Electronic band structure of Bi5O7NO3 and its methyl orange removal mechanism European Journal of Chemistry 13 (3) (2022) 337-350 European Journal of Chemistry ISSN 2153-2249 (Print) / ISSN 2153-2257 (Online) – Copyright © 2022 The Authors – Atlanta Publishing House LLC – Printed in the USA. This work is published and licensed by Atlanta Publishing House LLC – CC BY NC – Some Rights Reserved. https://dx.doi.org/10.5155/eurjchem.13.3.337-350.2297 European Journal of Chemistry View Journal Online View Article Online Electronic band structure of Bi5O7NO3 and its methyl orange removal mechanism Eshraq Ahmed Abdullah * Department of Chemistry, Faculty of Education, Taiz University, Taiz, 009674, Yemen * Corresponding author at: Department of Chemistry, Faculty of Education, Taiz University, Taiz, 009674, Yemen. e-mail: ali123456yemen@gmail.com (E.A. Abdullah). 10.5155/eurjchem.13.3.337-350.2297 Received: 21 June 2022 Received in revised form: 15 July 2022 Accepted: 23 July 2022 Published online: 30 September 2022 Printed: 30 September 2022 A detailed study of the electronic band structures and partial density of states of Bi5O7NO3 with different exchange correlation functionals was performed using the generalized gradient approximation. Bi5O7NO3 has two direct energy gap transitions of 2.84 and 3.66 eV at the experimental lattice parameters, revealing a semiconductor characteristic of a crystal. Molecular Mechanics; however, tends to underestimate the band-gap energies with indirect characters. This deviation is due to the slight decrease in the cell edges and the significant increase in the β angle during the optimization process. The mechanism of removal of methyl orange and its derivatives by the Bi5O7NO3 unit cell, which has the same experimental UV- Vis band gap, was later investigated through a DMol3 module. To do that, frontier molecular orbitals, global reactivity parameters, and electrostatic potential surface maps were evaluated. The high values of the electrophilicity indexes hint that the dyes are more reactive and can work as good electrophile species. A molecular packing of dye molecules and the ionic natural of Bi5O7NO3 generate a synergistic effect between π-π stacking, anion-π stacking, cation-π stacking and electrostatic interactions, which are thought to be the driven forces during dye removal. Bi5O7NO3 π-π Stacking Semiconductor Electrostatic interactions Electronic band structure Electrostatic potential surface Cite this: Eur. J. Chem. 2022, 13(3), 337-350 Journal website: www.eurjchem.com 1. Introduction In recent years, bismuth oxide and its Bi5O7NO3 oxynitride derivative have been chosen as potential candidates for a visible light-driven photocatalyst and as an adsorbent for the removal of colored organic compounds [1,2]. Therefore, the structural features of Bi5O7NO3 were the center of the previous experimental investigations. In detail, Abdullah et al. success- fully synthesized Bi5O7NO3 using a chemical precipitation method [3]. Characterization techniques revealed that the point of zero charge of Bi5O7NO3 in the orthorhombic crystal structure was found to be 9.7 implying that the positively charged surface of Bi5O7NO3 occupied a wide range of pH [3]. Bi5O7NO3 has a narrow band gap in the energy range of 2.7-2.9 eV with high charge carrier mobility, so it is a good photo- catalyst for utilizing visible light [4]. However, a proper description of the electronic structure of Bi5O7NO3 is still unaddressed in details. Recently, a band structure approach to semiconductor solid systems based on self-consistent Kohn- Sham density functional theory (DFT) has gained a great attention in theoretical physics and quantum chemistry [5,6]. This approach provides an effective way to estimate the electronic structure of a matter such as; band gap edges, the chemical nature of valence and conduction bands, and their ability to disperse in the matter. Therefore, the first key point of this study is to determine the electronic band structure of the Bi5O7NO3 unit cell using periodic DFT calculations. To do that, Bi5O7NO3 (Monoclinic, P21/c) was selected as a target crystal in this study. Its crystal structure consists of [𝐵𝐵𝐵𝐵𝐵𝐵]+∞ 2 layers that are linked through [𝐵𝐵𝐵𝐵4𝐵𝐵8]4− units to form a framework structure [7]. Nitrate groups fill the channels in this structure as shown in Figure 1a. The calculations have been carried out using the generalized gradient approximation (GGA) with the help of different exchange correlation functionals and k-point grids. In the global market, azo dyes represent a large proportion of applied dyes in printing, dyeing, textiles, paper, and plastics industries [8]. The discharge of large amounts of these dyes produces environmental risks due to their hard biodegra- dability [9,10]. Thus, the adsorption technique was selected as an economical method for dye removal due to its efficiency, simplicity in design and operation, and low energy consump- tion. In this regard, several adsorbent systems have been reported for dye wastewater treatment in recent years [11,12]. The ability of Bi5O7NO3 to work as an adsorbent has been described in the prior literature [1]. In this study, the Langmuir model showed that adsorption occurs through a monolayer chemisorption coverage and fits well the pseudo-second order kinetic model in which the intraparticle diffusion is the rate- determining step. The maximum removal ability is in the pH range of 6-8, while the minimum capacity appears at the more acidic and basic mediums conforming the electrostatic interac- tion between the positively charged Bi5O7NO3 surface and the anionic dye molecules. ABSTRACT RESEARCH ARTICLE KEYWORDS https://dx.doi.org/10.5155/eurjchem.13.3.337-350.2297 https://www.eurjchem.com/ https://dx.doi.org/10.5155/eurjchem.13.3.337-350.2297 mailto:ali123456yemen@gmail.com http://www.eurjchem.com/ https://crossmark.crossref.org/dialog/?doi=10.5155/eurjchem.13.3.337-350.2297&domain=pdf&date_stamp=2022-09-30 338 Eshraq Ahmed Abdullah / European Journal of Chemistry 13 (3) (2022) 337-350 2022 – European Journal of Chemistry – CC BY NC – DOI: 10.5155/eurjchem.13.3.337-350.2297 (a) (b) Figure 1. Schematic representation of (a) unoptimized and (b) optimized structures of the Bi5O7NO3 crystal. X-ray photoelectron spectroscopy results suggested that ion exchange is the dominant removal mechanism. However, how the dye can accumulate on the Bi5O7NO3 surface has never been addressed by the researchers before. This lack motivated us to select the second key point of this research by elucidating the adsorption mechanism of various structures of methyl orange dye on Bi5O7NO3 using the DMol3 module with the periodic DFT approach. 