3.4. 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.
3.4.1. Optimized structure and hydrogen bonding of D1
Table (1) and Fig. 3 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.
Figure 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.
The data in Table 1 and 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, 1.345and 1.329 Å. The selected angles in the tested dye O2C1N3 and N3C1N4 are found to be of the values 119.22o and 115.86o; while the respective angles in urea are found to be 120.34o and 118.29o [41, 42]. Thus, bonds are affected by the presence of two arms of D1 (Fig. 3) with sequence (right arm: C7 to H39) and (left arm: 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 10.9o degree right arm out of plane and the angle O2C1N4C40 is of 5.74o and degree left arm out of plane. This indicates that the carbon derivative is almost in the same molecular plane of urea. Also, atoms in angles C8C9C10C11, C11C12C13O25, C11C12N26N27, N26N27C28C29, N26N27C28C33 of the values 180,180, 179.9, -0.3, 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, C44C45C46O58 of values 180, 0.0 and 180.0 degrees respectively.
AIM theory calculations refer to the presence of hydrogen bonds in the skeleton of D1; that 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 (\({\nabla }^{2}\rho\)) 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.
Table 2. The calculated selected geometrical parameters (a.u) using B3lyp/6-311 + + G (d,p) level of theory, bond length (Å) and binding energy (kcal/mol) of DO26 dye (D1).
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. [44] demands; at BCP in which; \({\nabla }^{2}\rho and Hcript>\) for strong H-bonding of covalent character. It also should be \({\nabla }^{2}\rho >0\) And H < 0 for medium H-bond of partially covalent nature. Alternatively it should be \({\nabla }^{2}\rho >0\) 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, \({\nabla }^{2}\rho\) = 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\({\nabla }^{2}\rho\) is found to be negative and small in magnitude for strong covalent interactions, as in [Mn(III) porphyrin]Cl-trimethoprim complex (\({\nabla }^{2}\rho\) = -0.0786 a.u.) [45]; and as in bis-dithiazolyl dimers [46]. By using Eint = (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.
3.3.2. 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) are di-keto form (A, C13 = O25, C46 = O58), keto-enol forms (B and C) and di-enol forms (D and E) and corresponding four transition states (TS) (F-I) are suggested. The proposed relative potential energy surface diagram for different three tautomeric forms and TS of D1 (A–I), are represented in Fig. 4.
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, 6.54 Kcal/mol respectively. These data refer to the di-keto form of D1 is the most stable tautomer in the gas phase. This conclusion is confirmed by the calculated energy values of corresponding four transition states (TS) (F-I) with respect to A with 5.6, 5.65, 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), 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. 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 (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.
3.3.3. 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 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. Selected vibrational normal modes of analysis, including FT-IR values, for D1 obtained using B3LYP/6-311 + G (d,p) level of theory
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 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 (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 [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 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 [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 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− 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 (CH3–CO–NH–NH2) 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 (CH3–CO–NH–NH2) are found to be weak instead of intense band as previously reported [51]. The calculated frequencies belongs to N–N stretching has been practically detected at 1,300 and 1,250 cm− 1 respectively and bending vibrational deformation modes of the fragment of the same group has 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 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 is efficiently reproduces the experimental results and can be used for vibrational analysis of biomolecules with a sufficient confidence.
3.3.4. 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.
Table 4. Natural charge of selected atoms of DO26 dye1 (D1) at B3lyp/6-311 + + G(d,p) level of theory.
Table 4 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 SO3 groups. It also has been seen that the charge is around − 1.0 e on each atom. The maximum positive charges on sulpher atoms (S21 and S54 atoms of SO3 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 increase of charge on N27 and N27 as compared to 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.
3.3.5. FMOs analysis
Table 5 represents Frontier molecular orbitals (FMOs, Figure S4.) data. The represented calculated quantum chemical parameters values are EHOMO, ELUMO, energy gap (ΔEgap), ionization energy (I), electron affinity (A) and Dipole moment [53–55].
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 DO26 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 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 SO3 group of right arm. The dipole moment vector is representing the direction of the electronic charge transfer motion and it equals 10.98 D.
3.3.6. 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 (\({\chi }\) ) are related to the electron number (N) at constant external potential, v(r), respectively [53–55].
Also, Global electrophilicity index (ω), Global softness (S) and electronegativity (\({\chi }\) ) are computed based on HOMO and LUMO energy values for D1 using B3LYP/ 6-311 + + G(d,p) theory level of calculation [53, 54].
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 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 = 0.11 eV) and the Nueclophilicity index (N) is equals + 2.49 eV. These values indicate that the dye favor nucleophilic approximate 23 times more than electrophilic. Compound D1 possesses electronegativity (X), value of 0.51 eV as a measure for tendency of molecule to attract electrons means it has high softness values (0.51 eV) and showed high reactivity,
3.3.7. 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 mainly based calculation of the electronic density changes occurred during the molecule reactions. Usually Fukui functions f+ (r), f − (r) and f0 (r) are essentially calculated in three chemical situations such as electrophilic, nucleophilic and radical attacks [57, 60–62]. Where \({\text{q}}_{\text{k}}\left(\text{N}\right), {\text{q}}_{\text{k}}(\text{N}+1)\) and \({\text{q}}_{\text{k}}(\text{N}-1)\)are the atomic population on the kth atom for the neutral molecule, its anionic and cationic species respectively. Chattaraj et al. [63] defined the local quantity called philicity\({ \omega }_{k}^{\alpha }\) associated with a site k in a molecule with the assistance of corresponding condensed-to-atom variants of Fukui function, \({f}_{k}^{\alpha }\). Where α = +, − and 0 correspond to local philic quantities describing nucleophilic, electrophilic and radical attacks, respectively. The highest \({\omega }_{k}^{\alpha }\) corresponds to the most electrophilic site in a molecule. Softness \({s}_{k}^{\alpha }\)describe 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 \((\varDelta f\left(\text{r}\right))\) concerning electrophilic and nucleophilic capacity of a given atomic site in the molecule. Here \(\varDelta f\left(\text{r}\right)\) is the difference between the nucleophilic and electrophilic Fukui function. If \(\varDelta f\left(\text{r}\right)>0\) refers to nucleophilic attack. For \(\varDelta f\left(\text{r}\right)cript>\) 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 6–7.
The values of Fukui functions\({f}^{-}\left(\text{r}\right) \text{a}\text{n}\text{d} {f}^{+}\left(\text{r}\right)\) are presented in Table 6.