Biomechanical comparison of different rod-to-rod connectors to a conventional titanium- and cobalt chromium posterior spinal fixation system.

Introduction: Several types of rod-to-rod connectors are available for the extension of spinal fixation systems. However, scientific literature regarding the mechanical performance of different rod-to-rod connector systems is lacking. Research question: The goal of this study was to evaluate the mechanical characteristics of axial and lateral rod connectors in comparison to a conventional pedicle screw rod (titanium and cobalt chromium) construct. Material and method: Six types of instrumentations were investigated in a standardized test model to quantify the mechanical differences: 1: titanium rod; 2: titanium rod with axial connector; 3: titanium rod with lateral connector; 4: cobalt chromium rod; 5: cobalt chromium rod with axial connector; 6: cobalt chromium rod with lateral connector. All groups were tested in static compression, static torsion and dynamic compression and statistically compared regarding failure load and stiffness. Results: In static compression loading, the use of connectors increased the construct stiffness, but unaffected the yield load. The use of a cobalt chromium rod significantly increased by approximately 40% the yield load and stiffness in comparison to the titanium rod configurations. Under dynamic compression, a similar or higher fatigue strength for all tested groups in comparison to the titanium rod configuration was evaluated, with the exception of titanium rod with axial connector. Conclusion: Biomechanically, using rod connectors is a secure way for the extension of a construct and is mechanically equal to a conventional screw rod construct. However, in clinical use, attention should be paid regarding placement of the connectors at high loaded areas.

Single-Hydroxide Bridged Dimers of U and Np Actinyls: A Density Functional Study on Their Existence and Structure in Aqueous Solution.

With quantum chemical calculations at the density functional theory level, we examined the structure and the stability of diactinyl monohydroxo complexes [(AnO2)2(OH)]3+/+ in aqueous solution for An = U(VI), Np(VI), and Np(V). In particular, this study contributes to understanding the hydrolysis of Np(VI) and Np(V), which is less well characterized than for U(VI). [(UO2)2(OH)]3+ is a known hydrolysis complex of U(VI) at low pH. Although not yet found in experiments, [(NpO2)2(OH)]3+ is suggested to exist due to the similarity between Np(VI) and U(VI) complexes, while [(NpO2)2(OH)]+ is a hypothetical species thus far. Our calculations suggest that the An(VI) complexes favor the parallel orientation of actinyls, whereas for the Np(V) complex a perpendicular arrangement is stabilized by hydrogen bonds between aqua ligands and the actinyl oxygen atoms. The Np(VI) complex [(NpO2)2(OH)]3+ features a structure and stability similar to its U(VI) analogue. From calculated formation constants for An(VI) diactinyl monohydroxo complexes, we find qualitative agreement with the experiment for U(VI). Both An(VI) complexes are only slightly less stable than the separate mononuclear constituents, the actinyl aqua and the monohydroxo complex. For the Np(V) species [(NpO2)2(OH)]+, we calculated a considerably lower complexation constant than for its An(VI) analogues, but it is more stable against decay into its constituents. Thus, this complex may exist at about the pH where Np(V) hydrolysis starts at not too low Np(V) concentrations.

The effect of cement augmentation on pedicle screw fixation under various load cases : results from a combined experimental, micro-CT, and micro-finite element analysis.