2. Computational methods 2.1. Electronic structures of Bi5O7NO3 A total of 64 atoms of the Bi5O7NO3 crystal was optimized using a universal force field (UFF) as a Molecular Mechanics (MM) tool of a Forcite module implemented in a BIOVIA Material Studio 2017 package to achieve stable ground state parameters [13]. During this process, the nitrate groups were held rigid while the framework atoms were allowed to relax. The convergence tolerances were 1×10-5 kcal/mol for the total energy, 1×10-3 kcal/mol/Å for the force between the atoms and 1×10-5 Å for the maximum displacement. To gain the best understanding, the calculations were carried out with respect to the experimental lattice parameters [7]. In detail, the band gap value was first evaluated using the generalized gradient approximation with different exchange correlation functionals of Perdew, Burke and Ernzerhof (PBE), Hamprecht-Cohen- Tozer-Handy (HCTH/407) Becke-Lee-Yang-Parr (BLYP) in the DMol3 module [14,15]. The optimal functional was then examined at different Monkhorst-Pack grids of 1×1×1, 2×1×3, 2×1×4, and 3×1×5 to determine the impact of the Brillouin zone size. The electrons were treated using a DND 4.4 basis set and the effective core potential (ECP) approach. Finally, the electronic band structures and partial density of states were calculated for the optimized and unoptimized Bi5O7NO3 structures using the optimal functional and k-point grid. To verify the computational method, the UV-Vis diffuse reflectance spectrum (DRS) of the Bi5O7NO3 sample was recorded using a Perkin Elmer Lambda 35 UV-Vis spectrophotometer in the wavelength range of 200-800 nm. 2.2. Adsorption studies The adsorption study was carried out with the Bi5O7NO3 unit cell at the experimental lattice parameters, which has the same experimental UV-Vis band gap. To do that, methyl orange dyes (MO) in the structures of MO_H, MO_Na, and MO_zwitterion are first relaxed in the DMol3 module using the all-electrons approach at the GGA/HCTH level of theory. The self-consistent field convergence criteria of iteration processes are 1×10-5 Ha. Secondly, the relaxed MO molecules were copied on the Bi5O7NO3 unit cell. Interestingly, the Material Studio program copied four MO relaxed molecules, which are consistent with the number of Bi5O7NO3 molecules in each unit cell. The Material Studio program automatically controlled the position of the added molecules. Due to the prohibitive cost of the calculations, memory and disk storage requirements, only single point energy calculations with effective core potential (ECP) at the GGA/HCTH level of theory were conducted for adsorption systems. Finally, frontier molecular orbitals and electrostatic potential surface maps were acquired to investigate plausible adsorption sites. 2.3. Theoretical background In modern quantum chemistry, the solving of the Schrödinger wave function relies on the electron Hamiltonian (𝐻𝐻�) [16] that is given by the Equation (1), 𝐻𝐻� = 𝑇𝑇� + 𝑉𝑉�𝑒𝑒𝑒𝑒 + ∑ 𝑣𝑣(𝑟𝑟)𝑁𝑁 𝑖𝑖=1 (1) where 𝑣𝑣(𝑟𝑟) is the electron-nuclear attraction potential, 𝑇𝑇� is the kinetic energy operator and 𝑉𝑉�𝑒𝑒𝑒𝑒 is the electron-electron repulsion operator. This Hamiltonian can only be obtained for very small systems. Thus, Hohenberg-Kohn-Sham density functional theory was suggested as an alternative way to solve the Schrödinger equation. In this approach, the ground-state energy is approximated as a function of a non-interacting collection of electrons enclosed in a box that is influenced by an external potential 𝑣𝑣(𝑟𝑟). For a given 𝑣𝑣(𝑟𝑟), the ground state energy 𝐸𝐸𝐺𝐺𝐺𝐺 can be obtained by minimizing the electron density using a variational principle as follows, 𝐸𝐸𝐺𝐺𝐺𝐺 = 𝑚𝑚𝐵𝐵𝑚𝑚𝜌𝜌[∫𝑣𝑣(𝑟𝑟)𝜌𝜌(𝑟𝑟)𝑑𝑑𝑟𝑟 + 𝐹𝐹𝐻𝐻𝐻𝐻[𝜌𝜌(𝑟𝑟)]] (2) where 𝜌𝜌(𝑟𝑟) is a trail electron density and 𝐹𝐹𝐻𝐻𝐻𝐻[𝜌𝜌(𝑟𝑟)] is an unknown universal functional of 𝜌𝜌(𝑟𝑟) that must be approximated. In fact, this term equals to the sum of the Hartree energy 𝐸𝐸𝐻𝐻𝐻𝐻𝐻𝐻𝐻𝐻𝐻𝐻𝑒𝑒𝑒𝑒 and the exchange correlation energy 𝐸𝐸𝑥𝑥𝑥𝑥 , which Eshraq Ahmed Abdullah / European Journal of Chemistry 13 (3) (2022) 337-350 339 2022 – European Journal of Chemistry – CC BY NC – DOI: 10.5155/eurjchem.13.3.337-350.2297 contains a portion of the exact kinetic energy. Thus, the 𝐸𝐸𝐺𝐺𝐺𝐺 can be rewritten as 𝐸𝐸𝐺𝐺𝐺𝐺 = 𝑚𝑚𝐵𝐵𝑚𝑚𝜌𝜌[∫𝑣𝑣(𝑟𝑟)𝜌𝜌(𝑟𝑟)𝑑𝑑𝑟𝑟 + 𝐸𝐸𝐻𝐻𝐻𝐻𝐻𝐻𝐻𝐻𝐻𝐻𝑒𝑒𝑒𝑒[𝜌𝜌(𝑟𝑟)] + 𝐸𝐸𝑥𝑥𝑥𝑥[𝜌𝜌(𝑟𝑟)]] (3) For the electronic structure problem, the effective potential 𝑉𝑉𝑒𝑒𝑒𝑒𝑒𝑒is defined as a first derivative of the ground state energy in the Equation (3). This potential is used to build the Kohn-Sham DFT equation, which is one-electron Schrodinger like equation expressed by �− 1 2 ∇2 + 𝑉𝑉𝑒𝑒𝑒𝑒𝑒𝑒� ∅𝑖𝑖 = 𝜖𝜖𝑖𝑖∅𝑖𝑖 (4) where ∅𝑖𝑖 are the Kohn-Sham non-interacting electron orbitals and 𝜖𝜖𝑖𝑖 are the eigenvalues that determine the ground state energy. However, the wave function used to describe the electronic structure of crystalline solids must contain a lattice- periodic factor, 𝑢𝑢𝑘𝑘(𝑟𝑟) [17]. Thus, Bloch’s theorem suggests a shape of the periodic wave function by multiplying a lattice- periodic factor by a plane wave as follows, ∅𝑘𝑘(𝑟𝑟) = 𝑒𝑒𝑖𝑖𝑘𝑘𝐻𝐻𝑢𝑢𝑘𝑘(𝑟𝑟) (5) where 𝑘𝑘 is the quantum number that characterizes the wavefunction of a periodic system. The solution of the Kohn- Sham DFT equation using the Bloch theorem is known as the Periodic DFT approach. The ground state energy resulting from the Equation (4) is exact if the exchange correlation functional is known exactly. Unfortunately, this term has no exact expression. Thus, various attempts have been made by scientists to approximate it including; local, semi-local, and non-local approaches. 