Direct orange 26 dye environmental degradation: experimental studies (UV, mass, and thermal) in comparison with computational exploration hydrogen bonding analysis of TD-DFT calculations

The importance of this study stems from, it concentrates on new approach applying both practical and theoretical aspects to study structure stability of direct orange dye 26 (DO26) as an important dye widely used for dyeing of cotton or viscose for red orange direct printing. The stable dyes are so difficult to remove, decolorized and/or degrade, in pure solution or in wastewater samples, without using powerful removal environmental techniques electrochemical oxidations suggest and efficiently used in our Lab. Therefore, it is very important to compare between practical thermal and mass results as efficient techniques in studying dye stability, in comparison with theoretical results using Gaussian program for structural stability identification of DO26 dye, via careful inspection of various phenomena detected in its two symmetrical arms around urea center. Direct orange dye 26 (DO26) structure has been studied applying both practical spectroscopic and theoretical investigations. DFT-B3LYP/6–311 +  + G(d,p) calculations and the electronic vibrational properties are performed to investigate its structure stability and consequently its degradation and removal from its environmental media. Correlation is found between experimental and calculated data. An intra-molecular hydrogen bonding interaction had been detected and characterized in dye skeleton. The hydrogen bonding present in the dye structure affecting its vibrational properties had been discussed. Natural population analysis like HOMO and LUMO and high-quality molecular electrostatic potential plots along with various electronics had been presented at the same level of theory. Chemical reactivity descriptors from conceptual density functional theory point of view and structure activity relationship descriptor were obtained. The experimental UV/visible, FT-IR, mass and GC-mass spectral data of the dye DO26 (D1) had been presented. These data had been supported by TD-DFT calculations to simulate the experimental spectra with computing the natural transition orbitals (NTO) and the orbital composition. Actually there is a problem that the degradation of this dye in wastewater by different techniques leads to various unknown fragments, but on using theoretical possibilities, it can be expected what happened in practical work.


Introduction
Direct dyes are those of more than one azo group, phthalocyanine, stilbene, or oxazine containing compounds. In the color index, it is considered that the direct dyes form the second largest dye class with respect to the amount of different dyes [1]. DO26 is reddish orange to light yellowish red color textile dye. Therefore; DO26 can be used for dyeing cotton or viscose for red orange direct printing. It also can be used for silk, wool, polyvinyl alcohol, polyamide fiber fabric, and pulp dyeing [2][3][4][5]. The commercial dyestuff DO26 has a general formula C 33 H 22 N 6 Na 2 O 9 S 2 of M.Wt. = 756.67 g mol −1 [6].
Pollution of water by dyes is a serious problem in developed countries. Approximately, 1-10% or more of dyes are discharged into waste streams without treatment by the textile industry worldwide. The effluents from the textile dyeing industry contain many organic pollutants and are a serious environmental hazard because of their lasting color, high chemical oxygen demand, and non-biodegradability [6]. Therefore the understanding of spectroscopic vibrational, electronic structural, tautomerism, electronic excitation, chemical reactivity, and hydrogen bonding analysis of DO26 by applying both practical and theoretical techniques is a very important factor in studying its structural stability relationship and main target in the present research in removal of this dye from wastewater as great challenge.
DFT has been considered as an efficient tool for studying structural stability and vibrational properties of biomolecules [7,8]. DFT, when incorporated by proper functional exchange-correlation, provides sufficient confidence about the results. For computational low cost B3LYP, hybrid functions became popular because of its accuracy; it is combined with Becke's three parameter exchanges and with Lee, Yang, and Parr's correlation. The B3LYP function combined with 6-311 + + G(d,p) basis set were used to calculate structure and vibrational properties of direct dye DO26 molecule. In comparison, FTIR and UV-visible spectra of DO26 are shown good correlations between experimental and computational data. Most molecular calculated properties were electronic and thermodynamic. It also involved estimation of chemical reactivity and reaction paths. In DFT, also natural population analysis (NPA), HOMO, LUMO, and molecular electrostatic potential (MESP) surfaces were calculated. They were used to discuss resulting intra-molecular charge transfers and electron density distribution as main functions controlling the studied dye stability.
Hydrogen bonding plays a pivotal role in determining the structures stability and properties of biomolecules [9]. The study of hydrogen bonding phenomena had been successfully studied applying Bader's atoms in molecule [10]. The nature and strength of various types of hydrogen-bonded interactions had been efficiently described. The reliability and stability in the values of parameters have been studied, and it was found that they are almost independent of basis set on the use of functional B3LYP in DFT [11]. However, it has been noticed that B3LYP function estimates weak intramolecular interactions as well as charge transfer effects [11][12][13].

Chemicals and procedures
DO26 was purchased from Anil Dyes and Chemicals Industries (India). A Perkin Elmer lambda 4B spectrophotometer had been used for measurements of the UV/visible absorption spectra of the dye using 1.0 cm fused quartz cells at room temperature. A stock solution (400 mg/L) of direct orange textile dye with the M.Wt. = 756.67 g mol −1 was prepared by dissolving 200 mg in small amount of distilled water, and then the solution was completed to 500 mL measuring flask. Dilute aqueous solutions of (1.057 × 10 −3 M) DO26 were used for most measurements in 10 mL measuring flask. The FT-IR spectra of KBr discs containing D1 had been measured at wavenumber region 4000-400 cm −1 using FTIR 4100, JASCO spectrophotometer. Thermal analyses (TGA, DTG, and DTA) were carried out in dynamic nitrogen atmosphere (20 mL min −1 ) with a heating rate of 10 °C min −1 using Shimadzu system of DTG-60H thermal analyzers. Electron ionization (EI) mass spectrum (MS) for DO26 dye was obtained using Thermo Finnigan TRACE DSQ quadruple mass spectrometer with electron multiplier detector equipped with GCMS data system. The direct probe (DP) for solid material was used in this study. The sample was put into a glass sample micro-vial, by a needle (≈ 1 μg max), the vial installed on the tip of the DP containing heating cable and inserted into the evacuated ion source. The sample was ionized by an electron beam emitted from the filament, and the generated ions are being effectively introduced into the analyzer by the focusing and extractor lenses system. The mass spectrum was continuously scanned, and the obtained spectra were stored. EI mass spectra were obtained at ionizing energy value of 70 and 15 eV and ionization current of 60 μA, and vacuum is better than 10-6 torr. Agilent Technologies Agilent 6890 N GC/MS System coupled with a mass detector (5977B MSD -Network Mass Selective Detector) equipped with 70-eV electron impact (EI) mode was used for analyzing residual organic matters that extracted from treated solution for this experiment; a 30 cm column with an internal diameter of 0.25 mm was used. The stationary phase was actually bonded to the interior of the glass capillary, eliminating the need for packing a solid support in the column. The mass spectrometer and GC are controlled by MassHunter Acquisition software. Most instrumental analyses were performed in Microanalytical Center Cairo University.

