Thermodynamic, electronic and structural properties of Cu/CeO2 surfaces and interfaces from first-principles DFT+U calculations

The thermodynamic, structural and electronic properties of Cu-CeO(2) (ceria) surfaces and interfaces are investigated by means of density functional theory (DFT+U) calculations. We focus on model systems consisting of Cu atoms (i) supported by stoichiometric and reduced CeO(2) (111) surfaces, (ii) dispersed as substitutional solid solution at the same surface, as well as on (iii) the extended Cu(111)/CeO(2)(111) interface. Extensive charge reorganization at the metal-oxide contact is predicted for ceria-supported Cu adatoms and nanoparticles, leading to Cu oxidation, ceria reduction, and interfacial Ce(3+) ions. The calculated thermodynamics predict that Cu adatoms on stoichiometric surfaces are more stable than on O vacancies of reduced surfaces at all temperatures and pressures relevant for catalytic applications, even in extremely reducing chemical environments. This suggests that supported Cu nanoparticles do not nucleate at surface O vacancies of the oxide, at variance with many other metal/ceria systems. In oxidizing conditions, the solid solutions are shown to be more stable than the supported systems. Substitutional Cu ions form characteristic CuO(4) units. These promote an easy and reversible O release without the reduction of Ce ions. The study of the extended CeO(2)(111)/Cu(111) interface predicts the full reduction of the interfacial ceria trilayer. Cu nanoparticles supported by ceria are proposed to lie above a subsurface layer of Ce(3+) ions that extends up to the perimeter of the metal-oxide interface.     

On the interaction of Mg with the (111) and (110) surfaces of ceria

The catalytic activity of cerium dioxide can be modified by deposition of alkaline earth oxide layers or nanoparticles or by substitutional doping of metal cations at the Ce site in ceria. In order to understand the effect of Mg oxide deposition and doping, a combination of experiment and first principles simulations is a powerful tool. In this paper, we examine the interaction of Mg with the ceria (111) surface using both angle resolved X-ray (ARXPS) and resonant (RPES) photoelectron spectroscopy measurements and density functional theory (DFT) corrected for on-site Coulomb interactions (DFT + U). With DFT + U, we also examine the interaction of Mg with the ceria (110) surface. The experiments show that upon deposition of Mg, Ce ions are reduced to Ce(3+), while Mg is oxidised. When Mg is incorporated into ceria, no reduced Ce(3+) ions are found and oxygen vacancies are present. The DFT + U simulations show that each Mg that is introduced leads to formation of two reduced Ce(3+) ions. When Mg is incorporated at a Ce site in the (111) surface, one oxygen vacancy is formed for each Mg to compensate the different valencies, so that all Ce ions are oxidised. The behaviour of Mg upon interaction with the (110) surface is the same as with the (111) surface. The combined results provide a basis for deeper insights into the catalytic behaviour of ceria-based mixed oxide catalysts.     

Electronic and atomistic structures of clean and reduced ceria surfaces

The atomistic and electronic structures of oxygen vacancies on the (111) and (110) surfaces of ceria are studied by means of periodic density functional calculations. The removal of a neutral surface oxygen atom leaves back two excess electrons that are shown to localize on two cerium ions neighboring the defect. The resulting change of valency of these Ce ions (Ce4+ --> Ce3+) originates from populating tightly bound Ce 4f states and is modeled by adding a Hubbard U term to the traditional energy functionals. The calculated atomistic and electronic structures of the defect-free and reduced surfaces are shown to agree with spectroscopic and microscopic measurements. The preferential defect segregation and the different chemical reactivity of the (111) and (110) surfaces are discussed in terms of energetics and features in the electronic structure.     

