3.1 Geometries

The optimized geometries and calculated frequencies for EThF₂^- and EThF₂ at the SR-ZORA PBE/TZ2P level in comparison with previously reported values are provided in Table 1 and Table 2. All the studied anion and neutral molecules possess the Cs symmetry with a ¹A′ ground state for neutral molecules and ²A′ ground state for anions. Our calculated data are in accordance with previous values, suggesting that the PBE exchange correlational functional is suitable to analyze the current species. Single-point energy calculations through CCSD(T) in the Molpro 2012.1 package [35] using the optimized geometric structures at the B3LYP level for both anions and neutrals are performed to determine the electron affinity (EA) of the studied neutral molecules. The EA values for OThF₂, SThF₂, SeThF₂, and TeThF₂ are 1.20 eV, 1.59 eV, 1.66 eV, and 1.96 eV, respectively. The calculated geometries and frequencies under the Gaussian 09/DFT level are provided in the supplementary information. The bond length of Th-E increases along the series from OThF₂ to TeThF₂ both in the anion and neutral molecules, while the bond length of Th-F exhibits an opposite trend. The calculated results also indicate a decrease in the bond angles and bond lengths from the anions to the corresponding neutral molecules, which can be attributed to singly occupied molecular orbitals (SOMOs) of the anions possessing non-negligible anti-bonding character. The calculated bond length of Th-O in the OThF₂ neutral molecule is 1.895 Å, which is slightly longer than the previously reported result of 1.886 Å [10] at the B3LYP level; therefore, it would be meaningful to study the properties of different functionals in complexes including the thorium atom. Ours as well as the previously calculated bond length of Th-O bond are similar in value for the ThO triple bond length (1.89 Å) obtained from atomic radii [36]. Our recent calculated bond lengths at the SR-ZORA PBE/TZ2P level for Th-S, Th-Se, and Th-Te in SThF₂, SeThF₂, and TeThF₂ neutral molecules are 2.423 Å, 2.583 Å, and 2.821 Å, respectively; these are higher than the calculated bond lengths of di-atomic molecules ThS (¹Σ⁺, 2.343 Å), ThSe (¹Σ⁺, 2.495 Å), and ThTe (¹Σ⁺, 2.731 Å) at the same level. Moreover, the calculated bond lengths of Th-F in EThF₂ are all greater than that in ThF₂, as shown in Table 3.

3.2 Orbital analyses

Fig. 1 shows the contour plots of the Kohn-Sham MOs of OThF₂. The correlation diagram is presented in Fig. 2. The 10a′ molecular orbital, which is the highest occupied molecular orbital (HOMO), mainly stems from O 2p atomic orbitals (AOs), with modest contributions from Th 6d and 5f AOs, indicating a σbond between Th and O. The O 2p AOs mixed with Th 6d and 5f AOs, resulting in a weak π bonding 6a′′ (HOMO-1) molecular orbital. HOMO-2 (9a′) is another π orbital arising from the interactions of the 2p AO of oxygen with 6d and 5f AOs of thorium. Hence, the Kohn-Sham MO analysis suggests that the Th-O bond has two weak π bonds and one σbond in the OThF₂ molecule, which is nearly same as the bonds in other terminal thorium chalcogens included complexes. [13-15] NBO studies provide additional proof for the existence of multiple bonding in OThF₂. As displayed in Table 5, there are three bonding orbitals between Th and O, where the oxygen atom (mainly 2p atomic orbital (AO)) devotes around 84% to the Th-O bond; the rest originates from the mixing of Th 5f and 6d AOs, with more contribution from 6d orbitals than 5f orbitals. Because fluorine has high electronegativity, it is supposed that the AOs of oxygen would prefer to overlap more with the thorium AOs.

Fig. 1Full-screen View

(Color online) Contour plots of Kohn-Sham MOs of OThF₂ (isosurf = 0.05 a.u).

Fig. 2Full-screen View

Qualitative molecular orbital energy level diagram of OThF₂. The energy of atomic orbitals was shifted up with 6.21 eV.

Fig. 3 shows the contour plots of the Kohn-Sham MOs of SThF₂, and the correlation diagram is presented in Fig. 4. The 6a′′ (HOMO) molecular orbital is largely composed of S 3p AOs, Th 6d_π AOs and a bit Th 5f AOs, suggesting a weak π bond between Th and S. The 3p AO of S interacts with 5f-6d hybridized AOs of Th, forming a weak π bonding 10a′ (HOMO-1) molecular orbital. Moreover, a weak σbonding 9a′ (HOMO-2) molecular orbital is formed between Th and S through the overlap between 6d AO of Th and 3p AO of S; thus, identical to Th-O, Th-S shows two weak π bonds and a σbond in SThF₂.

Fig. 3Full-screen View

(Color online) Contour plots of Kohn-Sham MOs of SThF₂ (isosurf = 0.05 a.u).

Fig. 4Full-screen View

Qualitative molecular orbital energy level diagram of SThF₂. The energy of atomic orbitals was shifted up with 5.87 eV.

