Experimental and Computational Study of Pyrogenic Carbonaceous Matter Facilitated Hydrolysis of 2,4-Dinitroanisole (DNAN).

This study investigated the reaction pathway of 2,4-dinitroanisole (DNAN) on the pyrogenic carbonaceous matter (PCM) to assess the scope and mechanism of PCM-facilitated surface hydrolysis. DNAN degradation was observed at pH 11.5 and 25 °C with a model PCM, graphite, whereas no significant decay occurred without graphite. Experiments were performed at pH 11.5 due to the lack of DNAN decay at pH below 11.0, which was consistent with previous studies. Graphite exhibited a 1.78-fold enhancement toward DNAN decay at 65 °C and pH 11.5 relative to homogeneous solution by lowering the activation energy for DNAN hydrolysis by 54.3 ± 3.9%. This is supported by our results from the computational modeling using Car-Parrinello simulations by ab initio molecular dynamics/molecular mechanics (AIMD/MM) and DFT free energy simulations, which suggest that PCM effectively lowered the reaction barriers by approximately 8 kcal mol-1 compared to a homogeneous solution. Quaternary ammonium (QA)-modified activated carbon performed the best among several PCMs by reducing DNAN half-life from 185 to 2.5 days at pH 11.5 and 25 °C while maintaining its reactivity over 10 consecutive additions of DNAN. We propose that PCM can affect the thermodynamics and kinetics of hydrolysis reactions by confining the reaction species near PCM surfaces, thus making them less accessible to solvent molecules and creating an environment with a weaker dielectric constant that favors nucleophilic substitution reactions. Nitrite formation during DNAN decay confirmed a denitration pathway, whereas demethylation, the preferred pathway in homogeneous solution, produces 2,4-dinitrophenol (DNP). Denitration catalyzed by PCM is advantageous to demethylation because nitrite is less toxic than DNAN and DNP. These findings provide critical insights for reactive adsorbent design that has broad implications for catalyst design and pollutant abatement.

Assessing Gas-Phase Ion Reactivity of 50 Elements with NO and the Direct Application for 239Pu in Complex Matrices Using ICP-MS/MS.

Understanding the reactivity of metal cations with various reaction gases in inductively coupled plasma tandem mass spectrometry (ICP-MS/MS) is important to determine the best gas to use for a given analyte/interference pair. In this study, nitric oxide (NO) was investigated as the reaction gas following previous experimental designs. The reactions with 50 elements were investigated to examine periodic trends in reactivity, validate theoretical modeling of reaction enthalpies as a method to screen reactant gases, and provide a baseline data set for potential in-line gas separation methods. ICP-MS/MS studies involving actinides are typically limited to Th, U, and Pu, with analyses of Np and Am rarely reported in the literature. To date, only two previous methods have investigated the use of NO in ICP-MS/MS analyses. To showcase the utility of NO, a method was developed to measure 239Pu in the presence of environmental matrix constituent and other actinides, like what could be expected from postdetonation debris, with no chemical separation prior to analysis. 239Pu+ was reacted to form 239Pu16O+, eliminating interferences derived from the sample matrix by measuring the 239Pu+ intensity at m/z = 255 (239Pu16O+). To validate NO for 238U1H+ interference removal in environmental matrices, standard reference materials were diluted to 1 mg/g of solution and spiked to 0.05 pg/g of 239Pu and 1 µg/g 238U (Pu/U = 5 × 10-8). Measured 239Pu concentrations were within 6% of the spiked value. These results demonstrate that reliable 239Pu measurements can be made at levels relevant to nuclear forensics without the need for extensive chemical matrix separation prior to analysis.

Development and application of hybrid AIMD/cDFT simulations for atomic-to-mesoscale chemistry.

