Quantum Chemical Analysis of Uranium Trioxide Conformers

The shapes of two hypothetical conformers of uranium trioxide UO3 were analyzed by DFT calculations and the structures of localized molecular orbitals (LMOs). It was shown that differences between the Y- and T-shapes of UO3 were due mainly to the different contributions of the U 6pz- and 6px-orbitals to the corresponding LMOs and to the formation of specifi cally shaped regions of higher electron density in the vicinity of this atom.

Without disregarding completely the possibility that the two equilibrium confi gurations of UO 3 could be an artefact due to assumptions used in the calculation, we postulated that the existence of such stable shapes did not contradict quantum mechanical concepts about the structure of molecular compounds and the formation of chemical bonds and could be explained in terms of localized molecular orbitals (LMOs). It is well known that LMOs can correspond to atomic cores, chemical bonds, or unshared electron pairs [15]. If the shape of the LMOs refl ects the type and direction of the chemical bond, then an analysis of the contributions of various AOs to a given LMO and a comparison of analogs of LMOs for different compounds (or conformers of a single compound) of similar electronic structures enables the specifi cs of their steric structures to be determined.
Calculation Method. Equilibrium structures were optimized and force fi elds and vibrational eigen frequencies were calculated in the harmonic approximation for UO 3 conformers and UO 2 2+ using the applied quantum chemical program GAMESS-US [16,17]. The MacMolPlt [18] and ORTEP [19] programs were used to visualize the obtained results. The relativistic effective core potential (RECP) LANL2DZ [20] was used to approximate the U atom by replacing 78 inner electrons (Large Core approximation); specially developed DZ basis sets for this RECP, for the other U electrons. The O atoms were described based on standard full-electron correlation-consistent Dunning basis families cc-pVnZ and cc-pCVnZ [21]. The RECP and corresponding basis sets were generated using the Extensible Computational Chemistry Environment Basis Set Database [22][23][24]. The hybrid exchange-correlation functional B3LYP was also used in all calculations [25][26][27]. The approximation used in the calculations was also successful for modeling the structure and vibrational spectra of U-containing compounds (UO 2 Cl 2 , UCl 4 , and their complexes) [28,29]. LMOs were constructed by the Edmiston and Ruedenberg method [30]. Two types of designations were used for spherical functions with a non-zero l value, i.e., with Cartesian projections or with an |m l | value. The signs "+" or "-" in this instance corresponded to the combination sum or difference of functions with m l with opposite signs. A general set was used for the f-orbitals. Thus, alternative designations p 0 , p +1 , and p -1 corresponded to the set of spherical functions p z , p x , and p y ; . In each instance, the designations were chosen due to convenience and appearance. Results and Discussion. UO 3 can be viewed as the simplest example of equatorial coordination of O to UO 2 2+ [31]. This approach is refl ected in one of the names for UO 3 , i.e., uranyl oxide. Therefore, structural features of the UO 3 conformers can be determined by relying on concepts about the uranyl electronic structure, which was studied several times by quantum chemistry at various theory levels [13,[32][33][34][35][36][37][38]. It was shown that uranyl U=O bonds have σ-and π-type features. The σ-type orbitals are formed by overlap of 6d 0 -and 7s-orbitals (symmetric MO) or 5f 0 -and 6p 0 -orbitals (asymmetric MO) of U with hybrid sp z -orbitals of O atoms. The π-type MOs are formed by overlap of 6d xz -and 6d yz -orbitals (symmetric MO) or 6p x -, 6p y -, 2 5 xz f -, and 2 5 yz f -orbitals (asymmetric MO) of U with O 2p x -and 2p y -orbitals. The π-electrons are localized near the O atoms so that the order of the uranyl bonds is intermediate between a value of 2 and 3.
The active space for uranyl ion in the Large Core RECP approximation consists of 28 electrons that form 14 LMOs. Three of them (U I , U II , and U III ) correspond to 1s-orbitals of O atoms and 6s-orbitals of the U atom; another two (U V and U VI ), to U 6p x -and 6p y -orbitals. These LMOs are localized on the atoms, i.e., do not correspond to chemical bonds. They will not be further examined. The remaining 9 LMOs are divided into three groups. The fi rst of these consists of LMO U IV ; the second, 6 LMOs (U VII , U VIII , U IX , U X , U XII , U XIII ); the third, 2 LMOs (U XI , U XIV ). The U IV LMO (Fig. 2a) is formed from U 6p 0 -(66%) and 5f 0 -orbitals (1%) and O s-(28%) and p 0 -orbitals (5%) (here and henceforth the separate AOs are rounded to units of %) and is a σ-orbital. Each LMO of the pair U XI and U XIV (Fig. 2c) is localized on one of the uranyl bonds and is formed from U 6s-(3%), 7s-(2%), 6p 0 -(21%), 6d 0 -(7%), 5f 0 -orbitals (28%) and s-(7%) and p 0 -orbitals (32%) of the corresponding O atom and is also a σ-type orbital. The six remaining LMOs are divided into triplets (U VII , U XII , U XIII and U VIII , U IX , U X ) localized on each of the uranyl bonds (Fig. 2b). The LMOs of each triplet are rotated relative to each other around the z axis by 120°. All aforementioned types of active subshells of U with m l = 0, ±1 in addition to s-(26%) and p 0 -orbitals (59%) of the corresponding O atom contribute to these LMOs. Of the U AOs, the U 6p x -(1%), 6p y -(1%), 6p z -(8%), 6d +1 -(2%), 6d -1 -(1%), and 5f +1 -orbitals (1%) contribute most to the U VII -orbital. LMOs of this type are π-orbitals. In general, uranyl LMOs are in agreement with concepts about the electronic structure of this compound [13,[32][33][34][35][36][37][38]. The calculated order of the uranyl bonds is 2.38.
