On the Linear Geometry of Lanthanide Hydroxide (Ln-OH, Ln=La-Lu)
ABSTACT. Lanthanide hydroxides are key species in a variety of catalytic processes and in the preparation of corresponding oxides. This work explores the fundamental structure and bonding of the simplest lanthanide hydroxide, LnOH (Ln=La-Lu), using density functional theory calculations. Interestingly, the calculations predict that all structures of this series will be linear.Furthermore, these results indicate a valence electron configuration of s 2 p 4 for all LnOH compounds, suggesting that the lanthanide-hydroxide bond is best characterized as a covalent triple bond.
INTRODUCTION<!>COMPUTATIONAL DETAILS<!>RESULTS AND DISCUSSIONS<!>CONCLUSIONS<!>ASSOCIATED CONTENT
<p>Lanthanide compounds exhibit unique electronic and magnetic properties yielding a wide diversity of high-impact applications. [1][2][3][4][5] Lanthanides and, in particular, their corresponding hydrides, oxides, and hydroxides are known to efficiently facilitate important fundamental chemical transformations. Specific reactions catalyzed by such lanthanide species include oxidative dehydrogenation of alkenes, exchange of deuterium, and oxygen exchange. [1][2][3][4][5][6][7][8][9][10][11][12][13][14] While the unique magnetic and optical properties of lanthanides have been attributed to partially filled 4f shells, it has been shown that these metal orbitals are essentially unaffected in ligand bonding and are, at most, weakly involved in chemical bonding. Indeed, their poor overlap with ligand orbitals results in very little energy stabilization. [15][16][17] Instead, bonding in such species is driven by 6s and 5d orbitals. 18 The question of covalent bonding in f element complexes has been an active research area for some time. [19][20][21][22][23][24] Work by B. Roos and P. Pyykkoo suggested lanthanide carbene (LnCH2 + ) compounds exhibit double bond character. 25 Bonding was found to involve 5d lanthanide orbitals while the 4f orbitals serve as spin counterweights and as an electron reservoir. Interestingly, studies on small actinide molecules have shown different bonding behavior, where, unlike lanthanides, 5f orbitals can significantly contribute to bonding. For instance, Kovacs has shown that AnO3 exhibits actinide-oxygen bonds include contributions from actinide 5f orbitals. 26 Similar studies performed on AnC2 and AnCl3 have also implicated actinide 5f orbitals in bond formation. [26][27][28][29][30][31][32] Motivated by our lab's recent interest in metal oxide clusters, [33][34][35][36][37][38] we were intrigued by an apparent dearth of literature exploring the structure and bonding of lanthanide hydroxides. With the goal of exploring the full series, we note the inclusion of PmOH; while included here for completeness, Pm is unstable and thus PmOH is not likely to be experimentally studied. Hydroxide complexes play an important role in catalysis, biological systems, and in materials science. [4][5]11 Thus, knowledge of bonding in such complexes will provide a more complete understanding of reaction mechanisms and enhance the development of new catalysts and new materials. 39 Of particular interest here is the series of LnOH complexes, which allows for the study of the fundamental aspects of hydroxide bonding with lanthanide metals. Furthermore, such cluster species serve as models for electronically strained defect sites on surfaces. 40 In support of this use of small molecules and clusters as models for such sites, Baker and coworkers recently demonstrated the highly localized nature of the electronic structure of metal oxides. 41 In this study, density functional theory (DFT) is used to examine the electronic structure of lanthanide hydroxides. In particular, this report examines the ground state of each Ln-OH (Ln=La-Lu) followed by an in-depth investigation of the nature of the lanthanide-hydroxide bond.</p><p>Relating this result to the well-studied structure and bonding of transition metal hydroxides, [42][43][44][45][46][47][48][49][50] we observe a similarity with early transition metal hydroxide bonding. Specifically, we show that the nature of the lanthanide hydroxide bond involves important π-bonding.</p><!><p>Calculations were carried out using a local development version of the Gaussian suite of electronic structure programs. 51 The B3PW91 density functional was employed [52][53][54][55][56][57] using the unrestricted spin formalism for open shell cases. The segmented all-electron relativistically contracted zeroth-order regular approximation (SARC-ZORA) basis set was used for all lanthanide centers. 