Many important chemical processes involve reactivity and dynamics in complex solutions. Gaining a fundamental understanding of these reaction mechanisms is a challenging goal that requires advanced computational and experimental approaches. However, important techniques such as molecular simulation have limitations in terms of scales of time, length, and system complexity. Furthermore, among the currently available solvation models, there are very few designed to describe the interaction between the molecular scale and the mesoscale. To help address this challenge, here, we establish a novel hybrid approach that couples first-principles plane-wave density functional theory with classical density functional theory (cDFT). In this approach, a region of interest described by ab initio molecular dynamics (AIMD) interacts with the surrounding medium described using cDFT to arrive at a self-consistent ground state. cDFT is a robust but efficient mesoscopic approach to accurate thermodynamics of bulk electrolyte solutions over a wide concentration range (up to 2M concentrations). Benchmarking against commonly used continuum models of solvation, such as SMD, as well as experiments, demonstrates that our hybrid AIMD-cDFT method is able to produce reasonable solvation energies for a variety of molecules and ions. With this model, we also examined the solvent effects on a prototype SN2 reaction of the nucleophilic attack of a chloride ion on methyl chloride in the solution. The resulting reaction pathway profile and the solution phase barrier agree well with experiment, showing that our AIMD/cDFT hybrid approach can provide insight into the specific role of the solvent on the reaction coordinate.

NWChem: Recent and Ongoing Developments.

This paper summarizes developments in the NWChem computational chemistry suite since the last major release (NWChem 7.0.0). Specifically, we focus on functionality, along with input blocks, that is accessible in the current stable release (NWChem 7.2.0) and in the "master" development branch, interfaces to quantum computing simulators, interfaces to external libraries, the NWChem github repository, and containerization of NWChem executable images. Some ongoing developments that will be available in the near future are also discussed.

Degradation of Chloroform by Zerovalent Iron: Effects of Mechanochemical Sulfidation and Nitridation on the Kinetics and Mechanism.

Chloroform (CF) is a widely used chemical reagent and disinfectant and a probable human carcinogen. The extensive literature on halocarbon reduction with zerovalent iron (ZVI) shows that transformation of CF is slow, even with nano, bimetallic, sulfidated, and other modified forms of ZVI. In this study, an alternative method of ZVI modification─involving simultaneous sulfidation and nitridation through mechanochemical ball milling─was developed and shown to give improved degradation of CF (i.e., higher degradation rate and inhibited H2 evolution reaction). The composite material (denoted as S-N(C)-ZVI) gave synergistic effects of nitridation and sulfidation on CF degradation. A complete chemical reaction network (CRN) analysis of CF degradation suggests that O-nucleophile-mediated transformation pathways may be the main route for the formation of the terminal nonchlorinated products (formate, CO, and glycolic polymers) that have been used to explain the undetected products needed for mass balance. Material characterizations of the ZVI recovered after batch experiments showed that sulfidation and nitridation promoted the formation of Fe3O4 on the S-N(C)-ZVI particles, and the effect of aging on CF degradation rates was minor for S-N(C)-ZVI. The synergistic benefits of sulfidation and nitridation on CF degradation were also observed in experiments performed with groundwater.

Symmetry Breaking with the SCAN Density Functional Describes Strong Correlation in the Singlet Carbon Dimer.

The SCAN (strongly constrained and appropriately normed) meta-generalized gradient approximation (meta-GGA), which satisfies all 17 exact constraints that a meta-GGA can satisfy, accurately describes equilibrium bonds that are normally correlated. With symmetry breaking, it also accurately describes some sd equilibrium bonds that are strongly correlated. While sp equilibrium bonds are nearly always normally correlated, the C2 singlet ground state is known from correlated wave function theory to be a rare case of strong correlation in an sp equilibrium bond. Earlier work that calculated atomization energies of the molecular sequence B2, C2, O2, and F2 in the local spin density approximation (LSDA), the Perdew-Burke-Ernzerhof (PBE) GGA, and the SCAN meta-GGA, without symmetry breaking in the molecule, found that only SCAN was accurate enough to reveal an anomalous under-binding for C2. This work shows that spin symmetry breaking in singlet C2, which involves the appearance of net up- and down-spin densities on opposite sides (not ends) of the bond, corrects that underbinding, with a small SCAN atomization-energy error more like that of the other three molecules, suggesting that symmetry breaking with an advanced density functional might reliably describe strong correlation. This article also discusses some general aspects of symmetry breaking and the insights into strong correlation that symmetry breaking can bring. The normally correlated low-lying triplet excited state has the right vertical excitation energy in SCAN but not in LSDA or PBE, where the triplet is a false ground state. Fractional occupation numbers are found only for the symmetry-unbroken singlet and only in LSDA and PBE GGA.

