Author Correction: Electro-catalytic amplified sensor for determination of N-acetylcysteine in the presence of theophylline confirmed by experimental coupled theoretical investigation

The 1,l/-bis(2-phenylethan-1-ol)ferrocene, 1-butyl-3-methylimidazolium hexafluoro phosphate (BMPF6) and NiO-SWCNTs were used to modify carbon paste electrode (BPOFc/BMPF6/NiO-SWCNTs/CPE), which could act as an electro-catalytic tool for the analysis of N-acetylcysteine in this work. The BPOFc/BMPF6/NiO-SWCNTs/CPE with high electrical conductivity showed two completely separate signals with oxidation potentials of 432 and 970 mV for the first time that is sufficient for the determination of N-acetylcysteine in the presence of theophylline. The BPOFc/BMPF6/NiO-SWCNTs/CPE showed linear dynamic ranges of 0.02–300.0 μM and 1.0–350.0 μM with the detection limit of ~ 8.0 nM and 0.6 μM for the measurement of N-acetylcysteine and theophylline, respectively. In the second part, understanding the nature of interaction, quantum conductance modulation, electronic properties, charge density, and adsorption behavior of N-acetylcysteine on NiO–SWCNTs surface from first-principle studies through the use of theoretical investigation is vital for designing high-performance sensor materials. The N-acetylcysteine molecule was chemisorbed on the NiO–SWCNTs surface by suitable adsorption energies (− 1.102 to − 5.042 eV) and reasonable charge transfer between N-acetylcysteine and NiO–SWCNTs.

Sigma-Aldrich. Single wall carbon nanotubes functionalized with COOH was purchased from Neutrino Company, Iran. The BPOFc and NiO/SWCNTs were synthesized according to papers reported by Karimi-Maleh et al. 48,49 . An Autolab PGSTAT 12, potentiostat/galvanostat system with NOVA software was used for recording all of the voltammetric signals. The Zeiss-EM10C-100 kV and X' Pert Pro instruments were used for TEM and XRD investigation, respectively. MAP analysis of nanocomposite was recorded by a FESEM instrument model MIRA3TESCAN-XMU with Page and linear analysis software.
Fabrication of BPOFc/BMPF6/NiO-SWCNTs/CPE. 0.01 g BPOFc + 0.05 g NiO-SWCNTs + 0.94 g graphite was dispersed in diethyl ether. At room temperature, the solvent evaporated and then paraffin oil and BMPF6 oils were used for the preparation of paste. The BPOFc/BMPF6/NiO-SWCNTs/CPE paste was inserted in a glass tube with copper wire as a conductor of electricity.
Real sample preparation. The water and pharmaceutical serum samples were purchase from the local market and pharmacy and directly used for electrochemical analysis. Tablet samples were purchased from local pharmacy and then were completely ground and homogenized. Next, their calculated values were weighed and then dissolved in 50 mL of water/ethanol solution and the mixture was filtered for real sample analysis.
Computational details. The electronic and structural properties of N-acetylcysteine adsorbed onto a NiO-SWCNTs surface was investigated using the plane-wave DFT calculations as implemented in the Cambridge Serial Total Energy Package code 50 . The generalized gradient approximation (GGA) of the Perdew-Burke-Ernzerhof (PBE) functional 51 and ultrasoft pseudopotentials 52 were used to describe the exchange-correlation and core-valence electron. The adsorption energies were calculated using the dispersion correction by Grimme 53 , since van der Waals interactions were anticipated to affect the adsorption energies. A vacuum gap of 20 Å was used to prevent the interactions between the periodic slabs perpendicular to the surface, resulting in a simulation supercell of 10.393 × 8.520 × 35.073 Å 3 . The Monkhorst-Pack 54 with k-mesh of 4 × 1 × 1 was used to sample the Brillouin zone. The wave functions of the valence electron were described using a plane-wave basis set with a cut-off energy of 400 eV. To account for the metallic behavior of NiO 2 (the oxidation states of each element in NiO 2 are + 4 (Ni) and -2 (O)), the atomic positions were optimized via the BroydeN-Fletcher-Goldfarb-Shanno scheme 55 with an energy convergence criterion, force, and displacement of less than 10 −6 eV/atom, 0.3 eV/Å, and 0.01 Å, respectively. However, all other atoms and lattice vectors on the top layer of the slab were allowed to relax, since surface adsorption occurred on the topmost layer. The Hirshfeld's analysis 56 was used to evaluate the charge transfer between N-acetylcysteine and NiO-SWCNTs.