The surface dependence of CO adsorption on Ceria

An understanding of the interaction between ceria and environmentally sensitive molecules is vital for developing its role in catalysis. We present the structure and energetics of CO adsorbed onto stoichiometric (111), (110), and (100) surfaces of ceria from first principles density functional theory corrected for on-site Coulomb interactions, DFT+U. DFT+U is applied because it can describe consistently the properties of both the stoichiometric and reduced surfaces. Our major finding is that the interaction is strongly surface dependent, consistent with experiment. Upon interaction of CO with the (111) surface, weak binding is found, with little perturbation to the surface or the molecule. For the (110) and (100) surfaces, the most stable adsorbate is that in which the CO molecule bridges two oxygen atoms and pulls these atoms out of their lattice sites, with formation of a (CO(3)) species. This results in a strong modification to the surface structure, consistent with that resulting from mild reduction. The electronic structure also demonstrates reduction of the ceria surface and consequent localization of charge on cerium atoms neighboring the vacancy sites. The surface-bound (CO(3)) species is identified as a carbonate, (CO(3))(2-) group, which is formed along with two reduced surface Ce(III) ions, in good agreement with experimental infrared data. These results provide a detailed investigation of the interactions involved in the adsorption of CO on ceria surfaces, allowing a rationalization of experimental findings and demonstrate further the applicability of the DFT+U approach to the study of systems in which reduced ceria surfaces play a role.     

SO2 on TiO2(110) and Ti2O3(102) nonpolar surfaces: a DFT study

Density functional molecular cluster calculations have been used to investigate the interaction of SO(2) with defect-free TiO(2)(110) and Ti(2)O(3)(102) surfaces. Adsorbate geometries and chemisorption enthalpies have been computed and discussed. Several local minima have been found for TiO(2)(110), but only one seems to be relevant for the catalytic conversion of SO(2) to S. In agreement with experiment, the bonding of SO(2) to Ti(2)O(3)(102) is much stronger than that on TiO(2)(110). Moreover, our results are consistent with the surface oxidation and the formation of strong Ti-O and Ti-S bonds. On both substrates, the bonding is characterized by a two-way electron flow involving a donation from the SO(2) HOMO into virtual orbitals of surface Lewis acid sites (), assisted by a back-donation from surface states into the SO(2) LUMO. However, the localization of surface states and the strength of back-donation are very different on the two surfaces. On TiO(2)(110), back-donation is weaker, and it involves unsaturated bridging O atoms, while on Ti(2)O(3)(102), it implies the -based valence band maximum and significantly weakens the S-O bond.     

Effects of deposited Pt particles on the reducibility of CeO2(111)

The interaction of Pt particles with the regular CeO(2)(111) surface has been studied using Pt(8) clusters as representative examples. The atomic and electronic structure of the resulting model systems have been obtained through periodic spin-polarized density functional calculations using the PW91 exchange-correlation potential corrected with the inclusion of a Hubbard U parameter. The focus is on the effect of the metal-support interaction on the surface reducibility of ceria. Several initial geometries and orientations of Pt(8) with respect to the ceria substrate have been explored. It has been found that deposition of Pt(8) over the ceria surface results in spontaneous oxidation of the supported particle with a concomitant reduction of up to two Ce(4+) cations to Ce(3+). Oxygen vacancy formation on the CeO(2)(111) surface and oxygen spillover to the adsorbed particle have also been considered. The presence of the supported Pt(8) particles has a rather small effect (～0.2 eV) on the O vacancy formation energy. However, it is predicted that the spillover of atomic oxygen from the substrate to the metal particle greatly facilitates the formation of oxygen vacancies: the calculated energy required to transfer an oxygen atom from the CeO(2)(111) surface to the supported Pt(8) particle is only 1.00 eV, i.e. considerably smaller than 2.25 eV necessary to form an oxygen vacancy on the bare regular ceria surface. This strongly suggests that the propensity of ceria systems to store and release oxygen is directly affected by the presence of supported Pt particles.     

Reaction of SO2 with AuCeO2(111): importance of O vacancies in the activation of gold

Synchrotron-based high-resolution photoemission was used to study the adsorption and chemistry of SO(2) on AuCeO(2)(111) and AuO(x)CeO(2) surfaces. The heat of adsorption of the molecule on Au nanoparticles supported on stoichiometric CeO(2)(111) was 4-7 kcalmol larger than on Au(111). However, there was negligible dissociation of SO(2) on the AuCeO(2)(111) surfaces. The full decomposition of SO(2) was observed only after introducing O vacancies in the ceria support. AuO(x)CeO(2) surfaces were found to be much less chemically active than AuCeO(2)(111) or AuCeO(2-x)(111) surfaces. The active sites in {Au + AuO(x)}ceria catalysts should involve pure gold nanoparticles in contact with O vacancies.     