Computational Predictions of the Hydrolysis of 2,4,6-Trinitrotoluene (TNT) and 2,4-Dinitroanisole (DNAN).

Hydrolysis is a common transformation reaction that can affect the environmental fate of many organic compounds. In this study, three proposed mechanisms of alkaline hydrolysis of 2,4,6-trinitrotoluene (TNT) and 2,4-dinitroaniline (DNAN) were investigated with plane-wave density functional theory (DFT) combined with ab initio and classical molecular dynamics (AIMD/MM) free energy simulations, Gaussian basis set DFT calculations, and correlated molecular orbital theory calculations. Most of the computations in this study were carried out using the Arrows web-based tools. For each mechanism, Meisenheimer complex formation, nucleophilic aromatic substitution, and proton abstraction reaction energies and activation barriers were calculated for the reaction at each relevant site. For TNT, it was found that the most kinetically favorable first hydrolysis steps involve Meisenheimer complex formation by attachment of OH- at the C1 and C3 arene carbons and proton abstraction from the methyl group. The nucleophilic aromatic substitution reactions at the C2 and C4 arene carbons were found to be thermodynamically favorable. However, the calculated activation barriers were slightly lower than in previous studies, but still found to be ΔG‡ ≈ 18 kcal/mol using PBE0 AIMD/MM free energy simulations, suggesting that the reactions are not kinetically significant. For DNAN, the barriers of nucleophilic aromatic substitution were even greater (ΔG‡ > 29 kcal/mol PBE0 AIMD/MM). The most favorable hydrolysis reaction for DNAN was found to be a two-step process in which the hydroxyl first attacks the C1 carbon to form a Meisenheimer complex at the C1 arene carbon C1-(OCH3)OH-, and subsequently, the methoxy anion (-OCH3) at the C1 arene carbon dissociates and the proton shuttles from the C1-OH to the dissociated methoxy group, resulting in methanol and an aryloxy anion.

Pentavalent Uranium Incorporated in the Structure of Proterozoic Hematite.

Characterizing the chemical state and physical disposition of uranium that has persisted over geologic time scales is key for modeling the long-term geologic sequestration of nuclear waste, accurate uranium-lead dating, and the use of uranium isotopes as paleo redox proxies. X-ray absorption spectroscopy coupled with molecular dynamics modeling demonstrated that pentavalent uranium is incorporated in the structure of 1.6 billion year old hematite (α-Fe2O3), attesting to the robustness of Fe oxides as waste forms and revealing the reason for the great success in using hematite for petrogenic dating. The extreme antiquity of this specimen suggests that the pentavalent state of uranium, considered a transient, is stable when incorporated into hematite, a ubiquitous phase that spans the crustal continuum. Thus, it would appear overly simplistic to assume that only the tetravalent and hexavalent states are relevant when interpreting the uranium isotopic record from ancient crust and contained ore systems.

Resolving Configurational Disorder for Impurities in a Low-Entropy Phase.

Hematite (α-Fe2O3) exerts a strong control over the transport of minor but critical metals in the environment and is used in multiple industrial applications; the photocatalysis community has explored the properties of hematite nanoparticles over a wide range of transition metal dopants. Nonetheless, simplistic assumptions are used to rationalize the local coordination environment of impurities in hematite. Here, we use ab initio molecular dynamics (AIMD)-guided structural analysis to model the extended X-ray absorption fine structure (EXAFS) of Cu2+- and Zn2+-doped hematite nanoparticles. Specific defect-impurity associations were identified, and the local coordination environments of Cu and Zn both displayed considerable configurational disorder that, in aggregate, approached Jahn-Teller-like distortion for Cu but, in contrast, maintained hematite-like symmetry for Zn. This study highlights the role of defects in accommodating impurities in a nominally low-entropy phase and the limits to traditional shell-by-shell fitting of EXAFS for dopants/impurities in unprecedented bonding environments.

Quantum Solvers for Plane-Wave Hamiltonians: Abridging Virtual Spaces Through the Optimization of Pairwise Correlations.