AIMS: Anchorage of pedicle screw rod instrumentation in the elderly spine with poor bone quality remains challenging. Our study aims to evaluate how the screw bone anchorage is affected by screw design, bone quality, loading conditions, and cementing techniques. METHODS: Micro-finite element (µFE) models were created from micro-CT (µCT) scans of vertebrae implanted with two types of pedicle screws (L: Ennovate and R: S4). Simulations were conducted for a 10 mm radius region of interest (ROI) around each screw and for a full vertebra (FV) where different cementing scenarios were simulated around the screw tips. Stiffness was calculated in pull-out and anterior bending loads. RESULTS: Experimental pull-out strengths were excellently correlated to the µFE pull-out stiffness of the ROI (R2 > 0.87) and FV (R2 > 0.84) models. No significant difference due to screw design was observed. Cement augmentation increased pull-out stiffness by up to 94% and 48% for L and R screws, respectively, but only increased bending stiffness by up to 6.9% and 1.5%, respectively. Cementing involving only one screw tip resulted in lower stiffness increases in all tested screw designs and loading cases. The stiffening effect of cement augmentation on pull-out and bending stiffness was strongly and negatively correlated to local bone density around the screw (correlation coefficient (R) = -0.95). CONCLUSION: This combined experimental, µCT and µFE study showed that regional analyses may be sufficient to predict fixation strength in pull-out and that full analyses could show that cement augmentation around pedicle screws increased fixation stiffness in both pull-out and bending, especially for low-density bone. Cite this article: Bone Joint Res 2021;10(12):797-806.

Hydration Structure and Hydrolysis of U(IV) and Np(IV) Ions: A Comparative Density Functional Study Using a Modified Continuum Solvation Approach.

We studied the hydration and the first hydrolysis reaction of U(IV) and Np(IV) ions in an aqueous environment, applying a relativistic density functional method together with a recently proposed variant of a continuum solvation model where the solute cavities are constructed with effective atomic radii, based on charge-dependent scaling factors. In this way, one obtains improved solvation energies of charged species. We demonstrate that solute cavities, constructed with scaled atomic radii as described, permit one to calculate hydrolysis constants of acceptable accuracy. As a consequence, one is also able to estimate free hydration energies of U(IV) and Np(IV) in adequate agreement with empirical data. According to the model calculations, U(IV) is coordinated by eight to nine water molecules, while the preferred coordination number of Np(IV) is 8. For the highly charged ions under study, the modified solvation model simultaneously yields improved geometries, hydration energies, and hydrolysis constants.

Interdisciplinary Round-Robin Test on Molecular Spectroscopy of the U(VI) Acetate System.

A comprehensive molecular analysis of a simple aqueous complexing system-U(VI) acetate-selected to be independently investigated by various spectroscopic (vibrational, luminescence, X-ray absorption, and nuclear magnetic resonance spectroscopy) and quantum chemical methods was achieved by an international round-robin test (RRT). Twenty laboratories from six different countries with a focus on actinide or geochemical research participated and contributed to this scientific endeavor. The outcomes of this RRT were considered on two levels of complexity: first, within each technical discipline, conformities as well as discrepancies of the results and their sources were evaluated. The raw data from the different experimental approaches were found to be generally consistent. In particular, for complex setups such as accelerator-based X-ray absorption spectroscopy, the agreement between the raw data was high. By contrast, luminescence spectroscopic data turned out to be strongly related to the chosen acquisition parameters. Second, the potentials and limitations of coupling various spectroscopic and theoretical approaches for the comprehensive study of actinide molecular complexes were assessed. Previous spectroscopic data from the literature were revised and the benchmark data on the U(VI) acetate system provided an unambiguous molecular interpretation based on the correlation of spectroscopic and theoretical results. The multimethodologic approach and the conclusions drawn address not only important aspects of actinide spectroscopy but particularly general aspects of modern molecular analytical chemistry.

Combined EXAFS Spectroscopic and Quantum Chemical Study on the Complex Formation of Am(III) with Formate.

The complexation of Am(III) with formate in aqueous solution is studied as a function of the pH value using a combination of extended X-ray absorption fine structure (EXAFS) spectroscopy, iterative transformation factor analysis (ITFA), and quantum chemical calculations. The Am LIII-edge EXAFS spectra are analyzed to determine the molecular structure (coordination numbers; Am-O and Am-C distances) of the formed Am(III)-formate species and to track the shift of the Am(III) speciation with increasing pH. The experimental data are compared to predictions from density functional calculations. The results indicate that formate binds to Am(III) in a monodentate fashion, in agreement with crystal structures of lanthanide formates. Furthermore, the investigations are complemented by thermodynamic speciation calculations to verify further the results obtained.

