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).
How do we obtain converged molecular orbitals with the all-electron method ?
The default SCF automatic occupation scheme does not work. SCF iterations are interrupted with message about too many changes in the SCF occupation, meaning that no convergence was achieved. Another route has to be taken.
Note that is tutorial shows different way for obtaining convergence than another one for \(UF_6^{-}\), The anion, which is based upon relativistic effective core potentials.
Atomic start and the autooccupation¶
We demostrate the atomic start combined with the automatic occupation scheme, which successfully give 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.
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).