UF6 molecule

\(UF_6\) (146 electrons, \(O_h\) symmetry) is known compound connected with the uranium enrichment. We shall investigate UF6 as the closed-shell (singlet) state and in the highest D2h* computational symmetry (UF6.v2z.D2h.mol).

Note that is tutorial shows different ways for obtaining convergence than another one for \(UF_6^{-}\), The anion, which is based upon relativistic effective core potentials.

Atomic start

We demostrate the atomic start combined with the automatic occupation scheme, which successfully gives converged state with the occupation of (E1g,E1u)=(72,74), see the input file, x2c_a4p.atstart_scf_autoocc_2fs.inp, and the output file.

Input files for corresponding F,U atomic runs are F.v2z.D2h.mol, F.x2c.scf_2fs.inp, U.v2z.D2h.mol, x2c.scf_autoocc.inp. Output files from these (F,U) atomic runs are F.x2c.scf_2fs_F.v2z.D2h.out and x2c.scf_autoocc_U.v2z.D2h.out.

Note that it is not necessary to specify proper atomic configuration of the U atom as the auto-occupation scheme does the job and produces suitable starting MOs.


It is possible to obtain proper orbital occupation thanks to the implemented atomic potential start and avoid the lenghty atomic start procedure given above.

The autooccupation gives the lowest SCF energy, see the output file x2c_a4p.scf_autoocc_UF6.v2z.D2h.out, the input file, x2c_a4p.scf_autoocc.inp, and resulting MO coefficients, DFPCMO.UF6.x2c_a4p.scf.v2z.

Verification of the occupation

Next, we have to verify that this occupation of spinors gives the lowest energy. For that, we perform several atomic-start based SCF calculations with different occupation schemes. Results - occupations and SCF energy - are collected in the following table:

occupation SCF energy
68, 78 not converged
70, 76 -28636.011248088082
72, 74 -28636.624880692940
74, 72 -28635.715232162675
76, 70 -28634.793937853457

We see that manually assigned occupation of 72,74 gives the lowest energy, what is the proof of the correct autooccupation settings (see one input file, UF6.x2c_a4p.atstart_scf_autoocc_72_74).

Geometry optimization

The UF6 geometry optimization, thanks to the high Oh symmetry, requires change of one parameter only - the U-F bond distance.

To carry out the UF6 structure optimization with the BP86 functional effectively, let us first obtain starting set of (DFT) molecular orbitals. For that, we first run single point DFT step with molecular orbitals file from the previous SCF step and reuse them for the DFT-geometry optimization. See the BP86 input file, UF6.x2c_a4p.bp86_72_74.inp, and the geometry optimization input, UF6.geomopt.x2c_a4p.bp86_72_74.inp.

Thanks to this MO start, number SCF iterations during the geometry optimization cycle is less than 10, see the corresponding output file.

The final U-F bond distance obtained with the X2c-BP86-v2z method is 2.020A (experimental distance is 1.999A).

Test script

The Dirac Python test script for this tutorial is test. Pay attention to comments and commented lines to be able to reproduce this tutorial’s demostrative calculations.