Electrochemical oxidation of DO26 dye and GC-mass identification of its degradation products
The main electrochemical degradation process was investigated in cylindrical glass cell with electrolyte volume of 50 mL. The electrolyte was prepared from direct orange 26 (DO26) dye, using graphite electrodes at optimum conditions 6 g/L NaCl as electrolyte and pH = 2 at current intensity 40 mA. To enhance the mass transport and to maintain a uniform concentration of the electrolyte, the reactor solution was constantly stirred at 100 rpm using a magnetic stirrer. The electrochemical treatment was operated for 30 min using graphite electrodes as anode and as cathode. Both anode and cathode were fixed at same distance of 2 cm both sides of the cell and immersed in the electrolyte.
Gas chromatography that coupled with mass spectrometry (GC-MS) was used for the identification products resulting from electro-oxidation of DO26 dye. Samples of the DO26 dye solutions after the electro-oxidation were collected, extracted using dichloromethane [14,15], and effluent with n-hexane (1 mL). Effluents were collected and analyzed in GC/MS system. Analyst fragments were separated in GC using an Agilent HP-5 ms Ultra Inert capillary column (30.0 m × 0.25 mm × 0.25 μm). The temperature program began at 50 °C and increased at the rate of 8 °C min −1 up to 250 °C with holding time of 3 min for each increment. Helium was used as carrier gas with a flow rate of 1.0844 mL min −1 . Detection in MS followed the separation. A sample of 1 μL volume was injected in splitless mode.

Computational details
The Gaussian 09 W software package [16] had been used for theoretical calculations. The molecular geometry for the studied compound had been fully optimized using density functional theory B3LYP method by using 6-311 + + G(d,p) basis set [17,18], where (B3) [19][20][21] stands for Becke's three parameters combined with gradient-corrected functions of Lee, Yang, and Parr (LYP) [22]. During geometry optimization, no symmetry constrains had been applied [23,24]. The choice of basis set 6-311 + + G(d, p) is mainly due to its flexibility, accuracy, consistent, and better performance when using diffused Gaussian type triple-ζ potential [25,26]. The vibrational frequencies have been determined and checked and proved that all structures correspond to true minima of the potential energy surface at the same level of theory.
The Gaussian 09 W software package has been used for NBO calculations using NBO 3.1 program implemented in the same program. The GaussView version 5.0.9 [27] involving Chemcraft version 1.6 package [28] had been used throughout this work to optimize the structures of tested compounds. In addition, the Multiwfn v3.8 software program [29] has been used to compute quantum chemical descriptors from point of view of conceptual density functional theory (CDFT). The Multiwfn v3.8 software program [29] has been also used for atoms in molecule (AIM) analysis. The vertical linear-response TD-DFT approximation [30] has been also used for calculation of the first 80 low-lying excited states. The polarizable continuum model (PCM) [31,32] has been included in all steps of a modeling of bulk solvent effects.
Computing the natural transition orbitals (NTOs) [33] has been used in analyzing the electronic properties of tested molecules excited states. The molecular fragments to occupy (occ.NTOs) and virtual natural transition orbitals (virt NTOs) had been performed by the orbital composition analysis taking into consideration the Hirshfld percent contributions. The Multi-wave function v3.8 software program [29] had been used to estimate the electronic transitions between the ground state (S 0 ) and the low-lying singlet excited states (S n ). In order to study the charge redistribution due to the excitations in tested molecules, the variation in dipole moment with respect to ground state (ΔμCT) [29] and the charge transfer length (Δr) [34,35] was computed.
The VMD 1.9 program [35] has been used for rendering the color mapped isosurface graphs of electrostatic potential (ESP) of the ground states of the studied dye, based on the data outputted by Multiwfn program. The VibAnalysis code [36,37] with corresponding to VEDA program [38] has been used for calculation of the potential energy distribution (PED) for various vibrational normal modes of the studied DO26 dye (D1).