Uranyl adsorption at solvated edge surfaces of 2 : 1 smectites. A density functional study.

We systematically studied the adsorption of uranyl(vi) on two common edge surfaces, (010) and (110), of 2 : 1 smectite clay minerals, using standard periodic DFT models. To describe various types of permanently charged clay minerals, we introduced charged defects into the initially neutral layer of pyrophyllite, cation substitutions in tetrahedral (beidellitic) and octahedral (montmorillonitic) sheets. Comparing uranyl(vi) species at various sites of these two types of surfaces, we found that structural parameters of such adsorption complexes are essentially determined by the surface chemical groups forming the adsorption site, not by the type of the clay mineral. Even for sites involving a substituted cation we noticed only a weak effect of the substitution on the geometric parameters. Geometry optimization resulted in adsorbed uranyl or uranyl hydroxide, with coordination numbers of 4 or 5. However, in most cases the same species was determined on the same type of site, independent of the substitutions. Optimization of adsorbed uranyl leads to hydrolysis at sites close to a AlOH(-1/2) surface group, resulting in uranyl monohydroxide as adsorbate and protonation of the AlOH(-1/2) group. While most species are equatorially five-coordinated, coordination 4 is preferred when uranyl adsorbs on mixed AlO(H)-SiO(H) sites. Calculated formation energies of surface complexes do not single out a preferred species or site, but point to an equilibrium of several species. Comparison to experiment and consideration of pH conditions suggests AlOHOH and AlOH-SiO sites of (010) surfaces and AlOmOH, SiOOm, and AlOH-SiO sites of (110) surfaces as most probable for uranyl adsorption.

The DFT+Umol method and its application to the adsorption of CO on platinum model clusters.

Semi-local DFT approximations are well-known for their difficulty with describing the correct site preference for the adsorption of CO molecules on (111) surfaces of several late transition metals. To address this problem originating from a residual self-interaction in the CO LUMO, we present the DFT+Umol approach which generalizes the empirical DFT+U correction to fragment molecular orbitals. This correction is applied to examine CO adsorption energies at various sites on the (111) facets of cuboctahedral clusters Ptm(CO)8 (m = 79, 140, 225). The DFT+Umol correction leaves the electronic ground state of metal clusters, in particular their d-band structure, essentially unchanged, affecting almost exclusively the energy of the CO LUMO. As a result, that correction is significantly stronger for complexes at hollow sites, hence increases the propensity for adsorption at top sites. We also analyze competing edge effects on the (111) facets of the cluster models.

Uranyl adsorption on solvated edge surfaces of pyrophyllite: a DFT model study.

In a computational study we addressed the adsorption of uranyl UO(2)(2+) on solvated (110) and (010) edge surfaces of pyrophyllite, applying a density functional approach to periodic slab models. We explored bidentate adsorption complexes on various partially deprotonated adsorption sites: octahedral Al(O,OH), tetrahedral Si(O,OH), and mixed AlO-SiO. Aluminol sites were determined to be most favorable on the (110) surface of pyrophyllite, while on the (010) surface mixed AlO-SiO sites are preferred. The structural parameters of all low-energy complexes on both surfaces agree rather well with EXAFS results for the structurally similar mineral montmorillonite. We calculate the average U-O distance to surface and aqua ligand oxygen atoms to increase with the increasing coordination number of uranyl whereas EXAFS results indicate the opposite trend. According to our results, several adsorption species, with different coordination numbers on different edge faces, may coexist on clay minerals. This computational finding rationalizes why earlier spectroscopic studies indicated the existence of more than one adsorption species, whereas a single type of adsorption complex was suggested from most EXAFS results.

Improving Upon String Methods for Transition State Discovery.

