS-CASPT2 results (with) and CASSCF results (without).