2.3.1. The generalized gradient approximation (GGA) A semi-local approximation, GGA, is introduced to avoid the problem occurring for the rapidly varying electron densities of many materials. The electron density of a system is corrected by including its gradient, ∇𝜌𝜌(𝑟𝑟) [18,19]. The functional form of the GGA is usually taken as a correction to local density approximation (LDA) and it is divided into two separate parts; the exchange part and the correlation part as follows 𝐸𝐸𝑥𝑥𝑥𝑥𝐺𝐺𝐺𝐺𝐺𝐺 = 𝐸𝐸𝑥𝑥𝐺𝐺𝐺𝐺𝐺𝐺 + 𝐸𝐸𝑥𝑥𝐺𝐺𝐺𝐺𝐺𝐺 (6) The GGA exchange part takes the form of 𝐸𝐸𝑥𝑥𝐺𝐺𝐺𝐺𝐺𝐺(𝜌𝜌) = ∫𝜌𝜌(𝑟𝑟) 𝜖𝜖𝑥𝑥 𝑢𝑢𝑢𝑢𝑖𝑖𝑒𝑒[𝜌𝜌(𝑟𝑟)]𝐹𝐹𝑥𝑥𝐺𝐺𝐺𝐺𝐺𝐺(𝑠𝑠)𝑑𝑑𝑟𝑟 (7) where the energy density for the uniform electron gas �𝜖𝜖𝑥𝑥 𝑢𝑢𝑢𝑢𝑖𝑖𝑒𝑒� and the reduced gradient (s) are defined, respectively, as 𝜖𝜖𝑥𝑥 𝑢𝑢𝑢𝑢𝑖𝑖𝑒𝑒[𝜌𝜌(𝑟𝑟)] = −3𝑒𝑒2 4𝜋𝜋 �3𝜋𝜋2𝜌𝜌(𝑟𝑟)� 1 3 (8) 𝑠𝑠 = � ∇𝜌𝜌(𝐻𝐻) 2(3𝜋𝜋2) 1 3𝜌𝜌(𝐻𝐻) 4 3 � (9) The mathematical description of the exchange enhancement factor 𝐹𝐹𝑥𝑥𝐺𝐺𝐺𝐺𝐺𝐺, which is used to correct the exchange energy over its LDA value for a given electron density differs as the functional used to approximate the problem differ. In the PBE functional, the 𝐹𝐹𝑥𝑥𝐺𝐺𝐺𝐺𝐺𝐺 has a formula of 𝐹𝐹𝑥𝑥𝑃𝑃𝑃𝑃𝑃𝑃(𝑠𝑠) = 1 + 𝜅𝜅 − 𝜅𝜅 �1+𝜇𝜇𝑠𝑠 2 𝜅𝜅 � (10) where 𝜅𝜅 = 0.804,𝜇𝜇 = 0.2195 and 0 < 𝑠𝑠 < 3. When the reduced gradient approaches zero, the exchange gradient correction cancels the gradient correction of the correlation term. Thus, the GGA exchange returns to the LDA exchange. However, in the case of the BLYP functional, the exchange enhancement factor takes the form of 𝐹𝐹𝑥𝑥𝑃𝑃88(𝑠𝑠) = 1 + 𝛽𝛽𝑥𝑥(𝑠𝑠)2 𝐶𝐶[1+6𝛽𝛽𝑥𝑥(𝑠𝑠) 𝑠𝑠𝑖𝑖𝑢𝑢ℎ−1(𝑥𝑥(𝑠𝑠))] ; 𝑥𝑥 = 2(6𝜋𝜋2) 1 3𝑠𝑠 (11) where C and 𝛽𝛽 are empirical fitting parameters. The GGA correlation part takes the form of 𝐸𝐸𝐶𝐶𝐺𝐺𝐺𝐺𝐺𝐺 = ∫ 𝑑𝑑3𝑟𝑟 𝜌𝜌(𝑟𝑟)�𝜖𝜖𝑥𝑥 𝑢𝑢𝑢𝑢𝑖𝑖𝑒𝑒(𝑟𝑟𝑠𝑠, 𝜉𝜉) + 𝐻𝐻(𝐻𝐻𝑠𝑠,𝜉𝜉,𝐻𝐻)� (12) where the function 𝐻𝐻(𝐻𝐻𝑠𝑠,𝜉𝜉,𝐻𝐻) has a complicated formula for each functional [20]. The 𝐻𝐻(𝐻𝐻𝑠𝑠,𝜉𝜉,𝐻𝐻) for the PBE functional takes the form of 𝐻𝐻(𝐻𝐻𝑠𝑠,𝜉𝜉,𝐻𝐻) = 𝛾𝛾∅3𝑙𝑙𝑚𝑚 �1 + 𝛽𝛽 𝛾𝛾 𝑡𝑡2 � 1+𝐺𝐺𝐻𝐻2 1+𝐺𝐺𝐻𝐻2+𝐺𝐺2𝐻𝐻4 �� (13) In which, 𝑟𝑟𝑠𝑠 = � 3 4𝜋𝜋𝜌𝜌 � 1 3 , 𝜉𝜉 = �𝜌𝜌𝛼𝛼−𝜌𝜌𝛽𝛽� 𝜌𝜌 , 𝑡𝑡 = �∇��⃗ 𝜌𝜌� 2𝑘𝑘𝑠𝑠𝜌𝜌∅ ,∅ = 1 2 �(1 + 𝜉𝜉)2 3� + (1 − 𝜉𝜉)2 3� �, 𝐴𝐴 = 𝛽𝛽 𝛾𝛾 �𝑒𝑒𝑥𝑥𝑒𝑒�−𝜖𝜖𝑥𝑥 𝑢𝑢𝑢𝑢𝑖𝑖𝑒𝑒/𝛾𝛾∅3� − 1� −1 , 𝛾𝛾 = 0.031091,𝛽𝛽 = 0.066725 . The LYP correlation functional is derived by considering short-range effects in the two-particle density matrix [21]. The functional is transformed by 𝜖𝜖𝐶𝐶𝐿𝐿𝐿𝐿𝑃𝑃 = − 4𝐻𝐻 1+𝑑𝑑𝜌𝜌− 1 3 � 𝜌𝜌𝛼𝛼𝜌𝜌𝛽𝛽 𝜌𝜌 − 211 3⁄ 𝐶𝐶𝐹𝐹𝑎𝑎𝑎𝑎𝑎𝑎(𝜌𝜌)𝜌𝜌𝛼𝛼𝜌𝜌𝛽𝛽�𝜌𝜌𝛼𝛼 8 3⁄ + 𝜌𝜌𝛽𝛽 8 3⁄ � + 𝜕𝜕𝜖𝜖𝐶𝐶 𝐿𝐿𝐿𝐿𝐿𝐿 𝜕𝜕𝛾𝛾𝛼𝛼𝛼𝛼 𝛾𝛾𝛼𝛼𝛼𝛼 + 𝜕𝜕𝜖𝜖𝐶𝐶 𝐿𝐿𝐿𝐿𝐿𝐿 𝜕𝜕𝛾𝛾𝛼𝛼𝛽𝛽 𝛾𝛾𝛼𝛼𝛽𝛽 + 𝜕𝜕𝜖𝜖𝐶𝐶 𝐿𝐿𝐿𝐿𝐿𝐿 𝜕𝜕𝛾𝛾𝛽𝛽𝛽𝛽 𝛾𝛾𝛽𝛽𝛽𝛽� (14) where 𝜌𝜌𝛼𝛼 is the spin up density, 𝜌𝜌𝛽𝛽 is the spin down density, 𝛾𝛾𝛼𝛼𝛼𝛼 , 𝛾𝛾𝛽𝛽𝛽𝛽 , 𝛾𝛾𝛼𝛼𝛽𝛽 are the related gradient densities, and the constants take values of 𝐶𝐶𝐹𝐹 = 3 10 (3𝜋𝜋2)2 3� ,𝑎𝑎 = 0.04918,𝑎𝑎 = 0.132, 𝑐𝑐 = 0.2533,𝑑𝑑 = 0.349 while 𝑎𝑎(𝜌𝜌) equals 𝑎𝑎(𝜌𝜌) = 𝑒𝑒−𝑐𝑐𝜌𝜌 −1 3� 1+𝑑𝑑𝜌𝜌− 1 3� 𝜌𝜌−11 3� . In the case of the HCTH functional, the exchange – correlation form can be obtained by factorizing the post-local spin density approximation (𝐹𝐹𝐿𝐿𝐺𝐺𝐿𝐿𝐺𝐺) [22] as follows 𝐸𝐸𝑥𝑥𝑥𝑥 = ∑ ∑ 𝐶𝐶𝑞𝑞,𝛾𝛾 ∫𝐹𝐹𝐿𝐿𝐺𝐺𝐿𝐿𝐺𝐺,𝛾𝛾�𝜌𝜌𝛼𝛼 ,𝜌𝜌𝛽𝛽�𝑓𝑓𝛾𝛾 𝑞𝑞�𝜌𝜌𝛼𝛼 ,𝜌𝜌𝛽𝛽 , 𝑥𝑥𝛼𝛼2, 𝑥𝑥𝛽𝛽2�𝑑𝑑𝑟𝑟𝑚𝑚 𝑞𝑞𝛾𝛾 (15) In which 𝑓𝑓𝛾𝛾 𝑞𝑞 is the perturbation from the uniform electron gas, 𝑥𝑥𝛼𝛼 and 𝑥𝑥𝛽𝛽 are coefficients, which fit to atomic data. When Equation (15) is applied up to the fourth order, 15 linear coefficients can be easily parameterized by minimizing the error function, 𝛺𝛺 as follows, 𝛺𝛺 = ∑ 𝑎𝑎𝑚𝑚(𝐸𝐸𝑚𝑚𝑒𝑒𝑥𝑥𝐻𝐻𝑥𝑥𝐻𝐻 − 𝐸𝐸𝑚𝑚𝐻𝐻−𝐺𝐺)2𝑢𝑢𝑃𝑃 𝑚𝑚 + ∑ 𝑎𝑎𝑙𝑙,𝐺𝐺𝑢𝑢𝐺𝐺 𝑙𝑙,𝑥𝑥 �𝜕𝜕𝑃𝑃𝑙𝑙 𝐾𝐾−𝑆𝑆 𝜕𝜕𝑥𝑥 � 2 + ∑ 𝑎𝑎𝑗𝑗,𝑣𝑣 𝑢𝑢𝑣𝑣 𝑗𝑗,𝜎𝜎 ∫�𝑣𝑣𝑗𝑗,𝜎𝜎 𝑍𝑍𝑍𝑍𝑃𝑃 + 𝑘𝑘𝑗𝑗,𝜎𝜎 − 𝑣𝑣𝑗𝑗,𝜎𝜎 𝐻𝐻−𝐺𝐺�2 𝜌𝜌𝑗𝑗,𝜎𝜎 2 3� 𝑑𝑑𝑟𝑟 (16) The first summation corresponding to the energy errors, which can be calculated as a difference between the exact and the calculated Kohn-Sham energies of a property. While the second term defines the gradient error, which equals zero at the equilibrium geometry. The final term describes the exchange- correlation potential errors that are mostly fit by the Zhao- Morrison-Parr method at high ab initio densities. 340 Eshraq Ahmed Abdullah / European Journal of Chemistry 13 (3) (2022) 337-350 2022 – European Journal of Chemistry – CC BY NC – DOI: 10.5155/eurjchem.13.3.337-350.2297 Table 1. Bi5O7NO3 lattice parameters determined using the UFF Molecular Mechanics simulation. The calculated values are compared with the current experimental results of the un-optimized structure. Cell parameters UFF molecular mechanics Experimental lattice [7] a (Å) 8.3698 8.5846 b (Å) 23.0286 23.3846 c (Å) 5.2597 5.5422 𝛼𝛼 (°) 90 90 𝛽𝛽 (°) 110.956 108.103 𝛾𝛾 (°) 90 90 Cell volume (Å3) 946.71 1057.51 Table 2. Band gaps evaluation using different exchange correlation functionals and k-point grids Band gap (eV) at GGA/Gamma-point Experiment Predicted Functional PBE BLYP HCTH UV-Vis Un-optimized 2.664 2.615 2.775 2.82 2.7-2.9 [4] Optimized 1.306 1.429 1.418 3.1 [2] Band gap (eV) at GGA/HCTH level of theory k-point grid Coarse 2×1×3 Medium 2×1×4 Fine 3×1×5 Un-optimized 2.843 2.843 2.843 Optimized 1.508 1.508 1.508 The constant 𝑘𝑘𝑗𝑗,𝜎𝜎 shows the effect of quantum-mechanical integer discontinuity. All these contributions should be weigh- ted by suitable weights of 𝑎𝑎𝑚𝑚, 𝑎𝑎𝐿𝐿,𝐺𝐺 and 𝑎𝑎𝑗𝑗,𝑣𝑣 , respectively. 