Density functional theory (DFT) investigation of the oxidative degradation of NaAsO2 via hydroxyl radical

Arsenic is an environmentally ubiquitous health hazard due to its toxicity combined with its natural abundance and heavy industrial applications. Due to its role in cardiovascular disease, neurotoxicity, and various cancers, it is important to understand environmental fate of arsenic-containing compounds to take steps towards remediation. Sodium arsenite (NaAsO2) is one such compound that has been used worldwide as an herbicide, rodenticide, and insecticide. It is also toxic by ingestion, inhalation, and skin absorption. In aqueous environments, arsenite (As(III))-containing compounds can be oxidized to the less-toxic arsenate (As(V)) form. We have investigated the oxidation of sodium arsenite in water solution at the density functional theory level using the Minnesota 06 hybrid (M06-2X) functional and Pople basis sets (6-31G(d,p) and 6-311G(d,p)) with polarizable continuum model (PCM) solvation approach. Our computational results indicate that the oxidation mechanism of NaAsO2 by hydroxyl radical proceeds via sequential addition reactions where sodium arsenite (III) converts to sodium arsenate (V) via an arsenic (IV) intermediate.

Arsenic has been identified as a group I human carcinogen by the World Health Organization and is a highly toxic nonessential element that is often categorized alongside mercury, lead, and cadmium [6,20]. Inorganic arseniccontaining compounds are generally more toxic than organic compounds, and typically, As(III) is more toxic than As(V) [21][22][23]. Additionally, no chemical or biological pathways to degrade inorganic arsenics into harmless small molecules exist. They can be transformed into other compounds that are less toxic than their parent compounds [14]. Remediation of arsenics from groundwater often involves oxidation, adsorption, coagulation-flocculation, ion-exchange, and membrane processes [24].
It has been reported that As(V)-containing compounds react preferentially with Al 3+ , Fe 3+ , Mn 2+ , and Mn 4+ containing compounds that can often be found as metal oxides in sediment deposits [13]. Arsenate-containing compounds have been shown to be removed in some amounts from aquatic environments via soil adsorption [25]. Therefore, in addition to being generally less toxic, As(V) is shown to be less mobile than As(III) in regard to water transport [3]. It is for this reason that much attention has been drawn to the oxidation of As(III) compared to As(V) [9,26,27].
Of the As(III) containing compounds, arsenous acid (H 3 AsO 3 ) is one of the most widely studied compounds [14]. It has been shown that H 3 AsO 3 can be oxidized to H 3 AsO 4 utilizing ozone, molecular oxygen, activated H 2 O 2 , photochemical oxidation, permanganate, Mn(III/IV) oxide, iron oxides, ferrate, among others [14]. It has been reported that the oxidation of As(III) proceeds through the formation of an unstable As(IV) complex before achieving the As(V) oxidation state [28].
While arsenite-containing compounds can be readily oxidized to the less toxic arsenate compounds, computational studies have focused on arsenous acid and its anion (AsO 3 3− ). Sodium arsenite (NaAsO 2 ) is another arsenitecontaining compound that has been used as an herbicide, rodenticide, and insecticide; however, little has been published with regard to the oxidation of NaAsO 2 [9,14,29]. However, a rate constant for the oxidation of the arsenite anion from this compound by hydroxyl radical (OH • + AsO 2 − → As(IV)) was found to be 9.0 × 10 9 L mol −1 s −1 [30,31]. In order to investigate this process and compare to available experimental data, we have performed density functional theory calculations to determine the mechanism of oxidation for sodium arsenite via hydroxyl radical.

