鄭 東 袁相愛(ài) 馬 晶

（南京大學(xué)化學(xué)與化工學(xué)院，南京大學(xué)理論與計(jì)算化學(xué)研究所，南京 210046）

鄰位甲基紅水溶液的光譜性質(zhì)隨pH值的變化：含時(shí)密度泛函理論計(jì)算與實(shí)驗(yàn)研究

鄭 東 袁相愛(ài) 馬 晶*

（南京大學(xué)化學(xué)與化工學(xué)院，南京大學(xué)理論與計(jì)算化學(xué)研究所，南京 210046）

探明影響甲基紅光譜性質(zhì)的各種因素，有助于拓寬偶氮苯衍生物在有機(jī)光電器件中的應(yīng)用。采用密度泛函理論和實(shí)驗(yàn)相結(jié)合的方法研究了溶液酸堿性和溶劑水對(duì)鄰位甲基紅水溶液光譜的影響。溶液pH從13.1逐漸降低至0.5，鄰位甲基紅水溶液的最大吸收波長(zhǎng)從430 nm紅移至520 nm。在不同酸堿條件下，主要有三種物種共存于甲基紅水溶液中，它們分別是雙質(zhì)子化的甲基紅o-H2MR+（強(qiáng)酸性條件下），單質(zhì)子化的甲基紅o-HMR （弱酸條件下）和堿性甲基紅o-MR–（堿性條件下），通過(guò)密度泛函理論計(jì)算研究了三種不同形式的電子結(jié)構(gòu)特征。采用含時(shí)密度泛函理論計(jì)算了甲基紅偶極躍遷允許的最低激發(fā)能，分別采用連續(xù)介質(zhì)模型和分子簇模型研究水溶劑對(duì)甲基紅電子結(jié)構(gòu)和光譜性質(zhì)的影響。在酸性條件下，o-H2MR+和o-HMR分子內(nèi)氫鍵導(dǎo)致π共軛體系平面性增強(qiáng)，因而光譜紅移。而在堿性條件下，溶劑對(duì)o-MR–的光譜有顯著影響：極性o-HMR和o-MR–與水分子的偶極–偶極相互作用導(dǎo)致光譜進(jìn)一步紅移。

鄰位甲基紅；紫外/可見(jiàn)吸收光譜；pH；氫鍵；溶劑效應(yīng)；密度泛函理論；含時(shí)密度泛函理論

1 Introduction

Azobenzene and its derivatives have attracted long-term interest. The azobenzene has two different conformations, cis （Z）and trans （E）. The trans isomer （E） with two arene rings aligned in opposite side around the N＝N double bond is usually more stable than the cis isomer （Z）. The light-driven transcis isomerization allows the wide usage of azobenzene as the organic dyes, molecular switches, molecular shuttles, molecular motors, metal ion chelators, protein probes, rotors in photo regulation of biological molecules, or nanoscale optical storage device, etc.1Among these various materials, methyl red （MR） is a typical dye, which has three isomers with carboxylic acid anchoring in different positions （i.e., ortho-, meta-, and para-substituted phenyl rings）. Ortho-methyl red （o-MR） has been used in many fields such as the paper and textile industries, ink-jet printing, and acid-base indicators2.

o-MR works as a pH indicator in the range of 4.4–6.2, with a typical color change from yellow in basic or neutral solution to red in acidic solution. The acid dissociation constant （Ka） of the o-MR can be determined by a spectrophotometric method. Several experimental reports have been published on the Kaof equilibrium between dissociated and undissociated forms in the pH ranging from 2 to 8.3,4Until now, there are two kinds of models to derive pKavalues from UV/Vis absorption spectra （Fig.1）. In the earlier work done by Tobey3, the pKawas determined on the basis of monoacid model, assuming the neutral form （o-HMR）and the basic form （o-MR–） coexisted in o-MR aqueous solutions at various pH values （Fig.1（a）. Since then, this model has been widely used by many groups, and the pKavalue of o-MR in aqueous solution was measured to be 5.05 ± 0.05 in the temperature range of 298.15–303.15 K3. In the last decade, another form, positively charged o-H2MR+, was involved in binary acid model to determine pKa1of the equilibrium between o-H2MR+and o-HMR （Fig.1（b））. The pKa1of o-MR in aqueous solution was reported to be 2.10 ± 0.01 at room temperature4. The species involved in each acid-base equilibrium of o-MR in aqueous solution tend to be a resonance hybrid of a hydrogenbonded structure. It is hard to evaluate the effect of hydrogen bond on the pKavalues.