Results and discussions
Thermal analyses of TGA and DTA analyses of DO26 dye powder: The thermal analyses data of DO26 textile dye is shown in Fig. 1.
Thermal analyses data of direct orange 26 (DO26) refer to its stability when heated from 25 to 1000 °C with practical total weight loss of 93.24%. Figure 1a refers to its TGA, which shows three weight losses. The first loss of practical % = 3.2% starts at 31.40 °C to end at 334.76 °C; which can be assigned to loss of the water of crystallization and coordinated water.
It appears in DTG (Fig. 1b) as one loss exactly at 59.60 °C. This loss appears as two exothermic peaks appear in DTA curve (Fig. 1c) in temperature range from 113 to 400 °C exactly at 113.74, and 324.99 °C. Therefore, the first loss seems to occur in two consecutive steps. The second weight loss occurs in temperature range from 334.76 to 644.64 °C of practical weight loss % = 3.83% (Fig. 1a), which may be due to the release of N 2 gas (estimated weight loss % = 3.70%). It appears in DTG (Fig. 1b) as two losses exactly at 438.27 and 640.76 °C. This loss appears in DTA (Fig. 1c) at 636.23 °C as small endothermic peak. It may be attributed to the degradation of the azo bonds (-N = N-), which links between naphthalene and benzene rings. The third weight loss appears that, DO26 dye decomposed mainly (C 33 H 22 N 2 O 8 S 2 ) within the temperature range from 644.64 to 1000.42 °C with practical weight loss % = 86.21% (estimated weight loss % = 84.32%). It appears as a sharp large peak exactly at 967.11 °C in DTG (Fig. 1b) and as small endothermic peak at 808.54 °C in DTA (Fig. 1c). The residual mass which represent 6.76% may be referred to sodium oxide (Na 2 O with estimated weight % = 8.19%). The thermal degradation of the dye at temperature range up to 1000 °C refers to its very high stability, and it required very efficient degradation tools like chemical or electrochemical oxidation to be removed from environment wastewater which is actually performed in another paper. Most of these thermal fragments are correlated to most of fragment ions appeared in mass spectra of pure powder dye and of GCmass of dye of electro-oxidation of degradation products fragment ions.

Mass spectra of powder DO26 dye
Mass spectral fragmentation of DO26 textile dye molecule using EI-MS at 70 eV is shown in Fig. 2.
The results in Fig. 2 and in supplementary Fig. S1 show two m/z values first one at m/z = 756, which is mainly related to the disodium salt of the dye of molecular formula: C 33 H 22 N 6 Na 2 O 9 S 2 of mol mass 756.67 and another peak at m/z = 734, which is mainly attributed to molecular ion of the dye without sodium of general formula C 33 H 24 N 6 O 9 S 2 + and mol mass = 735.7 g/mol. These results and its fragmentation refer to its pure form and the possibility to decompose to several fragment ions on mass measurements. Most of these molecular and fragment ions are appeared like those appear at m/z = 57, 71, 85, 105, and 111 in thermal degradation of dye in its powder form. Some of these fragment ions are appeared in GC-mass spectra of electro-oxidized dye products.

Spectral and electrochemical oxidation results
UV/Vis spectra of DO26 dye and its actual textile wastewater sample treated by electrochemical oxidation/reduction reaction in one cell using graphite electrodes as both anode and cathode at different time intervals (Fig. S1) refer to; after 4 min of electrolysis under chosen optimum conditions with 49.84% decolourization with high decomposition of the azo group. Also it shows 83.22% decolourization of DO26 actual sample after 12 min of electrochemical oxidation/reduction. This decolorization is lower than the decolorization of the dye dissolved in distilled water 97.77%. Less decolorization attributed to field additives is used to coat the dye to textiles by physical and especially chemical reaction which gives more stability for the dye in its medium. The degradation and color removal of DO26 dye occurred only in the presence of chloride. Thus, the decolorization of the dye is due to its main reaction with the generated chlorine/hypochlorite, in which the chlorine/hypochlorite oxidizes the dye and it is then reduced to chloride ion [39] such as DO26 + OCl − → CO 2 + H 2 O + Cl − + by-products. On the other hand, in cathodic compartment, the reaction assumed to take place as follows: 2H 2 O + 2 e − → H 2 + 2 − OH, and so the dye chromogenic (N = N) groups were reduced to give ≈ 30% with no significant COD reduction.
The GC-MS results show that at a retention time of 14.21 min, benzene diazonium with molecular ion peak with m/z 105 resulted from the main degradation of DO26 dye (Fig. S2). The benzene fragment with m/z 77 at retention time 10.445 min has been obtained directly by oxidation from benzene diazonium [40]. A non-hydroxylated fragment, dichlorobenzene, peak with m/z 148 at retention time 16.53 min and mono-hydroxylated fragment, pentachlorophenol, peak with m/z 267 at retention time 31.06 min were obtain from the progressive chlorination of simple by-products as benzene. The ion peak having retention time 16.20 min was identified as α-naphthol with m/z 144 resulted from the further electrochemical oxidation of the other identified intermediates, 1,2,6-trihydroxy naphthalene sulfonate with m/z = 255.8, and 3-amino-7-(carboxyamino) naphthalene-2-sulfonic acid with m/z = 281 at retention time 27.75 and 33.33 min, respectively. So, the cleavage of the DO26 dye may take place symmetrically or asymmetrically. The main degradation of DO26 dye in this study occurred asymmetrically by breakage the bond between the nitrogen of azo group and the carbon of 2-hydroxy-3-naphthalenesulfonate ring. To assess the practical environmental work, it seems reasonable to support the above data by correlation with theoretical calculation and give main reasons of its high stability, which required more powerful environmental removal tools like thermal, chemical, and/ or electrochemical oxidation.

Density functional theory (DFT) studies
The molecular electrostatic potential maps, bond lengths, bond angles, and dihedral angles as the optimized geometrical parameters were calculated. Also natural charges, natural population analysis, reactivity descriptors, and energetic were computed. All of these calculated parameters were analyzed for the studied dye DO26 both in water and gas phases of the ground state and compared with the practical, thermal, and spectroscopic data (UV-Vis, FT-IR, and GC-MS). Figure 3 presents the computed parameters of DO26 in this work, such as optimized geometry, numbering system, and vector of the dipole moment. The values of computed parameters of DO26 dye (D1) were obtained using B3lyp/6-311 + + G (d,p).