Probing the 4f states of ceria by tunneling spectroscopy

Low-temperature scanning tunneling microscopy and spectroscopy have been employed to analyze the local electronic structure of the (111) surface of a ceria thin film grown on Ru(0001). On pristine, defect-free oxide terraces, the empty 4f states of Ce(4+) ions appear as the only spectral feature inside the 6 eV oxide band gap. In contrast, occupied states are detected between -1.0 and -1.5 eV below E(Fermi) in conductance spectra of different point and line defects, such as surface oxygen vacancies, grain boundaries and step edges. They are assigned to partially filled 4f states localized at the Ce(3+) ions. The presence of excess electrons indicates the oxygen-deficient nature of the direct oxide environment. The f state spectroscopy with the STM allows us to probe the spatial distribution of Ce(3+) ions in the ceria surface, providing unique insight into the local reduction state of this chemically important material system.     

Crystal structure and spectroscopic properties of Na(2)K(6)(VO)(2)(SO(4))(7)

Red-brown crystals of a new mixed alkali oxo sulfato vanadium(V) compound Na(2)K(6)(VO)(2)(SO(4))(7), suitable for X-ray determination, have been obtained from the catalytically important binary molten salt system M(2)S(2)O(7)-V(2)O(5) (M = 80% K and 20% Na). By slow cooling of a mixture with the mole fraction X(V(2)O(5)) = 0.24 from 325 degrees C, i.e., just below the liquidus temperature, to the solidus temperature of around 300 degrees C, a dark reddish amorphous phase was obtained containing crystals of the earlier described V(V)-V(IV) mixed valence compound K(6)(VO)(4)(SO(4))(8) and Na(2)K(6)(VO)(2)(SO(4))(7) described here. This compound crystallizes in the tetragonal space group P4(3)2(1)2 (No. 96) with a = 9.540(3) A, c = 29.551(5) A at 20 degrees C and Z = 4. It contains a distorted VO(6) octahedron with a short V-O bond of 1.552(6) A, a long one of 2.276(5) A trans to this, and four equatorial V-O bonds in the range 1.881(6)-1.960(6) A. The deformation of the VO(6) octahedron is less pronounced compared to that of the known oxo sulfato V(V) compounds. Each VO(3+) group is coordinated to five sulfate groups of which two are unidentately coordinated and three are bidentate bridging to neighboring VO(3+) groups. The length of the S-O bonds in the S-O-V bridges of the two unidentately coordinated sulfato groups are 1.551(6) A and 1.568(6) A, respectively, which are unusually long compared to our earlier measurements of sulfate groups in other V(III), V(IV), and V(V) compounds.     

Dual-stimuli responsive behaviors of diblock polyampholyte PDMAEMA-b-PAA in aqueous solution

The rheological behaviour of aqueous suspensions of boehmite (AlO(OH)) modified with different Ce-salts (Ce(NO(3))(3), CeCl(3), Ce(CH(3)COO)(3) and Ce(2)(SO(4))(3)) was investigated at a fixed Ce/Al molar ratio (0.05). Freshly prepared boehmite suspensions were near-Newtonian and time-independent. A shear-sensitive thixotropic network developed when Ce-salts with monovalent anions were introduced in the nanoparticle sols. The extent of particle aggregation dramatically increased with ageing for Ce(NO(3))(3) and CeCl(3) whereas an equilibrium value was reached with Ce(CH(3)COO)(3). The addition of Ce(2)(SO(4))(3) with divalent anions involved no thixotropy but rather a sudden phase separation. The combined data set of IRTF and DRIFT spectra indicated that free NO(3)(-) anions of peptized boehmite adsorb on the nanoparticle surface by H-bond. The introduction of Ce-salts in the boehmite sol led to the coordination between Ce(3+) ions and NO(3)(-) anions adsorbed on boehmite i.e. to [Ce(NO(3))(4)(H(2)O)(x)](-) complex. Such coordination led to a thixotropic behaviour which was lower with Ce(NO(3))(3) compared to CeCl(3) and Ce(CH(3)COO)(3). In contrast, Ce(2)(SO(4))(3) formed insoluble complexes with dissolved aluminium species. The formation of H-bonded surface nitrate complexes was found to play a decisive role on the particle-particle interactions and consequently on the rheological behaviour of the sols.     