Transition state discovery via application of string methods has been researched on two fronts. The first front involves development of a new string method, named the Searching String method, while the second one aims at estimating transition states from a discretized reaction path. The Searching String method has been benchmarked against a number of previously existing string methods and the Nudged Elastic Band method. The developed methods have led to a reduction in the number of gradient calls required to optimize a transition state, as compared to existing methods. The Searching String method reported here places new beads on a reaction pathway at the midpoint between existing beads, such that the resolution of the path discretization in the region containing the transition state grows exponentially with the number of beads. This approach leads to favorable convergence behavior and generates more accurate estimates of transition states from which convergence to the final transition states occurs more readily. Several techniques for generating improved estimates of transition states from a converged string or nudged elastic band have been developed and benchmarked on 13 chemical test cases. Optimization approaches for string methods, and pitfalls therein, are discussed.

Comparative density functional study of the complexes [UO2(CO3)3]4- and [(UO2)3(CO3)6]6- in aqueous solution.

With a relativistic all-electron density functional method, we studied two anionic uranium(VI) carbonate complexes that are important for uranium speciation and transport in aqueous medium, the mononuclear tris(carbonato) complex [UO(2)(CO(3))(3)](4-) and the trinuclear hexa(carbonato) complex [(UO(2))(3)(CO(3))(6)](6-). Focusing on the structures in solution, we applied for the first time a full solvation treatment to these complexes. We approximated short-range effects by explicit aqua ligands and described long-range electrostatic interactions via a polarizable continuum model. Structures and vibrational frequencies of "gas-phase" models with explicit aqua ligands agree best with experiment. This is accidental because the continuum model of the solvent to some extent overestimates the electrostatic interactions of these highly anionic systems with the bulk solvent. The calculated free energy change when three mono-nuclear complexes associate to the trinuclear complex, agrees well with experiment and supports the formation of the latter species upon acidification of a uranyl carbonate solution.

Uranyl monocarboxylates of aromatic acids: a density functional model study of uranyl humate complexation.

Using a scalar relativistic all-electron density functional method, we studied uranium(VI) complexation with benzoic acid and its derivatives in aqueous solution as models of uranyl humates. We explored monodentate, bidentate, and chelate coordination of various isomers of methyl and hydroxyl substituted benzoic acid ligands. Monodentate complexes were determined to be energetically preferred as long as entropy effects were neglected. However, bidentate structures were favored at the Gibbs free energy level. Coordination of aromatic carboxylic acids tends to be weaker than that of aliphatic ones, while structural characteristics were determined to be quite similar. Optimized geometries yield uranyl bonds and U-C distances in agreement with EXAFS results for monocarboxylate of benzoate and p-hydroxy benzoate. Average uranyl-oxygen distances to equatorial ligands, U-O(eq), are shorter than in experiment, which is tentatively rationalized by variations in the coordination numbers. As for aliphatic monocarboxylate complexes studied earlier, U-O(eq) values of benzoic acid derivatives do not discriminate mono- and bidentate coordinated species. Structures and energies determined support the interpretation of uranyl humate complexes as bidentate carboxylate species with fivefold coordination of uranyl.

CO coordination at XNi4 clusters with impurities X = H, C, O. A density functional study.

We report a computational investigation of CO adsorption on small nickel clusters that contain single impurity atoms H, C, or O. At bare Ni 4 and clusters with H or O impurity, the most stable coordination of the probe molecule is on top of a Ni atom which interacts with the impurity. The CNi 4 cluster is an exception where 3-fold coordination of CO was determined to be more stable than that on top, however, by 4 kJ/mol only. Our results suggest that the heteroatoms X (X = H, C, O) affect only weakly the reactivity of the cluster with respect to CO; the binding energy of CO in the most stable complexes (CO)XNi 4 increases at most by 10% compared to the value for bare Ni 4, 194 kJ/mol. The impurity induces a small decrease of the CO infrared frequency shift for on-top coordinated CO, compared to Ni 4, because of partial oxidation of the metal moiety. A notable difference is predicted for clusters that contain a C impurity because of the different preferred coordination mode which results in a strong CO frequency red shift of approximately 300 cm (-1). The calculated characteristic CO frequency shifts may be helpful in identifying experimentally clusters with impurity atoms.

