Dirac-Fock one-centre expansion calculations on the molecular model systems ThH4 and UH6

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Dirac-Fock one-centre expansion calculations on the molecular model systems ThH4 and UH6

P. Pyykkö, J. Desclaux

To cite this version:

P. Pyykkö, J. Desclaux. Dirac-Fock one-centre expansion calculations on the molecular model systems ThH4 and UH6. Journal de Physique Colloques, 1979, 40 (C4), pp.C4-222-C4-223.

�10.1051/jphyscol:1979469�. �jpa-00218865�

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JOURNAL DE PHYSIQUE Colloque C4, supplément au n" 4, Tome 40, avril 1979, page C4-222

Dirac-Fock one-centre expansion calculations on the molecular model systems ThH

⁴

and UH

⁶

P. Pyykko and J. P. Desclaux (*)

Department of Physical Chemistry, Abo Akademi, SF-20500 Abo (Turku), Finland (*) D R F / C P N , C . E . N . G . , 85 X, F-38041 Grenoble Cedex, France

Résumé. — On présente certains résultats de calculs relativistes Dirac-Fock à un centre pour les systèmes modèles ThH4 et UH». Les hybridations, les distributions radiales et l'influence des 5f sur la distance de liaison sont discutées. Une valeur de 30 pm est prédite pour la contraction actinidique.

Abstract. — Relativistic Dirac-Fock one-centre expansion calculations are presented for the molecular-model systems Thl-L and UH6. The hybridizations, the radial distributions and the effect of the 5f : s on the bond length are discussed. A value of 30 pm is predicted for the actinoid contraction.

Relativistic effects influence strongly the chemi- cal properties of the latter half of the periodic system (for a review, see e.g. Ref. [1]). We are studying these effects by Dirac-Fock one-centre expansion calculations on the covalent model hydri- des MH„. These seem to be sufficiently realistic so that e.g. the covalent radii of the central atom may be obtained [2]. For the MH„ systems (M = Ti, Zr, Hf, Th, Cr, Mo, W), the calculated M-H bond lengths differ in the average from the experimental

ET UH6(7s27p6r„+(6d)4)

6 6^r v, <f

68- \ y ^

- 2 8 0 7 1 . 7 2 - lo—"'^

I UH6(7s2(r^r-)(7p+5f)6rg(6d)4) 40- V / -2 8072.44- °—LO--

'22.4pm¹

Cp Contraction due to me 5P.s

8 2_ (106)H6(7s27p 65f1 4r;(6d)4) '.86- \ . - / I -4 0725 88- ^--b-^ |

2 9 5 p m

K — H

Actinoid contraction

i i i_J i i i i I i i L _ J I i i

3.5 4.0 4.5 R [ M - H ] [a u.]

Fig. 1. — Dirac-Fock potential energy curves for U H , (without and with the 5f functions) and for (106)H6. The total energy £T( R ) is given in atomic units.

M-X by 16, 39, - 3, 42, 55 and 75 pm (picometers) for X = H^b„^di!.(BHJ, C(o-), F, CI, Br and I, respecti- vely. This suggests a hydridic hydrogen covalent radius of 58 pm. Then a comparison between UH6(f°) and (106)H6(f"') (see Fig. 1) may be used to get a value of 30 pm for the actinoid contraction of bond lengths. A comparison between ThH„ and (104)H, (taken from Ref. [3]) leads to the same value. As seen from figure 1, adding the 5f : s shortens the U-H bond by 22 pm. For ThH⁴ the corresponding value is only 8 pm.

The hybridizations of ThH⁴ and UH⁶ are shown in table I. The electron configurations mentioned in the table caption are the relativistic equivalents of the (a,)2 (t2)6 and (tlu)6 (eg)4 ground states of ThH4(Td) and UH6(Oh), respectively. We emphasize that the ThH4 5f : s are centred on the hydrogens while the UH6 5f : s exhibit both an inner radial density maximum around 1.3 a.u. and an outer one at the ligands. Although all these orbitals s-f are partially a description of the hydrogens in the one-centre model used, they also are partially true 7s, 7p, 6d and 5f orbitals of the metal atom. It is thus quite appro- priate to speak of s-p-d hybridization of Th and s-p- d-f hybridization of U in the present molecular model systems.

The 7p shells are more diffuse than the 6d shells.

Table I. — Hybridizations for ThH4 at R = 3.868 a.u. assuming the electron configuration F6(s + f)2 (7\ + r„) (p + d + f)6 and for UH„ at R = 3.8 a.u. assuming the electron configuration

(7s)²(r; + r-)(^P + f)⁶(r;(d))⁴.

System Hybridization ThH⁴ 7s^{0 8 ,}7p^{0 8 7}6d^{, 9 2}5f^{0 4 0}

UH⁶ 7s¹ 7p""6d² 5f'⁵⁶

Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:1979469

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DIRAC-FOCK ONE-CENTRE EXPANSION CALCULATIONS C4-223

Therefore their norm, N(7p), increases with in- configuration other originally unoccupied but ener- creasing R. Adding the 7p : s to the basis increases getically accessible A 0 : s (here 7p) that provide very considerably the long-range force on the hydro- sufficient bonding at the various R : s involved in gens. This suggests that a good hydrogenation cata- the reaction. A more detailed discussion will appear lyst should have, close to its ground state electron shortly [ 2 ] .

References

[I] PYYKKO, P . , Adv. Quantum Chem. 11 (in press).

[23 PYYKKO, P. and DESCLAUX, J. P., Chem. Phys. (in press).

[ 3 ] PYYKKO, P. and DESCLAUX, J. P., Chem. Phys. Lett. 50 (1977) 503.