Corresponding Orbitals Derived from Periodic Bloch States for Electron Transfer Calculations of Transition Metal Oxides

An approach for modeling electron transfer in solids and at surfaces of iron-(oxyhydr)­oxides and other redox active solids has been developed for electronic structure methods (i.e., plane-wave density functional theory) capable of performing calculations with periodic cells and large system sizes efficiently while at the same time being accurate enough to be used in the estimation of the electron-transfer coupling matrix element, <i>V</i>_<i>AB</i>, and the electron transfer transmission factor, κ_el. This method is an extension of the valence bond theory electron transfer method for molecules and clusters implemented by Dupuis and others and used extensively by Rosso and co-workers in which scaled corresponding orbitals derived from the Bloch states are used to calculate the off-diagonal matrix elements <i>H</i>_<i>AB</i> and <i>S</i>_<i>AB</i>. A key development of the present work is the formulation of algorithms to improve the accuracy of the integration of the exact exchange integral in periodic boundary conditions. This method is demonstrated on model systems for electron small polaron transfer in iron-(oxyhydr)­oxides, including bare Fe²⁺–Fe³⁺ ions, and in [Fe³⁺(OH₂)₂ (OH^–)₂)]_<i>n</i>^<i>n</i>+ chains representing the common edge-sharing Fe octahedral motif in these materials

Strengthening of the Coordination Shell by Counter Ions in Aqueous Th⁴⁺ Solutions

The presence of counterions in solutions containing highly charged metal cations can trigger processes such as ion-pair formation, hydrogen bond breakages and subsequent re-formation, and ligand exchanges. In this work, it is shown how halide (Cl^–, Br^–) and perchlorate (ClO₄^–) anions affect the strength of the primary solvent coordination shells around Th⁴⁺ using explicit-solvent and finite-temperature ab initio molecular dynamics modeling methods. The 9-fold solvent geometry was found to be the most stable hydration structure in each aqueous solution. Relative to the dilute aqueous solution, the presence of the counterions did not significantly alter the geometry of the primary hydration shell. However, the free energy analyses indicated that the 10-fold hydrated states were thermodynamically accessible in dilute and bromide aqueous solutions within 1 kcal/mol. Analysis of the results showed that the hydrogen bond lifetimes were longer and solvent exchange energy barriers were larger in solutions with counterions in comparison with the solution with no counterions. This implies that the presence of the counterions induces a strengthening of the Th⁴⁺ hydration shell

Importance of Counteranions on the Hydration Structure of the Curium Ion

Using density functional theory based ab initio molecular dynamics and metadynamics, we show that counterions can trigger noticeable changes in the hydration shell structure of the curium ion. On the basis of the free energies of curium–water coordination, the eight-fold coordination state is dominant by at least 98% in the absence of counteranions and in the presence of chloride and bromide counteranions. In addition, the solvent hydrogen bond (HB) lifetimes are relatively longer. In contrast, the solvent hydrogen bond (HB) lifetimes are relatively shorter in the presence of perchlorate counteranions, with the nine-fold and eight-fold states existing in an 8/2 ratio, which is in good agreement with the reported ratio measured by X-ray scattering experiments. To our knowledge, this is the first time that molecular simulations have shown that counteranions can directly affect the first hydration shell structure of a cation

Predicting Reduction Rates of Energetic Nitroaromatic Compounds Using Calculated One-Electron Reduction Potentials

The evaluation of new energetic nitroaromatic compounds (NACs) for use in green munitions formulations requires models that can predict their environmental fate. Previously invoked linear free energy relationships (LFER) relating the log of the rate constant for this reaction (log­(<i>k</i>)) and one-electron reduction potentials for the NAC (<i>E</i>¹_NAC) normalized to 0.059 V have been re-evaluated and compared to a new analysis using a (nonlinear) free-energy relationship (FER) based on the Marcus theory of outer-sphere electron transfer. For most reductants, the results are inconsistent with simple rate limitation by an initial, outer-sphere electron transfer, suggesting that the linear correlation between log­(<i>k</i>) and <i>E</i>¹_NAC is best regarded as an empirical model. This correlation was used to calibrate a new quantitative structure–activity relationship (QSAR) using previously reported values of log­(<i>k</i>) for nonenergetic NAC reduction by Fe­(II) porphyrin and newly reported values of <i>E</i>¹_NAC determined using density functional theory at the M06-2X/6-311++G­(2d,2p) level with the COSMO solvation model. The QSAR was then validated for energetic NACs using newly measured kinetic data for 2,4,6-trinitrotoluene (TNT), 2,4-dinitrotoluene (2,4-DNT), and 2,4-dinitroanisole (DNAN). The data show close agreement with the QSAR, supporting its applicability to other energetic NACs