58 This basis set provides an efficient alternative to effective core potentials in many routine DFT studies of similar species. Moreover, the SARC-ZORA basis set provides a balanced treatment of different electronic configurations of lanthanides. [58][59][60] The Dunning-style correlation consistent basis set, aug-cc-pVTZ, was used for both hydrogen and oxygen centers. [61][62] To account for relativistic effects, the second-order Douglass-Kroll-Hess scalar relativistic correction was employed during geometry optimizations and frequency calculations. 63 Geometry optimizations were carried out using standard methods and all nature of all potential energy surface stationary points was confirmed by second-derivative calculations. 64 In all cases, the stability of converged Kohn-Sham determinants was verified. [65][66] Fragment-based orbital perturbation theory analysis was performed on all molecules using the Natural Bond Orbital program (NBO6). 67</p><!><p>To explore the structure and bonding of LnOH, we began by calculating minimum energy structures for each member of the series. Table 1 presents the geometric parameters of optimized LnOH structures. The lanthanide-oxygen bond lengths range from 1.90 to 2.09 Å and the O-H bond is consistently ~0.95Å through the series. For all species, the Ln-O-H bond angle is linear, suggesting two possible bonding descriptions. Either the compounds are covalently bound with the oxygen center adopting a sp hybridization and the Ln-OH bond featuring π-bonding character, or the system is best described as ionic and bound by a charge/dipole interaction. In an effort to fully characterize the Ln-hydroxide bond and understand the observed linear structure, three analyses have been carried out. Specifically, this study examines the canonical molecular orbitals (MOs) predicted by DFT, considers an analysis of ionic bond character, and employs a perturbational fragment MO analysis. [68][69] Figure 1 shows the MO diagram of europium hydroxide, which is shown as a representative case for the LnOH series. The MO diagrams for the 14 other members of this series are substantially the same, with changes in the number of valence electrons resulting in a change of electron count in 4f, 5d, and 6s based non-bonding orbitals. In addition to the differences in 4f occupations, GdOH and LuOH exhibit doubly-occupied 6s based non-bonding MOs. LaOH also has a doubly occupied 6s metal-based MO and an empty 4f manifold unlike the other LnOH species. The MO diagrams of CeOH, PrOH, NdOH, and PmOH share the common feature of a singly-occupied 5d orbital as the highest occupied MO (HOMO). Importantly, the relative energetic ordering of bonding and antibonding orbitals is unchanged across the full Ln series and, consequently, the Ln-(OH) bond order remains constant. Noteworthy are additional nearby low-energy states located for CeOH, NdOH, and PmOH. Indeed, multiple states for these species lie within a window of roughly 0.1 eV, which underscores how close-lying the 4f, 5d and 6s orbitals are in these molecules. In all cases, though, the minimum energy structure remains linear and the Ln-(OH) bond order is unchanged (vide infra). Full details regarding such states are provided in the Supporting Information. Examination of the bonding orbitals supports assignment of the Ln-OH bond order as 3.</p><p>Specifically, the MO diagram includes an occupied s bonding orbital and two degenerate doublyoccupied p. The metal-based 4f and 6s orbitals are predominantly non-bonding. The 6s orbital is singly-occupied across the lanthanide hydroxide series except for LaOH, GdOH, and LuOH where the 6s based MO is doubly occupied as stated earlier, while 4f occupation changes with the atomic number of the lanthanide. A Mulliken population analysis (Supporting Information, Table S7)</p><p>shows, as might be expected, that the bonding orbitals are mostly ligand based. Indeed, in both s and π bonds the contribution from Ln centered atomic orbital basis functions can be as small as 3%. The Mulliken analysis further shows that metal participation in bonding primarily involves p and d Ln atomic orbitals, though the bonding in some members of the series includes some metal f-orbital character.</p><p>In order to explore the strength of the LnOH p MOs (Fig. 1), we investigated the dependence of the Ln-OH bond length with respect to changes in the Ln-O-H angle. Three specific LnOH cases were chosen: CeOH, EuOH, and YbOH. The bond lengths were relaxed while constraining the Ln-O-H angle to 109.5° and 120°. Table 2 shows the results of these calculations.