For many-body methods such as MCSCF and CASSCF, in which the number of one-electron orbitals is optimized and independent of the basis set used, there are no problems with using plane-wave basis sets. However, for methods currently used in quantum computing such as select configuration interaction (CI) and coupled cluster (CC) methods, it is necessary to have a virtual space that is able to capture a significant amount of electron-electron correlation in the system. The virtual orbitals in a pseudopotential plane-wave Hartree-Fock calculation, because of Coulomb repulsion, are often scattering states that interact very weakly with the filled orbitals. As a result, very little correlation energy is captured from them. The use of virtual spaces derived from the one-electron operators has also been tried, and while some correlations are captured, the amount is quite low. To overcome these limitations, we have been developing new classes of algorithms to define virtual spaces by optimizing orbitals from small pairwise CI Hamiltonians, which we term as correlation optimized virtual orbitals with the abbreviation COVOs. With these procedures, we have been able to derive virtual spaces, containing only a few orbitals, which are able to capture a significant amount of correlation. The focus in this manuscript is on using these derived basis sets to target full CI (FCI) quality results for H2 on near-term quantum computers. However, the initial results for this approach were promising. We were able to obtain good agreement with FCI/cc-pVTZ results for this system with just 4 virtual orbitals, using both FCI and quantum simulations. The quality of the results using COVOs suggests that it may be possible to use them in other many-body approaches, including coupled cluster and Møller-Plesset perturbation theories, and open up the door to many-body calculations for pseudopotential plane-wave basis set methods.

From NWChem to NWChemEx: Evolving with the Computational Chemistry Landscape.

Since the advent of the first computers, chemists have been at the forefront of using computers to understand and solve complex chemical problems. As the hardware and software have evolved, so have the theoretical and computational chemistry methods and algorithms. Parallel computers clearly changed the common computing paradigm in the late 1970s and 80s, and the field has again seen a paradigm shift with the advent of graphical processing units. This review explores the challenges and some of the solutions in transforming software from the terascale to the petascale and now to the upcoming exascale computers. While discussing the field in general, NWChem and its redesign, NWChemEx, will be highlighted as one of the early codesign projects to take advantage of massively parallel computers and emerging software standards to enable large scientific challenges to be tackled.

Toward Quantum Computing for High-Energy Excited States in Molecular Systems: Quantum Phase Estimations of Core-Level States.

This paper explores the utility of the quantum phase estimation (QPE) algorithm in calculating high-energy excited states characterized by the promotion of electrons occupying core-level shells. These states have been intensively studied over the last few decades, especially in supporting the experimental effort at light sources. Results obtained with QPE are compared with various high-accuracy many-body techniques developed to describe core-level states. The feasibility of the quantum phase estimator in identifying classes of challenging shake-up states characterized by the presence of higher-order excitation effects is discussed. We also demonstrate the utility of the QPE algorithm in targeting excitations from specific centers in a molecule. Lastly, we discuss how the lowest-order Trotter formula can be applied to reducing the complexity of the ansatz without affecting the error.

Using Atom Dynamics to Map the Defect Structure Around an Impurity in Nano-Hematite.

The bulk behavior of materials is often controlled by minor impurities that create nonperiodic localized defect structures due to ionic size, symmetry, and charge balance mismatches. Here, we used transmission electron microscopy (TEM) of atom-resolved dynamics to directly map the topology of Fe vacancy clusters surrounding structurally incorporated U6+ in nanohematite (α-Fe2O3). Ab initio molecular dynamic simulations provided additional independent constraints on coupled U, Fe, and vacancy mobility in the solid. A clearer understanding of how such an apparently incompatible element can be accommodated by hematite emerged. The results were readily interpretable without the need for sophisticated data reconstruction methods, model structures, or ultrathin samples, and with the proliferation of aberration-corrected TEM facilities, the approach is accessible. Given sufficient z-contrast, the ability to observe impurity-vacancy structures by means of atom hopping can be used to directly probe the association of impurities and such defects in other materials, with promising applications across a broad range of disciplines.

Reduction of 1,2,3-trichloropropane (TCP): pathways and mechanisms from computational chemistry calculations.