Optimized structure and hydrogen bonding of D1
The results in Fig. 3 refer to the maximum C-C bond length (among others) of 1.454 Å in naphthalene ring system that in good agreement with the reported value of 1.42 Å [41,42]. The bond angle C37-C36-C27 calculated is found to be 119.75 Å; it shows excellent agreement with the reported value of 119.4 Å [41,42]. The dye D1 is considered urea derivative fragment in which the urea calculated bonds C1-O2, C1-N3, and C1-N4 give values of 1.223, 1.393, and 1.377 Å. The corresponding practical values of these bonds in D1 are found to be 1.245, 1.345, and 1.329 Å.
The selected angles in the tested dye O2C1N3 and N3C1N4 are found to be of the values 119.22° and 115.86°, while The computed values of dihedral angles around central urea derivatives are represented in Table 1. These data show that the angle N4C1N3C7 is of 10.9° right arm out of plane and the angle O2C1N4C40 is of 5.74° left arm out of plane. This indicates that the carbon derivative is almost in the same molecular plane of urea. Also it is detected that, atoms in angles C8C9C10C11, C11C12C13O25, C11C12N26N27, N26N27C28C29, and N26N27C28C33 of the values 180,180, 179.9, − 0.3, and 179.76 degree refer to the planarity of right arm component due to symmetry of the molecular structure. The left arm one is almost planar, which represented by angles N60C61C62C63, C41C42C47C48, and C44C45C46O58 of values 180, 0.0, and 180.0 degrees, respectively.
The presence of hydrogen bonds in the skeleton of D1 follows Koch and Popelier criterion [43]. The hydrogen bonding requires the existence of bond critical point (BCP) for the "proton donor (H) and acceptor (A)" contact. Applying this theory to DO26, it shows a lot of intra-molecular hydrogen bonding interaction O25-H39, O58-H72, O2-H50, O23H20, O74-H53 in diazo-carbonyl fragment in two arms. The application of this theory [43] actually required the value of electron density (q) in the range 0.002-0.040 a.u., and corresponding Laplacian ( ∇ 2 ) should be 0.024-0.139 a.u. These parameters have been calculated for the studied D1 at BCP with sequence O25…H39, O58…H72, O2… Fig. 3 The optimized geometry of DO26 dye (D1) compounds using B3LYP/6-311 + + G(d,p) level of theory, the numbering system, and vector of dipole moment DO26 dye (D1) H50, O23…H20, O74…H53 along with geometrical parameters of H-bonds and the data obtained are presented in Table 1.
There are three types of H-bonds have been detected in the basis of D1 topology [44] via calculated parameters. The characterization has been followed Rozas et al.'s [44] demands, at BCP in which ∇ 2 andH < 0 for strong H-bonding of covalent character. It also should be ∇ 2 > 0 and H < 0 for medium H-bond of partially covalent nature. Alternatively it should be ∇ 2 > 0 and H > 0 for weak H-bond. From the presented data in Table 2, it is clear that Laplacian of charge density is positive for all BCP, ∇ 2 = 0.15, 0.15, 0.066, 0.061, 0.062, and 0.047. Also the energy density H < 0 for the first two N27H39…O25 and N60H72…O58 and others is H > 0 suggesting the interaction to be medium H-bond of partially covalent nature in N27H39…O25 and N60H72…O58 and weak in nature for all other BCP. The value of ∇ 2 is found to be negative and small in magnitude for strong covalent interactions, as in [Mn(III) porphyrin] Cl-trimethoprim complex ( ∇ 2 = − 0.0786 a.u.) [45] and as in bis-dithiazolyl dimers [46]. By using E int = (V) at BCP as proposed by Espinosa et al. [47], the energy of interactions occur in tested dye has been theoretically calculated. The estimated interaction energy values of hydrogen bonding in the given dye for bonds O25…H39, O58…H72, O2… H50, O23…H20, O74…H53 are found to be − 12.36, − 12 .41, − 3.8, − 3.53, and − 3.57 kcal/mol, respectively. These data indicate the medium H-bond interactions for N27H39… O25 and N60H72…O58 bonds, and other bond are of week interaction [48]. The binding energy more accurate values have been obtained by applying another prediction equation [49], and the found values for bonds O25…H39, O58…H72, O2…H50, O23…H20, O74…H53 are found to be − 8.78, − 8.8, − 3.26, − 2.73, and − 2.8 kcal/mol respectively.

The tautomeric relative stability of D1
From the above calculations and practical work data, the depicted three different tautomeric forms of the DO26 (D1) dye (Fig. S3)  The data in Fig. 4 give great benefit in explaining structural behavior of the studied dye and its stability. The DFT calculations reveal that the stability order of different forms (A-E) of the DO26 dye is A > B > C > D = E as given by their calculated relative energy values of 0.0, 3.24, 3.29, and 6.54 kcal/mol, respectively. These data indicate that the diketo form of D1 is the most stable tautomer in the gas phase. This conclusion is confirmed by the calculated energy values of the corresponding four transition states (TS) (F-I) with respect to A with 5.6, 5.65, and 8.9 kcal/mol, respectively, which have stability order of F < G < H = I. The stability of the di-keto form (A) relative to the keto-enol (B), enolketo (C), and the di-enol (D) forms may be attributed to the increasing in the strain effects within the moiety of these forms. There is a transfer of the single proton between the oxygen atoms (O25 or O58). On the other hand, proton is moved in opposite directions relative to the nitrogen atoms (N 27 or N 60 ) (forms B and C). It is also noticed that form C is less stable than form B, which may be attributed to the electrostatic attraction between the proton and the oxygen atom. The stability of A (the di-keto form) may be attributed to the planarity of right and left part arms for central carbonyl group C1 = O2.