A theoretic insight into the catalytic activity promotion of CeO2 surfaces by Mn doping

In this paper, we investigated the primary reduction and oxygen replenishing processes over Mn substitutionally doped CeO(2)(111) surfaces by density functional theory with the on-site Coulomb correction (DFT + U). The results indicated that Mn doping could make the surface much more reducible and the adsorbed O(2) could be effectively activated to form superoxo (O(2)(-)) and/or peroxo species (O(2)(2-)). The Mn doping induced the Mn 3d-O 2p gap state instead of Ce 4f acting as an electrons acceptor and donor during the first oxygen vacancy formation and O(2) replenishing, which helped to lower the formation energy of the first and second oxygen vacancies to -0.46 eV and 1.40 eV, respectively. In contrast, the formation energy of a single oxygen vacancy in the pure ceria surface was 2.08 eV and only peroxo species were identified as the O(2) molecule adsorbed. Our work provides a theoretical and electronic insight into the catalytic redox processes of Mn doped ceria surfaces, which may help to understand the enhanced catalytic performances of MnO(x)-CeO(2) oxides, as reported in previous experimental works.     

Interaction of hydrogen with cerium oxide surfaces: a quantum mechanical computational study

The interaction of the (110) and (111) surfaces of ceria (CeO(2)) with atomic hydrogen is studied with ab initio calculations based on density functional theory. A Hubbard U term added to the standard density functional allows to accurately describe the electronic structure of the two surfaces. The minimum energy configuration for the adsorbed H on each of the two surfaces is obtained. An O-H-O bridge is formed on the (110) surface, whereas an axial tricoordinated OH group results on the (111) surface. For both surfaces, the adsorption of an H atom is accompanied by the reduction of a single Ce ion (which is one of the nearest neighbors of the adsorbed atom) and by a substantial outward protrusion of the O atom(s) directly bound to H. The adsorption of atomic H on the (110) and (111) surfaces is energetically favored by -150.8 and -128.3 kJ/mol, respectively, with respect to free molecular H(2). The calculated frequencies for the OH stretching vibrational mode are 3100 cm(-1) for the (110) surface and 3627 cm(-1) for the (111) surface. The latter value is in excellent agreement with experimental data reported in the literature.     

A theoretical study of surface reduction mechanisms of CeO(2)(111) and (110) by H(2).

Reaction mechanisms for the interactions between CeO(2)(111) and (110) surfaces are investigated using periodic density functional theory (DFT) calculations. Both standard DFT and DFT+U calculations to examine the effect of the localization of Ce 4f states on the redox chemistry of H(2)-CeO(2) interactions are described. For mechanistic studies, molecular and dissociative local minima are initially located by placing an H(2) molecule at various active sites of the CeO(2) surfaces. The binding energies of physisorbed species optimized using the DFT and DFT+U methods are very weak. The dissociative adsorption reactions producing hydroxylated surfaces are all exothermic; exothermicities at the DFT level range from 4.1 kcal mol(-1) for the (111) to 26.5 kcal mol(-1) for the (110) surface, while those at the DFT+U level are between 65.0 kcal mol(-1) for the (111) and 81.8 kcal mol(-1) for the (110) surface. Predicted vibrational frequencies of adsorbed OH and H(2)O species on the surfaces are in line with available experimental and theoretical results. Potential energy profiles are constructed by connecting molecularly adsorbed and dissociatively adsorbed intermediates on each CeO(2) surface with tight transition states using the nudged elastic band (NEB) method. It is found that the U correction method plays a significant role in energetics, especially for the intermediates of the exit channels and products that are partially reduced. The surface reduction reaction on CeO(2)(110) is energetically much more favorable. Accordingly, oxygen vacancies are more easily formed on the (110) surface than on the (111) surface.     

Synthesis of highly active sulfate-promoted rutile titania nanoparticles with a response to visible light