Despite the numerous experimental studies exploring the influence of pH values on UV/Vis spectra of o-MR in organic solvent-water mixtures, a complementary computational effort to model such influence is lacking. The effects of carboxylic group substitution and protonation on the structures and conformations of MR isomers have been studied by density functional theory （DFT） and time dependent DFT （TD-DFT） calculations5. Intramolecular hydrogen bond was found in the structure of neutral o-MR, whereas m- and p-MR cannot form intramolecular hydrogen bond6. The effect of pH values on the evolution of spectral features is correlated with the structural change of o-MR in aqueous solution by using semiempirical INDO/CIS-S （intermediate neglect of differential orbital/configuration interaction spectroscopic-Single excitation） calculations on a conformation ensemble taken from sequential Monte Carlo/quantum mechanical approach7. It is still difficult to make a quantitative interpretation of the acid-base behavior of o-MR solutions by using sophisticated ab initio electronic structure calculations.

This work was motivated by the questions of what is the relationship between red shifting of the spectra and pH decreasing of o-MR aqueous solution, and what is the influence of intramolecular or intermolecular hydrogen bonds on UV/Vis spectra.

Fig.1 Monoacid model and binary acid model of o-MR in acidbasic equilibrium

As a first step, the UV/Vis absorption spectra of o-MR aqueous solution were experimentally measured at a wide pH range. The previous experiments were mostly based on monoacid model, and the UV/Vis spectra of o-MR were repor-ted with a very limited range of pH from 2 to 8. Here to illustrate the contribution of the o-H2MR+to the spectra, the pH range was set to be 0.5–13.1. DFT calculations were then performed on diprotic form o-H2MR+, nonionic form o-HMR, and the basic form o-MR–, respectively. TD-DFT was employed to calculate the UV/Vis spectra of three forms of o-MR. According to the population of the three forms at various pH values, the spectra of o-MR with different pH values were simulated. Intramolecular hydrogen bond is found in the structure of o-HMR （neutral form） and diprotic form （o-H2MR+）, which can increase the planarity of conformation and hence contribute to the red shift in the absorption spectra. Both PCM and explicit solvent models are applied to study the solvent effects on electronic structures, especially the lowest dipole-allowed vertical excitation energy, similar to what has been done for the bithiophene derivatives8. The study of optical properties of azo dyes has potential impacts on the controllable fabrication of optoelectronic device, since the photoisomerization of o-MR on TiO2nanoparticles has been explored and applied to fabricate dye-sensitized solar cells9.

2 Experimental and computational details

2.1 Materials and measurements

The neutral form of o-MR was purchased from commercial sources and used without further purification. Other chemicals used in this study were reagent grade. A laboratory stock solution made by dissolving 1.86 × 10–2g of crystalline methyl red in 100 mL volumetric flask with distilled water. The standard solution of o-MR for use in the actual experiment is made by adding 5 mL stock solution and diluting to 50 mL with distilled water. The acidity of the test solutions was adjusted by adding an appropriate amount of solutions which were progressive diluted from HCl （1 mol·L–1）, so the concentrations of acid solutions were set to 10–1, 10–2, 10–3, 10–4, 10–5mol·L–1, respectively. The solution in acid conditions was prepared by diluting a mixture of 5 mL standard o-MR solution and 45 mL of various concentration of HCl solution to 50 mL. As for the base conditions, the same procedure was taken to adjust the pH values using 1 mol·L–1NaOH solution. The investigated pH fell into the range from 0.5 to 13.1. All pH measurements were made with a pB-10 digital pH meter （Sartorius, Germany） at room temperature. The UV/Vis spectra of o-MR aqueous solution at different pH values were recorded with a Shimadzu UV-3600 double-beam spectrophotometer using a quartz glass cell with a path length of 10 mm at room temperature. Several parallel and independent tests were carried out. All experimental spectra showed the same tendency that spectra of o-MR in acid condition were more red shifted comparing with the spectra in base condition. The color of o-MR aqueous solutions changed little after 48 h.

Recently, the UV/Vis spectra of m-MR were reported for more diluted aqueous solutions of 1.537 × 10–5mol·L–1at various acidities （pH = 2.51–7.27）10. Despite o-MR and m-MR had different carboxylic acid anchoring positions, the experimental UV/Vis absorption spectra exhibited the similar properties. In this work, we will use theoretical calculations to rationalize the change in spectra with various different pH values （0.5–13.1）.

2.2 Computational details

All calculations were performed using the Gussian09 program11. The structures of three different forms of o-MR with and without the presence of water solvent molecules were optimized using the DFT method at the 6-31+G（d） basis set.

