Author: Andrew Wong
1. Abstract
The purpose of this post is to study the dissociation of NO2 to NO and O on Fe (110) surface by performing a transition state search using the nudged elastic band method. A reaction energy diagram was constructed to evaluate the activation barrier for this particular reaction. The properties and geometry of the transition state were then studied by comparing it to the proposed initial and final states.
2. Introduction
NO2 reduction is an important area of research as its reaction path leads to the production of several industrially vital products, such as NH3 and N2O [1]. The reduction of NO2 into NH3 is important for environmental applications, such as water remediation projects. Additionally, research on Fe as a catalyst in NO2 reduction is of particular interest, especially in the applications of electrocatalysis in environmental systems. [2]. Using the nudged elastic band method, the purpose of this post is to utilize density functional theory calculations (DFT) to determine the transition state to reduce NO2, nitrogen dioxide, to NO, nitric oxide, and O, atomic oxygen, on an Fe (110) surface. Fe as a catalyst was selected for its catalytical desirable properties and is the most optimal pure candidate for the Haber-Bosch process of reducing N2 to NH3 [3].
3. Methodology
3.1 Calculation Parameters
A plane wave basis set with pseudo potentials in the Vienna Ab initio Simulation Package (VASP) was used to perform all DFT calculations. The Perdew, Burke, and Ernzerhof functional (PBE) was selected to model the electron-electron exchange and correlation energies. The projector augmented-wave (PAW) method was implemented to represent the ion-core electron interactions [5]. The Monkhorst-Pack method was utilized to model the K-point grid. An Fe core radius of 2.4 Bohrs (1.27 Å) with a panel of 8 valence electrons ( 3d6 and 4s2) was chosen with an electronic convergence tolerance of 2E-06 eV in all calculations. For all calculations, a cutoff energy of 450 eV was selected as this was seen to be optimal energy cutoff value during the geometry optimization calculations of the molecules and the Fe surface.
3.2 Model Parameter
From previous post, a 4 layer 3 x 3 Fe (110) surface was used and optimized as it is the most stable termination facet of Fe [2]. The slab was modeled with a vacuum region of approximately 10 Å with a k-point mesh of 5 x 5 x 1 and cutoff energy of 450 eV. To imitate the bulk Fe, the bottom two layers of the slab were fixed. Lastly, dipole corrections and selective dynamics were used.
3.3 Transition State Search Algorithm
Transition State searches in this post employ the Climbing Image Nudged Elastic Band Method (NEB) to determine the transition state [4]. Geometry optimizations of the initial and final states were performed at a k-point mesh of 5 x 5 x 1 and cutoff energy of 450 eV. The reactant and product states were defined as NO2 to NO and O. Figure 1 below displays the optimized initial, transition, and final states.
Figure 1. Top and side views of initial, transition, and final states of NO2 reducing to NO and O
Blue: Nitrogen Red: Oxygen, Purple: Iron
Based on the optimized structures of the reactant and product states, eight linearly interpolated images were created to determine the transition state. Once the tangential forces of the highest energy image is less than the absolute value of 0.05 eV/Å, the transition state search is complete. An animation of this particular transition state search is shown below.
Movie 1: Transition state search of reducing NO2 to NO and O using eight linearly interpolated images from NEB Method. Red: O, Blue: N, Purple: Fe
4. Results and Discussion
Once the transition state search was complete, a reaction energy diagram was constructed to determine the transition state and the activation barrier of this reaction. Using the eight linearly interpolated images, energies were plotted below in figure 2 relative to the reactant state.
Figure 2: Reaction Energy Diagram for transition state search of NO2 to NO + O
From the transition state search, This transition state was confirmed as it had a single imaginary zero-point vibrational frequency value. From figure 2, the activation barrier was determined to be a value of 0.72 eV. Additionally, this reaction is energetically downhill favorable as the difference between the product and reactant state is approximately 2 eV.
During the trial transition state search, It is important to note that when using four linearly interpolated images, the NEB method missed a saddle point between the initial image and the first interpolated image. This was confirmed as the first image did not have an imaginary vibration frequency value during zero-point vibrational energy calculations. As a result, another transition state search was performed by creating an additional four images by linearly interpolating the original initial state and the first interpolated image. A reaction diagram including the 8 linearly interpolated images is shown below in figure 2.
As seen in figure 2, the transition state was concluded to be more similar the initial state than final state. Figure 3 was constructed to compare the bond lengths between the reactant and transition state.
Figure 3: Comparing bond lengths between Initial and Transition State. Red: O, Blue: N, Purple: Fe
As seen in figure 3, the NO bond length between oxygen atom 1 in the reactant and transition state is approximately the same. However, the NO bond of oxygen atom 1 rotated out of the plane approximately 90 degrees in the transition state, primarily contributing to the increase of 0.72 eV in energy. Additionally, the N atom began to adsorb between the adjacent Fe atom. Both of these observations most likely occurred to allow the oxygen atom 1 to rotate above the nitrogen atom like in the final proposed state. For the NO bond interaction between oxygen atom 2, elongation of the NO bond and stronger adsorption towards the Fe surface occurred. Specifically, the bond length increased by 0.2 Å to allow this atom to dissociate from the NO2 and adsorb more strongly to the Fe surface atoms.
5. Conclusion
Using the NEB method, a transition state with an activation barrier of 0.72 eV was found for the reduction of NO2 to NO and O. Although a particular transition state for the NO2 reduction was found, it is important to note that the NEB method are local minimization calculations. As local minimization calculations, it cannot confirm whether other transition states that are between the initial and final states also exist [7]. Particular caution should be considered when using the NEB method around the saddle point as using not a sufficient number of images can neglect a transition state during the transition state search. Based on a particular DFT adsorption study, the reaction barrier differed by approximately 0.1 eV [8]. Improvements on this transition search can be made by allowing the NO to adsorb onto the hollow site in the product state, the most stable site, rather than the short bridge site. Overall, the dissociation of NO2 onto the Fe (110) is an energetically favorable reaction with an activation barrier of 0.72 eV.
6. Citations
[1] Liu, Jin-Xun, et al. “Activity and Selectivity Trends in Electrocatalytic Nitrate Reduction on Transition Metals.” ACS Catalysis, vol. 9, no. 8, 2019, pp. 7052–7064., doi:10.1021/acscatal.9b02179.
[2] Maheshwari, Sharad, et al. “Elementary Kinetics of Nitrogen Electroreduction on Fe Surfaces.” AIP Publishing, AIP Publishing LLC, 28 Jan. 2019, aip.scitation.org/doi/full/10.1063/1.5048036.
DOI: 10.1021/acscentsci.6b00272
[4] G. Henkelman, H. Jónsson, Improved tangent estimate in the nudged elastic band method for finding minimum energy paths and saddle points, The Journal of Chemical Physics, 113 (2000) 9978-9985.
[5] Init.at. “Vienna Ab Initio Simulation Package.” VASP, www.vasp.at/.
[6] Rostgaard, and Carsten. “The Projector Augmented-Wave Method.” ArXiv.org, 12 Oct. 2009, arxiv.org/abs/0910.1921.
[7] Scholl, David S. and Steckel, Janice A. “Density Functional Theory: A Practical Introduction” Wiley (2009).
[8] Xu, Lang, et al. “Atomic and Molecular Adsorption on Fe(110).” Surface Science, North-Holland, 12 Sept. 2017, www.sciencedirect.com/science/article/pii/S0039602817305988?via=ihub.