The stability of N-acetylcysteine adsorption on the NiO-SWCNTs surface was evaluated by calculating the adsorption energy (E ads ): where E LUMO and E HOMO are the energies of the LUMO and HOMO, respectively. The electronic sensitivity of the NiO-SWCNTs towards the adsorption of N-acetylcysteine was assessed by calculating the change in the HLG 58 : where E g1 and E g2 represent the HLG before and after adsorption.

Results and discussion
NiO/SWCNTs characterization. The elemental analysis of NiO-SWCNTs is shown in Fig. 1. The existence of C, Ni and O elements confirm the purity of synthesized NiO-SWCNTs nano-composites by the recommended procedure. The decoration of NiO/NPs at functional SWCNTs was characterized by TEM method (Fig. 2A). The presence of nickel oxide nanoparticles on the single-wall carbon nanotubes surface is well represented in Fig. 2A. In contrast, the XRD patterns of NiO-SWCNTs confirm the occurrence of (002) at 2θ ~ 26° plane relative to carbon nanotubes and other planes, i.e. (2) www.nature.com/scientificreports/ Electro-catalytic determination of N-acetylcysteine by BPOFc/BMPF6/NiO-SWCNTs/ CPE. The electro-oxidation of N-acetylcysteine with thiolic structure is relative to pH of solution. The electrocatalytic interaction between BPOFc and N-acetylcysteine was optimized by recording signals of 1.0 mM drug at BPOFc/BMPF6/NiO-SWCNTs/CPE surface with pH ranges of 4.0-8.0. According to obtained data (not shown), it is observed that maximum electro-catalytic interaction could occur at pH = 7.0 and this pH was chosen as the best condition. The signal for the oxidation of 1.0 mM N-acetylcysteine was recorded at BPOFc/NiO-SWCNTs/CPE (Fig. 3, curve b), BPOFc/BMPF6/CPE (Fig. 3, curve c), BPOFc/BMPF6/NiO-SWCNTs/ CPE (Fig. 3, curve d), BMPF6/ NiO-SWCNTs/CPE (Fig. 3, curve e), BMPF6/CPE (Fig. 3, curve f), NiO-SWCNTs/CPE ( Fig. 3 curve g) and CPE (Fig. 3, curve h). On the other hand, BPOFc/BMPF6/NiO-SWCNTs/CPE exhibited an oxidation/reduction signal with ∆Ep = 130 mV that confirms quasi-reversible behavior of BPOFc/BMPF6/NiO-SWCNTs/CPE in the aqueous solution (curve a). The increasing oxidation signal of BPOFc/BMPF6/NiO-SWCNTs/CPE and simultaneous decrease in reduction signal of mediator after addition of 1.0 mM N-acetylcysteine, confirms an EC / interaction 59,60 between mediator and N-acetylcysteine on the surface of BPOFc/BMPF6/NiO-SWCNTs/ CPE. The comparison of the electro-catalytic oxidation signal of N-acetylcysteine at the surface of BPOFc/ BMPF6/NiO-SWCNTs/CPE with its signal at BPOFc/NiO-SWCNTs/CPE and BPOFc/BMPF6/CPE confirmed that the conductivity of electrode surface could be enhanced by the existence of NiO-SWCNTs and BMPF6. This increase in conductivity helps to improve oxidation current and decrease oxidation potential. In addition, the comparison of the electro-catalytic oxidation signal of N-acetylcysteine at the surface of BPOFc/NiO-SWCNTs/ CPE with its signal at BPOFc/BMPF6/CPE shows that reduction in oxidation potential at the surface of BPOFc/ NiO-SWCNTs/CPE is more than its reduction at the surface of BPOFc/BMPF6/CPE. This point can be related to the high viscosity of BPOF, which makes it difficult to access the electrode surface. On the other hand, oxidation signal of N-acetylcysteine showed a weak signal at the surface of CPE. After modification of CPE with NiO-SWCNTs or BPOFc, the oxidation signal of N-acetylcysteine was improved, that