The azobenzene derivatives have two geometric isomers（Z/E） with two arene rings aligned in two different orientations around the N＝N double bond. In general, the trans isomer of an azobenzene derivative is known to have a nearly coplanar structure of two phenyl rings and the azo group. In the cis isomer, however, the two phenyl rings are twisted out of plane of the azo group due to the steric hindrance between phenyl hydrogen. We investigated the possible conformers of the cis and trans isomers of o-MR with and without intramolecular hydrogen bond between the carboxylic hydrogen and the azo nitrogen. Fig.2 showed the DFT optimized geometries of trans and cis isomers and the energy difference relative to o-HMR-transa conformation. Conformers with intramolecular hydrogen bond are expected to be more stable than the ones without intramolecular hydrogen bond. The conformers of both o-HMR-trans-a and o-HMR-cis-a had intramolecular hydrogen bond, which were described by the interatomic distance （rN…H） and the bond angle of O1－H1…N1（∠O－H…N） in Table 1. o-HMR-trans-a is highly stabilized by an intramolecular hydrogen bond with the six membered ring conformation. The N1…H1distance is predicted to be 0.172 nm and the O1－H1…N1angle is 151° at B3LYP/6-31+G（d） level in gas phase.

Fig.2 Optimized structures of o-HMR isomers and energy differences relative to the most stable o-HMR-trans-a conformation

The influence of the 6-31+G（d,p） basis set on the description of intramolecular hydrogen bond was also tested. The B3LYP/6-31+G（d,p） calculation of the most stable o-HMR-trans-a conformer shows little difference in skeleton structure but stronger intramolecular hydrogen bond （rN…H= 0.169 nm；∠O－H…N = 152°） than that predicted by using 6-31+G（d）basis set. The B3LYP/6-31+G（d） calculation on cis isomer, o-HMR-cis-a, suggests a weak intramolecular hydrogen bond（rN…H= 0.176 nm； ∠O－H…N = 145°）. This result is in agreement with the previous calculated results （rN…H= 0.170 nm,∠O－H…N = 153°）5at the B3LYP/6-31+G（d,p） level. But the early theoretical predictions by HF/6-31G* with GAMESS software showed a much weaker hydrogen bonding （trans: rN…H= 0.1831 nm； cis: rN…H= 0.1916 nm）12between the carboxylic hydrogen and the azo nitrogen.

From Table 1, one can find that the bond length of the azo group （－N＝N－） and the angle between the two arene rings changed little upon conformational changing from o-HMR-trans to o-HMR-cis, while the dihedral angel θ2（C8－N2＝N1－C6） changed dramatically from 180° to 13° upon trans-to-cis isomerization. In trans isomers, o-HMR-trans-a is the lowest energy conformer, the calculated relative energies of o-HMR-trans-b and o-HMR-trans-c with respect to o-HMR-trans-a are 22.2 and 23.0 kJ·mol–1, respectively. The cis isomers are less stable than the trans ones with the calculated relative energies of o-HMR-cis-a and o-HMR-cis-b with respect to o-HMR-trans-a being 68.2 and 79.1 kJ·mol–1, respectively. In the following subsections, we will concentrate on the electronic structures of trans conformations.

In addition, the comparison between different DFT functionals was made on the following characteristic parameters: the bond lengths of C8－N2（r1）, N1＝N2（r2）, and N1－C6（r3）, the dihedral angles of C9＝C8－N2＝N1（θ1）, C8－N2＝N1－C6（θ2）and N2＝N1－C6＝C1（θ3）, the hydrogen bond distance between H1and N1, and the angle O1－H1…N1, as shown in Table 1. It can be seen that different DFT functionals had little influence on the selected structural parameters of o-HMR-trans-a conformation.

To simulate the UV/Vis spectra of o-MR aqueous solution at different pH conditions, time dependent density functional theory （TD-DFT） is used to calculate the low-lying excitation energies of the dipole-allowed transitions for the different forms of o-MR. The spectra calculated with different DFT functionals in gas phase and polarized continuum model （PCM） were shown in Fig.3. Despite the influence of the choice of different DFT functionals on geometry structures was negligible, different functionals gave different predictions on UV/Vis spectra for o-HMR-trans-a conformation. All the selected functionals are typical hybrid functionals with the difference between each other mainly lying in the percentage of exact exchange （B3LYP: 20%； CAM-B3LYP: 19%–65%； wB97XD: 22.2%–100%；M06-2X: 54%； LC-wPBE: 0–100%）. Among them, CAMB3LYP, wB97XD, and LC-wPBE are range separated hybrids that include an increasing fraction of exact exchange when the interelectronic distance increases. It was demonstrated that increasing the amount of exact exchange included in the exchange correlation functional tends to increase the predicted transition energies13. M06-2X including larger amounts of exact exchange （54%） provide a more localized description of the excited state, and subsequently larger transition energies. Range separated hybrids （CAM-B3LYP, wB97XD, and LC-wPBE）with high percentage of long range exact exchange may also overestimate the transition energy. In the following TD-DFTcalculations, the B3LYP with the percentage of 20% exact exchange will be employed.

