Integrals

4.1 Calculating one- and two-electron integrals with SEWARD. 

4.1.1 Prepare SEWARD input.

• In the inputs directory, check files seward.input.head and seward.input.embedding. 

• Symmetry used: D2h; actual symmetry: Oh.

• Relativistic Hamiltonian: second order Douglas-Kroll-Hess.

• The cluster: basis sets.

  • Pr          Pr.ano-rcc.Roos.25s22p15d11f4g2h.9s8p5d4f3g2h.       QZP the lanthanide activator; all-electron basis set

  • F8          F.ano-rcc.Roos.14s9p4d3f2g.5s4p3d.                           QZP-3f2g the ligands; all-electron basis set 

  • 12Ba2+  Ba.ECP.Seijo.27s23p.1s1p.0e-AIMP-BaF2-Ba.                basis functions for orthogonalization between cluster MOs and 12Ba neighbors

  • Int6        5s                                                                               optimized for BaF2 :Yb2+ 13 A2u state basis functions at interstices to allow delocalitation towards them

• The cluster: geometry.

  • Pr is at 0,0,0. 

  • F is at :xB:, :yB:, :zB:; the geometry script shell will give the value dPr-F/√3 to all these three parameters.

  • Ba is at lattice sites.

  • The three symmetry planes of D2h produce the whole PrF8Ba12 cluster.

• The embedding:

  • Ab initio model potentials (AIMP): one-electron operators in the Hamiltonian. The AIMPs incorporate the quantum mechanical effects of (Ba2+; F−) frozen closed-shell Hartree Fock wavefunctions obtained in preparatory self-consistent- embedded-ions calculations. Note that orthogonality functions are used in the nearest 12 Ba2+ to fulfill strong orthogonality with occupied Ba2+ external wave- functions. They are taken from libs/AIMPLIB library

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* E.4.3. BaF2 (BaF2)

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* E.4.3.a. BaF2 (a=6.2001 A)

*   Structure:

*     R.W.G. Wyckoff, Crystal Structures, 2nd. ed.

*     (Interscience, New York, 1967), Vol. 1.

*     (Fluorite; Oh5-Fm3m; a=6.2001 A)

*   Embedding potentials:

*         L.Seijo, Z.Barandiaran, to be published

*         Out of SCEI DKH-HF calculations

*     /Ba.ECP.Seijo.0s.0s.0e-AIMP-BaF2-Ba.

*     /Ba.ECP.Seijo.27s23p.1s1p.0e-AIMP-BaF2-Ba.

*     /F.ECP.Seijo.0s.0s.0e-AIMP-BaF2-F.

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• External lattice ions occupy experimental crystal structure sites.

• All ions within a cube of 7x7x7 unit cells, cetered at the impurity site, are rep- resented by total ion embedding AIMPs. They have been obtained in Self- Consistent-Embedded-Ion (SCEI) Hartree-Fock calculations.

• An additional set of 2697 symmetry-independent point charges is used to ensure that the Ewald potential is reproduced within the cluster volume. 

4.1.2 Run SEWARD at different Pr-F distances.

• Go to the shells directory.

• Update variable LOGNAME in file j.head.

• Use the shells to submit jobs and to calculate integrals setting the $GeomLab parameter to actual dPr-F values in Angstrom. Use Shannon-Prewitt ionic radii mismatch to set a reasonble initial grid for the energy-distance curves.

  • Update file CLUSTER with the name given to the embedded cluster, e.g. PrF8Ba12.

  • Update file GEOMSHELL with the name of the script shell used to handle the actual geometry of the cluster. We will use AB2C2D2.D2h.geom.sh in this case. This script shell is in directory ./geom and will be invoked by the job file, prior to the calculation of SEWARD in order to prepare its final input file.

  • Edit j.calculation and uncomment only the “ksh run.integ.sh” line among all the lines that run programs.

  • Edit prepare.jobs, update the variable $Distance list with the list of dPr−F values in Angstrom, and invoke it. It will use files j.head, j.calculation, and j.tail to prepare a number of job files $Cluster.$Geomlab.job that are ready to be submitted to the batch queue system for calculation. It also updates file do.submit; it can be updated by commenting out lines corresponding to previous runs. Invoke this file to submit all the jobs to be executed in a working machine $machine. Note that this file is useful to keep a record of the jobs submitted.

4.1.3 Printout of SEWARD.

• • When the calculations of integrals are done, go to the printouts directory.

  • Grep the rc= value of all printouts. It should be 0. It is advisable to move all the *.integ.output files to a convenient subdirectory, like printouts/INTEG.

  • Check basis set data (cf. MOLCAS ANO-RCC and local AIMPLIB libraries)

  • Note symmetry adaptation of the atomic basis sets at the end of the printout.

  • Occupied AOs transform as follows:

   D2h blocks (irreps)                     D2h-Oh correspondence:

    1   2   3   4   5   6   7   8       D2h: 1          2,3,5      4,6,7     8

    ag  b3u b2u b1g b1u b2g b3g au      Oh:  a1g,a2g,eg t1u,t2u    t1g,t2g   a1u,a2u,eu

                                           Oh irreps of symmetry adapted orbitals:

Pr

s   1   0   0   0   0   0   0   0      ->    a1g

p   0   1   1   0   1   0   0   0      ->               t1u

d   2   0   0   1   0   1   1   0      ->    eg t2g

f   0   2   2   0   2   0   0   1      ->               t1u,t2u              a2u

8F

s   1   1   1   1   1   1   1   1      ->    a1g        t1u        t2g       a2u

p   3   3   3   3   3   3   3   3      ->    a1g,eg     2t1u,1t2u  2t2g,t1g  a2u,eu

4.1.4 Integral files

• The integral files and other important files that are produced by MOLCAS up to this level must be available for any of the following calculations of wave functions and energies. Depending on the case, they can be either kept in disk or recalculated again. This is a lot of storage, so, when temporarily kept, they stay in the working machine scratch directory $WorkDir and are never copied to the user machine.