Ion Association in AlCl₃ Aqueous Solutions from Constrained First-Principles Molecular Dynamics

The Car–Parrinello-based molecular dynamics (CPMD) method was used to investigate the ion-pairing behavior between Cl^– and Al³⁺ ions in an aqueous AlCl₃ solution containing 63 water molecules. A series of constrained simulations was carried out at 300 K for up to 16 ps each, with the internuclear separation (<i>r</i>_Al–Cl) between the Al³⁺ ion and one of the Cl^– ions held constant. The calculated potential of mean force (PMF) of the Al³⁺–Cl^– ion pair shows a global minimum at <i>r</i>_Al–Cl = 2.3 Å corresponding to a contact ion pair (CIP). Two local minima assigned to solvent-separated ion pairs (SSIPs) are identified at <i>r</i>_Al–Cl = 4.4 and 6.0 Å. The positions of the free energy minima coincide with the hydration-shell intervals of the Al³⁺ cation, suggesting that the Cl^– ion is inclined to reside in regions with low concentrations of water molecules, that is, between the first and second hydration shells of Al³⁺ and between the second shell and the bulk. A detailed analysis of the solvent structure around the Al³⁺ and Cl^– ions as a function of <i>r</i>_Al–Cl is presented. The results are compared to structural data from X-ray measurements and unconstrained CPMD simulations of single Al³⁺ and Cl^– ions and AlCl₃ solutions. The dipole moments of the water molecules in the first and second hydration shells of Al³⁺ and in the bulk region and those of Cl^– ions were calculated as a function of <i>r</i>_Al–Cl. Major changes in the electronic structure of the system were found to result from the removal of Cl^– from the first hydration shell of the Al³⁺ cation. Finally, two unconstrained CPMD simulations of aqueous AlCl₃ solutions corresponding to CIP and SSIP configurations were performed (17 ps, 300 K). Only minor structural changes were observed in these systems, confirming their stability

Mechanisms and Kinetics of Alkaline Hydrolysis of the Energetic Nitroaromatic Compounds 2,4,6-Trinitrotoluene (TNT) and 2,4-Dinitroanisole (DNAN)

The environmental impacts of energetic compounds can be minimized through the design and selection of new energetic materials with favorable fate properties. Building predictive models to inform this process, however, is difficult because of uncertainties and complexities in some major fate-determining transformation reactions such as the alkaline hydrolysis of energetic nitroaromatic compounds (NACs). Prior work on the mechanisms of the reaction between NACs and OH^– has yielded inconsistent results. In this study, the alkaline hydrolysis of 2,4,6-trinitrotoluene (TNT) and 2,4-dinitroanisole (DNAN) was investigated with coordinated experimental kinetic measurements and molecular modeling calculations. For TNT, the results suggest reversible formation of an initial product, which is likely either a Meisenheimer complex or a TNT anion formed by abstraction of a methyl proton by OH^–. For DNAN, the results suggest that a Meisenheimer complex is an intermediate in the formation of 2,4-dinitrophenolate. Despite these advances, the remaining uncertainties in the mechanisms of these reactionsand potential variability between the hydrolysis mechanisms for different NACsmean that it is not yet possible to generalize the results into predictive models (e.g., quantitative structure–activity relationships, QSARs) for hydrolysis of other NACs

Tuning Band Gap Energies in Pb₃(C₆X₆) Extended Solid-State Structures

A detailed plane-wave density functional theory investigation of the solid-state properties of the extended organometallic system Pb₃C₆X₆ for X = O, S, Se, and Te has been performed. Initial geometry parameters for the Pb–X and C–X bond distances were obtained from optimized calculations on molecular fragment models. The Pb₃C₆X₆ extended-solid molecular structures were constructed in the space group <i>P</i>6/<i>mmm</i> on the basis of the known structure for X = S. Ground-state geometries, band gap energies, densities of states, and charge densities were calculated with the PBE-generalized gradient exchange-correlation functional and the HSE06 hybrid exchange-correlation functional. The PBE band gap energies were found to be lower than the HSE06 values by >0.7 eV. The band energies at points of high symmetry along the first Brillouin zone in the crystal were larger than the overall band gap of the system. Pb₃C₆O₆ was predicted to be a direct semiconductor (Γ point) with a PBE band gap of 0.28 eV and an HSE06 band gap of 1.06 eV. Pb₃C₆S₆ and Pb₃C₆Se₆ were predicted to have indirect band gaps. The PBE band gap for Pb₃C₆S₆ was 0.98 eV, and the HSE06 band gap was 1.91 eV. The HSE06 value is in good agreement with the experimentally observed band gap of 1.7 eV. Pb₃C₆Se₆ has a PBE band gap of 0.56 eV and a HSE06 band gap of 1.41 eV. Pb₃C₆Te₆ was predicted to be metallic with both of the PBE and HSE06 functionals. A detailed analysis of the PBE band structure and partial density of states at two points before and after the metallic behavior reveals a change in orbital character indicative of band crossing in Pb₃C₆Te₆. These results show that the band gap energies can be fine-tuned by changing the substituent X atom

