A DFT analysis of electronic, reactivity, and NLO responses of a reactive orange dye: the role of Hartree-Fock exchange corrections

An experimental and theoretical study based on DFT/TD-DFT approximations is presented to understand the nature of electronic excitations, reactivity, and nonlinear optical (NLO) properties of reactive orange 16 dye (RO16), an azo chromophore widely used in textile and pharmacological industries. The results show that the solvent has a considerable influence on the electronic properties of the material. According to experimental results, the absorption spectrum is formed by four intense transitions, which have been identified as π→π∗\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$\pi \rightarrow \pi ^{*}$\end{document} states using TD-DFT calculations. However, the TD-DFT results reveal a weak n→π∗\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$n\rightarrow \pi ^{*}$\end{document} in the low-lying spectral region. Continuum models of solvation indicate that these states suffer from bathochromic (ca. 15 nm) and hypsochromic shifts (ca. 4 nm), respectively. However, the expected blue shift for the absorption n→π∗\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$n\rightarrow \pi ^{*}$\end{document} is only described using long-range or dispersion-corrected DFT methods. RO16 is classified as a strong electrophilic system, with electrophilicity ω > 1.5 eV. Concerning the nucleophilicity parameter (N), from vacuum to solvent, the environment is active and changes the nucleophilic status from strong to moderate nucleophile (2.0 ≤ N ≤ 3.0 eV). The results also suggest that all electrical constants are strongly dependent on long-range and Hartree-Fock exchange contributions, and the absence of these interactions gives results far from reality. In particular, the results for the NLO response show that the chromophore presents a potential application in this field with a low refractive index and first hyperpolarizability ca. 214 times bigger than the value usually reported for urea (β = 0.34 × 10− 30 esu), which is a standard NLO material. Concerning the solvent effects, the results indicate that the polarizability increases ∼20×10−24\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$\sim 20 \times 10^{-24}$\end{document} esu from gas to solvent while the first hyperpolarizability is calculated as ∼45×10−30\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$\sim 45 \times 10^{-30}$\end{document} esu, ca. 180%, regarding the vacuum. The results suggest RO16 is a potential compound in NLO applications. Graphical Abstract The frontier molecular orbitals, and the inverse relation between the energy-gap (Egap) and the first hyperpolarizability (β) The frontier molecular orbitals, and the inverse relation between the energy-gap (Egap) and the first hyperpolarizability (β)


Introduction
Since it was discovered in the 1960s [1], nonlinear optics (NLO) has figured as a prominent field in the science of materials. Organic and inorganic chromophores with higher NLO response can be used to built a variety of devices, such as field-effect transistors [2,3], light-emitting diodes [4,5], solar cells [6][7][8], and sensors [9,10] that can improve logical circuits. The biggest advantage of such devices is their data energies [14][15][16], pertinent feature for devices like solar cells, for instance.
Due to the features discussed above, the science of materials has invested many efforts into developing and discovering new compounds with enhanced NLO behavior. In this race, organic chromophores have shown superior performance. First, they present a higher limit of rupture when exposed to high-power lasers. Moreover, organic molecules allow greater miniaturization capacity compared to inorganic materials. Finally, organic compounds can be conveniently modified by chemical synthesis, improving their NLO feature. Between such dyes, one can cite chalcones [17,18], and squaraines [19,20].
However, as any experimental attack is expensive and demands much time, it is imperative to model the molecular NLO behavior using molecular modeling and quantum mechanics techniques. Within this scenery, Density Function Theory (DFT) [21,22] has gained special emphasis. In the DFT days, the old functionals faced problems like the description of van der Waals forces, longrange corrections, and including the Hartree-Fock exchange term. Nowadays, these problems have been solved, and DFT methods have been used to describe a series of molecular properties like reactivity, electronic excitations, and the NLO behavior of diverse chromophores [23][24][25][26]. Moreover, DFT and other quantum chemical approximations have been combined to liquid and solid-state simulations, giving information concerning how the environment affects the optical properties of a chromophore [16,27,28].