Normal mode analysis and FT-IR of D1
The vibrational normal mode analysis confirm that the most of the calculated frequencies of the optimized geometry of D1 ( Fig. 4) are found to be real. Consequently; the D1 optimized geometry corresponds to a true minimum energy in the PES. The obtained frequency values applying the present theoretical model are scaled with a factor of 0.96 [50] to avoid errors due to neglect of inharmonic terms. All the vibrational modes are properly assigned applying the basis of PED. By using free VibAnalysis code [46,47] with corresponding to VEDA program [48], the various vibrational normal modes have been calculated. The calculated FTIR frequency intensities and assignments listed in Table S1 are selected in normal modes up to 400 cm −1 . All normal modes with all details up to 400 cm −1 are presented in Table S1 as supplementary information. Figure 5 presents simulated FT-IR spectra at 400 to 4000 cm −1 for DO26 in comparison with experimental results. The DO26 (D1) has two similar arms for the urea derivatives. Each arm is substituted naphthalene and benzene ring linked by diazonium fragment (= N-NH-). The N-H stretching frequencies of the rings are calculated and found to be in the range 3,473-3,133 cm −1 , which is in good agreement with the found values in literature [51] of 3,200 and 3,500 cm −1 with strong or medium intensities.
N-H stretching vibration with a PED of almost 90-100% is calculated at 3,473, 3,450, 3,138, and 3,133 cm −1 and presented in Table 3. The FT-IR practical value corresponding to this band is found to be 3,466 cm −1 . However, the NH group in acetyl-hydrazine molecule (CH 3 -CO-NH-NH 2 ) is detected at 3,445 cm −1 and confirmed by the calculated one found at 3,640 cm −1 by DFT [52]. The N-H stretching band is apparently shifted due to hydrogen bonding with oxygen O25 or O58 attached to naphthalene ring. The inter-molecular hydrogen bonding in D1 is stronger than intra-molecular Hydrogen-bonding as indicated by difference in calculated and experimental frequencies of the same dye.
The rings C-H stretching frequencies at the wavenumber range 3,117-3,024 cm −1 have been calculated. The C-H stretching of C49H50 group near to the C = O of central urea has been detected at 3, 086 cm −1 , which were found to be at 3,000 and 3,100 cm −1 with medium intensities in the published work [51]. The calculated C = C stretching vibrations and its mixing with other modes of naphthalene rings are found in lower region at frequency values of 1,574 and 1,559 cm −1 , respectively. These theoretically calculated values are also correlated with that reported in literature [51] in which strong absorption band of naphthalene right arm has been detected at 1,571 cm −1 and falling range of 1,600-1,500 cm −1 .
The C-H bending of ring systems frequencies in plane and out of plane are calculated and found to be ascertained with C-C stretching region. The calculated C-H vibrational mode of strong intensity for naphthalene ring is found to be at 1,120 cm −1 . The naphthalene ring torsion modes are always found in even lower frequency region [51].
The CH 2 stretching vibrations of weak intensities in the dye skeleton are detected at 2,954 and 2,907 cm −1 . The CH 2 bending vibration has been detected at 1,464 cm −1 . The C-H lying between N14 and R3 stretching vibration has been practically detected as strong intensity band at 2,904 cm −1 . The calculated C = O stretching band has been theoretically calculated at 1,625 cm −1 , which actually fit the practically detected in FTIR value of D1 at 1,638 cm −1 . These data are found to be in good correlation with the C = O stretching as a very strong band in the region 1,680-1,640 cm −1 previously reported elsewhere [51]. The C-N and C = N stretching vibrations coupled with N-H scissoring and CCN and HNN twisting vibrations, respectively, in acetyl-hydrazine molecule (CH 3 -CO-NH-NH 2 ) are calculated and found to be 1,499 and 1,428 cm −1 . These theoretically calculated values are actually correlated with the practically detected values in the wavenumber range at 1,460-1,430 cm −1 in the FT-IR of tested dye. All of these bands of acetyl-hydrazine molecule (CH 3 -CO-NH-NH 2 ) are found to be weak instead of intense band as previously reported [51]. The calculated frequencies belong to N-N stretching have been practically detected at 1,300 and 1,250 cm −1 , respectively, and bending vibrational deformation modes of the fragment of the same group have been practically detected at 1,352 and 680 cm −1 . The theoretically calculated and experimental FT-IR frequencies of D1 at 400-4000 cm −1 are listed in Table 3 and graphically represented in Fig. 6. Figure 6 shows a correlation between theoretically calculated (Table S1) and the practically detected frequencies in FT-IR of the dye DO26. These data show good and correlation exists with a coefficient of 0.9991. Such a correlation proved that the DFT/B3LYP scheme of theoretical calculation in the field of spectroscopy efficiently reproduces the experimental results and can be used for vibrational analysis of biomolecules with a sufficient confidence.

Natural charges and natural population analysis (NPA) of D1
The NPA scheme at B3LYP/6-311 + + G(d, p) level had been used in theoretical calculation of atomic charges of the investigated molecule (D1) in gas. These charges are ranged from − 1.001 to 2.299 e, and the data obtained are depicted in Table S2. The obtained results proved that this scheme is more reliable due to its low basis set dependency. Table S2 shows that the carbon atoms in the skeleton of the dye DO26 are either carrying positive or negative charges; it depends on its position. The negative charges are concentrated on O23, O24, O25, O55, O56, and O57 oxygen atoms of SO 3 groups. It also has been seen that the charge is around − 1.0 e on each atom. The maximum positive charges on sulfur atoms (S21 and S54 atoms of SO 3 groups) have been detected. The nitrogen and oxygen atoms of urea and diazonium fragments are negatively charged, and consequently they accept electrons. It is also noticed that the harge increases on N27 and N27 atoms than that on N26 and N59. The decrease in charge on O25 and O58 may be due to electron density transfer from proton donors N27H39 and N60H72 to proton acceptors O25 and O58 involved in hydrogen bonding. It is finally noticed that charges on hydrogen atoms have positive values. Table 2 represents Frontier molecular orbitals (FMOs, Figure S4) data. The represented calculated quantum chemical parameters values are E HOMO , E LUMO , energy gap (ΔE gap ), ionization energy (I), electron affinity (A), and Dipole moment [53][54][55].