Computational methods
Gaussian16 [32] was used to carry out quantum mechanical calculations of the reaction mechanisms of the transformation of sodium arsenite to sodium arsenate through an arsenic (IV) intermediate state (Scheme I).
Density functional theory calculations were performed using the Minnesota 06 hybrid functional (M06-2X) [33] with the 6-31G(d,p) [34][35][36][37][38][39] and 6-311G(d,p) [39][40][41][42] basis sets. Effect of water solvation was considered using the polarizable continuum model (PCM) with the default (Scheme I) parameters for water (ε = 78.3553) as available in Gauss-ian16 [43,44]. Harmonic vibrational frequencies were used to determine that structures resided at either a minima or transition state on the potential energy surface as indicated by the presence of no imaginary frequencies or one imaginary frequency, respectively. The synchronous transit-guided quasi-Newton (STQN) method [45,46] was used as necessary to search for transition states using the QST2 and QST3 keywords in addition to manual potential energy scans. The QST2 method uses the reactant and product geometries alone as input to attempt to search for the transition state. The QST3 method uses the reactant and product geometries as well as an initial guess geometry for the transition state to attempt to search for the transition state.

Results and discussion
Initial optimizations of the reactant structures NaAsO 2 and OH • were performed separately to obtain starting geometries. These structures were then combined, with the two molecules placed approximately 3.00 Å apart (distance measured between the arsenic of the NaAsO 2 and the oxygen of the OH • ). The combined structures were then allowed to relax to obtain a starting orientation of the molecules. However, upon optimization, the hydroxyl group immediately moved to within bonding distance (1.79 Å) of the As atom of the arsenite complex. We then performed a relaxed potential energy scan of the bond between the arsenic and the hydroxyl radical. Our calculations showed a continual increase in potential energy as the hydroxyl group was pulled away from the arsenic, breaking the As-OH bond, with no definitive peaks to indicate a potential transition state (Fig. S1). The procedure of pulling the intermediate or product of a reaction apart is sometimes easier in cases where the intermediate or product is more stable than the reactant, and there is a little to no activation barrier between the two.
Explicit water molecules were added to stabilize the hydroxyl radical in a starting configuration where the reactants were at least 3.00 Å apart. Initial attempts were made with two explicit water molecules to save computational time, but the results were very similar to the calculations with no explicit water molecules. A recent study on H 3 AsO 3 oxidation by OH • used four water molecules to create a hydrogen bonding around the complex [28], which we decided to adopt for our system (Fig. 1a).
We performed a relaxed potential energy scan of the As-OH bond formation (Fig. 2a). We again found that the product appears to rapidly form with no clear indication of a transition state in the potential energy surface. We do see a large drop in energy in the reaction coordinate points surrounding ~2.18 Å. However, this drop in energy appears to be a result of slight movements of the atoms as the OH • begins to coordinate in closer proximity to the As atom. We attempted to optimize the structure to a transition state using opt = TS on data points surrounding this region, but all attempts resulted to the product structure with no imaginary frequencies, and thus, no transition state was found. Therefore, our data suggests that when in close proximity to OH • , the initial oxidation step of NaAsO 2 is a barrierless process.
A second hydroxyl radical was then added to the system along with a fifth explicit water molecule (Fig. 1b).
Optimizations for this system began with the hydroxyl radical roughly 3.00 Å away from the intermediate As(IV) complex. The optimization proceeded directly to the product with a bond forming between the hydroxyl radical and the arsenic. We then attempted a relaxed scan of the potential energy surface by breaking the bond between the As and the oxygen atom of the second hydroxyl radical (Fig. 2b).
The potential energy scans did show a small peak around 2.20 Å which could have been indicative of a transition state. However, upon close inspection of the structures from the The optimized structure of the sodium arsenate product after oxidation by the second hydroxyl including five explicit solvent molecules. c The optimized structure of sodium arsenate product after oxidation by the second hydroxyl including ten explicit solvent molecules Fig. 2 Relative potential energy change in response As-OH bond formation utilizing M06-2X/6-31G(d,p) and M06-2X/6-311G(d,p). Geometry was allowed to relax at each step. Implicit solvation was accounted for using the PCM approach with default parameters for water in Gaussian16. Individual reaction conditions are as follows: a first addition of OH • with formation of the As-OH bond in Fig. 1a using four explicit water molecules arranged within hydrogen bond-ing distance to the reactants. b Second addition of OH • and formation of the As-OH bond in Fig. 1b using five explicit water molecules arranged within hydrogen bonding distance to the reactants. c Second addition of OH • and formation of the As-OH bond in Fig. 1c using ten explicit water molecules arranged within hydrogen bonding distance to the reactants relaxed scans, it was discovered that this small increase and subsequent drop in the potential energy surface is a result of changes in the hydrogen bonding network which resulted in water molecules moving to other parts of the system (Fig. S2). Attempts were made to perform transition state calculations on the structures found at the peak and on either side of the peak. However, attempts to optimize a transition state (opt = TS) resulted in the final As(V) product. The resulting structure also had no imaginary frequencies indicating the structure found was a minima and not a transition state. The structure on the left side of the peak was used as the reactant structure along with the optimized product in a QST2 calculation to search for the elusive transition state; however, these calculations either failed to optimize or optimized to the As(V) product (NaH 2 AsO 4 ). Finally, QST3 calculations were performed using the data used for the QST2 for the reactant and product input, and the guess for the transition state was taken from the highest point on the peak. These calculations also optimized to the product with no imaginary frequencies rather than a transition state.
These results indicate that this oxidation step may also proceed as a barrierless addition of hydroxyl radical to the arsenic (IV) intermediate to form the arsenate (V) product. However, to determine if increasing solvation would stabilize a potential transition state, we performed a test calculation with the double amount of explicit water molecules. We performed a potential energy scan identical to the one shown in Fig. 2b but included ten water molecules (Figs. 1c and 2c).
The PES shows a much smoother curve from 1.70 to 2.20 Å with no indication of the peaks found in the previous calculation with only five explicit waters. However, we do see a similar peak near 2.33 Å when the 6-311G(d,p) basis set was used. It was at this point in this calculation that the sodium atom moved to the other side of the molecule, and in subsequent steps, a bond began to form between the arsenic and the oxygen of another water molecule. Further optimization of this structure revealed a bond between this water and the arsenic complex accompanied by another series of protonation/deprotonation events. The water bonding to the arsenic lost its proton to another water, which caused a domino effect of protons being transferred between water molecules until the originally designated hydroxyl radical was protonated and thus transformed into a water molecule. Overall, this shows that it is highly preferential for this oxidation to occur even if it must happen by implicating the hydrogen bond network of waters.