In particular, azo dyes are an interesting case. Azo compounds are π-systems made up of aromatic rings connected by azo-bridges (−N=N−) which behave like an entire push-pull system, favoring the electronic polarization. Because of their reactivity, one often applies these chromophores as antiviral and antifungal drugs [29][30][31]. The reactive orange (RO16) present in Figure 1 is one of such chromophores which has attracted attention due to its use in the textile industry. For this reason, there is great concern about how to remove this chromophore from water effluents [32][33][34]. However, almost nothing is known about its electronic properties.
For the first time, this work presents a discussion of the optical properties of an azo dye known as reactive orange 16 (RO16) shown in Figure 1. Via experimental analysis, DFT, and Time-Dependent DFT calculations, it characterizes the electronic absorption and emission spectra. Quantum mechanical results account for solvent effects, longrange (LC) interactions, and Hartree-Fock exchange (HFE) contributions. The experimental report reveals four strong excitations, which have been characterized as π → π * absorptions. However, the TD-DFT analysis reports that the lowest absorption energy belongs to a weak n → π * state. Moreover, this state is not experimentally observed once it is covered by an intense π → π * one.
Concerning the NLO behavior, RO16 presents great potentialities. For instance, the first hyperpolarizability is ca. 214 times bigger than that value reported for urea (β = 0.34 × 10 −30 esu) [35,36], which is a standard NLO material. These results suggest RO16 is a promise as NLO material. Finally, the satisfactory description of the RO16 photophysics and NLO behavior depends on including LC and HFE corrections.

Theoretical details
Although azo dyes can be stable either in trans as cis geometries, trans-isomers are those with the highest NLO response [27], the focus of this work. The molecular geometries of the reactive orange 16 at the ground and the first excited states were optimized within the framework of density functional theory using the Coulomb attenuated version of the B3LYP method (CAM-B3LYP) approximation [37] and the standard 6-311++G(d,p) basis set [38][39][40][41][42]. However, before performing DFT optimizations, we first performed a scan varying the three most relevant torsion angles of the chain containing the sulfur atoms (C24-C25-S28-C30, S28-C30-C32-O33, and O30-C32-O33-S34) to determine the most energetically favorable conformations using the semi-empirical PM3 methods. Then, a posterior analysis of the infrared spectra showed that all vibrational frequencies are positive, confirming that the molecular geometry is on a glocal minimum of energy.
Concerning including thermodynamic conditions and explicit solvent molecules, this approach improves the results for electronic excitations and NLO response. However, there is a practical limitation: electrical properties like NLO effects are additive properties [51]. Thus, the first hyperpolarizability for a dimmer, for instance, will be twice that obtained for a monomer, which is a problem if one is interested in discussing only the reference molecule. As the major focus is to relate the UV-Vis to NLO behavior, we avoided this technical difficulty and adopted conducting version of the polarizable continuum model (C-PCM) [52] to simulate the water solvent.
The NLO effects arise when the light interacts with the matter. In such a case, one can expand the energy of the system in the Taylor series: In this equation, μ 0 is the permanent dipole moment vector given by The following terms are the dipole polarizability (α) and the first hyperpolarizability (β). These parameters can be obtained by satisfying the Hellmann-Feynman theorem and taking the partial derivative concerning the electric field [53] and After obtaining the tensor component, it is usual to discuss the dipole polarizability using the concept of isotropic ( α ) and anisotropic (Δα) contributions and The theoretical polarizability can infer the refractive index (n) using the Lorentz-Lorenz equation [54,55] where V mol is the molecular volume. The static version first hyperpolarizability is a tensor given for a cubic matrix (3 × 3 × 3) with 27 elements. However, appropriate symmetry rules (β ijj = β jij = β jj i ) [56] reduces this number to 10 distinct elements which are combined to give the static β total where β x = β xxx + β xyy + β xzz β y = β yyy + β yxx + β yzz (9) β z = β zzz + β zxx + β zyy .