FMOs analysis
The HOMO (ionization potential I =-E HOMO ) energy value usually determines the donating power of electrons of the tested group. Its high value indicates the ease of donating electron to the unoccupied orbital of the receptor molecule, which means measure oxidation potential (1.72 eV) for the proposed dye. The small value of E LUMO (electron affinities A =-E LUMO ).means more able to accept electron which means less reduction potential (− 0.70 eV) for the proposed dye. The calculated E HOMO of the tested dye is found to be − 1.724 eV, which is located on the SO 3 group system of right arm. On the other hand, the E LUMO of DO26 is found to be 0.696 eV, which is mainly contributed by all left arm of the dye molecule. The energy (ΔE gap ) between HOMO and LUMO usually described the chemical reactivity of the molecule. In the present study, ΔE gap is found to be 2.42 eV, which indicates the high reactivity of the compound in oxidation reduction reaction. Hence the dye is highly reactive and recommends being use in dye sensitized solar cell (DSSC). The ionization potential I and electron affinity A are so important parameters. The determination of these two important parameters allows the calculation of the global reactivity descriptors. The A and I parameters depend mainly on the one-electron HOMO and LUMO orbital energy values. The molecule of less I value will be the better electron donor, while the molecule of high I value will be the better electron acceptor. From Table 2, it has 1.72 eV value of I and A is − 0.7 eV, and electronegativity is equal 0.51 eV. Figure 7 represents Frontier molecular orbitals of the studied DO26 dye compounds (D1).
The data in Fig. 7 show that the dispersion of charge densities of HOMOs and LUMOs indicate charge transfer to naphthalene with azo-phenyl ring (left arm of urea derivatives) from SO 3 group of right arm. The dipole

Global reactivity descriptors of D1
The nature of chemical interactions and chemical reactivity of atoms, ions or molecules are considered important to explain the reactivity of the molecular dye DO26 (D1). The CDFT, quantum chemical descriptors like chemical hardness (η), electronic chemical potential (µ), and electronegativity ( χ ) are related to the electron number (N) at constant external potential, v(r), respectively [53][54][55].
The computed GRD reactivity descriptors of the compound D1 are represented in Table 5. These data have been considered very important to explain the reactivity and stability of studied DO26 (D1). D1 has t value of η = 1.21 eV of chemical hardness and the softness value (0.41 eV), which indicates softness and chemical reactivity of studied. The results obtained are in good correlation with the find HOMO-LUMO band energy gaps of the synthesized dye. The calculated chemical potential (μ) value of the studied dye DO26 (D1) presented in Table 3 means it has high chemical potential value (− 0.5 eV), which refers to the high charge transfer occurs within tested dye.
The electrophilicity index (ω) is a thermodynamic parameter that measures energy changes in a chemical system saturated by adding electrons. It described the chemical reactivity of a system. The calculated data presented in Table 3 proved that D1 has electrophilicity index value (ω = 0.11 eV) and the nucleophilicity index (N) is equals + 2.49 eV. These values indicate that the dye favor nucleophilic approximate 23 times more than electrophilic. The Dye D1 possesses electronegativity (X) of the value = 0.51 eV as measured for tendency of molecule to attract electrons. This means that it has high softness values and showed high reactivity,

Local reactivity descriptor of D1
To understand the chemical reactivity and site selectivity of theoretically tested compounds, it is very important to use the concepts of local and global reactivity descriptors [56,57]. The Fukui function is the first derivative of the electronic density ρ(r) of a system with respect to the number of electrons (N) at a fixed external potential ν(r) as defined by Yang and Mortier (1986) [58].
The local descriptors such as electrophilic and nucleophilic Fukui functions had been more clarified by Parr and Yang [59,60]. The calculation of Fukui functions is very important to determine the active sites of the DO26 dye (D1). It is mainly based on calculation of the electronic density changes occurred during the molecule reactions.
Usually the Fukui functions f + (r), f -(r) and f 0 (r) are essentially calculated in three chemical situations such as electrophilic, nucleophilic, and radical attacks [57,[60][61][62], where q k (N), q k (N + 1), and q k (N − 1) are the atomic population on the k th atom for the neutral molecule, its anionic and cationic species, respectively. The research done by Chattaraj et al. [63] defined the local quantity called philicity k associated with a site k in a molecule with the assistance of corresponding condensed-to-atom variants of Fukui function, f k , where α = + , − , and 0 correspond to local philic quantities describing nucleophilic, electrophilic, and radical attacks, respectively. The highest k corresponds to the most electrophilic site in a molecule. Softness s k function described the reactivity of atoms in molecules had been proposed by Lee et al. [22,63]. Morell and Labbe et al. [64] proposed another dual descriptor (Δf (r)) concerning electrophilic and nucleophilic capacity of a given atomic site in the molecule. Here Δf (r) is the difference between the nucleophilic and electrophilic Fukui function. If Δf (r) > 0 refers to nucleophilic attack. For Δf (r) < 0 , it is favored for an electrophilic attack. The calculated data using the above equations at the level B3LYP/6-311 + + G (d,p) for Fukui functions indices, dual descriptor, condensed local softness, local, and relative electrophilicity of DO-26 are given in Tables 3-4.
The values of Fukui functions f − (r)andf + (r) are presented in Table 3.
From these data, it can be stated that the most electrophilic active sites in DO26 molecule are located on O55, O56, and O57. Likewise, the active sites susceptible for nucleophilic attacks in the same dye are C7, C9, C10, C11, O25, N26, N27, N59, and N60.
The same conclusion can be reached considering the dual descriptor Δf (r) regarding electrophilic and nucleophilic attack, also from the philicity indices Table (4).
The characteristic differences between the calculated values of parameters is mainly attributed the redistribution of electron density inside molecules due to high electronegativity of N and O atoms in skeleton, also the effect of -C = O… HN, -SO 3 −1 groups. The obtained results of the calculated functions are in good agreement with the last population analysis and computed HOMO and LUMO energies.
By using implemented code in Multi-wave function v3.8 software program [38], condensed local softness, local electrophilicity/nucleophilicity index, and relative electrophilicity/nucleophilicity have been also calculated for each atom in the studied molecule from CDFT point of view to complete the picture of the studied dye map. The careful inspection of these data revealed that the dye molecule had the donation and the back-donation processes at their active center (O55, O56, O57, C7, C9, C10, C11, O25, N26, N27, N59, and Table 4 Values of the condensed local softnesses (Hartree*e), relative electrophilicity/nucleophilicity (dimensionless) and the condensed local electrophilicity (ElectroP)/nucleophilicity  Tables 3, and 4. According to these results, one can conclude that the studied dye possesses lot of active centers to interact with pocket protein surface, through donating electrons to orbitals and back donation process. The calculated local descriptors data revealed that the theoretical variation efficiencies of the investigative molecules agree well with the available experimental data in the same work.