Highly active sulfate-promoted rutile titania (SO(4)(2-)/TiO(2)) with smaller band gap was prepared by an in situ sulfation method, that is, under moderate conditions, sulfate-promoted rutile titania was directly obtained via precipitating Ti(SO(4))(2) in NaOH solution followed by peptizing in HNO(3) without the phase transformation from anatase to rutile. Thus, the negative impacts of phase transformation from anatase to rutile on the structure, surface, and photoactivity properties of the catalysts due to higher calcination temperature can be avoided. The catalysts were characterized by means of thermal analysis, Brunauer-Emmett-Teller analysis (BET), X-ray diffraction (XRD), scanning electron microscopy (SEM), Fourier transform infrared spectroscopy (FT-IR), X-ray photoelectron spectroscopy (XPS), UV-visible spectroscopy, FT-IR pyridine adsorption, and temperature-programmed desorption (TPD). The results show sulfate species are sensitive to the variation of calcination temperature. In the process of peptizing, sulfate species are homogeneously dispersed throughout the bulk of catalysts, allowing sulfate species to penetrate into the network of TiO(2) effectively. After being calcined at 300 degrees C, sulfate species occupy oxygen sites to form Ti-S bonds, as evidenced by XPS results. As calcination temperature is further increased to 600 degrees C or above, the active sulfate species on the catalyst surface are destroyed, and the sulfate species in the network of TiO(2) are expelled out onto the surface to form inactive sulfate species. Thus, Ti(3+) defects will be produced on the catalyst surface. Accompanying this process, surface area is decreased promptly, and crystalline size is greatly increased via two fast growth phases due to the decomposition of sulfate species with different binding forces. Most importantly, the band gap of SO(4)(2-)/TiO(2) is remarkably shifted to the visible light region due to the formation of Ti-S bonds, and with increasing calcination temperature the visible light absorption capability is reduced due to breakage of Ti-S bonds. The excellent photoactivity of 300 degrees C calcined SO(4)(2-)/TiO(2) can be explained by its small crystalline size, high surface area, loose and porous microstructure, and the generation of Br?nsted acidity on its surface.     

Charge transfer and formation of reduced Ce3+ upon adsorption of metal atoms at the ceria (110) surface

The modification of cerium dioxide with nanoscale metal clusters is intensely researched for catalysis applications, with gold, silver, and copper having been particularly well studied. The interaction of the metal cluster with ceria is driven principally by a localised interaction between a small number of metal atoms (as small as one) and the surface and understanding the fundamentals of the interaction of metal atoms with ceria surfaces is therefore of great interest. Much attention has been focused on the interaction of metals with the (111) surface of ceria, since this is the most stable surface and can be grown as films, which are probed experimentally. However, nanostructures exposing other surfaces such as (110) show high activity for reactions including CO oxidation and require further study; these nanostructures could be modified by deposition of metal atoms or small clusters, but there is no information to date on the atomic level details of metal-ceria interactions involving the (110) surface. This paper presents the results of density functional theory (DFT) corrected for on-site Coulomb interactions (DFT+U) calculations of the adsorption of a number of different metal atoms at an extended ceria (110) surface; the metals are Au, Ag, Cu, Al, Ga, In, La, Ce, V, Cr, and Fe. Upon adsorption all metals are oxidised, transferring electron(s) to the surface, resulting in localised surface distortions. The precise details depend on the identity of the metal atom. Au, Ag, Cu each transfer one electron to the surface, reducing one Ce ion to Ce(3+), while of the trivalent metals, Al and La are fully oxidised, but Ga and In are only partially oxidised. Ce and the transition metals are also partially oxidised, with the number of reduced Ce ions possible in this surface no more than three per adsorbed metal atom. The predicted oxidation states of the adsorbed metal atoms should be testable in experiments on ceria nanostructures modified with metal atoms.     

Density functional studies of model cerium oxide nanoparticles

Density functional plane-wave calculations have been performed to investigate a series of ceria nanoparticles (CeO2-x)(n), n Ce3+ reduction have been accounted for through the use of an effective on-site Coulomb repulsive interaction within the so-called DFT+U approach. Twelve nanoparticles of up to 2 nm in diameter and of both cuboctahedral and octahedral forms are chosen as representative model systems. Energetic and structural effects of oxygen vacancy formation in these nanoparticles are discussed with respect to those in the bulk and on extended surfaces. We show that the average interatomic distances of the nanoparticles are most significantly affected by the creation of oxygen vacancies. The formation energies of non-stoichiometric nanoparticles (CeO2-x)(n) are found to scale linearly with the average coordination number of Ce atoms; where x < 0 species, containing partially reduced O atoms, are less stable. The stability of octahedral ceria particles at small sizes, and the predicted strong propensity of Ce cations to acquire a reduced state at lower coordinated sites, is supported by interatomic potential-based global optimisations probing the low energy isomers of the Ce19O32 nanoparticle.     