Regarding the reactivity of the chromophore, one can deal with global and local parameters. One mainly discusses the global reactivity in terms of the chemical potential (μ), ionization energy (IP), electron affinity (EA), hardness (η), electrophilicity (ω), and nucleophilicity. The first five parameters are calculated as [57]: and For the nucleophilicity (N) index, we adopt an empirical scale developed for closed-shell systems based on the HOMO energies, defined as [58,59]: In the equation above, the calculations are performed on the tetracyanothylene (TCNE) molecule, also obtained within the CAM-B3LYP/6-311++G(d,p) formalism. The local reactivity parameters if often discussed using the Fukui functions, which describe the selectivity or reactivity of an atomic site or a region in a chemical chromophore. These parameters are given by [60] F + k = q k (N + 1) − q k (N), for nucleophilic attack (16) and , for electrophilic attack, (17) where q k (N), q k (N + 1), and q k (N − 1) are the electronic populations on the kth atomic site for N, N + 1, N − 1 electron systems, respectively. Other two relevant parameters are the relative nucleophilic (f nu = |F + k /F − k |) and electrophilic (f el = |F − k /F + k |) indexes. When f nu > f el , the atomic site is inclined to perform a nucleophilic attack. In another way, f el > f nu the atom is prone to an electrophilic attack on a nucleophilic site [60][61][62][63][64]. Concerning the solvent effects on the electronic properties, the results were obtained using the conducting version of the polarizable continuum model (C-PCM) [65]. Finally, all electronic calculations were carried out in Gaussian 09 package [66]. We used the software GaussSum [67] to perform the Partial Density of States (PDOS) analysis.

Experimental details
Reactive orange dye 16 (RO-16), ID: 24858342, with a molecular weight of 617.54 g/mol was purchased from Sigma-Aldrich Company, Saint Louis, USA, with the content of 70%. Initially, a solution of 50 mL of RO-16 was prepared at a concentration of 10 mg/L. Then, the measurement was performed in a brand spectrophotometer (Digital Double Beam -GTA -101) in a quartz cuvette with an optical path of 1 cm and 1 ml.

Electronic excitations
The experimental absorption spectrum of the RO16 in water is shown in Figure 2. According to this spectrum, four absorption bands can be observed: two in the visible region, with their maxima wavelengths (λ max ), centered at 493 and 388 nm, and two in the ultraviolet region with λ max at 296 and 253 nm. These two bands in the visible region were assigned as n → π * , and the two bands in the UV region as π → π * [68]. The obtained spectrum for RO16 agrees very well with previous results reported in the literature [68][69][70]. The bands at 493 and 388 nm are attributed to the chromophore, and azo group [70]. In comparison, the bands at 296 and 253 nm are related to the structure of gamma acetylated and aromatic rings [70], respectively. Table 1 shows the maximum wavelengths (λ max ) and oscillator strength of the five lowest transitions of orange 16 calculated in vacuum and water using different methods. As can be seen, in the gas phase, B3LYP provides two Fig. 2 Absorption spectra of reactive orange 16 calculated in vacuum and water using different methods (B3LYP, CAM-B3LYP, M06-2X, and wB97XD) and the same basis set 6-311++G(d,p). In water, the spectra were obtained using the solvent described by C-PCM with the same level of QM calculation Table 1 Maximum wavelengths (λ/nm), oscillator strength (f ) of the five lowest transitions of reactive orange 16 calculated in vacuum and water using different methods (B3LYP, CAM-B3LYP, M06-2X, and ωB97XD) and the same 6-311++G(d,p) basis set Normally, from gas to solvent, n → π * states suffer a hypsochromic effect [16,71], and for RO16, this behavior is not different. Comparing the gas phase and in water B3LYP results, it was observed that the weak n → π * transition exhibits a blue shift of 4 nm, and was found inverted concerning the position of the second transition. This small blue shift was also observed with the other methods (CAM-B3LYP, M06-2X, and ωB97XD), but the n → π * transition was not inverted. Generally, from gas to solvent, n → π * states suffer a hypsochromic effect [16,71], and for RO16, this behavior is no different. Comparing the gas phase and in water B3LYP results, it was observed that the weak n → π * transition exhibits a blue shift of 4 nm and was found inverted concerning the position of the second transition. This slight blue shift also was observed with the other methods (CAM-B3LYP, M06-2X, and ωB97XD), but the n → π * transition was not inverted.