Let us examine the T-and Y-shapes of UO 3 . The active space for UO 3 in the approximation given above is limited to 38 electrons that form 19 LMOs. The following correspondence occurs between the Cartesian systems for the trioxide and uranyl: x, y, z (trioxide) ↔ z, x, y (uranyl). Therefore, for example, the analog of the p 0 -(p z -) orbital for the uranyl U atom is the p +1 -(p x -) orbital of the trioxide U atom. For the T-shape of the trioxide, the LMOs T I , T II , T IV , T VIII , and T XV are analogs of U I , U II , U III , U V , and U VI LMOs of uranyl, respectively, with T III localized on the third O atom and T VII , on all three O atoms. These LMOs are not examined further. The remaining 12 LMOs can be separated into fi ve groups: one LMO (T V ), one LMO (T VI ), six LMOs (T X , T XI , T XII , T XIII , T XIV , T XVI ), three LMOs (T IX , T XVII , T XVIII ), and one LMO (T XIX ).
The T V LMO (Fig. 3a) is an analog of U IV . It is formed from U 6p x -orbitals (62%) in addition to s-(33%) and p xorbitals (4%) of uranyl O atoms. The total contribution of U and O orbitals to non-zero z-projections (d xz , f xz 2 , etc.) is ~1%. The T VI LMO has no analog among the uranyl LMOs. It is localized mainly on the bond to the third O atom and has a clearly pronounced section of increased electron density (lobe) between the uranyl bonds (Fig. 3b). The shape of this σ-type LMO is due to the dominant contribution of the U 6p z -orbital (67%) in addition to 2s-and 2p z -orbitals of the third O atom (25%). The contributions of the uranyl O s-and p z -orbitals to this LMO are ~7%. The next six LMOs (T X , T XI , T XII , T XIII , T XIV , T XVI ) are analogs of the sextet of U orbitals. They are also split into three triplets (T X , T XI , T XIII are localized on a one uranyl bond; T XII , T XIV , T XVI , on the other) and encompass each of these bonds from three sides. In contrast with the uranyl case, the examined trioxide LMOs are not fully equivalent because the uranyl group is not axially symmetric. All aforementioned types of active U subshells with m l = 0, ±1, ±2, ±3 in addition to 2s-(6%) and p x -, p y -, and p z -orbitals (75%) of the corresponding O atom contribute to these LMOs. The U AOs that contribute most to the T XII orbital (Fig. 3c) are the 6p x -(3%), 6d +2 -(1%), 6d -2 -(2%), 5f +1 -(2%), 5f +3 -(2%), and 5f -3 -orbitals (3%). The next three LMOs are π-type (T IX , T XVII , T XVIII ) and are localized on the bond to the third O atom. They also encompass this bond from three sides and are not fully equivalent because of the presence of an xz symmetry plane for the trioxide. Like for the π-type LMOs of the uranyl bonds, all aforementioned types of active U subshells with m l = 0, ±1, ±2, ±3 in addition to 2s-(16%) and p x -, p y -, p z -orbitals (65%) of the third O atom contribute to this type of LMO. The U AOs that contribute most to the T XVIII -orbital (Fig. 3d) are the 6p z -(6%), 6d -2 -(2%), 5f 0 -(2%), 5f +1 -(1%), and 5f -1 -orbitals (4%). The remaining LMO T XIX is also localized on the bond to the third O atom.