could be related to high conductivity of mediators at the surface of CPE. In addition, after modification of CPE with NiO-SWCNTs and www.nature.com/scientificreports/ BPOFc, a better oxidation signal for N-acetylcysteine that is relative to synergic effect of the two mediators at surface of CPE is observed. The electro-catalytic oxidation signal of 1.0 mM N-acetylcysteine was recorded at the BPOFc/BMPF6/NiO-SWCNTs/CPE surface in a scan rage between 2-20 mV/s (Fig. 4 insert). As shown in Fig. 4, a linear relation between electro-catalytic current of N-acetylcysteine at the BPOFc/BMPF6/NiO-SWCNTs/CPE surface with ν, which confirmed an adsorption process for the oxidation of N-acetylcysteine at BPOFc/BMPF6/NiO-SWCNTs/ CPE surface was observed.
A Tafel plot of BPOFc/BMPF6/NiO-SWCNTs/CPE in the presence of 1.0 mM N-acetylcysteine is shown in Fig. 5. The electron transfers coefficient (α) value was measured as ~ 0.516 by the Tafel equation.
The differential pulse voltammetry method was used for the investigation of N-acetylcysteine and theophylline in the concentration range of 0.02 to 300.0 μM (sensitivity 0.2079 μA/μM and R 2 = 0.9961) and 1.0-350.0 μM  www.nature.com/scientificreports/ (sensitivity 0.1643 μA/μM and R2 = 0.9975), respectively. The detection limit (3σ) was set at ~ 8.0 nM and 0.6 μM for N-acetylcysteine and theophylline at the surface of BPOFc/BMPF6/NiO-SWCNTs/CPE as a novel electrochemical sensor using (LOD = 3S b /m) equation. The BPOFc/BMPF6/NiO-SWCNTs/CPE displayed better dynamic range or the limit of detection for determination of N-acetylcysteine compared to another electrochemical methods suggested ( Table 1). The differential pulse voltammograms of different concentration of N-acetylcysteine and theophylline were measured at the BPOFc/BMPF6/NiO-SWCNTs/CPE surface (Fig. 6A). The voltammograms showed two oxidation peaks separated at potentials of ~ 432 mV and 970 mV that is relative to oxidation of N-acetylcysteine and theophylline, respectively. Figure 6B,C showed the plots of oxidation current vs. concentration of drugs. As can be seen, the sensitivity for the simultaneous investigation of N-acetylcysteine and theophylline is equal to 0.2078 and 0.1627 μA/μM, which are comparable with sensitivity obtained for the two drugs in linear dynamic range determination. This study revealed that a concurrent determination of N-acetylcysteine and theophylline is possible at BPOFc/BMPF6/NiO-SWCNTs/CPE surface with no interference.
The stability of BPOFc/BMPF6/NiO-SWCNTs/CPE was also checked in the presence of 10.0 μM N-acetylcysteine + theophylline solution. BPOFc/BMPF6/NiO-SWCNTs/CPE was stored at the laboratory temperature, and the electro-catalytic signal of BPOFc/BMPF6/NiO-SWCNTs/CPE had no apparent decrease in the first fifteen days. Compared with its first electro-catalytic signal, the response sensitivity remained at 96% after 50 days. The obtained results confirmed good stability of BPOFc/BMPF6/NiO-SWCNTs/CPE as a new electrochemical sensor.
To check the selectivity of BPOFc/BMPF6/NiO-SWCNTs/CPE, the interference effects of some usual biological, cationic, and anionic compounds are investigated in the solution containing 10.0 μM N-acetylcysteine + theophylline. The results indicated that 1000-fold of K + , F -, Na + , Br − and Ca 2+ and 600-fold of glucose, phenylalanine, and urea have no major influence on the investigation of 20.0 μM N-acetylcysteine.