2.3.2. Molecular mechanics method The molecular mechanics method is a non-electron Hamiltonian approach, which deals with a molecule or solid as a collection of atoms that held together. The ground-state energy in the molecular mechanics approach is evaluated in terms of the force constants that describe the interatomic interactions. Different Molecular Mechanics force fields are incorporated in the Material Studio software modules such as; the universal force field (UFF), the condensed phase optimized molecular potentials for atomic simulation studies (COMPASS) and the Deriding [23]. In the UFF code, the functional form of the total energy is given by 𝐸𝐸𝐻𝐻𝑈𝑈𝐹𝐹𝐹𝐹 = 𝐸𝐸𝑅𝑅 + 𝐸𝐸𝜃𝜃 + 𝐸𝐸∅ + 𝐸𝐸𝑤𝑤 + 𝐸𝐸𝑣𝑣𝑑𝑑𝑣𝑣 + 𝐸𝐸𝑒𝑒𝑙𝑙 (17) = 1 2 𝑘𝑘𝐼𝐼𝐼𝐼�𝑟𝑟 − 𝑟𝑟𝐼𝐼𝐼𝐼� 2 + 𝑘𝑘𝐼𝐼𝐼𝐼𝐻𝐻 ∑ 𝐶𝐶𝑢𝑢𝐶𝐶𝐶𝐶𝑠𝑠𝐶𝐶𝑚𝑚 𝑢𝑢=0 + 𝑘𝑘𝐼𝐼𝐼𝐼𝐻𝐻𝐿𝐿 ∑ 𝐶𝐶𝑢𝑢𝐶𝐶𝐶𝐶𝑠𝑠𝑚𝑚∅𝐼𝐼𝐼𝐼𝐻𝐻𝐿𝐿𝑚𝑚 𝑢𝑢=0 + 𝑘𝑘𝐼𝐼𝐼𝐼𝐻𝐻𝐿𝐿�𝐶𝐶0 + 𝐶𝐶1𝐶𝐶𝐶𝐶𝑠𝑠𝑎𝑎𝐼𝐼𝐼𝐼𝐻𝐻𝐿𝐿 + 𝐶𝐶2𝐶𝐶𝐶𝐶𝑠𝑠2𝑎𝑎𝐼𝐼𝐼𝐼𝐻𝐻𝐿𝐿� + 𝐷𝐷𝐼𝐼𝐼𝐼 �−2 �𝑥𝑥𝐼𝐼𝐼𝐼 𝑥𝑥 � 6 + �𝑥𝑥𝐼𝐼𝐼𝐼 𝑥𝑥 � 12 �+ 332.0637 𝑄𝑄𝑖𝑖𝑄𝑄𝑗𝑗 𝜀𝜀𝑅𝑅𝑖𝑖𝑗𝑗 (18) where 𝐶𝐶 is the periodic angle in a Fourier expression, 𝐶𝐶𝑢𝑢 is the expansion coefficient, 𝑎𝑎𝐼𝐼𝐼𝐼𝐻𝐻𝐿𝐿 is the angle between IL axis and IJKL plane, 𝐷𝐷𝐼𝐼𝐼𝐼 is the van der Waals depth, 𝑥𝑥𝐼𝐼𝐼𝐼 is the van der Waals bond length, 𝑄𝑄𝑖𝑖 , 𝑄𝑄𝑗𝑗 are the atomic charges in electron units, 𝑅𝑅𝑖𝑖𝑗𝑗 is the distance in Angstrom and 𝜀𝜀 is the dielectric constant. The first term describes the bond stretching between atoms in the molecule or solid. The following three terms use the Fourier Cosine expansion to describe angle bonding, torsion about bonds, and inversions. The non-bonded interactions; van der Waals and electrostatic, which determine attraction and repulsion forces are described in the last two terms. The functional form of the Deriding force field is very similar to that of the UFF. Thus, it usually yields similar results. However, the contribution of the torsion term in the functional form of the COMPASS force field outweighs the van der Waals contribution. Thus, it is more important to predict the vibrational frequencies compared to UFF and Deriding force fields [24]. 3. Results and discussion 3.1. Electronic structures of Bi5O7NO3 Figure 1 illustrates the Bi5O7NO3 crystal structure at the experimental lattice parameters (unoptimized structure) and the UFF optimized structure. The optimized unit cell remained in a monoclinic phase with a space group P21/c in the gas phase. The calculated lattice parameters for the optimized Bi5O7NO3 are compared with the experimental parameters of the unoptimized structure reported by Ziegler et al. in Table 1 [7]. As can be seen, the calculated lattice parameters are slightly shorter along the directions and the β angle shows an increase of 2.853°. The crystal structure underwent a moderate shrinkage, with a 10.5% decrease in the volume of the unit cell. 3.1.1. The functional effect Table 2 presents detailed results for the evaluation of the band gaps of the unoptimized and UFF optimized structures of Bi5O7NO3 with the PBE, BLYP and HCTH exchange correlation functionals. In general, the calculation results match the theoretical trend of the band gap values in the order of HCTH > PBE [25]. There is a slight deviation in the gap value for the BLYP functional. The HTCH functional can reproduce the experimental energy band gap of 2.82 eV in the case of the un- optimized structure. The value also shows close agreement with the predicted value reported by Yu et al. [4]. This is due to the fact that the HTCH functional employs 15 internal parameters for band structure calculations [26]. This finding indicates that the HTCH functional is reliable and much suitable to compute the band structure [27,28]. However, in the case of the UFF optimized structure, the HTCH and BLYP functionals underestimate the experimental results by 50%. This deviation may be due to an underestimation of the lattice constants and an overestimation of the β angle. 3.1.2. The k-point grid effect The effect of a reciprocal space on a band gap value was addressed by the quality sets of Coarse, Medium and Fine grids as well as the G– point that marks the origin of the reciprocal lattice. In comparison with a G– point, Table 2 exhibits a marginal development of the band gap values using a 2×1×3 grid. Energy gaps remain invariant with 2×1×4 and 3×1×5 k- point meshes. That is, the energy gap value of Bi5O7NO3 is relatively independent of the number of k-points sampled of the Brillouin zone. 3.1.3. Electronic band structure Figure 2 demonstrates the electronic band structures of the optimized and unoptimized Bi5O7NO3 obtained at the GGA/HCTH level of theory using the 2×1×3 k-point grid. The electronic band structures of Bi5O7NO3 were determined when the Fermi energy level is set to be zero and the solid vertical Eshraq Ahmed Abdullah / European Journal of Chemistry 13 (3) (2022) 337-350 341 2022 – European Journal of Chemistry – CC BY NC – DOI: 10.5155/eurjchem.13.3.337-350.2297 (a) (b) Figure 2. Electronic band structures for (a) un-optimized and (b) optimized Bi5O7NO3 structures Figure 3. A Tauc plot of Bi5O7NO3 extracted from the UV-Vis analysis. The linear fit regions evaluate the band gaps by 2.82, 3.66, and 2.57 eV at the x-axis intercept for Bi5O7NO3 before and after MO dye adsorption, respectively. lines describe the symmetry points of the monoclinic Bi5O7NO3 Brillouin zone. The results indicate that the unoptimized structure of Bi5O7NO3 has a band gap of 2.843 eV, verifying its ability to absorb a visible light. Under the UFF relaxation process, the states in the conduction band come closer to the Fermi level and significantly reduce the band gap to 1.508 eV, indicating that the unoptimized structure is more ionic in nature and has a large charge transfer property [29]. This makes Bi5O7NO3 as a promising visible-light-driven photo- catalyst. The conduction band minimum (CB) and the valence band maximum (VB) of the un-optimized structure were located at the G symmetry point indicating the presence of direct band gap allowed transitions. On the contrary, the conduction band minimum of the optimized structure was obtained near the Z symmetry point, whereas the valence band maximum is linked to the B symmetry point, creating an indirect band gap feature. 