</p><p>For these three specific lanthanide hydroxides, the bond length decreases as the angle increases from 109° to the equilibrium value of 180°. This indicates that as the bond angle relaxes towards the linear minimum energy geometry, the sum of the covalent radii of the atoms decrease.</p><p>Following Pyykko, [70][71][72] we interpret a decrease in the additive covalent radii as an indirect measure of an increase in bond order. Thus, the results of Table 2 indicate the bond order in the optimized linear structures is higher than in the bent structures. As mentioned above, the lanthanide-hydroxide linear geometry also could be due to electrostatic charge-dipole interactions. To explore this possibility, we compared optimized Ln-OH bond lengths with sums of Ln + and OHionic radii. 73 An ideal ionic bond length is the sum of ionic radii of the two ions, and this value is expected to be appreciably larger than the associated covalent bond length. For the lanthanide ionic radii, where multiple radii are reported, we consider the smallest ionic radii for each lanthanide given by Shannon. 74 The reported ionic radii by Shannon correspond to higher oxidation states (+2, +3, and +4) of the studied lanthanides. While the required Ln + and OHare missing, we can estimate their values by considering changes in ionic radii of ions as their oxidation states and coordination numbers change. A detailed description of the determination of the proper values of ionic radii for Ln + and OHis provided in the supporting information. Table 3 gives effective ionic radii and optimized bond lengths given by our DFT calculations for the LnOH series. In all cases, the optimized bond lengths are much shorter than the corresponding (ideal) LnOH ionic bond length. These results suggest Ln-OH bonding is not predominantly ionic in nature. To more fully quantify the ionic character of the Ln-OH bond, we calculated the percent ionic character of the bond for each member in the series. 73 Specifically, dipole moments evaluated as part of our DFT calculations have been compared with dipoles evaluated classically between Ln cations and the hydroxide anion. For purely ionic systems, one would expect the ions to be Ln + and OH -. As shown in Table 4, the ionic character of the Ln-(OH) bond varies with the lanthanide.</p><p>For LaOH, which has zero f orbital population, the ionic character of the metal-hydroxide bond is essentially zero, suggesting the metal-hydroxide bond is purely covalent. The metal-hydroxide ionic bond character for the rest of the series varies from 5% at LuOH to 17% at YbOH. Stepping across the period from Ce to Eu, with a half-filled f shell, the ionic character of this bond increases.</p><p>Another periodic trend of increasing ionic character is also observed as one moves across the series from Gd to Yb. These trends may be understood by considering the occupation of f-based nonbonding MOs. In addition, the classical idealized dipole moment was calculated at two other cases (shown in Table 4). Specifically, in one case the center of the OH dipole fragment was taken to be at the midpoint of the O-H bond and in the other case the charge center was placed at the hydrogen nucleus. In both cases, the calculated dipole moment was larger than the dipole moment obtained from DFT calculations. The dipole moments resulting from these additional cases also resulted in a small percent ionic character (see Supporting Information).</p><p>To consider the extent of Ln-(OH) bond covalency, we performed a fragment based orbital perturbation study based on the Natural Bonding Orbital (NBO) model. 75 Specifically, the metal center (in the +1 oxidation state) and hydroxide ligand (-1 charge) were defined as separate fragments for the NBO fragment orbital second-order perturbation model. Table 5 reports NBO based second-order perturbation stabilization energies arising from inter-fragment occupiedunoccupied interactions. [67][68][69]75 As seen in the MO diagram discussed above (Fig. 1), the LnOH series shows both s and π bonding interactions. The NBO analysis (Fig. 2 and Table 5) supports this characterization. Indeed, the NBO study indicates that the s bond is formed from hydroxide lone pair donation into the empty lanthanide 5dz2. In the second-order treatment of the model the stabilization energies from this bonding interaction are 11.2-25.4 kcal/mol. The NBO analysis also shows two significant interactions corresponding to π bonding between the lanthanides and hydroxide ligand. Such interactions result from lanthanide 5dxz and 5dyz orbitals interacting with hydroxide 2px and 2py orbitals. The calculated stabilization energies due to these π interactions range from 6.0 to 11.0 kcal/mol.