The ability of the BPOFc/BMPF6/NiO-SWCNTs/CPE was investigated for the study of N-acetylcysteine and theophylline in the tablet samples by standard addition technique. The obtained data are shown in Table 2. The     (Fig. 7). Several types of C-C bonds were observed in the SWCNTs with different bond lengths of 1.40-2.44 Å (bonds shared between two hexagons) and 1.44 Å (the bond shared between a hexagon and pentagon), which were comparable with other studies 62 . The Ni-O bond length of 2.10 Å was in agreement with the earlier results (2.08 Å) 63 . The electronic properties of NiO and SWCNTs were described based on the HLG. The band structure of NiO in Fig. 8 revealed that the SWCNT is a semiconductor with an E g of 0.67 eV. The LUMO and HOMO of the SWCNT were − 5.01 and − 5.81 eV, respectively.
From the DOS plot of NiO, an HLG of 0.80 eV was revealed. The obtained PDOS results showed that the 3d orbitals of the surface Ni were mainly located at the HOMO, while at the LUMO, the hybridization was mostly contributed by Ni 4 s orbitals. The PDOS results suggested that the Ni 3d orbitals play a key influence on the adsorption process.
Several configurations were explored to find the most feasible adsorption sites where four local minima were obtained (Fig. 9).
Based on the E ads calculations, the four configurations of N-acetylcysteine adsorption onto NiO-SWCNTs were exothermic processes with negative adsorption energies ranging between − 1.102 and − 5.042 eV (Table 3). Moreover, the adsorption energy varies owing to the interactions of N-acetylcysteine molecule with several adsorption sites with the NiO-SWCNTs. As presented in Table 3, the four relaxed configurations with more negative adsorption energy values and small interaction distances (ranging from 1.689 to 1.980 Å) between the N-acetylcysteine and NiO-SWCNTs, signify strong interactions and stability. This strong interaction indicates that the NiO-SWCNTs is a prominent sensor for the adsorption of N-acetylcysteine with good response to all the adsorption sites considered. Moreover, the more negative adsorption energy value suggests that the reaction will release more energy. Among these configurations, the most stable (SNA3) is where the acidic end is bonded strongly with the interfacial Ni atoms of the substrate [64][65][66] .
The interaction between the N-acetylcysteine molecule and NiO-SWCNTs was anticipated to alter the electronic property of N-acetylcysteine, which could be understood by the variation in its energy band gap [67][68][69] . The electronic property of N-acetylcysteine molecule was studied based on the HLG and density of states (DOS) spectrum (Fig. 10). The DOS of N-acetylcysteine molecule possesses a broad HOMO and LUMO separated by a wide HLG (Fig. 10). After adsorption, the N-acetylcysteine molecule introduced sharp occupied bands in the HLG of all the configurations. The TDOS results revealed similar changes, which indicated that NiO-SWCNTs might be an effective sensor towards the N-acetylcysteine molecule. The adsorption of N-acetylcysteine molecule shifted the HOMO levels to a higher energy, whereas the LUMO levels remained unaffected. Thus, the HLG value of N-acetylcysteine molecule was significantly reduced compared to its isolated molecule. The average HLG variation (|ΔHLG| (%)) upon adsorption of N-acetylcysteine molecule onto NiO-SWCNTs surface is connected with the sensitivity of adsorbent, as well as modifying its electrical conductivity. The |ΔHLG| (%) of 63.09, 68.33, 69.83, and 65.84% for configurations SNA1, SNA2, SNA3, and SNA4, respectively (see Table 3), signified high sensitivity of NiO-SWCNTs towards the adsorption of N-acetylcysteine molecule on its surface. From the HLG variation result, it was established that the sensing response of NiO-SWCNTs towards N-acetylcysteine molecule was observed to be rather higher for SNA3 configuration. Further understanding into the bonding mechanisms between the N-acetylcysteine molecule and NiO-SWCNTs was obtained by analyzing the DOS of N-acetylcysteine molecule before and after adsorption onto the NiO-SWCNTs surface (Fig. 10). After adsorption, the DOS of N-acetylcysteine molecule was broadened owing to the strong hybridization with the adsorbed Ni ion. This showed a chemisorption state of N-acetylcysteine molecule.  www.nature.com/scientificreports/ where σ , k, E g and T are the electrical conductivity, Boltzmann's constant, bandgap energy and thermodynamic temperature, respectively. According to this equation, smaller HLG values lead to a larger electrical conductivity. The electrical conductivity before adsorption was 2.86 × 10 -9 . Therefore, the electrical conductivity of SNA1, SNA2, SNA3 and SNA4 configurations was higher after adsorption.