This result shows that long-range interactions are essential if one desires to describe n → π * states. In contrast, for the other four transitions, we observe a redshift of the entire spectrum. With the B3LYP, this redshift was 21, 12, 3, and 1 nm from the gas phase to water, and for the other methods (CAM-B3LYP, M06-2X, and ωB97XD), the average values were 14, 6, 4, and 4 nm, respectively. From vacuum to solvent, one observes that the environment increases the oscillator strength values for these four transitions compared to the gas phase. This effect is expected since water is a very polar solvent [72]. Such property usually causes both a bathochromic shift in π − π * absorptions and increases its oscillator force. The 5th transition presents the most significant increase in this property.
Comparing the experimental results, we observe that the best agreement with observed two first π → π * transitions is obtained with B3LYP, giving wavelengths differences of 10 and 8 nm for the 2nd and 3rd transitions. For the other π → π * transitions (4th and 5th), this best agreement was obtained with CAM-B3LYP, with these values of 13 and 12 nm, which also agrees with M06-2X and ωB97XD results. Thus, our results show that the use of a non-longrange DFT functional (B3LYP) provides an appropriate description of the 2nd and 3rd transitions. The corrected functionals provide a satisfactory description of the 4th and 5th transitions of RO16 in water.
However, if one considers only the theoretical fitting of the experimental spectra, for a first view, B3LYP sounds to give the best performance. However, it is not true. This method is an old hybrid-functional that does not account for crucial interactions like long-range and van der Waals forces, and some recent results have attested the relevance of these interactions in the description of the photophysics of a chromophore. For some fused-ring systems [71], the solvent induces a crossing between the two lowest n−π * and π −π * transitions. However, such effect only is obtained for ab initio CIS(D) and CCS(D) Hamiltonians, as well as those DFT methods corrected for long-range and/or van der Waals forces, like CAM-B3LYP and B97D.
For the case of the RO16 molecule, one observes B3LYP predicts a wrong photophysical behavior crossing the two lowest n − π * and π − π * absorption lines (see Table  1). However, none other more DFT method confirms this behavior. Consequently, the B3LYP prediction does not match the RO16's photophysics. Table 2 shows the results obtained for the molecular dipole moment (μ), dipole polarizability (α), molecular volume (V mol ), and the refractive index (n) for the RO16 molecule in a water solvent, using different approaches of quantum mechanics and the C-PCM, which is an adequate continuum model to discuss NLO parameters. This discussion considers three effects: the influence of longrange interactions, the role of Hartree-Fock exchange, and the effects of the solvent.

Dipole moment and dipolar polarizability
The long-range corrections (LC) polarize the reference molecule, increasing its dipole moment. For instance, the B3LYP results predict a value of 2.59 D for μ. However, after including LC corrections using the CAM-B3LYP functional, the molecular dipole increases to 2.65 D. The inclusion of HF exchange causes similar effects. For instance, the Minnesota family of density functionals (M06-L, M06, M06-2X, and M06-HF) accounts for zero, 24%, Fig. 3 The evolution of the refractive index, dipole moment, dipole polarizability, and the first hyperpolarizability ( n, μ, α , and β total ) as function of the Hartree-Fock exchange 54%, and 100% of HF exchange. They predict the dipole moment as 2.53, 2.57, 2.67, and 2.87 D, respectively. Such effects are better realized in Figure 3a.
Concerning the solvent effects, Table 2 also allows for comparing the values obtained for μ, α, and n. In the particular case of the dipole moment in both gas (2.19 D) Table 2 The molecular dipole moment (μ/D), the components of the dipolar polarizability (α/10 −24 esu), molecular volume (V mol ), and the refractive index (n) calculated for different degrees of quantum chemistry and the 6 and solvent (2.67 D) using the M06-2X method. These values indicate a polarization effect of ca. 17%, concerning the gas-phase value, and agree with other data that predict polarization effects which can achieve 30% or even 40% [28,[73][74][75].
Contrasting the dipole moment, the dipolar polarizability (α) also presents an opposite correlation concerning the inclusion of long-range corrections and HF exchange terms in DFT methods. For instance, from B3LYP to CAM-B3LYP, the isotropic α varies from 87.83 × 10 −24 to 81.92 × 10 −24 esu. Moreover, considering the systematic inclusion of HF exchange, the Minnesota functionals predict that decreases from 89.10 × 10 −24 to 77.69 × 10 −24 esu, which is a variation of 13%. Figure 3b points out such behavior.
By combining α , and the molecular volume (V mol ), one can obtain the refractive index (n) throughout the Lorentz-Lorenz equation [54,55]. Analyzing the results showed in Table 2 one can observe that the B3LYP prediction (n = 2.41) is not realistic once this functional overestimates n concerning the other methodologies. However, including long-range corrections using the CAM-B3LYP model, one obtains n = 2.10. On the other side, the Minnesota family of functionals shows that the refractive index decreases regarding the inclusion of the HF exchange term, achieving a value of 2.07 using the M06-HF method and the C-PCM model.
As the refractive index (n = c/v) is the ratio between the light speed in the vacuum and a particular environment, lower n values designate great capacity of data transference. The results for the RO16 molecule are stimulating. For instance, refractive indexes of 1.76 and 1.89 respectively for the cis and trans isomers of an azo-azomethine dye [27]. Valverde [76], and Hodgkinson [77] have estimated refractive indexes of 1.71 and 2 for crystallized chalcones and pristine oxide, respectively.
Concerning the solvent effect (see Table 2), from vacuum to an aqueous environment, the solute polarization due to solvent acts improving all quantities. For instance, the isotropic contributions for the polarizability increases from 61.85 × 10 −24 to 81.30 × 10 −24 esu, which is a variation of ca. 31% concerning the gas-phase value. Both Δα and n show similar trend. Table 3 shows the values obtained for the first hyperpolarizability (β total ) under static conditions. Again, these results consider three points: the effects of long-range corrections, including Hartree-Fock exchange, and the solvent contributions. Concerning the role of long-range corrections, the CAM-B3LYP results predict a value of 66.88 × 10 −30 esu for β total , which is an improvement of 29% regarding the value of 93.87 × 10 −30 esu predicted using B3LYP.

First hyperpolarizability
The systematic inclusion of HF exchange also causes a decrease in the first hyperpolarizability. For instance, the M06-L functional does not consider any percent of HF contributions and predicts 108.21 × 10 −30 esu for β total . However, the other Minnesota functionals, M06, and M06-2X functionals, which propose respectively zero, 27%, and 54% of HF exchange, predict 87.64 × 10 −30 , 72.73 × 10 −30 . and 55.54 × 10 −30 esu. As one can observe, from M06-L to M06-HF methods, the HFE corrections improve in ca. 49% the description of β total . This behavior is better observed in Figure 3b.
As most organic NLO chromophores are large molecules that can demand great computational power, we tested the performances of the PM6 and PM7 semi-empirical methods. From Table 3, one can observe that both approximations reproduce all aspects assigned by DFT methods. For instance, they are assertive when predicting that the most contribution for the first hyperpolarizability comes from β x . However, the PM6 estimate (β total = 68.06 × 10 −30  [35,36], a well known optical material. Through individually presents low NLO response, this property is enhanced in crystal, once β is an addictive parameter [78,79]. RO16 also presents a good performance concerning the paranitro aniline molecule, which is other typical donor-acceptor compound with NLO applications that presents β total estimated between 6.27×10 −30 [80] and 8.86×10 −30 esu [81]. Thus, all results show that RO16 is really suitable for optical applications. Considering the contributions of the solvent, it is clear that the environment presents a powerful influence on the first hyperpolarizability. For instance, Table 3 shows the results obtained using the M06-2X functional in vacuum and water solvent, considering the C-PCM solvent model. From gas to solvent, the energy gap decreases from 5.10 to 5.02 eV. However, as Oudar and Chemla [82] have shown, the first hyperpolarizability is an inverse function of the energy gap, being approximated like β ∝ Δμf/ΔE 3 , where f is the oscillator force corresponding to the energy transition ΔE and Δμ is the difference between the dipole moment in the excited and ground states. Quantitatively, Figure 4 better explores the inverse relationship between the first hyperpolarizability and the energy gap. Thus, it is expected that a slight variation in the energy gap generates a considerable improvement in β total . According to the M06-2X results, the first hyperpolarizability changes Concerning the charge transfer characteristics, the analysis of the molecular orbitals and the respective HOMO-LUMO gap shows this process. From Figure 4, one observes that the frontier orbitals are mainly localized in different molecular regions. However, there is an overlap between them. This feature facilitates an eventual charge transfer process. The energy gap (E gap ), which is around 5 eV, shows a wide band-gap semiconductor-like behavior and from the gas phase to the solution, E gap calculated with the M06-2X DFT method decreases ca. 0.07 eV, which can improve the charge transfer effect.
Finally, it is important to do a reflection about other contributions to the optical response. For the entire work, we have used gas-phase geometry. However, the molecular relaxation due to solvent can affect both electronic excitations and the NLO response of a material. In particular, the greatest effect occurs on π − π * transitions, increasing moderately its bathochromic shift and its corresponding oscillator force [72]. Throughout the Oudar and Chemla two-level model [53], one knows that a bathochromic shift generates an increase in the NLO parameters. Thus, including such effects could improve the optical response.

PDOS analysis
The Partial Density of States (PDOS) is a function that brings reliable information about the electronic structure of the material [83][84][85][86][87][88]. To understand the individual contributions of specific atoms to PDOS and how their contributions change when those atoms are within a chemical group, the O and N atoms were analyzed individually, and their results were plotted against the chemical group curves as Azo (−N=N−), SO 2 , C rings, SO 3 Na(Position 1), and SO 3 Na(Position 2). The choice of O and N as isolated atoms is due to their high electronegativity and their presence in the main functional groups mentioned above. All the other atoms are majority H and were classified as Allothers. The results in the vacuum and under PCM implicit water solvent environment were compared. Figure 5 shows the contribution of isolated O and N atoms to the PDOS is low and has relevant values only in the region of occupied orbitals. This behavior does not change from vacuum to the implicit solvent environment. The Azo group has a significant contribution nearly to the occupied orbitals. It has a peak at the LUMO orbital, which means the HOMO-LUMO transition arises from the C rings to an orbital that has a component in the Azo group. The PDOS of the SO 2 group has no appreciable change from vacuum to the implicit water environment. C rings have the most important contribution to PDOS. This effect occurs because aromatic rings present a great abundance of π electrons, which are less bonded to the nuclei, being strongly polarizable by the environment. One can observe that the water compresses the peaks. Near virtual orbitals region, it is clear the tendency to unite the peaks close to 0.0 eV. Observing these peaks around 3.0 eV, it is also possible to note this phenomenon. Figure 5 shows the contribution of isolated O and N atoms to the DOS is low. They have relevant values only close to the occupied orbitals. This behavior does not change from vacuum to water. The Azo group has a significant contribution just about the occupied orbitals. It has a peak at the LUMO orbital, which means the HOMO-LUMO transition arises from the C rings to an orbital that has a component in the Azo group. The PDOS of the SO 2 group has no appreciable change from vacuum to water. C rings have the major contribution in all PDOS plots. This effect occurs because aromatic rings present a great abundance of π electrons, which are less bonded to the nuclei, being strongly polarizable by the environment. It can be observed that the implicit environment compresses the peaks. Around virtual orbitals, it is clear the tendency to unite the peaks close to 0.0 eV. Observing peaks around 3.0 eV, one can also note this phenomenon. They experience the tendency to merge their peaks in all spectra under the effects of the PCM water solvent.

Reactivity
Global reactivity descriptors Table 4 shows the results obtained for the global reactivity descriptors obtained for the RO16 molecule. From these results, one can observe that the solvent plays a relevant in the molecular reactivity. For instance, by analyzing the M06-2X data obtained at gas and solvent, one concludes that the chemical potential increases from −4.58 eV in vacuum to −4.78 eV in a solvent. The ionization potential (IP) and electron affinity (EA) increase to 7.29 eV (ca. 2.24%) and 2.27 eV (ca. 12%) in an aqueous environment. Consequently, the system becomes more reactive when embedded in a solvent. Concerning the chemical hardness (η), this parameter decreases from 2.55 eV (vacuum) to 2.51 eV (solvent). Although the concept of polarizability is different for physicists and chemists, polarizability, α and η has been often connected by a relation of linear regression [25,89,90]. Thus, an increase in the chemical hardness of the material denotes a decreasing the dipole polarizability, as well as in the refractive index.