Fig.3 Calculated UV/Vis absorption spectra of o-HMR using B3LYP，CAM-B3LYP， LC-wPBE， wB97XD， M062X in gas phase and in PCM model， in comparison with experimental result at pH = 2.9 with the concentration of 0.069 mmol·L-1

In comparison with the calculated spectra in gas phase, the spectra calculated in PCM model （dieletric constant ε = 78.3）were closer to the experimental results for all the selected DFT functionals. In Fig.3, we take the experimental spectrum at pH = 2.9 to make a comparison with the calculated results, because the neutral o-HMR is a dominant species with the percentage, δ（o-HMR）, of 86% in solutions. The details will be given in the subsection 3.4, and all the calculated spectra are presented in the original form without any scaling fit to experiments. It will be shown that the solvent effect on the calculated UV/Vis spectra is significant because the o-HMR is polarized by the－N（CH3）2and －COOH substituents lying at the two ends of π-conjugated system, resulting in stronger intramolecular charge transfer and large dipole moment. To test the influence of the intermolecular hydrogen bonding interactions on the spectra of o-MR with different pH values of solutions, the explicit water cluster model is also adopted in this work. Therefore, both two kinds of solvent models, PCM and explicit solvent cluster models are used to model the absorption spectra of the o-H2MR+, o-HMR, o-MR–in aqueous solutions within the framework of TD-DFT. The calculation results will provide useful information to understand the red-shift in UV/Vis spectra with the decrease of pH values.

3 Results and discussion

3.1 Experimental UV/Vis spectra of o-HMR in aqueous solutions at different pH values

In the earlier study of the solution of 0.74 mmol·L–1o-MR ethanol-water mixtures, their pH values were adjusted by HOAc-NaAc buffer system range from 2 to 8.3In the work of Drummond4, the pKabetween o-HMR and o-H2MR+was also determined by spectrographic technique. The investigation of spectra in previous two works focused on the determination of pKavalues in acid-base equilibrium, and the studied UV/Vis spectra of o-MR solutions were reported with a very limited pH range. In this work, we take three forms of o-MR （o-H2MR+, o-HMR, o-MR–） into consideration. The pH values of the investigated solutions fall into range from 0.5 to 13.1, much wider than the previous work. As shown in Fig.1 the o-H2MR+form can be involved in the acid-base equilibria of o-MR aqueous solutions in strong acid conditions.

The experimental UV/Vis absorption spectra of 0.069 mmol·L–1o-MR aqueous solutions at various pH values （from 1.2 to 13.1） were measured at 300–600 nm intervals, with the results shown in Fig.4（a）. As displayed in Fig.4, o-MR aqueous solutions with different pH values exhibited different colors. When the pH of the solutions is lower than 2.9, the dye presented red color. The solution color changed to orange around pH = 5.3, and then yellow in the pH range from 6.8 to 13.1. In the pH range from 1.2 to 2.9, an obvious absorption peak around 520 nm could be obtained. The absorption intensity at 520 nm decrease with the increase of pH values, and the peak of 520 nm almost disappeared when the pH of the solution was around 5.3. In the higher pH solution, an absorption peak at shorter wavelength around 430 nm appeared and the absorption peak at 430 nm obviously increased from pH = 7.2 to pH = 13.1. Fig.4（b） shows the spectra of o-MR with a different concentration, i.e., Co-MR= 0.072 mmol·L–1. The similar trend of red-shift of maximum absorption band upon the pH decreasing was also demonstrated in the measurement with a higher solution concentration.

According to the monoacid model, the two absorption peaks observed in the experimental spectra were usually ascribed tothe absorption maxima of the acid and basic forms of o-MR of 520 nm and 428 nm, respectively. It will be shown in subsection 3.4 that the maxima absorption bands of diprotic o-H2MR+and nonionic o-HMR forms in the binary acid model are close to each other and merged together into a broad band around 520 nm.