Oxidising CO to CO2 using ceria nanoparticles

We calculate, using simulated amorphisation and recrystallisation (A&R), that ceria (CeO2) nanoparticles, about 8 nm in diameter, comprise a high concentration of labile surface oxygen species, which we suggest will help promote the oxidation of CO to CO2. In particular, the ceria nanoparticle contains a high proportion of reactive {100} surfaces, surface steps and corner sites. When reduced to CeO1.95, the associated Ce3+ species and oxygen vacancies decorate step, corner and {100} sites in addition to plateau positions on {111}. The energetics of CO oxidation to CO2, catalysed by a ceria nanoparticle, is calculated to be lower compared with CO oxidation associated with the lowest energy surface (i.e. CeO2(111)) of the corresponding 'bulk' material. Our calculated morphologies for the ceria nanoparticles are in accord with experiment.     

Adsorption and reaction of methanol on stoichiometric and defective SrTiO3(100) surfaces

The adsorption and reaction of methanol (CH(3)OH) on stoichiometric (TiO(2)-terminated) and reduced SrTiO(3)(100) surfaces have been investigated using temperature-programmed desorption (TPD), X-ray photoelectron spectroscopy (XPS), and first-principles density-functional calculations. Methanol adsorbs mostly nondissociatively on the stoichiometric SrTiO(3)(100) surface that contains predominately Ti(4+) cations. Desorption of a monolayer methanol from the stoichiometric surface is observed at approximately 250 K, whereas desorption of a multilayer methanol is found to occur at approximately 140 K. Theoretical calculations predict weak adsorption of methanol on TiO(2)-terminated SrTiO(3)(100) surfaces, in agreement with the experimental results. However, the reduced SrTiO(3)(100) surface containing Ti(3+) cations exhibits higher reactivity toward adsorbed methanol, and H(2), CH(4), and CO are the major decomposition products. The surface defects on the reduced SrTiO(3)(100) surface are partially reoxidized upon saturation exposure of CH(3)OH onto this surface at 300 K.     

The reaction between ZnO and molten Na2S2O7 or K2S2O7 forming Na2Zn(SO4)2 orK2Zn(SO4)2, studied by Raman spectroscopy and x-ray diffraction

Reactions between solid zinc oxide and molten sodium or potassium pyrosulfates at 500 degrees C are shown by Raman spectroscopy to be 1:1 reactions leading to solutions. By lowering the temperature of the solution melts, colorless crystals form. Raman spectra of the crystals are given and tentatively assigned. Crystal structures of the monoclinic salts at room temperature are given. Na(2)Zn(SO(4))(2): space group = P2/n (No. 13), Z = 8, a = 8.648(3) Angstroms, b = 10.323(3) Angstroms, c = 15.103(5) Angstroms, beta = 90.879(6) degrees, and wR(2) = 0.0945 for 2748 independent reflections. K(2)Zn(SO(4))(2): space group = P2(1)/n (No.14), Z = 4, a = 5.3582(11) Angstroms, b = 8.7653(18) Angstroms, c = 16.152(3) Angstroms, beta = 91.78(3) degrees , and wR(2) = 0.0758 for 1930 independent reflections. In both compounds, zinc is nearly perfectly trigonally bipyramidal, coordinated to five oxygen atoms, with Zn-O bond lengths ranging from 1.99 to 2.15 Angstroms, equatorial bonds being slightly shorter on the average. The O-Zn-O angles are approximately 90 degrees and 120 degrees . The sulfate groups connect adjacent Zn(2+) ions, forming complicated three-dimensional networks. All oxygen atoms belong to nearly perfect tetrahedral SO(4)(2-) groups, bound to zinc. No oxygen atom is terminally bound to zinc; all zinc oxygens are further connected to sulfur atoms (Zn-O-S bridging). In both structures, some oxygen atoms are uniquely bound to certain S atoms. The sulfate group tetrahedra have quite short (1.42-1.45 Angstroms) terminal S-O bonds in comparison to the longer (1.46-1.50 Angstroms) Zn-bridging S-O bonds. The Na(+) or K(+) ions adopt positions between the ZnO(5) hexahedra and the SO(4) tetrahedra, completing the three-dimensional network of the M(2)Zn(SO(4))(2) structures. Bond distances and angles compare well with literature values. Empirical correlations between S-O bond distances and average O-S-O bond angles follow a previously found trend.