3.1.4. The UV-Vis analysis To verify the computational method, the Tauc method, which relies on a linear fitting of Equation (19), was used to determine the optical absorption edge near the band gap values [30,31]. (𝛼𝛼ℎ𝜈𝜈)1 𝑢𝑢⁄ = 𝐴𝐴�ℎ𝜈𝜈 − 𝐸𝐸𝑔𝑔� (19) where ℎ is Planck’s constant, 𝜈𝜈 is the photon’s frequency, 𝛼𝛼 is the absorption coefficient, 𝐸𝐸𝑔𝑔 is the band gap and 𝐴𝐴 is the proportionality constant. In Figure 3, a sharper and more linear edge is obtained when the exponent 1 𝑚𝑚⁄ equals two indicating indirect allowed transitions. The Tauc plot shows that Bi5O7NO3 has a band gap value of 2.82 eV. 342 Eshraq Ahmed Abdullah / European Journal of Chemistry 13 (3) (2022) 337-350 2022 – European Journal of Chemistry – CC BY NC – DOI: 10.5155/eurjchem.13.3.337-350.2297 (a) (b) Figure 4. PDOS plots of (a) unoptimized and (b) optimized Bi5O7NO3 structures. This value is identical to the theoretical gap of the unoptimized structure. However, the band gap of the optimized structure is 46% less than this value. The underestimation behavior is a common band gap problem due to self-interaction errors. However, this study illustrates that the underestimation behavior did not occur significantly on the monoclinic phase of Bi5O7NO3 at the experimental lattice parameters. The most attractive point in the UV-Vis analysis is the presence of two distinct allowed transitions of photons. The second allowed transitions that occur at 3.66 eV experimentally assign to the 𝑚𝑚 → 𝜋𝜋∗ energy transitions of nitrate groups [32]. In the calculated band structures, this gap can be assigned to the allowed transitions between the Bi5O7NO3 valence band and a second conduction band, which produce a direct band gap of 3.2 eV and an indirect band gap of 2.3 eV for the unoptimized and optimized structures, respectively. 3.1.5. The PDOS analysis of Bi5O7NO3 To gain a deeper insight into the nature of the bands and to know how the atomic orbitals are combined to form the bonding and antibonding bands, the PDOS study was carried out at the GGA/HCTH level of theory. The obtained PDOS in Figure 4 illustrates that the band located above the Fermi level (CB) has the Bi 6p character with a minor contribution of the O 2p and N 2p orbitals. The highest band below the Fermi level (VB) consisted mainly of the O 2p orbitals with little contri- bution from the Bi 6p and Bi 6s orbitals. Hybridization between these orbitals making the valence band of Bi5O7NO3 to be largely dispersed [33]. However, Andriyevsky et al. ascribed this energy dispersion to the presence of nitrate groups [34]. This dispersion produces the best mobility of photocarries and makes Bi5O7NO3 as a promising photocatalytic system [35]. Experimentally, there are two band gaps in Figure 3. According to the PDOS results, the first band gap is arising from the allowed transitions occurred between valence band maximum and the N 2p and O 2p orbitals in the conduction band, while the second band gap is due to the allowed transitions taking place between the valence band maximum and the Bi 6p orbitals in the conduction band. There is a clear separation of the O 2p orbitals of the nitrate groups in the optimized structure. This occurs because of the UFF relaxation criteria dealt with nitrate groups as a single component in motion. This splitting proves that the upper of the valence band of Bi5O7NO3 shows a contribution of O2p orbitals bonded to nitrate groups, which is in excellent agreement with Huang et al. [36]. The narrow band gap in the optimized structure is due to the ability of the Bi 6p orbitals to move toward a lower energy level and its overlap- ping behaviour with the O2p and N2p orbitals, as shown in Figure 4 (b). The band below the VB shows a mixture of O 2p, N 2p, and Bi 6s states. The last band located in the energy range of –16 → –21 eV has an O 2s character, which is slightly affected by some N 2p states. Clearly, the resulted states are quite flat and tight on k-space of Bi5O7NO3 indicating the ionic nature of the Bi5O7NO3 framework and a weaker p-d interaction. 3.2. Adsorption studies According to Figure 5, there is a difference in the adsorption position of the dye molecules. MO_H dye molecules have perpendicular attached along the b direction of the Bi5O7NO3 framework at the edge of the azo groups. Therefore, the benzene-4-sulfonic acid groups remain outside the cell. In general, there are two regions of interaction. The first region is governed by the phenyl −𝑁𝑁(𝐶𝐶𝐻𝐻3)2 fragment at the top and bottom of the unit cell. Whereas the second region occurs when two methyl orange molecules are slipped stacking in the middle of the unit cell. Eshraq Ahmed Abdullah / European Journal of Chemistry 13 (3) (2022) 337-350 343 2022 – European Journal of Chemistry – CC BY NC – DOI: 10.5155/eurjchem.13.3.337-350.2297 (a) (b) (c) Figure 5. Preferable adsorption sites of MO dyes onto the Bi5O7NO3 unit cell (a) MO_H/Bi5O7NO3, (b) MO_Na/Bi5O7NO3 and (c) MO_Zwitterion/Bi5O7NO3. In the case of MO_Na and MO_zwitterion, the dye molecules have parallel adsorbed along the b direction. Two dye mole- cules were completely encapsulated by the Bi5O7NO3 frame- work. A steric effect; however, prevents a complete encapsula- tion of the other two molecules. Therefore, benzene-4-sulfonate groups remain outside the cell. 3.2.1. Frontier molecular orbitals of the adsorbates Frontier molecular orbitals are mostly described by the highest energy orbital that is still occupied by electrons (HOMO) and the lowest energy orbital that has enough space to accept electrons (LUMO) [37]. Figure 6 illustrates that the HOMO orbital of the MO_H optimized structure is completely localized on the azo group of the dye, indicating that the excitation takes place from 𝑚𝑚 and 𝜋𝜋 orbitals of nitrogen atoms. However, before the optimization process, the HOMO lobe is localized along the −𝑁𝑁 = 𝑁𝑁 − phenyl− 𝑁𝑁(𝐶𝐶𝐻𝐻3)2 fragment. The presence of electron donor groups (−𝐶𝐶𝐻𝐻3) in the HOMO lobe leads to increase the energy level of the HOMO orbitals [38]. Since a low energy gap between HOMO and HOMO-1 energy levels, aromatic rings can consider as a second center of the electron donation. In the case of the optimized MO_Na dye molecule, the center of donation resides in dimethyl amine and sulfonate groups for HOMO and HOMO-1 lobes, respectively. The introduction of a low electronegativity sodium atom on the HOMO lobe of the un-optimized MO_Na leads to a sharper increase in the energy level of the frontier orbitals. For the MO_zwitterion dye, the center of donation is localized on the sulfonate group, which is enhanced by a small or large π-bond in the HOMO-1 region for the unoptimized and optimized dye molecules, respectively. The ability of the sulfonate groups to work as a center of donation agrees well with the research work done by Saleh et al. [39]. The shape of the LUMO level declares that the electron-receiving center mainly distributes over the entire dye molecules. 