Molecular electrostatic potential map (MEP)
Electrostatic potential (ESP) on molecular van der Waals surfaces have emerged as powerful tools in predicting, interpreting, and rationalizing trends in different areas of chemistry [65] as well as in drug design and molecular biology [66].
ESP-mapped surfaces of the studied compound, D1, are shown in Fig. 8.
Module of Multi-wave function program is used for the quantitative molecular surface analysis, and it is capable of partitioning the whole van der Waals surface into multiple fragments. It also allows discussion of the characteristics of the ESP distribution of studied dye D1.
It can be asserted on the basis of ESP-mapped that an electrophile is attracted towards negative region of diazonium and urea center fragment with -SO 3 − , while a nucleophilic attack favors the electropositive region. These values indicate the same results from NPA and local reactivity descriptors analysis mentioned in above sections.

Electronic absorption spectra
Direct orange 26 dye (D1) has been synthesized and confirmed to possess antibacterial and application in printing and dyeing [67,68]. To analyze how the UV-visible spectrum of D1 is varied, the experimental absorption electronic spectra in water solvent and computed are depicted in Fig. 9. The calculated absorption maximum wavelengths (λ max ), electronic excitation energies (ΔE), and oscillator strengths (f) of D1 in water are given in Table 5    π π * electronic transitions between the ground state (S0) and six low-lying singlet excited states (Sn) of DO26 dye (D1). The data obtained in Fig. 10 of the computed natural transition orbitals (NTOs) indicate that these electronic transitions can be assigned as π-π * transitions.
The Hirshfeld population analysis is used to calculate percent contributions of molecular fragments to occupied and unoccupied natural transition orbitals in the electronic transitions between the ground state (S0) and six low-lying singlet excited states (Sn) of D1 obtained at the PCM-B3LYP (water)/6-311 + + G(d,p) level of approximation and depicted in Table 6.
These data of molecular orbital compositions are essentially based on the percent contributions of urea center, naphthalene right arm (Napth_R), naphthalene left arm (Napth_L), azo-phenyl right arm (Azoph_R), and azo-phenyl  Table 5 Absorption maximum wavelengths (λ max ), electronic excitation energies, and oscillator strengths of D1 in water  left arm (Azoph_L) molecular fragments to the occupied and virtual NTOs. The first transition (S 0 → S 1 ) is related to electrons' occupied NTO of p z and p x orbitals that mainly localized on O55, O56, and O57 of the sulfonic group (S54-(O55, O56, and O57)) with contributions of ~ 26%, 30%, and 32%, respectively. From these data, it is obvious that π-bonding interaction exists between the p z orbitals of these atoms. The unoccupied NTO is composed of p z orbitals mainly localized on C13, O25, and N26 of the active group in right naphthalene group with contributions of ~ 10%, 9.5%, and 17%, respectively. From these data, it is obvious that π*-antibonding interaction exists between the p z orbitals of these atoms. It is clear from data presented in Table 7, that the electron density ππ* transition from left arm to right arm by around 17% of electron localized over the entire molecule.
The second transition (S 0 → S 2 ) is related to electrons' occupied NTO of p z , p x , and p y orbitals mainly localized on O22, O23, and O24 of the sulfonic group (S21-(O22, O23 and O24)) with contributions of ~ 31%, 25%, and 33%, respectively, as a result of π-bonding interaction exists between the p sub-orbitals of these atoms. The non-occupied NTO are composed of p z orbitals that mainly localized on C13, O25, and N26 of the active group in right naphthalene group as S 0 → S 1 . A π*-antibonding interaction exists between the p z orbitals of these atoms is mainly related on electron density ππ* transition from left arm to right arm by around 20% of electron localized over the entire molecule.
For the third transition (S 0 → S 3 ), the occupied NTO the π-bonding interaction is concentrated between the p z orbitals of urea center and left naphthalene arm with 22 and 41%, respectively. The unoccupied NTO is composed of p z orbitals that mainly localized on the right naphthalene group and azo-phenyl with contributions of ~ 30% and 23%, respectively. A π*-antibonding transition may be assigned as ππ*.interaction exists between the p z orbitals of these atoms.
The fourth transition (S 0 → S 1 ), as a result of electrons' occupied NTO, is mainly localized on right arm group (C7-H39) with contributions of naphthalene group ~ 47% and azo-phenyl 50%. The π-bonding interaction is due to ππ* transition and exists between the p z orbitals of these range atoms. The unoccupied NTO is found to be mainly localized on right naphthalene group with contributions of ~ 94%. It is mainly occurred due to π*-antibonding interaction exists between the p z orbitals of these atoms.
The fifth transition (S 0 → S 5 ), as a result of electrons' occupied NTO, is mainly localized on left arm of naphthalene and azo-phenyl with contributions of ~ 56% and 41%, respectively, and attributed to π-bonding interaction exists between the p sub-orbitals of these atoms. The non-occupied NTO is composed of p z orbitals and mainly localized on right naphthalene group with contribution of ~ 90%. A π*-antibonding transition may be assigned as ππ* interaction exists between the p z orbitals of these atoms.
For the 6th transition (S 0 → S 6 ), it is essentially related to the occupied NTO π-bonding electron interactions exist between the p z orbitals of urea center and left naphthalene arm with 47 and 31%. Consequently, the non-occupied NTO is composed of p z orbitals mainly localized on left naphthalene group and azo-phenyl left part with contributions of ~ 45% and 31%, respectively; resulting in π*-antibonding interaction leading to ππ* transition exists between the p z orbitals of these atoms.
These detailed discussions are confirmed by Fig. 10, which illustrate natural transition orbitals (NTOs) occupied and unoccupied due to transitions between the ground state (S0) and six low-lying singlet excited states (Sn) of DO26 dye (D1) obtained at the PCM-B3LYP (water)/6-311 + + G(d,p) level of approximation. This detailed discussion clearly shows a π-bonding interaction among the specific groups of atoms as mentioned above. The NTOs data clearly discussed π-antibonding interactions among all these contributing species. The nature of vertical electronic transitions in the studied compound (D1) is analyzed via determining the topology of the molecular orbitals involved in these transitions. The NTOs of the first electronic transition (S0 → S1), associated with the ICT band, are given in Fig. 10. It is noticed that both occupied and virtual NTOs demonstrate the typical π-type molecular orbital characteristic. They are clearly delocalized over the entire molecule including the two arms. The details of the active space of molecular orbital wave function representation and its surfaces are presented in supporting information for details in supplementary (Figs S3-S4 and Table S3).
In order to study the extent of charge transfer (CT) or charge redistribution during the excitations, the Δr index and variation of dipole moment (Δμ CT ) of excited state with respect to ground state are computed for the studied molecules using Multiwfn code [29]. The obtained data refer to six transitions and calculated parameters are given in Table 7. Table 7 Charge transfer (CT) length (Δr) and variation in dipole moment (Δμ CT ) indices of the six electronic excitations for the studied D1 obtained at the PCM-B3LYP (water)/6-311 + + G(d,p) level of approximation. The data in Tables 6 and 7 refer to the variation in the electron density distribution of the occupied NTOs as a symmetry reason to the electron-donating or accepted ability of two arms, which considered as a good evidence of the intramolecular charge transfer nature.
Correlation between theoretical and practical spectral and electrochemical oxidation results of DO26: The above results show good correlation between both practical and theoretical calculation in the following main points: 1-The thermal degradation of the dye at temperature range up to 1000 °C refer to its very high stability, and it required very efficient degradation tools like chemical or electrochemical oxidation to be removed from environment wastewater, which is actually performed in another paper. Most of these thermal fragments are correlated to most of fragment ions appeared in mass spectra of pure powder dye and of GC-mass of dye of electro-oxidation of degradation products. 2-The thermal degradation of DO26 refer to its high stability of its two symmetrical arms around urea center as correlated to theoretical ESP-mapped surfaces compound (D1) as it decomposed at very high temperature range as a result of charge concentration on some of its essential parts. The dipole moment change upon excitations (Δμ CT ) is another important factor to assess its CT behavior. 3-The UV-visible spectrum of D1 is varied; the experimental absorption electronic spectra in water solvent and computed are highly correlated. The calculated absorption maximum wavelengths (λ max ), electronic excitation energies (ΔE), and oscillator strengths (f) of D1 in water correlated effectively with the corresponding experimental values. The data obtained of the computed natural transition orbitals (NTOs) indicate that these electronic transitions can be assigned as π-π* transitions. These detailed discussions are confirmed, which illustrate natural transition orbitals (NTOs) occupied and unoccupied due to transitions between the ground state (S0) and six low-lying singlet excited states (Sn) of DO26 dye (D1) obtained at the PCM-B3LYP (water)/6-311 + + G(d,p) level of approximation.
4-The simulated FT-IR spectra at 400 to 4000 cm −1 for DO26 in comparison with experimental results refer to the fact that the dye has two similar arms for the urea derivatives. Each arm is substituted naphthalene and benzene ring linked by diazonium fragment (= N-NH-). The N-H stretching frequencies of the rings are calculated and found to be in the range 3,473-3,133 cm −1 , which is in good agreement with the found values in of 3,200 and 3,500 cm −1 with strong or medium intensities. The inter-molecular hydrogen bonding in D1 is stronger than intra-molecular H-bonding as indicated by difference in calculated and experimental frequencies of the same dye.