Density functional model studies of uranyl adsorption on (001) surfaces of kaolinite.

The adsorption of uranyl on two types of neutral (001) surfaces of kaolinite, tetrahedral Si(t) and octahedral Al(o), was studied by means of density functional periodic slab model calculations. Various types of model surface complexes, adsorbed at different sites, were optimized and adsorption energies were estimated. As expected, the Si(t) surface was found to be less reactive than the Al(o) surface. At the neutral Al(o) surface, only adsorption at protonated sites is calculated to be exothermic for inner- as well as outer-sphere adsorption complexes, with monodentate coordination being preferred. Adsorption energies as well as structural features of the adsorption complexes are mainly determined by the number of deprotonated surface hydroxyl groups involved. Outer-sphere complexes on both surfaces exhibit a shorter U-O bond to the aqua ligand of uranyl that is in direct contact with the surface than to the other aqua ligands. This splitting of the shell of equatorial U-O bonds is at variance with common expectations for outer-sphere surface complexes of uranyl.

Impurity effects on small Pd clusters: a relativistic density functional study of Pd4X, X = H, C, O.

We carried out relativistic density functional calculations to investigate systematically the effect of main group element impurities H, C, and O on a Pd4 cluster. We determined a bridging coordination for Pd4H as most stable, whereas several other local minima are energetically close. The interaction of C with Pd4 is strong enough to restructure the cluster, resulting in two Pd2 units bridged by 4-fold coordinated C, but other isomers are again almost degenerate. Nearly degenerate isomers of Pd4O exhibit 2- and 3-fold coordination of O. In the most stable structures, the binding energies of the impurities, 295 kJ/mol for Pd4H, 655 kJ/mol for Pd4C, and 367 kJ/mol for Pd4O, are large enough to allow bond breaking of common small molecules when they interact with an ensemble of Pd4 clusters. Interestingly, the noteworthy relativistic effect on the properties of Pd4 also affects the interaction with impurity atoms. Comparison with other metals reveals similarities with Ni4X and differences from Ir4H, Ir4C, and Pt4H.

Influence of single impurity atoms on the structure, electronic, and magnetic properties of Ni5 clusters.

With a gradient-corrected density functional method, we have studied computationally the influence of single impurity atoms on the structure, electronic, and magnetic properties of Ni5 clusters. The square-pyramidal isomer of bare Ni5 with six unpaired electrons was calculated 23 kJ/mol more stable than the trigonal bipyramid in its lowest-energy electronic configuration with four unpaired electrons. In a previous study on the cluster Ni4, we had obtained only one stable isomer with an O or an H impurity, but we located six minima for ONi5 and five minima for HNi5. In the most stable structures of HNi5, the H atom bridges a Ni-Ni edge at the base or the side of the square pyramid, similarly to the coordination of an H atom at the tetrahedral cluster Ni4. The most stable ONi5 isomers exhibit a trigonal bipyramidal structure of the Ni5 moiety, with the impurity coordinated at a facet, (micro3-O)Ni5, or at an apex edge, (micro-O)Ni5. We located four stable structures for a C impurity at a Ni5 cluster. As for CNi4, the most stable structure of the corresponding Ni5 complex comprises a four-coordinated C atom, (micro4-C)Ni5, and can be considered as insertion of the impurity into a Ni-Ni bond of the bare cluster. All structures with C and five with O impurity have four unpaired electrons, while the number of unpaired electrons in the clusters HNi5 varies between 3 and 7. As a rough trend, the ionization potentials and electron affinities of the clusters with impurity atoms decrease with the coordination number of the impurity. However, the position of the impurity and the shape of the metal moiety also affect the results. Coordination of an impurity atom leads to a partial oxidation of the metal atoms.