3.2.2. The chemical reactivity Density functional theory is a modern tool used to provide theoretical insights into the chemical reactivity of adsorbate matter [40-42]. The molecular reactivity of dye molecules was investigated in terms of the Koopmans’ theorem by measuring the ability of dye molecules to acquire electrons. Thus, different physical parameters such as; the chemical hardness (η), the chemical potential (μ), the electronegativity value (χ), the electrophilicity index (ω) and the maximum number of electrons that an electrophile can acquire have been extracted. These global indexes were approximated from HOMO (𝐸𝐸𝐻𝐻) and LUMO (𝐸𝐸𝐿𝐿) energies using the following equations. 𝜇𝜇 = −𝜒𝜒 = 𝑃𝑃𝐻𝐻+𝑃𝑃𝐿𝐿 2 (20) 𝜂𝜂 = 𝑃𝑃𝐿𝐿−𝑃𝑃𝐻𝐻 2 (21) 𝑎𝑎 = 𝜇𝜇2 2𝜂𝜂 (22) ∆𝑁𝑁𝑚𝑚𝐻𝐻𝑥𝑥 = −𝜇𝜇 𝜂𝜂 (23) The calculated energies of the HOMO and LUMO orbitals, along with the corresponding values of the physical parameters for the study systems, are listed in Table 3. According to Fukui’s theory, a high-energy value of the HOMO orbital suggests a better capability of the MO_Na dye to donate electrons. Whereas a low-energy value of the LUMO level indicates a great tendency of the MO_Zwitterion dye to accept electrons [43,44]. Almost all dyes show smaller energy gaps in comparison to Bi5O7NO3 in the sequence of MO_Zwitterion < MO_Na < MO_H implying their high chemical reactivity and a strong intermolecular charge transfer during the adsorption process [45,46]. The minimum energy gap of the MO_Zwitterion can structurally be attributed to the conjugation length increase, which makes the LUMO level lower. The tendency of electrons to escape from the dye is measured by the chemical potential (μ) or the electronegativity value (χ). The electronegativity values of all dyes are high except for the unoptimized MO_Na dye molecule. This finding indicates the capability of the dyes to accept electrons from Bi5O7NO3 when they are brought together. However, the low electronegativity value of the un-optimized MO_Na is due to the presence of a low electronegativity sodium atom in its HOMO lobe structure [47]. 344 Eshraq Ahmed Abdullah / European Journal of Chemistry 13 (3) (2022) 337-350 2022 – European Journal of Chemistry – CC BY NC – DOI: 10.5155/eurjchem.13.3.337-350.2297 ELUMO = -3.223 eV ↕ Egap = 1.853 eV EHOMO = -5.076 eV EHOMO-1 = -5.203 eV ELUMO = -3.276 eV ↕ Egap = 1.416 eV EHOMO = -4.692 eV EHOMO-1 = -5.979 eV (a) (d) ELUMO = -3.350 eV ↕ Egap = 0.788 eV EHOMO = -4.138 eV EHOMO-1 = -4.851 eV ELUMO = -0.769 eV ↕ Egap = 0.36 eV EHOMO = -1.129 eV EHOMO-1 = -1.758 eV (b) (e) ELUMO = -4.440 eV ↕ Egap = 0.506 eV EHOMO = -4.946 eV EHOMO-1 = -5.724 eV ELUMO = -5.132 eV ↕ Egap = 0.291 eV EHOMO = -5.423 eV EHOMO-1 = -5.639 eV (c) (f) Figure 6. Frontier molecular orbitals of MO_H, MO_Na, and MO_zwitterion dye molecules (a, b, c) optimized structures and (d, e, f) unoptimized structures (Isovalue of 0.03). Eshraq Ahmed Abdullah / European Journal of Chemistry 13 (3) (2022) 337-350 345 2022 – European Journal of Chemistry – CC BY NC – DOI: 10.5155/eurjchem.13.3.337-350.2297 Table 3. Calculated physical parameters of dye molecules at the GGA/HCTH level of theory Structure 𝑬𝑬𝑯𝑯 (𝐞𝐞𝐞𝐞) 𝑬𝑬𝑳𝑳 (𝐞𝐞𝐞𝐞) 𝑬𝑬𝒈𝒈𝒈𝒈𝒈𝒈 (𝐞𝐞𝐞𝐞) 𝝁𝝁 (𝐞𝐞𝐞𝐞) 𝝌𝝌 (𝐞𝐞𝐞𝐞) 𝜼𝜼 (𝐞𝐞𝐞𝐞) 𝝎𝝎 (𝐞𝐞𝐞𝐞) ∆𝑵𝑵𝒎𝒎𝒈𝒈𝒎𝒎 ECT Optimized MO_H -5.076 -3.223 1.853 -4.150 4.150 0.927 9.292 4.479 0.268 MO_Na -4.138 -3.350 0.788 -3.744 3.744 0.394 17.789 9.503 -4.760 MO_Zwitterion -4.946 -4.440 0.506 -4.693 4.693 0.253 43.526 18.549 -13.80 Bi5O7NO3 -4.330 -2.823 1.507 -3.577 3.577 0.754 8.488 4.747 Unoptimized MO_H -4.692 -3.276 1.416 -3.984 3.984 0.708 11.209 5.627 -2.86 MO_Na -1.129 -0.769 0.360 -0.949 0.949 0.180 2.502 5.272 -2.50 MO_Zwitterion -5.423 -5.132 0.291 -5.278 5.278 0.146 95.711 36.271 -33.5 Bi5O7NO3 -5.362 -2.519 2.843 -3.941 3.941 1.422 5.462 2.772 Figure 7. Absorption spectra of MO dye structures Similarly, high values of the electrophilicity index (ω) illustrate the ability of dyes to work as good electrophile species during adsorption. To support the above findings, the electrophilicity-based charge transfer (ECT) method was used to determine the direction of a charge transfer. The ECT values were calculated using the following Equation 𝐸𝐸𝐶𝐶𝑇𝑇 = ∆𝑁𝑁maxBi5O7NO3 − ∆𝑁𝑁max𝑑𝑑𝑑𝑑𝑒𝑒 (24) When a dye molecule approaches the Bi5O7NO3 unit cell, there are two ECT possible values; greater or less than zero. If the ECT value is greater than zero, the charge will flow from the dye to Bi5O7NO3. Whereas if the ECT value is less than zero, the charge tends to move towards the dye molecule [48]. In general, the calculated ECT values of all dyes considered were negative, indicating that the electrons will transfer from the Bi5O7NO3 unit cell to the dye molecule during adsorption. Although the unoptimized methyl orange dye structures are more reactive compared to others, the calculated optical spectra in Figure 7 indicate that the optimized dye structures give a good fit with the experiment in the available methyl orange spectrum range. Therefore, only the optimized MO dye structures were selected to study the adsorption mechanism in the following sub- sections. 3.2.3. Band structures of Dye/Bi5O7NO3 adsorption systems The calculated band structures of dye/Bi5O7NO3 systems are illustrated in Figure 8. After adsorption, the dyes introduce sharp occupied molecular energy levels in the band gap region of Bi5O7NO3. The predicted band gap value is zero for all study systems. This indicates that adsorption of dye molecules elevates the electron concentration near the Fermi level of the Bi5O7NO3 unit cell, and adsorbed systems are metallic [49]. However, the analysis made of the MO/Bi5O7NO3 UV-Vis spectrum in Figure 3 reveals the presence of one band gap with a significant red shift to 2.57 eV. These results prove that the MO dye molecules influence the band gap energy of Bi5O7NO3. Unfortunately, there are no reports available in the literature on the MO/Bi5O7NO3 band structure. Therefore, a direct comparison is difficult. 