For the Y-shape of the trioxide, LMOs Y I , Y II , Y III , Y IV , Y VII , Y VIII , and Y XVIII are analogs of T III , T II , T I , T IV , T VII , T VIII , and T XV , respectively, of the T-shape LMOs and are not further examined. The remaining 12 LMOs can be divided into six groups of one LMO (Y V ), one LMO (Y VI ), six LMOs (Y IX , Y X , Y XIII , Y XVI , Y XVII , Y XIX ), two LMOs (Y XI , Y XIV ), one LMO (Y XII ), and one LMO (Y XV ). LMO Y V is an analog of T VI . It is also localized mainly on the bond to the third O atom. However, it does not have the lobe characteristic of T VI (Fig. 4a). This is due to the smaller contribution of the U 6p z -orbital (60%) and more substantial contributions of the uranyl O s-and p z -orbitals (14%) while preserving the previous contribution of the s-and p z -orbitals of the third O atom (24%). LMO Y VI (Fig. 4b) is an analog of T V . It is formed from U 6p x -orbitals (66%) in addition to uranyl O s-(30%) and p x -orbitals (1%). The total contribution of U and O orbitals to non-zero z-projections is ~3%. The next six LMOs of the Y-shape (Y IX , Y X , Y XIII , Y XVI , Y XVII , Y XIX ) are obviously analogs of the corresponding sextet of T-shape orbitals and have similar characteristics. LMOs Y IX , Y XIII , and Y XVII are localized on one uranyl bond; Y X , Y XVI , and Y XIX , on the other. Like for the T-shape, all aforementioned types of active U subshells with m l = 0, ±1, ±2, ±3 in addition to 2s-(8%) and p x -, p y -, p z -orbitals (70%) of the corresponding O atoms contribute to such LMOs. The U AOs 6p x -(4%), 6p z -(4%), 6d 0 -(2%), 6d -1 -(1%), 6d -2 -(1%), 5f 0 -(1%), 5f +1 -(3%), 5f +2 -(1%), 5f -2 -(2%), 5f -3 -orbitals (1%) contribute most to the Y XVII -orbital (Fig. 4f). The pair of LMOs Y XI and Y XIV and another LMO Y XII of the Y-shape are analogs of   three π-type LMOs of the T-shape that are localized on the bond to the third O atom (T IX , T XVII , and T XVIII ). LMO Y XII (Fig. 4d), in contrast with T XVIII (Fig. 3d), is symmetric relative to the xz plane and; therefore, is placed into a separate group. All aforementioned types of active U subshells with m l = 0, ±1, ±2, ±3 in addition to 2s-(8%) and p x -and p z -orbitals (67%) of the third O atom contribute to the Y XI and Y XIV LMOs. The U AOs 7s-(2%), 6p z -(3%), 6d 0 -(2%), 6d +1 -(2%), 5f 0 -(6%), and 5f +1 -orbitals (4%) contribute most to the Y XI -orbital (Fig. 4c). The structure of the Y XII LMO is simpler. It is formed from U 6d -1 -(4%) and 5f -1 -orbitals (7%) and p y -orbitals (88%) of the third O atom. The remaining LMO of the Y-shape, Y XV , has no analog among the T-shape LMOs and is formed from U and uranyl O AOs with non-zero x-projections, i.e., 6p x -(60%), 6d +1 -(3%), 5f +1 -(7%), and 5f +3 -orbitals (1%) of the U atom and 2s-(15%) and p x -and p z -orbitals (14%) of the uranyl O atoms. A characteristic feature of the Y XV -orbital (Fig. 4e) is the presence of two lobes localized at corners formed by the uranyl bonds and the bond to the third O atom.
Thus, in our opinion, important factors for stabilizing the T-shape of the trioxide are the substantial contributions of the 6p z -orbital to σ-type LMOs T VI and T XIX localized on the bond to the third O atom and forming lobes situated between the uranyl bonds and thereby repelling them from each other. In turn, the dominant contribution of the 6p x -orbital to LMO Y XV that is responsible for forming the lobes that press the uranyl bonds toward each other can stabilize the Y-shape of the trioxide.
Conclusions. Quantum chemical modeling in terms of density functional theory LANL2DZ/B3LYP/cc-pVDZ predicted the existence of two stable conformers of molecular UO 3 . We attempted to explain this phenomenon on the basis of concepts of LMOs because their shape and structure refl ect features of the electronic and geometric structures of molecular systems. Analytical results for LMOs of uranyl and the two shapes of UO 3 indicated that U AOs contribute most to the σ-type bonds; the O AOs, to the π-type. As a result, π-type LMOs in the trioxide preserve mainly the structure and shape of the corresponding U orbitals. The principal differences in LMOs of the T-and Y-shapes of UO 3 are related to the different contributions of U AOs and those of the third O atom in the molecular plane for the Y-shape and the lack of such localization for the T-shape. These differences of LMOs are refl ected directly in the structures of the two shapes of UO 3 .
The existence of the examined conformers is hypothetical in nature. Experimental confi rmation of the stability of the Y-and T-shapes of UO 3 would be a unique example of a bistable molecular system with the bond angle as the coordinates of large-amplitude intramolecular motion.