Fig.4 Experimental UV/Vis spectra of （a） 0.069 mmol·L-1and （b） 0.072 mmol·L-1o-MR solutions at different pH conditions

In order to understand the influence of different pH values on UV/Vis absorption spectra, we carried out a series of DFT calculations on the electronic structures of different forms of o-MR with and without the consideration of solvent effect.

3.2 Nonionic o-MR: the role of intramolecular hydrogen bond

Hydrogen bonding plays an important role in a variety of physicochemical phenomena. It was worthwhile to mention that intramolecular O－H…N hydrogen bond was formed in o-HMR-trans-a conformation, and the conformations of o-HMR-trans-b and o-HMR-trans-c did not have such an intramolecular hydrogen bond. The conformational stability of o-HMR-trans-a can be understood in terms of molecular structure, in particular the intramolecular hydrogen bond. We then calculated the UV/Vis spectra of the three conformations, respectively. The calculated UV/Vis spectra of o-HMR-trans-a conformation were more red shifted than the conformations without intramolecular hydrogen bond （Fig.5）. What made such a difference Conformers of the trans isomer have a nearly planar structure, with only a small distortion to reduce the electron repulsion between the carboxylic group and the azo group. In the selected three conformations, the intramolecular hydrogen bond of o-HMR allows all the non-hydrogen atoms of o-HMR-trans-a （except the N-substituted tails） to be essentially coplanar. But the other two conformations, o-HMR-trans-b and o-HMR-trans-c, are out of planarity with the dihedral angel θ2and θ3aparting from the 180° （Table 1）. Therefore, intramolecular hydrogen bond can increase the planarity of πconjugated conformation, leading to the red shift in the absorption spectra.

In certain circumstances, however, intermolecular hydrogen bond formed in the solute-solvent interactions, and the interplay between intramolecular and intermolecular hydrogen bonding interactions may also affect the absorption spectra, which will be addressed in the following subsection.

3.3 Protonated and deprotonated forms of o-MR

The red color of o-MR solution was usually associated with the protonated o-H2MR+, the orange was from neutral o-HMR, the yellow was from deprotonated o-MR–. The alterations of the conjugation of the whole D-π-A system of o-MR were considered as the main reason for the color change at different pH values, corresponding to the reversible equilibrium between protonation and deprotonation processes.

Fig.5 Calculated UV/Vis absorption spectra of different isomers o-HMR-trans with and without intramolecular hydrogen bond using TDDFT with （a） CAM-B3LYP and （b） B3LYP functionals

Fig.6 depicts the optimized geometry and dipole moment of the three forms of o-MR （i.e., o-H2MR+, o-HMR, and o-MR–） at both 6-31+G（d） and 6-31+G（d,p） levels. As mentioned before,the more sophisticated basis set like 6-31+G（d,p） did not cause much changes in the optimized geometry. As expected, the πconjugated systems of o-MR are polarized by the donor （D） and acceptor （A） substituents, resulting in non-zero dipole moment. Such a D-π-A compound may be described as a resonant form between a neutral from and a charge-separated form. This phenomenon has been found in the other D-π-A systems.8,14,15The azo N－N bonds in all the three structures （o-H2MR+: 0.129 nm； o-HMR: 0.127 nm； o-MR–: 0.126 nm） calculated at B3LYP/6-31+G（d） level are observed to be longer than that of typical Car－N＝N－Carbonds （0.1255 nm）16. The N2－C8linkage bonds are short than the typical Nazo－Carbond length value（0.1431 nm）16. The o-H2MR+exhibits an obvious quinoid structure. The side view of all o-MR species show that all structures exhibit planarity except o-MR–in gas phase. Our recent research indicated that planar conformation can cause red-shift of UV/Vis spectra for oligofluorenes17. Here, we will also show that the enhanced planarity of diprotic o-H2MR+rationalize the red shift of absorption spectra as pH decreases. The coplanar structure of the phenyl rings and the azo group is expected to be favorable for the internal hydrogen bonding formation of o-MR via six membered ring conformation. The internal hydrogen bonding in the trans form of o-MR would be stronger, which in turn weakens the external hydrogen bonding with solvent water molecules. In addition, three forms of o-MR, o-H2MR+, o-HMR, o-MR–, present different magnitudes of dipole moment both in gas phase and PCM model, implying the different polarity of different form.