3.2.4. The PDOS analysis of the Dye/Bi5O7NO3 adsorption systems To describe how the density of states changes after adsorption, we carried out the projected density of states. Before adsorption, the PDOS of Bi5O7NO3 near the Fermi level are caused by mixing atomic orbitals of Bi 6p, O 2p and N 2p in the conduction band and the O 2p orbitals in the valence band. However, after adsorption, Figure 9 shows that the bands on the edge of the Fermi level are derived from the combination of these orbitals with the C 2p and H 1s orbitals of the dye molecules. Due to the high mixing of the 2p orbitals, the O 2p orbitals move upward while the Bi 6p orbitals move downward [33]. The band gap region has been built by the overlapping of the O2p, Bi 6p, C 2p, and H 1s orbitals, so the MO/Bi5O7NO3 adsorption systems have metallic characteristics. 3.2.5. The electrostatic potential surface map The electrostatic potential surface (EPS) map is a measure of non-covalent interactions when a positive test charge interacts with a molecule [50]. Therefore, EPS map is a useful tool, which illustrates how does the charge distribute over the molecule? Figure 10 depicts the EPS maps of the MO dye molecules and the Bi5O7NO3 unit cell ranging from red to blue. The red color has a negative charge and works as a preferred site for the electrophilic reaction. The blue color has a positive charge, which can be used for the nucleophilic reaction. The yellow and green regions represent the neutral electrostatic potential in which the electronegativity difference is not so great [42,48]. https://www.mdpi.com/2075-163X/12/3/387/htm#fig_body_display_minerals-12-00387-f003 346 Eshraq Ahmed Abdullah / European Journal of Chemistry 13 (3) (2022) 337-350 2022 – European Journal of Chemistry – CC BY NC – DOI: 10.5155/eurjchem.13.3.337-350.2297 (a) (b) (c) Figure 8. Band structures of the adsorbed systems (a) MO_H/Bi5O7NO3, (b) MO_Na/Bi5O7NO3, and (c) MO_zwitterion/ Bi5O7NO3. The negative charge region of the MO_H dye distributes over the −𝑁𝑁 = 𝑁𝑁 − phenyl− 𝑆𝑆𝐵𝐵3− fragment, while a region of positive charge appears over the phenyl− 𝑁𝑁(𝐶𝐶𝐻𝐻3)2 fragment and hydrogen atoms. In the case of the MO_Na dye, the negative charge is concentrated on the aromatic carbons, nitrogen, and oxygen atoms of the sulfonate group whereas the positive charge is due to sulfur, sodium, and hydrogen atoms. There is a small negative charge on both −𝑆𝑆𝐵𝐵3− group and the lone electron pair on the −𝑁𝑁 = 𝑁𝑁+𝐻𝐻 group in the MO_Zwitterion dye. The EPS map of Bi5O7NO3 before adsorption shows that the regions of negative and positive charges distribute over the whole area of the unit cell. According to Figure 11, the Bi5O7NO3 EPS map differs after adsorption. The EPS map of the MO_H/Bi5O7NO3 shows only positive charge regions, which localize on bismuth atoms of [𝐵𝐵𝐵𝐵𝐵𝐵]+∞ 2 layers. This behavior indicates that the positive charge phenyl− 𝑁𝑁(𝐶𝐶𝐻𝐻3)2 fragment of the MO_H dye can neutralize the negative regions of the Bi5O7NO3 unit cell. The dye adsorption is completely occurred through the electrostatic character. There is a clear decrease in a net positive charge of the Bi5O7NO3 unit cell, although the negative charge regions of the dye remain outside the cell indicating the presence of electron rich centers. Figure 11 attributes this lack to the effect of aromatic rings π-π stacking and nitrate - azo π-stacking. The EPS maps of the MO_Na/Bi5O7NO3 and MO_Zwitterion/Bi5O7NO3 show both positive and negative EPS regions. However, these regions are only distributed on the opposite corners and in the middle of the unit cell. Eshraq Ahmed Abdullah / European Journal of Chemistry 13 (3) (2022) 337-350 347 2022 – European Journal of Chemistry – CC BY NC – DOI: 10.5155/eurjchem.13.3.337-350.2297 (a) (b) (c) Figure 9. PDOS plots of the adsorbed systems (a) MO_H/Bi5O7NO3, (b) MO_Na/Bi5O7NO3, and (c) MO_zwitterion/ Bi5O7NO3 The electrostatic interaction that occurs between the negatively charged oxygen atoms of the nitrate groups and the positive charge localized on the hydrogen atoms works as the first driven force for the adsorption. Figure 12 shows that the intermolecular distances of two MO dyes are in the range ~2.8- 3.1 Å, which is still less than ~3.4-3.7 Å, the obtained distances for methyl orange removal through the π-π stacking mechanism over the carbonated Mg-Al layered double hydroxide on a Monte Carlo simulation [51]. This finding implies a strong π- stacking interaction of the adsorbed systems. The combination of the negative charge regions of the MO_Na dye and the 𝜋𝜋- stacking arising from the molecular packing works as the second driven force for the MO_Na dye adsorption. This synergistic interaction can neutralize the positive charge of the Bi5O7NO3 framework. Figure 12 clearly shows the presence of two stacking types on the MO_Na/Bi5O7NO3 system; the aromatic rings π-π stacking and the azo groups π-π stacking. Although the EPS map of the MO_Zwitterion dye has a large positive charge region on its surface, there is a little increase in the positive charge region on the MO_Zwitterion/Bi5O7NO3 system, which is implies strong 𝜋𝜋-stacking interactions. Actually, three types of interaction are observed in Figure 12. These interactions involve aromatic π-π stacking; cation-π stacking, in which −𝑁𝑁 = 𝑁𝑁+𝐻𝐻 group plays the cation role and anion-π stacking, which takes place between sulfonate groups and aromatic rings. The ability of the dye to bond to Bi5O7NO3 via hydrogen bonding may improve the removal of the dye. These results are in accordance with the findings of Ko et al. [51]. 