Conclusions
Our results suggest that the oxidation reaction proceeds via a barrierless addition of sodium arsenite (III) with OH • to form an intermediate As(IV) complex (NaHAsO 3 ). This As(IV) intermediate is then further oxidized to sodium arsenate (V) through a second barrierless addition of OH • . While information on the exact mechanism to our knowledge is lacking, it appears that this barrierless reaction is in line with the general statement in the literature which is that arsenite compounds can be readily oxidized to arsenates [14]. Additionally the published rate constant for the anion (OH • + AsO 2 − → As(IV)), 9.0 × 10 9 L mol −1 s −1 , indicates that the reaction happens very fast which further supports a barrierless reaction process [30,31].

Acknowledgements
The authors would like to thank Dr. Caitlin Bresnahan and Dr. Robert Lamb for providing feedback and guidance on the reaction mechanism calculations. The use of trade, product, or firm names in this report is for descriptive purposes only and does not imply endorsement by the U.S. Government. The tests described and the resulting data presented herein, unless otherwise noted, were obtained from research funded under the Installations and Operational Environments, Office of the Technical Director of the United States Army Corps of Engineers, and the Environmental Security Technology Certification Program of the Department of Defense by the USAERDC. Permission was granted by the Chief of Engineers to publish this information. The findings of this report are not to be considered as an official Department of the Army position unless so designated by other authorized documents. This work was supported by a grant of computer time from the DoD High Performance Computing Modernization Program at ERDC, Vicksburg, MS. This document has been approved for public release (Distribution Statement A) by the Engineer Research and Development Center.
Author contribution All authors contributed to the study conception and design. Computations, data collection, and analysis were performed by AMK. The first draft of the manuscript was written by AMK, and all authors commented on previous versions of the manuscript. All authors read and approved the final manuscript.
Funding This research was funded under the Installations and Operational Environments, Office of the Technical Director of the US Army Corps of Engineers.
Availability of data and material The datasets generated during and/or analyzed during the current study are available from the corresponding author on reasonable request.