Fig.6 Optimized geometry of o-MR species at B3LYP/6-31+G（d） level and the dipole moment in （a） gas phase and （b） PCM model

Fig.7 Optimized geometry of o-H2MR+， o-HMR， o-MR-with （a） 1H2O and （b） 2H2O cluster models

In addition, the water cluster model was introduced to investigate the intermolecular interactions between solute and water solvents. In the previous work of Costa et al.7the micro shell of the basic form （o-MR–） starting at 0.12 nm and has a peak at 0.17 nm and finishes at 0.20 nm. The micro shell of neutral form （o-HMR） starting at 0.14 nm and has a peak at 0.17 nm and finishes at 0.19 nm7. Accordingly, we take one or two water molecules into consideration, respectively. The results are shown in Fig.7, indicating that the intermolecular hydrogen bond affects the spectra of o-MR species, especially the basic form o-MR–. The electrostatic potential （ESP） images shown in Fig.8 give the hint of the favorable attacking mode of the water solvents to the polar groups of the o-MR at different pH conditions. The accumulation of water molecules is expected around carboxylic group, which is capable to form hydrogen bonds between the solute and solvent. The optimized geometry of o-MR species with one water （1H2O） and two water （2H2O） sys-tems are shown in Figs.7（a） and 7（b） in gas phase and PCM model, respectively. In gas phase, the intramolecular hydrogen bond of o-H2MR+has been weakened by the intermolecular hydrogen bond, while in o-HMR system just the opposite trend to that of o-H2MR+systems. In 1H2O model of o-H2MR+and o-MR–, there are two intermolecular hydrogen bonds formed between O and H atom. In the other systems only one intermolecular hydrogen bond formed between solute and water molecule. In 2H2O model, hydrogen bond network formed in all three forms of o-MR. The enhancement of intramolecular hydrogen bond is observed with the addition of water solvent molecule both in gas phase and PCM model. But both the intermolecular and intramolecular interactions are strengthened in PCM model compared to those in gas phase. In o-H2MR+with 1H2O or with 2H2O system, the position of water within PCM model was closer to the carboxyl group than the ones in gas phase. Again, the employment of 6-31+G（d,p） basis set gave similar results to those obtained by 6-31+G（d） basis set （Fig.7）.

From Fig.8 one can see that the positive charge of o-H2MR+is delocalized among the whole structure, the negative charge of o-MR–is mainly localized in –COO–group. The O atom of water molecule was positioned towards the H atom of carboxylic group in o-H2MR++ 1H2O system. And the H atom of water was positioned toward the O atom of carboxylic group in o-HMR + 1H2O and o-MR–+ 1H2O system. Such intermolecular and intramolecular hydrogen bonds may have some effects on UV/Vis spectra, which will be discussed later.

Fig.8 Optimized electrostatic potential （ESP） of o-MR species with and without the presence of solvent molecules

Fig.9 Distribution coefficient δ of o-H2MR+， o-HMR， o-MR-at different pH values

Fig.10 Simulated UV/Vis spectra based on the populations of o-H2MR+， o-HMR， o-MR-in various solutions at B3LYP/6-31+G（d） level with PCM model

3.4 Simulated UV/Vis spectra at different pH conditions

The o-MR aqueous solution is taken as a mixture of o-H2MR+, o-HMR, o-MR–with different populations. According to acid base equilibrium, the distribution coefficient, δ of o-H2MR+, o-HMR and o-MR–at different pH values can be estimated by formula （1）–（3）.

where Co-MRis the concentration of o-MR solution, and ［o-H2MR+］, ［o-HMR］ and ［o-MR–］ are the concentrations of three forms, respectively. The distribution coefficients of o-H2MR+, o-HMR, o-MR–were calculated by pH and pKaof o-MR （pKa1= 2.1, pKa2= 5.05）. The distribution diagram of the three forms of MR in aqueous solutions was constructed in Fig.9. It indicates that the fraction of neutral form （o-HMR） is always less than one at any pH value. It was found that o-MR is completely in the basic form （o-MR–） at pH > 8. The protonated form （o-H2MR+） is dominated at pH = 0. The neutral form （o-HMR） has a maximum fraction of 0.94 at pH = 3.6. Therefore, we cannot directly compare our calculated spectra of o-MR with the experimental spectra.

In order to simulate the variation of UV/Vis spectra of o-MR at various pH values, the populations （shown in Table 2） of three species of o-MR at certain pH values were used as the weights to assemble the calculated UV/Vis spectra at B3LYP/6-31+G（d） level within the framework of PCM. Shown in Fig.10 are the simulated UV/Vis spectra of o-MR at pH values ranging from 1.2 to 9.4. The simulated spectra show the same trend as the experimental spectra （Fig.4）. Although we considered the contributions of three forms （o-H2MR+, o-HMR, o-MR–） in the simulation of UV/Vis spectra of o-MR aqueous solutions, the maximum absorption bands of o-H2MR+and o-HMR were quite close to each other with almost the same intensity （Fig.11）. So the broad band at 520 nm in the experimental spectra may come from the overlapping of o-H2MR+and o-HMR absorption peaks.

Table 2 Calculated percentage of o-MR species at various pH values according to the formula （1）-（3）

Fig.11 Calculated UV/Vis spectra of three forms of o-MR using TD-DFT with B3LYP/6-31+G（d） in gas phase or in PCM model with and without the presence of solvent molecules

To test the solvent effects on the absorption spectra, we compare the TD-DFT results of three different forms, o-H2MR+（strong acid condition）, o-HMR （weak acid condition）, and o-MR–（basic condition） in both gas phase and PCM model, with and without the presence of the solvent molecules. The absorption spectra of basic o-MR–form are very sensitive to the pres-ence of water solvent molecules. The solute-solvent interaction makes the o-MR–spectra red-shift, especially in gas phase model.

In order to better understand nature of the transitions observed in spectra, the contours of the molecular orbitals （MOs）involved in the low-energy electronic transitions are shown in Fig.12. Both of the maximum absorption wavelength （λmax） of o-H2MR+, and o-HMR are featured almost exclusively HOMO → LUMO transitions, being characterized as the π →π* type. The energy gap between HOMO and LUMO of o-H2MR+is 2.67 eV, smaller than the other two species （o-HMR: 3.06 eV； o-MR–: 4.03 eV）. The calculated band gap with PCM model （in Fig.12 bracket） shows the same trend with the calculation in gas phase. In the water cluster model, the charge transfer between water molecule and o-H2MR+or o-HMR species is not obvious, while it is clear in o-MR–system. We notice that the discrepancy of spectra between o-MR–and o-HMR in PCM model is smaller than that in gas phase （Fig.12）.

Values in parentheses denote the band gap calculated with PCM model.

Although we introduced the two explicit water molecules in the solvent cluster model to simulate the UV/Vis spectra, the calculated results just qualitatively reproduced the experimental spectra. In fact, the larger cluster models are required to give better agreement with experiments. It seems that some portions of the short-ranged solute and solvent hydrogen bonding interactions are considered in the explicit solvent models. But the long-ranged electrostatics interactions in aqueous solutions failed to be covered by a limited number of solvent molecules in the present cluster model. In this case, the embedding of the explicit cluster models into the PCM is a comprise to take into account of both short and long ranged solvent–solute interactions, as shown in Fig.11（b）.

4 Conclusions

In this work, pH-dependence of optical property of o-MR has been studied both experimentally and theoretically. When the pH of o-MR decreased from 13.1 to 0.5, the maximum of the UV/Vis absorption spectra red shifted from 430 nm to 520 nm. Three main forms of o-MR （o-H2MR+, o-HMR, and o-MR–） coexisted in o-MR aqueous solutions at various pH values. The intramolecular hydrogen bond is found in trans forms of o-H2MR+and o-HMR, leading to the enhancement of π-conjugation and contributing to the red shift of spectra. Significant solvent effect occurs on the calculated UV/Vis spectra of o-MR–（under basic conditions）, as demonstrated by the calculations employing both PCM and explicit water cluster model. The polarity of o-HMR and o-MR–are stronger than that of o-H2MR+. Thus strong dipole–dipole interactions between o-MR species and solvent water molecule may also contribute to the red shift of the spectra. The understanding of the factors that affect the optical properties of o-MR may provide useful information to explore the wide usage of azo dyes in fabrications of optoelectronic device.

（1）Merino, E.； Ribagorda, M. Beilstein J. Org. Chem. 2012， 8, 1071. doi: 10.3762/bjoc.8.119

（2）Sahoo, C.； Gupta, A. K.； Pal, A. Desalination 2005， 181, 91. doi: 10.1016/j.desal.2005.02.014

（3）Tobey, S. W. J. Chem. Educ. 1958， 35, 514. doi: 10.1021/ed035p514

（4）Drummond, C. J.； Grieser, F.； Healy, T. W. J. Chem. Soc., Faraday Trans. 1989， 85, 561. doi: 10.1039/f19898500561

（5）Zhang, L.； Cole, J. M.； Waddell, P. G； Low, K. S.； Liu, X. G. ACS Sustain. Chem. Eng. 2013， 1, 1440. doi: 10.1021/sc400183t

（6）Wong, J. H.； Lee, S. Physica B 2012， 407, 232. doi: 10.1016/j.physb.2011.10.036

（7）Costa, S. C. S.； Gester, R. M.； Guimar?es, J. R.； Amazonas, J. G.；Nero, J. D.； Silva, S. B. C.； Galembeck, A. Opt Mater. 2008， 30 , 1432. doi: 10.1016/j.optmat.2007.08.008

（8）Meng, S. C.； Ma, J. J. Phys. Chem. B 2008， 112, 4313. doi: 10.1021/jp710456p

（9）Zhang, L.； Cole, J. M. Appl. Mater. Interface 2014， 6, 3742. doi: 10.1021/am500308d

（10）Khouri, S. I. J.； Abdel-Rahim, I. A.； Alshamaileh, E. M.；Altwaiq, A. M. J. Solution Chem. 2013， 42, 1844. doi: 10.1007/s10953-013-0068-9

（11）Frisch, M. J.； Trucks, G. W.； Schlegel, H. B.； et al. Gaussian 09, Revision B.01； Gaussian Inc.: Wallingford, CT, 2010

（12）Park, H. S.； Oh, K. S.； Kim, K. S.； Chang, T. J. Phys. Chem. B 1999， 103, 2355. doi: 10.1021/jp9838442

（13）Laurent, A. D.； Jacquemin, D. Int. J. Quantum Chem. 2013， 113, 2019. doi: 10.1002/qua.24438

（14）Giustetto, R.； Seenivasan, K.； Pellerej, D.； Ricchiardi, G.；Bordiga, S. Microporous and Mesoporous Materials 2012， 15, 167. doi: 10.1016/j.micromeso.2012.01.024

（15）Benedict, J. B.； Cohen, D. E.； Lovell, S.； Rohl, A. L.； Kahr, B. J. Am. Chem. Soc. 2006， 128, 5548. doi: 10.1021/ja0601181

（16）Allen, F. H.； Watson, D. G.； Brammer, L.； Orpen, A. G.； Taylor, R. Typical Interatomic Distances: Organic Compounds. In International Tables for Crystallography； International Union of Crystallography: Chester, England, 2006； Vol. A, pp 790–811.

（17）Yuan, X. A.； Zhang, W. W.； Xie, L. H.； Ma, J.； Huang, W.； Liu, W. J. J. Phys. Chem. B 2015， 119, 10316.

Rationalization of pH-Dependent Absorption Spectrum of o-Methyl Red in Aqueous Solutions: TD-DFT Calculation and Experiment Study

ZHENG Dong YUAN Xiang-Ai MA Jing*
（Institute of Theoretical and Computational Chemistry, School of Chemistry and Chemical Engineering, Nanjing University, Nanjing 210046, P. R. China）

The understanding of factors that affect the optical properties of azo dyes sheds insight to the design of noνel optoelectronic deνices. The effect of the acidity or alkalinity and the solνent on the absorption spectra of ortho-methyl red （o-MR） aqueous solutions was inνestigated using UV/Vis experiments and density functional theory （DFT） calculations. The spectra of o-MR aqueous solutions showed a red shift of the maximum absorption peak from 430 nm to 520 nm when the pH of the solution was decreased from 13.1 to 0.5. In νarious acidity or alkalinity conditions, three main forms of o-MR coexisted in the aqueous solutions, i.e., diprotic o-H2MR+（strong acid condition）, nonionic o-HMR （weak acid condition）, and o-MR–（basic condition）, whose electronic structures were studied by DFT. The lowest dipole-allowed excitation energies of o-MR in aqueous solutions haνe been estimated by performing timedependent density functional theory （TD-DFT） calculations. Both polarized continuum model （PCM） and explicit water cluster model were applied to study the solνent effects on the electronic structures and calculated spectra. The intramolecular hydrogen bond increases the planarity of o-H2MR+and o-HMR, leading to the enhancement of π-conjugation and, hence, a red shift in the spectra. Significant solνenteffects on the calculated UV/Vis spectra of o-MR–（under basic condition） were reνealed. Strong dipole–dipole interactions between the polar o-MR–and solνent water molecules may contribute to the red shift in the spectra.

o-Methyl red; UV/Vis spectrum; pH; Hydrogen bond; Solνent effect; DFT; TD-DFT

O641

10.3866/PKU.WHXB201512072

Received: October 14, 2015； Revised: December 6, 2015； Published on Web: December 7, 2015.

*Corresponding author. Email: majing@nju.edu.cn； Tel: +86-25-83597408.

The project was supported by the National Natural Science Foundation of China （21290192, 21273102）.

國(guó)家自然科學(xué)基金（21290192, 21273102）資助項(xiàng)目

?Editorial office of Acta Physico-Chimica Sinica