3.2.6. Adsorption energies The adsorption energy mostly reflects the stability of the adsorbed systems compared to pure molecules [52]. The adsorption energy per single dye molecule is defined as follows, 𝐸𝐸𝐻𝐻𝑑𝑑𝑠𝑠𝑎𝑎𝐻𝐻𝑎𝑎𝐻𝐻𝑖𝑖𝑎𝑎𝑢𝑢 = �𝐸𝐸𝑑𝑑𝑑𝑑𝑒𝑒/𝑃𝑃𝑖𝑖5𝑂𝑂7𝑁𝑁𝑂𝑂3 − �𝐸𝐸𝑃𝑃𝑖𝑖5𝑂𝑂7𝑁𝑁𝑂𝑂3 + 𝑚𝑚𝐸𝐸𝑑𝑑𝑑𝑑𝑒𝑒�� 𝑚𝑚⁄ (25) in which 𝐸𝐸𝑑𝑑𝑑𝑑𝑒𝑒/𝑃𝑃𝑖𝑖5𝑂𝑂7𝑁𝑁𝑂𝑂3 and 𝐸𝐸𝑃𝑃𝑖𝑖5𝑂𝑂7𝑁𝑁𝑂𝑂3 are the total energy of the Bi5O7NO3 unit cell with and without dye molecules, 𝐸𝐸𝑑𝑑𝑑𝑑𝑒𝑒 is the optimized energy of a single dye molecule before adsorption and 𝑚𝑚 is the number of adsorbed dye molecules. The adsorption energies are 8606.14, 7051.70 and 12698.1 eV for the MO_H/ Bi5O7NO3, MO_Na/Bi5O7NO3 and MO_zwitterion/Bi5O7NO3 systems, respectively. High positive energy values of dye adsorption confirm the presence of a strong endothermic chemisorption process, which is associated with the formation of bonds. This finding is in line with the previous experimental results [1]. The MO_zwitterion/Bi5O7NO3 system is bound more strongly than other adsorbed systems. This may be attributed to a greater stability of the dye arising from its ability to engage in hydrogen bond formation. 4. Conclusions Density functional theory and molecular mechanics calculations were conducted to explore the electronic proper- ties of Bi5O7NO3 unit cell. The HTCH 407 exchange correlation functional at the GGA level of theory is selected to be an efficient and more accurate approximation for the Bi5O7NO3 band gap at the experimental lattice parameters compared to PBE and BLYP functionals due to its highly parameterized. However, this 348 Eshraq Ahmed Abdullah / European Journal of Chemistry 13 (3) (2022) 337-350 2022 – European Journal of Chemistry – CC BY NC – DOI: 10.5155/eurjchem.13.3.337-350.2297 (a) (b) (c) (d) Figure 10. Electrostatic potential surface maps of (a) MO_H, (b) MO_Na, (c) MO_Zwitterion dye molecules and (d) the Bi5O7NO3 unit cell (isovalue = 0.016). (a) (b) (c) Figure 11. Electrostatic potential surface maps of (a) MO_H/Bi5O7NO3, (b) MO_Na/Bi5O7NO3, and (c) MO_Zwitterion/ Bi5O7NO3 (isovalue = 0.016). functional shows a 46% band gap underestimation in the case of the optimized structure of Bi5O7NO3 that is produced by the Molecular Mechanics simulation. Actually, Bi5O7NO3 at the experimental lattice parameters has two energy gaps. PDOS results ascribe the first band gap of 2.84 eV, which reproduces the experimental gap to the allowed transitions occurring between the valence band maximum and the N 2p and O 2p orbitals. Whereas the second gap of 3.22 eV, which is less by 0.44 eV from the UV-Vis value, assigns to the optical transitions that occur to the Bi 6p orbitals. The removal mechanism of methyl orange dye onto Bi5O7NO3 unit cell was explored using various MO dye structures and the DMol3 module of the Material Studio software at the GGA/HCTH level of theory. Electronegativity and energy gap values indicate that all dye molecules are more reactive and show a great tendency to accept electrons from Bi5O7NO3. Eshraq Ahmed Abdullah / European Journal of Chemistry 13 (3) (2022) 337-350 349 2022 – European Journal of Chemistry – CC BY NC – DOI: 10.5155/eurjchem.13.3.337-350.2297 (a) (b) (c) Figure 12. The intermolecular distance of the π-stacking interactions involved in dye removal using Bi5O7NO3 (a) MO_H, (b) MO_Na, and (c) MO_Zwitterion. This tendency produces a great mixing between the dyes and the Bi5O7NO3 orbitals, which turns the Bi5O7NO3 semi- conductor into a metallic material. The MO_zwitterion structure shows the most stable configuration of the dye molecule onto the Bi5O7NO3 unit cell because of its ability to engage in a hydrogen bond formation. Analysis of EPS maps and molecular packing distances suggests a multiple adsorption mechanism of methyl orange dyes on Bi5O7NO3. 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The full terms of this license are available at http://www.eurjchem.com/index.php/eurjchem/pages/view/terms and incorporate the Creative Commons Attribution-Non Commercial (CC BY NC) (International, v4.0) License (http://creativecommons.org/licenses/by-nc/4.0). By accessing the work, you hereby accept the Terms. This is an open access article distributed under the terms and conditions of the CC BY NC License, which permits unrestricted non-commercial use, distribution, and reproduction in any medium, provided the original work is properly cited without any further permission from Atlanta Publishing House LLC (European Journal of Chemistry). No use, distribution or reproduction is permitted which does not comply with these terms. Permissions for commercial use of this work beyond the scope of the License (http://www.eurjchem.com/index.php/eurjchem/pages/view/terms) are administered by Atlanta Publishing House LLC (European Journal of Chemistry). http://wojast.org/wp-content/uploads/%20Vol10-1/78_85_Mkpenie-et-al.pdf http://wojast.org/wp-content/uploads/%20Vol10-1/78_85_Mkpenie-et-al.pdf https://www.jetir.org/papers/JETIR1901468.pdf https://doi.org/10.1007/s11356-022-20050%E2%80%932 https://doi.org/10.1007/s11356-022-20050%E2%80%932 http://www.eurjchem.com/index.php/eurjchem/pages/view/terms http://creativecommons.org/licenses/by-nc/4.0 http://www.eurjchem.com/index.php/eurjchem/pages/view/terms 1. Introduction 2. Computational methods 2.1. Electronic structures of Bi5O7NO3 2.2. Adsorption studies 2.3. Theoretical background 2.3.1. The generalized gradient approximation (GGA) 2.3.2. Molecular mechanics method 3. Results and discussion 3.1. Electronic structures of Bi5O7NO3 3.1.1. The functional effect 3.1.2. The k-point grid effect 3.1.3. Electronic band structure 3.1.4. The UV-Vis analysis 3.1.5. The PDOS analysis of Bi5O7NO3 3.2. Adsorption studies 3.2.1. Frontier molecular orbitals of the adsorbates 3.2.2. The chemical reactivity 3.2.3. Band structures of Dye/Bi5O7NO3 adsorption systems 3.2.4. The PDOS analysis of the Dye/Bi5O7NO3 adsorption systems 3.2.5. The electrostatic potential surface map 3.2.6. Adsorption energies 4. Conclusions Disclosure statement ORCID and Email References PrintField10: PrintField11: PrintField12: PrintField13: PrintField14: PrintField15: PrintField16: PrintField17: PrintField18: PrintField19: PrintField110: PrintField111: PrintField112: PrintField113: PrintField20: PrintField21: PrintField22: PrintField23: PrintField24: PrintField25: PrintField26: PrintField27: PrintField28: PrintField29: PrintField210: PrintField211: PrintField212: PrintField213: