Computational Exploration of Spectroscopic and Hydrogen Bonding Analysis of Direct Orange 26 Dye in Combination with Experimental and TD-DFT Calculations.

: The importance of this study stems from, it concentrates on new approach applying both practical and theoretical aspects to study structure of Direct orange dye 26 (DO-26) as an important dye widely used for dyeing of cotton or viscose for red orange direct printing. It also can be used for silk, wool, polyvinyl alcohol, polyamide fiber fabric and pulp dyeing. It proficiently compare practical with theoretical results of structural identification of the given important dye, via carful inspection of various phenomena detected in its two symmetrical arms around urea center. Direct orange dye 26 (DO-26) structure has been studied applying both practical spectroscopic and theoretical investigations. DFT-B3LYP/6-311++G(d,p) calculations are performed to investigate its structure, and the electronic vibrational properties. Correlation is found between experimental and calculated data. An intra-molecular hydrogen bonding interaction had been detected and characterized in dye skeleton using Atoms-in-molecule analysis employment. 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, structure activity relationship descriptor were obtained. The experimental UV/Visible and FT-IR spectral data of the dye DO-26 (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. The variation of charge transfer length (Δr) and variation in its dipole moment with respect to ground state (Δ  CT ) had been computed in order to study the charge redistribution due to the excitations. Actually there is a problem that, 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  This research deals with both practical and theoretical aspects to study structure of Direct orange dye 26 (DO-26).  It is an important dye widely used for dyeing of cotton, silk, wool, polyamide fiber and pulp dyeing.  The experimental UV/Visible and FT-IR spectral data of the dye DO-26 (D1) had been presented.  This study involved carful inspection of various phenomena detected in its two symmetrical arms around urea center.  DFT-B3LYP/6-311++G(d,p) calculations are performed to investigate its structure, data These data show six absorption bands with maxima at 511 nm (ε = 13,395 M -1 .cm -1 ), 491 nm (ε = 14514 M -1 .cm -1 ), 416 nm (ε = 14514 M -1 .cm -1 ), 321 nm (ε = 6777 M -1 .cm -1 ), 302 nm (ε = 5440 M 1 .cm -1 ), and 267 nm (ε = 7077 M -1 .cm -1

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 DO-26 molecule. On comparison of FTIR and UV-Visible spectra of DO-26 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.
Hydrogen bonding plays a pivotal role in determining the structures and properties of biomolecules [9]. The study of hydrogen bonding phenomena had been successfully studied applying Bader's atoms-in-molecule (AIM) theory [10]. The nature and strength of various types of hydrogen-bonded interactions had been efficiently described by the AIM theory. The AIM theory is able to describe the change in electron density distribution in a molecule as a result of either bond formation or complex formation. The reliability and stability in the values of AIM 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]. The FT-IR spectra of KBr discs containing D1 had been measured at wavenumber region 4000 -400 cm -1 using FTIR 4100, JASCO spectrophotometer.

Computational details
The Gaussian 09W software package [14] 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 [15,16]. Where (B3) [17][18][19] stands for Becke's three parameters combined with gradient-corrected functions of Lee, Yang and Parr (LYP) [20], During geometry optimization no symmetry constrains had been applied [21,22]. 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 [23,24]. 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 09W software package has been used for NBO calculations using NBO 3.1 program implemented in the same program. The Gauss View version 5.0. 9 [25] involving Chemcraft version 1.6 package [26] had been used throughout this work to optimize the structures of tested compounds. In addition, the Multiwfn v3.8 software program [27] has been used to compute quantum chemical descriptors from point of view of conceptual density functional theory (CDFT). The Multiwfn v3.8 software program [27] has been also used for Atom in molecule (AIM) analysis. The vertical linear-response TD-DFT approximation [28] has been also used for calculation of the first 80 low-lying excited states. The Polarizable Continuum Model (PCM) [29,30] has been included in all steps of a modeling of bulk solvent effects.
Computing the natural transition orbitals (NTO) [31] have 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 [27] had been used to estimate the electronic transitions between the ground state (S0) and the low-lying singlet excited states (Sn). In order to study the charge redistribution due to the excitations in tested molecules; the variation in dipole moment with respect to ground state The VMD 1.9 program [33] 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 [34,35] with corresponding to VEDA program [36] has been used for calculation of the potential energy distribution (PED) for various vibrational normal modes of the studied DO-26 dye (D1).

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 D1 both in water and gas phases of the ground state and compared with the practical elemental analyses and spectroscopic data.  Figure 1 present the computed parameters of D1 in this work; such as optimized geometry, numbering system, vector of the dipole moment, bond lengths, bond angles and dihedral angles.  [37,38]. Thus, bonds are affected by the presence of two arms of D1 ( Figure 1) with sequence (right arm: C7 to H39) and (left arm:

Optimized structure and hydrogen bonding of D1
C40 to H58).
The computed values of dihedral angles around central urea derivatives are represented in Table 1. They show that, the angle N4C1N3C7 is of 10. Applying this theory to DO-26 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 [39] 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…H50, O23…H20, O74…H53 along with geometrical parameters of H-bonds and the data obtained are listed in Table 2. There are three types of H-bonds have been detected in the basis of D1 topology [40] via calculated parameters. The characterization has been followed Rozas et al. [40] demands; at BCP in which; ∇ 2 < 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

The tautomeric relative stability of D1
From the above calculations and practical work data; the depicted three different tautomeric   Kcal/mol respectively; which have stability order of F<G<H=I (see Figure 2). The stability of the di-keto form (A) relative to the keto-enol (B), enol-keto (C) and the di-enol (D) forms may be attributed to the increasing in the strain effects within the moiety of these forms. On inspection of supplementary material ( Figure S1), one can find 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 (N27 or N60) (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 ( Figure 1) are found to be real. Consequently; the D1 optimized geometry corresponds to a true minimum energy in the PES.  Table 3; 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.    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 (CH3-CO-NH-NH2), is detected at 3,445 cm -1 and confirmed by the calculated one found at 3,640 cm -1 by DFT [48]. 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 intramolecular H-bonding as indicated by difference in calculated and experimental frequencies of the same dye indicates that.
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 [47]. 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 [47] 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 [47].
The CH2 stretching vibrations of weak intensities in the dye skeleton are detected at 2,954 and 2,907 cm -1 . The CH2 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 -  Table 3 and graphically represented in Figure   4.  shows a correlation between theoretically calculated and the practically detected frequencies in FT-IR of the dye DO-26. 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 is 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 4. The obtained results proved that; this scheme is more reliable due to its low basis set dependency.

Values are mean ± SD triplicate assays
The HOMO (ionization potential I= -EHOMO) 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. The small value of ELUMO (electron affinities A = -ELUMO).means more able to accept electron. The calculated EHOMO of the tested dye is found to be -1.724 eV; which is located on the SO3 group system of right arm. On the other hand the ELUMO, of DO-26 is found to be 0.696eV; which is mainly contributed by all left arm of the dye molecule. The energy (ΔEgap) between HOMO and LUMO usually described the chemical reactivity of the molecule. In the present study, ΔEgap is found to be 2.42eV; 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 5, it has 1.72 eV value of I and A is -0.7 eV and electronegativity is equal 0.51 eV. Figure 5 represents Frontier molecular orbitals of the studied DO-26 dye compounds (D1).
These data have been considered very important to explain the reactivity and stability of studied  Table 5 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 5 proved that D1 has Electrophilicity index value (ω = 0. Where ∆ (r) is the difference between the nucleophilic and electrophilic Fukui function.
If ∆ (r) > 0 refers to nucleophilic attack. If ∆ (r) < 0 it may be 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 6-7.
According to these results, one can conclude that the studied dye possess 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       The data obtained in Figure 8 of the computed natural transition orbitals (NTOs) indicate that these electronic transitions can be assigned as π-π * transitions.

Electronic absorption spectra
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 9. Table 9. 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 using Hirshfeld population analysis.
These data of molecular orbital compositions are essentailly 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 left arm (Azoph_L) molecular fragments to the occupied and virtual NTOs.
The first transition (S0→S1), is related to electrons occupied NTO of pz and px 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 pz orbitals of these atoms. The unoccupied NTO is composed of pz 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 pz orbitals of these atoms. It is clear from data in 9, electron density ππ* transition from left arm to right arm by around 17 % of electron localized over the entire molecule.
The second transition (S0→S2), is related to electrons occupied NTO of pz, px and py orbitals mainly localized on O22, O23 and O24 of the sulphonic 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 pz orbitals that mainly localized on C13, O25 and N26 of the active group in right naphthalene group as S0→S1. A π*-antibonding interaction exists between the pz orbitals of these atoms is mainly related electron density ππ* transition from left arm to right arm by around 20 % of electron localized over the entire molecule.
For the third transition (S0→S3), the occupied NTO the π-bonding interaction is concentrated between the pz orbitals of urea center and left naphthalene arm with 22 and 41%, respectively. The un-occupied NTO is composed of pz 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 ππ*.interaction exists between the pz orbitals of these atoms.
The fourth transition (S0→S1), 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 ππ* transition and exists between the pz orbitals of these range atoms. The un-occupied NTO is found to be mainly localized right naphthalene group with contributions of  94%. It is mainly occurred due to π*-antibonding interaction exists between the pz orbitals of these atoms.
The fifth transition (S0→S5), 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 nonoccupied NTO is composed of pz orbitals and mainly localized on right naphthalene group with contribution  90%. A π*-antibonding transition may be assigned as ππ* interaction exists between the pz orbitals of these atoms.
For the 6 th transition (S0→S6), is essentially related to the occupied NTO π-bonding electron interactions exist between the pz orbitals of urea center and left naphthalene arm with 47 and 31%.
Consequently, the non-occupied NTO is composed of pz orbitals mainly localized left naphthalene group and azo-phenyl left part with contributions of  45% and 31%, respectively; resulting in π*antibonding interaction leading to ππ* transition exists between the pz orbitals of these atoms.
These detailed discussions are confirmed by Figure 8; 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 details discussion clearly shows a π-bonding interaction among the specific groups of atoms as mentioned above. The NTOs data clearly discussed πantibonding 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 Figure 8. 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 (see the supporting information for details in supplementary Figure S2 and Table S2.
These six transitions and calculated parameters are given in Table 10. The data in Tables 9-11      a PED <10 % are not included in assignments. b Symbols: ν = Stretching, δ = Bending, τ and γ = torsional motions, + = out of phase, -= in phase

Conclusions
Expressions represent: (direction of phase, percentage contribution in normal mode%) vibrational normal mode (Atom composition mode motions) Values are mean ± SD triplicate assays.

Figure 2
Using the B3LYP/ 6-311++G(d,p) of the DFT theory; the calculated surface relative potential energy values are given for the different tautomeric forms transformations of DO-26 dye (D1). FT-IR spectra of the DO-26 dye (D1) in the region 400-4000 cm-1: (a) Experimental spectra (b) simulated spectra.

Figure 4
Correlation between experimental FT-IR and simulated IR spectra in the region 4000-400 cm-1of the DO-26 dye (D1).

Supplementary Files
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