The characteristic pathway for degradation of halogenated aliphatic compounds in groundwater or other environments with relatively anoxic and/or reducing conditions is reductive dechlorination. For 1,2-dihalocarbons, reductive dechlorination can include hydrogenolysis and dehydrohalogenation, the relative significance of which depends on various structural and energetic factors. To better understand how these factors influence the degradation rates and products of the lesser halogenated hydrocarbons (in contrast to the widely studied per-halogenated hydrocarbons, like trichloroethylene and carbon tetrachloride), density functional theory calculations were performed to compare all of the possible pathways for reduction and elimination of 1,2,3-trichloropropane (TCP). The results showed that free energies of each species and reaction step are similar for all levels of theory, although B3LYP differed from the others. In all cases, the reaction coordinate diagrams suggest that ß-elimination of TCP to allyl chloride followed by hydrogenolysis to propene is the thermodynamically favored pathway. This result is consistent with experimental results obtained using TCP, 1,2-dichloropropane, and 1,3-dichloropropane in batch experiments with zerovalent zinc (Zn0, ZVI) as a reductant.

Reaction Energetics and 13C Fractionation of Alanine Transamination in the Aqueous and Gas Phases.

The alanine transaminase enzyme catalyzes the transfer of an amino group from alanine to α-ketoglutarate to produce pyruvate and glutamate. Isotope fractionation factors (IFFs) for the reaction +H3NCH(CH3)COO- + -OOCCH2CH2C(O)COO- ↔ CH3C(O)COO- + +H3NCH(CH2CH2COO-)COO- (zwitterionic neutral alanine + doubly deprotonated α-ketoglutarate ↔ pyruvate + zwitterionic glutamate anion) were calculated from the partition functions of explicitly and implicitly solvated molecules at 298 K. Calculations were done for alanine (noncharge separated, zwitterion, deprotonated), pyruvic acid (neutral, deprotonated), glutamic acid (noncharge separated, zwitterion, deprotonated, doubly deprotonated), and α-ketoglutaric acid (neutral, deprotonated, doubly deprotonated). The computational results, calculated from gas phase- and aqueous-optimized clusters with explicit H2O molecules at the MP2/aug-cc-pVDZ and MP2/aug-cc-pVDZ/COSMO levels, respectively, predict that substitution of 13C at the C2 position of alanine and pyruvic acid and their various forms leads to the C2 position of pyruvic acid/pyruvate being enriched in 13C/12C ratio by 9‰. Simpler approaches that estimate the IFFs based solely on changes in the zero-point energies (ZPEs) are consistent with the higher-level model. ZPE-based IFFs calculated for simple analogues formaldehyde and methylamine (analogous to the C2 positions of pyruvate and alanine, respectively) predict a 13C enrichment in formaldehyde of 7-8‰ at the MP2/aug-cc-pVDZ and aug-cc-pVTZ levels. A simple predictive model using canonical functional group frequencies and reduced masses for 13C exchange between R2C═O and R2CH-NH2 predicted enrichment in R2C═O that is too large by a factor of two but is qualitatively accurate compared with the more sophisticated models. Our models are all in agreement with the expectation that pyruvate and formaldehyde will be preferentially enriched in 13C because of the strength of their >C═O bond relative to that of ≡C-NH2 in alanine and methylamine. 13C/12C substitution is also modeled at the methyl and carboxylic acid sites of alanine and pyruvic acid, respectively.

Association of Defects and Zinc in Hematite.

Zn is an essential micronutrient that is often limited in tropical, lateritic soils in part because it is sequestered in nominally refractory iron oxide phases. Stable phases such as goethite and hematite, however, can undergo reductive recrystallization without a phase change under circumneutral pH conditions and release metal impurities such as Zn into aqueous solutions. Further, the process appears to be driven by Fe vacancies. In this contribution, we used ab initio molecular dynamics informed extended X-ray absorption fine structure spectra to show that Zn incorporated in the structure of hematite is associated with coupled O-Fe and protonated Fe vacancies, providing a potential link between crystal chemistry and the bioavailability of Zn.

Downfolding of many-body Hamiltonians using active-space models: Extension of the sub-system embedding sub-algebras approach to unitary coupled cluster formalisms.

In this paper, we discuss the extension of the recently introduced subsystem embedding subalgebra coupled cluster (SES-CC) formalism to unitary CC formalisms. In analogy to the standard single-reference SES-CC formalism, its unitary CC extension allows one to include the dynamical (outside the active space) correlation effects in an SES induced complete active space (CAS) effective Hamiltonian. In contrast to the standard single-reference SES-CC theory, the unitary CC approach results in a Hermitian form of the effective Hamiltonian. Additionally, for the double unitary CC (DUCC) formalism, the corresponding CAS eigenvalue problem provides a rigorous separation of external cluster amplitudes that describe dynamical correlation effects-used to define the effective Hamiltonian-from those corresponding to the internal (inside the active space) excitations that define the components of eigenvectors associated with the energy of the entire system. The proposed formalism can be viewed as an efficient way of downfolding many-electron Hamiltonian to the low-energy model represented by a particular choice of CAS. In principle, this technique can be extended to any type of CAS representing an arbitrary energy window of a quantum system. The Hermitian character of low-dimensional effective Hamiltonians makes them an ideal target for several types of full configuration interaction type eigensolvers. As an example, we also discuss the algebraic form of the perturbative expansions of the effective DUCC Hamiltonians corresponding to composite unitary CC theories and discuss possible algorithms for hybrid classical and quantum computing. Given growing interest in quantum computing, we provide energies for H2 and Be systems obtained with the quantum phase estimator algorithm available in the Quantum Development Kit for the approximate DUCC Hamiltonians.

Properties of perhalogenated {closo-B10} and {closo-B11} multiply charged anions and a critical comparison with {closo-B12} in the gas and the condensed phase.

closo-Borate anions [closo-BnXn]2- are part of the most famous textbook examples of polyhedral compounds. Substantial differences in their reactivity and interactions with other compounds depending on the substituent X and cluster size n have been recognized, which favor specific closo-borates for different applications in cancer treatment, chemical synthesis, and materials science. Surprisingly, a fundamental understanding of the molecular properties underlying these differences is lacking. Here, we report our study comparing the electronic structure and reactivity of closo-borate anions [closo-BnXn]2- (X = Cl, Br, I, n = 10, 11, 12 in all combinations) in the gas phase and in solution. We investigated the free dianions and the ion pairs [nBu4N]+[closo-BnXn]2- by gas phase anion photoelectron spectroscopy accompanied by theoretical investigations. Strong similarities in electronic structures for n = 10 and 11 were observed, while n = 12 clusters were different. A systematic picture of the development in electronic stability along the dimension X is derived. Collision induced dissociation shows that fragmentation of the free dianions is mainly dependent on the substituent X and gives access to a large variety of boron-rich molecular ions. Fragmentation of the ion pair depends strongly on n. The results reflect the high chemical stability of clusters with n = 10 and 12, while those with n = 11 are much more prone to dissociation. We bridge our study to the condensed phase by performing comparative electrochemistry and reactivity studies on closo-borates in solution. The trends found at the molecular level are also reflected in the condensed-phase properties. We discuss how the gas phase values allow evaluation of the influence of the condensed phase on the electronic stability of closo-borates. A synthetic method via an oxidation/chlorination reaction yielding [closo-B10Cl10]2- from highly chlorinated {closo-B11} clusters is introduced, which underlines the intrinsically high reactivity of the {closo-B11} cage.

Time Domain Simulations of Single Molecule Raman Scattering.

Nonequilibrium chemical phenomena are known to play an important role in single molecule microscopy and spectroscopy. Herein, we explore these effects through ab initio molecular dynamics (AIMD)-based Raman spectral simulations. We target an isolated aromatic thiol (thiobenzonitrile, TBN) as a prototypical molecular system. We first show that the essential features contained in the ensemble-averaged Raman spectrum of TBN can be reproduced by averaging over 18 short AIMD trajectories spanning a total simulation time of ∼60 ps. This involved more than 90 000 polarizability calculations at the B3LYP/def2-TZVP level of theory. We then illustrate that the short trajectories (∼3.3 ps total simulation time), where the accessible phase space is not fully sampled, provide a starting point for understanding key features that are often observed in measurements targeting single molecules. Our results suggest that a complete understanding of single molecule Raman scattering needs to account for molecular conformational flexibility and nonequilibrium chemical phenomena in addition to local optical fields and modified selection rules. The former effects are well-captured using the described AIMD-based single molecule Raman spectral simulations.

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, V AB, and the electron transfer transmission factor, κel. 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 H AB and S AB. 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)] nn+ chains representing the common edge-sharing Fe octahedral motif in these materials.