Ab Initio Molecular Dynamics of Uranium Incorporated in Goethite (α-FeOOH): Interpretation of X‑ray Absorption Spectroscopy of Trace Polyvalent Metals

Incorporation of economically or environmentally consequential polyvalent metals into iron (oxyhydr)­oxides has applications in environmental chemistry, remediation, and materials science. A primary tool for characterizing the local coordination environment of such metals, and therefore building models to predict their behavior, is extended X-ray absorption fine structure spectroscopy (EXAFS). Accurate structural information can be lacking yet is required to constrain and inform data interpretation. In this regard, ab initio molecular dynamics (AIMD) was used to calculate the local coordination environment of minor amounts of U incorporated in the structure of goethite (α-FeOOH). U oxidation states (VI, V, and IV) and charge compensation schemes were varied. Simulated trajectories were used to calculate the U L_III-edge EXAFS function and fit experimental EXAFS data for U incorporated into goethite under reducing conditions. Calculations that closely matched the U EXAFS of the well-characterized mineral uraninite (UO₂), and constrained the <i>S</i>₀² parameter to be 0.909, validated the approach. The results for the U-goethite system indicated that U­(V) substituted for structural Fe­(III) in octahedral uranate coordination. Charge balance was achieved by the loss of one structural proton coupled to addition of one electron into the solid (−1 H⁺, +1 e^–). The ability of AIMD to model higher energy states thermally accessible at room temperature is particularly relevant for protonated systems such as goethite, where proton transfers between adjacent octahedra had a dramatic effect on the calculated EXAFS. Vibrational effects as a function of temperature were also estimated using AIMD, allowing separate quantification of thermal and configurational disorder. In summary, coupling AIMD structural modeling and EXAFS experiments enables modeling of the redox behavior of polyvalent metals that are incorporated in conductive materials such as iron (oxyhydr)­oxides, with applications over a broad swath of chemistry and materials science

Iron Vacancies Accommodate Uranyl Incorporation into Hematite

Radiotoxic uranium contamination in natural systems and nuclear waste containment can be sequestered by incorporation into naturally abundant iron (oxyhydr)­oxides such as hematite (α-Fe₂O₃) during mineral growth. The stability and properties of the resulting uranium-doped material are impacted by the local coordination environment of incorporated uranium. While measurements of uranium coordination in hematite have been attempted using extended X-ray absorption fine structure (EXAFS) analysis, traditional shell-by-shell EXAFS fitting yields ambiguous results. We used hybrid functional <i>ab initio</i> molecular dynamics (AIMD) simulations for various defect configurations to generate synthetic EXAFS spectra which were combined with adsorbed uranyl spectra to fit experimental U L₃-edge EXAFS for U⁶⁺-doped hematite. We discovered that the hematite crystal structure accommodates a trans-dioxo uranyl-like configuration for U⁶⁺ that substitutes for structural Fe³⁺, which requires two partially protonated Fe vacancies situated at opposing corner-sharing sites. Surprisingly, the best match to experiment included significant proportions of vacancy configurations other than the minimum-energy configuration, pointing to the importance of incorporation mechanisms and kinetics in determining the state of an impurity incorporated into a host phase under low temperature hydrothermal conditions

Near-Quantitative Agreement of Model-Free DFT-MD Predictions with XAFS Observations of the Hydration Structure of Highly Charged Transition-Metal Ions

First-principles dynamics simulations (DFT, PBE96, and PBE0) and electron scattering calculations (FEFF9) provide near-quantitative agreement with new and existing XAFS measurements for a series of transition-metal ions interacting with their hydration shells via complex mechanisms (high spin, covalency, charge transfer, etc.). This analysis does not require either the development of empirical interparticle interaction potentials or structural models of hydration. However, it provides consistent parameter-free analysis and improved agreement with the higher-<i>R</i> scattering region (first- and second-shell structure, symmetry, dynamic disorder, and multiple scattering) for this comprehensive series of ions. DFT+GGA MD methods provide a high level of agreement. However, improvements are observed when exact exchange is included. Higher accuracy in the pseudopotential description of the atomic potential, including core polarization and reducing core radii, was necessary for very detailed agreement. The first-principles nature of this approach supports its application to more complex systems