The global electrophilicity (ω) and nucleophilicity (N) are other two relevant reactive parameters often discussed for a pharmacy candidate. According to Domingos and collaborators, a chromophore can be classified as marginal (x < 0.8 eV), moderate (0.8 ≤ x ≤ 1.5 eV), or even as a strong electrophile (x > 1.5 eV) [91]. Similarly, a compound can be assigned as marginal (N < 2.0 eV), moderate (2.0 ≤ N ≤ 3.0 eV), and a strong nucleophile (N > 3.0 eV) [58,59]. After considering these scales, one observes that the environment increases the electrophilicity from 4.11 to 4.55 eV, which allows to classify RO16 as a strong electrophile. However, one observes a opposite behavior for the nucleophilicity. From vacuum to solvent, N varies from 3.77 to 2.11 eV, changing the status from a strong to moderate nucleophile.
One can also observe that the absence of LC and HFE contributions overestimates ω. For instance, from B3LYP to CAM-B3LYP, one obtains ω = 6.68 eV and ω = 4.02 eV, respectively. Similar behavior is observed between M06-L (ω = 9.97 eV) and M06-2X (ω = 4.55 eV). These findings show that LC and HFE are essentials one desires to investigate the molecular reactivity. Regarding nucleophilicity, these interactions also are fundamentals. However, they actuate, decreasing the values of N. For instance, while B3LYP predicts 2.98 eV, the CAM-B3LYP method indicates 4.46 eV for N. Again, similar behavior is observed for M06-L and M06-2X, for instance.

Local reactivity descriptors
After determining the global reactivity parameters, the next step is to discover the independent behavior of each atomic site in the molecule. Figure 6 presents the plots for the relative nucleophilic and electrophilic indexes (f nu , f el ) obtained from the Fukui functions (F + k , F − k ) calculated from the Mulliken charges at the M06-2X/6-311++G(d,p) level of theory. Table 4 The global reactivity descriptors, the chemical potential (μ), ionization energy (IP), electron affinity (EA), chemical hardness (η), electrophilicity (ω), and nucleophilicity (N)  Figure 6 presents the natural and Mulliken population analysis, NPA and MPA, respectively. Typically, an azobridge is rich in π-electrons. Thus, this region is expected to be prone to perform a nucleophilic attack. Figure 6a confirms this statement. The NPA results also indicate that all elements placed in the fused aromatic rings are essentially electrophiles. However, the other aromatic ring presents an opposite behavior, being a nucleophilic region. Finally, the MPA showed in Figure 6 predicts similar results compared to those obtained from NPA. However, Mulliken charges sounds to overestimate or underestimate the indexes of some atoms.

Conclusions
Based on DFT/TD-DFT and semiempirical methods, this works presents a theoretical and experimental discussion of the optical and reactive properties of the reactive orange 16 dye. These results account for solvent contributions, long-range (LC), and Hartree-Fock exchange (HFE) corrections.
In the ground state, RO16 presents a wide absorption band placed in the visible region of the spectra. Clearly, this band is composed of four strong π → π * excitations, besides a weak n → π * line placed in the lowlying region of the spectra. Although the π → π * absorption suffers a clear redshift when embedded in a water solvent, the n → π * state presents a smooth blue shift. However, this behavior only is correctly described if long-range interactions under the form of Hartree-Fock exchange or dispersion corrections are considered in the calculations. The theoretical results also show that RO16 can be useful for a variety of NLO applications. In fact, according to DFT and semi-empirical calculations, the chromophore presents a strong NLO response. For instance, static approximations of the first hyperpolarizability (β total ) show values superior to those reported for standard NLO materials like p-nitroaniline and urea. Moreover, the current DFT calculations using the Lorentz-Lorenz equation, which connects the dipole polarizability (α) to the refractive index (n), show that the RO16 molecule presents lower n. However, those methods which do not account for LC or HFE do not describe the reality, overestimating the dipole polarizability, the refractive index, and the firsthyperpolarizability. Thus, such interactions are essential to better understand the NLO response of the RO16 molecule.

Conflict of interest
The authors declare no competing interests.