</p><p>The s and π stabilization energies increase with deceasing Ln-OH bond lengths (Table 1). However, rather than a single periodic trend being observed as one moves across the Ln series, our results show bimodal behavior. Moving across the series from Ce to Eu, results in decreasing stabilization energies. A second decreasing trend begins at Gd and continues to Yb. Both La and Lu, the two extremes of the lanthanide series, are outliers. Similar to the discussion above regarding the ionic character of Ln-(OH) bonds, Ce-Eu/Gd-Yb trends can be understood by considering 6s5d4f occupations.  Linear metal-hydroxide compounds are not unique to the lanthanide species described in this work. Early first row transition metal hydroxides, ScOH, TiOH, and VOH, are also known to exhibit a linear conformation. Those systems feature s bond donation from an oxygen lone pair to the empty metal 3dz2 orbital, as well as donation of two additional oxygen lone pairs to metal 3dxz and 3dyz orbitals. Thus, the bond order in those systems is 3, [42][43][44] just as our results suggest for LnOH.</p><p>Interestingly, the bonding changes as one moves from early to late transition metals.</p><p>Various studies on CuOH report weaker Cu-OH bonding than for the early transition metals. [45][46][47][48] Previous studies, supported by both experimental and DFT calculations, have also shown that CuOH exhibits a bent geometry, unlike ScOH, TiOH or VOH. [46][47] For example, Karzhavyi et al. reported a bent CuOH structure with a Cu-O-H angle of 107-110º in both a solid and a molecular calculation of CuOH. 48 Other previous work also suggest that zinc hydroxide exhibits a bent structure. [49][50] This difference in bonding trends between early and late transition metal hydroxides is due to differences in 5d occupation. As the d-orbital occupation increases, πdonation from the hydroxide lone pair orbitals becomes less favorable.</p><p>As mentioned, the LnOH species considered in this work have been motivated by recent fundamental bonding studies on gas phase lanthanide molecules and clusters. The analysis presented above suggests that in the case of multiple hydroxyl and oxo ligands coordination, one would expect a distortion of the Ln-O-H bond from its linear structure due to the inaccessibility of the lanthanide 5d orbitals. In recent studies, Chick Jarrold and coworkers presented the structure and bonding of various lanthanide oxides and hydroxides, some of which involve multiple lanthanide-oxygen bonds. 1,14,[76][77] In agreement with our results, their experimental photoelectron spectroscopic studies and supporting DFT calculations have shown that Ln(I) complexes (e.g.</p><p>EuOH 1 ) favor a linear geometry, while lanthanide complexes with a higher coordination number (two or more hydroxide ligands coordinated to the lanthanide center) and corresponding higher lanthanide oxidation state (+2, +3, etc.) yield bent Ln-O-H angles between 140 o and 160 o . 14,77</p><!><p>In this paper, DFT calculations have been used to explore the fundamental structure and bonding of lanthanide hydroxide complexes. For all members of this series, the minimum energy structure is a linear. An analysis of the canonical MOs establishes a metal-hydroxide bond order of 3, involving one sand two pbonding MOs. Additional analysis suggests that the percent ionic character of the bond varies with the lanthanide metal. Interestingly, the degree of ionic character is relatively small in all cases (ranging from < 1% to ~17%). A fragment based orbital perturbation study using the NBO model was employed to examine the strength of covalent bonding in the LnOH series. In agreement with the qualitative features of the canonical MOs, the NBO fragment orbital analysis identifies meaningful sand p-bonding interactions. Taken together, this work supports the assignment of the lanthanide-hydroxide bond as a triple bond.</p><!><p>Table providing total self-consistent energies, S 2 expectation values for all LnOH species discussed in the paper, descriptions of low-lying states located for select LnOH systems, and results from a Mulliken population analysis of the series of LnOH species.</p>