Conclusions
From the obtained data, it is concluded that it is very important to compare between practical thermal and mass results as efficient techniques in studying dye stability, with theoretical results using Gaussian program for structural stability identification of DO26 dye, via careful inspection of various phenomena detected in its two symmetrical arms around urea centre. DFT calculations have been carried out on DO26 dye (D1) applying the B3LYP/6-311G method to study the structure characters and vibrational analysis of the tested dye. Highly interesting correlation had been found between experimental and calculated parameters such as bond lengths and vibrational frequencies. Complete assignment of FT-IR spectra vibrational modes of DO26 (D1) is successfully performed at wavenumber range 400 to 4000 cm −1 . The AIM analyses actually revealed the presence of intra-molecular hydrogen bonding within two arms of the dye molecule. The obtained data successfully characterized them as medium and weak interactions. The effect of hydrogen bonding on structure and vibrational properties of the tested dye had been professionally also discussed. NBO analysis, HOMO-LUMO, and MESP plots had been used to explain chemical reactivity of DO26 dye (D1) molecule. Various electronic transition parameters have been calculated which actually provide further description and threw more lights on the chemical reactivity and direction of chemical reactions detected in the behavior of DO26. From the above calculations and practical work data, the depicted three different tautomeric forms of the DO26 (D1) dye are di-keto form (A, C 13 = O 25 , C 46 = O 58 ), keto-enol forms (B and C), and di-enol forms (D and E), and corresponding four transition states (TS) (F-I) are suggested. The theoretical calculation helps effectively to clarifying the thermal fragments correlation to most of fragment ions appeared in mass spectra of pure powder dye and of GC-mass of dye of electro-oxidation degradation products.
Supplementary information.