Fig. 5 shows the contour plots of the Kohn-Sham MOs of SeThF₂, and the correlation diagram is presented in Fig. 6. Of which, 6a′′ (HOMO) and 10a′ (HOMO-1) are molecular orbitals of two weak π bonds, mainly composed of 4p of Se and 6d of Th, in addition to a trace of Th-5f AOs. The interaction between 4p of Se and 6d of Th forms a weak σbonding 9a′ (HOMO-2) molecular orbital; thus, as in the previous two cases, we suggest the Th-Se bond possess two weak π bonds and a σbond in the SeThF₂ molecule.

Fig. 5Full-screen View

(Color online) Contour plots of Kohn-Sham MOs of SeThF₂ (isosurf. = 0.05 a.u).

Fig. 6Full-screen View

Qualitative Kohn-Sham molecular orbital energy level diagram of SeThF₂. The energy of atomic orbitals was shifted up with 5.78 eV.

The contour plots of the Kohn-Sham MOs of TeThF₂ and the correlated diagram are presented in Fig. 7 and Fig. 8, respectively. TeThF₂ has a bonding nature similar to the previous three molecules, and Th-Te bond possess two weak π bonds and one σbond in the TeThF₂ molecule. Similarly, multiple bonding in the SThF₂, SeThF₂, and TeThF₂ molecules can be observed through NBO research. As displayed in Table 5, three Th-S, Th-Se, or Th-Te bonding orbitals exist, in which the sulfur (mainly 3p AO), selenium (mainly 4p AO), or tellurium atom (mainly 5p AO) contributes more than 80% to the Th-S, Th-Se, or Th-Te chemical bond, respectively. Moreover, the remaining contributions are mainly attributed to the mixing of Th 5f and 6d AOs. Furthermore, the 5a′′ (HOMO-3) and 8a′ (HOMO-4) molecular orbitals are mainly composed of F-2p AOs with detectable contribution from Th-6d AOs, based on Figs. 1, 3, 5 and 7, suggesting there exists head-on interplay between the AOs of fluoride and thorium atoms. However, the interaction of Th and F is essentially weak for overpowering dedication from F-2p AOs; therefore, the effective bond order between Th and F atoms in these complexes could be viewed as less than one, as shown in Table 8.

Fig. 7Full-screen View

(Color online) Contour plots of Kohn-Sham MOs of TeThF₂ (isosurf = 0.05 a.u).

Fig. 8Full-screen View

Qualitative Kohn-Sham molecular orbital energy level diagram of TeThF₂. The energy of atomic orbitals was shifted up with 5.67 eV.

The relevant NBO computational results for the OThF₂ to TeThF₂ are compared with those for ThO to ThTe, as listed in Table 4 to Table 6. Table 4 shows the increment of Th-6d populations and the decrement of Th-5f population along both the series from OThF₂ to TeThF₂ and from ThO to ThTe, respectively. Moreover, the 6d and 5f population values in EThF₂ are higher than those in the corresponding ThE. A highly polarized multiple bond character for all Th-E bonds in EThF₂ and ThE can be observed from the NBO analyses. The multiple bonds have a significant contribution from Th in the Th-S, Th-Se, and Th-Te bonds as compared with the that in the Th-O bond, where both the π and σbonds have the same trends, suggesting a weaker covalency of the Th-O chemical bond compared to its counterparts, which is in accordance with the decrease in electronegativity from O to Te. From OThF₂ to TeThF₂ and ThO to ThTe, decreasing f character and increasing d character are observed in the Th-E chemical bonds; this trend is in accordance with the natural electron population in Th-6d AO and Th-5f AO. With the addition of two F atoms, the natural electron charges on the Th center in EThF₂ (E = O, S, Se, Te) becomes more positive than those in ThE (E = O, S, Se, Te) because of the strong electronegativity of F, thus forming a higher oxidation state of Th. Furthermore, natural electron charges on the Th center decrease from 2.45 to 2.16 along the series of EThF₂, which is consistent with the decreased donation from Th to E down the chalcogen group in the order O < S < Se < Te.

Furthermore, we performed the theoretical bond analyses of EThF₂ and EThF₂^- (E = O, S, Se, Te), as displayed in Table 7 and Table 8. Generally, the bond orders of Th-E and Th-F in OThF₂ are slightly lower than those in EThF₂ (E = S, Se, Te), in which the latter species have nearly the same bond order; the same trend occurs in EThF₂^- (E = O, S, Se, Te). Moreover, the bond orders of Th-E and Th-F in anions are lower than those in the corresponding neutral species, suggesting that the extra electron undermines the interaction between Th and E (E = O, S, Se, Te) as well as Th and F and that the SOMO of anions or the lowest unoccupied molecular orbital (LUMO) of the neutral molecules exhibit a non-negligible anti-bonding character, which are in accordance with the downward trend of bond lengths from the anions to the corresponding neutral ones.