To evaluate the interactions between the N-acetylcysteine and NiO-SWCNTs, the three-dimensional (3D) charge density difference was calculated, as given in Fig. 11.
In this 3D charge density difference plot, the electron enrichment and depletion are shown as blue and yellow isosurfaces, respectively. The electronic interaction largely occurred at the top of Ni atoms of the NiO-SWCNTs nanocomposite, which was in direct contact with the N-acetylcysteine molecule. The electrons transfering from the N-acetylcysteine molecule to NiO-SWCNTs indicated that the Ni atoms were oxidized during the adsorption process. Since the electron accumulation sites were mostly located at the interface, they confirmed that the bond between N-acetylcysteine molecule and NiO-SWCNTs was of a covalent nature. However, less electron density was observed at the NiO-SWCNTs interface, signifying that the SWCNTs was less influenced electronically by the interaction with NiO nanoparticle. The interactions between the N-acetylcysteine molecule and NiO-SWCNTs indicates a substantial charge transfer, which was evaluated grounded on the Hirshfeld charge analysis. The charge migration analysis of SNA1, SNA2, SNA3, and SNA4 configurations was found to be 1.11, 1.18, 1.21 and 1.14 |e|, respectively. A positive value of Hirshfeld charge analysis was observed for the four interaction sites considered in this study. This further confirmed electrons transfer from the N-acetylcysteine molecule to NiO-SWCNTs. The changes of work function connected to the charge transfer between N-acetylcysteine molecule and NiO-SWCNTs was used to evaluate the sensitivity of NiO-SWCNTs towards the adsorption of N-acetylcysteine molecule. The field emission property was altered due to the work function change of NiO-SWCNTs before and after the adsorption of N-acetylcysteine. According to Fig. 12, the work function of NiO-SWCNTs was decreased after N-acetylcysteine molecule adsorption due to the charge migration from the N-acetylcysteine molecule to the NiO-SWCNTs surface.

Conclusion
The electro-catalytic interaction between BPOFc and N-acetylcysteine was studied at the BPOFc/BMPF6/NiO-SWCNTs/CPE surface. The cyclic voltammograms data confirms the good selectivity and high sensitivity of BPOFc/BMPF6/NiO-SWCNTs/CPE for determination of N-acetylcysteine. Moreover, the most prominent adsorption site, sensitivity, conductivity, charge transfer, electronic and structural properties of N-acetylcysteine molecule adsorption onto NiO-SWCNTs surface was studied using DFT studies. The negative adsorption energies in the range of -1.102 to -5.042 eV and suitable charge transfer confirmed the stability of N-acetylcysteine adsorption at NiO-SWCNTs surface. In addition, the adsorption of N-acetylcysteine molecule was chemisorption. Therefore, the most prominent adsorption site of N-acetylcysteine molecule at NiO-SWCNTs surface  www.nature.com/scientificreports/ was when the acidic end of N-acetylcysteine molecule was adsorbed at NiO-SWCNTs surface. The theoretical investigation established the high electrical conductivity of NiO-SWCNTs and suggested this nano-composite as a conductive binder for modification of carbon paste electrode. The BPOFc/BMPF6/NiO-SWCNTs/CPE can be detected as N-acetylcysteine in the presence of theophylline with limits of detection 8.0 nM and 0.5 μM. The finding of this study offers useful information to design novel NiO-SWCNTs-based sensors for sensing toxic molecule.