Binary diffractive beam splitters with arbitrary diffraction angles.

Diffractive optical beam splitters designed with iterative Fourier transform type algorithms can produce only certain diffraction angles given by the spatial frequencies used for the computations, which are multiples of a certain base spatial frequency. We have developed a design algorithm that overcomes this limitation and can be used to compute binary diffractive elements with arbitrary diffraction angles. The simulated and experimentally measured properties of optical elements producing beam arrays in circular arrangements are presented and discussed.

Two hydrogen ligands on tetrairidium clusters: a relativistic density functional study.

Structural and energetic properties of Ir(4)H(2) have been determined by applying a relativistic density functional method. As previously obtained for Ir(4)H, terminal coordination of H ligands is preferred, in contrast to some other transition metals. Square-planar Ir(4) isomers with an H binding energy of up to 318 kJ mol(-1) per atom were determined as the most stable structures of Ir(4)H(2). Isomers with a tetrahedral or butterfly structure of the metal framework exhibit average H atom binding energies of up to approximately 300 kJ mol(-1). For all three types of isomers, a surprisingly large number of stable minima was identified. Unexpectedly, structural as well as energetic properties of Ir(4)H(2) complexes are very similar to Ir(4)H. Thus binding of an H atom to Ir(4) is only slightly affected by the presence of a second H ligand. In all cases examined, the reaction H(2)+ Ir(4)--> H(2)Ir(4) was found to be exothermic with reaction energies of up to 170 kJ mol(-1).

Structure, stability, electronic and magnetic properties of Ni4 clusters containing impurity atoms.

Using a gradient-corrected density functional method, we studied computationally how single impurity atoms affect the structure and the properties of a Ni4 cluster. H and O atoms coordinate at a Ni-Ni bond, inducing small changes to the structure of bare Ni4 which is essentially a tetrahedron. For a C impurity, we found three stable structures at a Ni4 cluster. In the most stable geometry, the carbon atom cleaves a Ni-Ni bond of Ni4, binding to all Ni atoms. Inclusion of the impurity atom leads to a partial oxidation of the metal atoms and, in the most stable structures, reduces the spin polarization of the cluster compared to bare Ni4. An H impurity interacts mainly with the Ni 4s orbitals, whereas the Ni 3d orbitals participate strongly in the bonding with O and C impurity atoms. For these impurity atoms, Ni 3d contributions dominate the character of the HOMO of the ligated cluster, in contrast to the HOMO of bare Ni4 where Ni 4s orbitals prevail. We also discuss a simple model which relates the effect of a H impurity on the magnetic state of metal clusters to the spin character (minority or majority) of the LUMO or HOMO of the bare metal cluster.

A density functional study of uranyl monocarboxylates.

We studied uranium(VI) monocarboxylate complexes by a relativistic density functional method using simple carboxylic acids as ligands, i.e. [UO2(OOCR)]+ (R = H, CH3, CH2CH3). These complexes exist in aqueous solution and, for R = CH3 and CH2CH3, may also be considered as models of uranyl complexated by humic substances. We investigated mono- and bidentate coordination modes. Short-range solvent effects were accounted for explicitly via aqua ligands of the first hydration shell and long-range electrostatic interactions were described via a polarizable continuum model. The calculated results for the uranyl U=O bond, the bond to aqua ligands, and the averaged uranium distances to equatorial oxygen atoms, U-Oeq, agreed quite well with EXAFS-derived interatomic distances. However, the uranyl-carboxylate bond was calculated to be notably shorter than the experimentally determined value. Experimental differences between mono- and bidentate coordination, obtained mainly from crystal structures, were qualitatively reproduced for the U-C distance but not for the average bond length, U-Oeq. We discuss these discrepancies between calculated and experimental results in some detail and suggest changes in the coordination number rather than variations of the coordination geometry as the main source of the experimentally observed variation of the U-Oeq distance.