Origin of the Absorption Band of Bromophenol Blue in Acidic and

Publication Date (Web): August 24, 2016. Copyright © 2016 American Chemical Society. *E-mail: [email protected]. Phone: 0046 8 55378418...
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Origin of the Absorption Band of Bromophenol Blue in Acidic and Basic pH: Insight from a Combined Molecular Dynamics and TD-DFT/ MM Study M. Chattopadhyaya,† N. Arul Murugan,† and Zilvinas Rinkevicius*,†,‡ †

Division of Theoretical Chemistry & Biology, School of Biotechnology, KTH Royal Institute of Technology, SE-106 91 Stockholm, Sweden ‡ Swedish e-Science Research Center (SeRC), KTH Royal Institute of Technology, SE-100 44 Stockholm, Sweden S Supporting Information *

ABSTRACT: We study the linear and nonlinear optical properties of a wellknown acid−base indicator, bromophenol blue (BPB), in aqueous solution by employing static and integrated approaches. In the static approach, optical properties have been calculated using time-dependent density functional theory (TD-DFT) on the fully relaxed geometries of the neutral and different unprotonated forms of BPB. Moreover, both closed and open forms of BPB were considered. In the integrated approach, the optical properties have been computed over many snapshots extracted from molecular dynamics simulation using a hybrid time-dependent density functional theory/molecular mechanics approach. The static approach suggests closed neutral ⇒ anionic interconversion as the dominant mechanism for the red shift in the absorption spectra of BPB due to a change from acidic to basic pH. It is found by employing an integrated approach that the two interconversions, namely open neutral ⇒ anionic and open neutral ⇒ dianionic, can contribute to the pHdependent shift in the absorption spectra of BPB. Even though both static and integrated approaches reproduce the pHdependent red shift in the absorption spectra of BPB, the latter one is suitable to determine both the spectra and spectral broadening. Finally, the computed static first hyperpolarizability for various protonated and deprotonated forms of BPB reveals that this molecule can be used as a nonlinear optical probe for pH sensing in addition to its highly exploited use as an optical probe.

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((TD-)DFT/MM) are the popular hybrid approaches2,3 that are routinely used to model the structure and response properties of molecules in homogeneous or heterogeneous environments, respectively. Depending upon whether the MM subsystem is polarizable or not, the schemes that describe the subsystem interactions are referred to as electrostatic embedding or polarizable electrostatic embedding. One can also combine these hybrid approaches with routine sampling approaches such as Monte Carlo and molecular dynamics to obtain a so-called integrated approach1−6 to model the structure and spectroscopic properties of molecules under ambient temperature and pressure. There exist many studies1−9 that test the performance of integrated approaches in modeling the electronic and magnetic properties of molecules in solvent and biostructure environments, and usually these methods fairly well capture the effect of the environment and the response of the material to specific environmental parameters. In the current work we study bromophenol blue, a popular pH

INTRODUCTION There is growing interest in the preparation and characterization of smart materials which are responsive to light, heat, pressure, and pH, since they have a wider range of applications in the health-care, clean environment, water treatment, and energy sectors. A careful investigation based on first principle theory to understand how do these materials respond to any thermodynamic condition or external fields will provide useful insight on designing novel materials for specific applications in health-care and technology. It is necessary to have a simple and optimal model that fairly mimics the system and accounts for all the effects to get insight into the stimuli responsive behavior of the system. Thanks to the development of hybrid approaches,1−3 which combine quantum and classical descriptions of the system, it is possible to study extended systems such as solute−solvent systems or molecules in heterogeneous environments. The hybrid approach allows dividing the total system into subsystems where a part of the system is described more accurately while the rest of the system is described in a coarse way. The interactions between the subsystems are described using an effective Hamiltonian. The time-independent and time-dependent density functional theory/molecular mechanics © 2016 American Chemical Society

Received: July 29, 2016 Revised: August 23, 2016 Published: August 24, 2016 7175

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C−O linkage, the BPB molecule can exist both in closed (sp3 hybridized state of the central C atom) and open (sp2 hybridized state of the central C atom) forms (refer to Figure 1). Overall, six different molecular forms of BPB were

indicator in water solvent, to understand the mechanism behind its pH sensing ability.10−13 The usual mechanism attributed to the functioning of an optical pH sensor14−17 is that it has a different optical response (absorption or emission maximum or fluorescence intensity) for different pH values. At the molecular level the change in pH leads to a change in the population of different protonated forms which are known to have characteristic absorption or fluorescence spectra. The probe molecule can exist in different protonated forms, namely neutral, zwitterionic, cationic, anionic, and dianionic forms, and it is often unknown which specific forms of this probe are responsible for the optical behavior in a given pH range. It is worth recalling that the pHdependent optical behavior of deGFP1 protein18 has been proposed due to a change in the relative population of the neutral and anionic forms of its chromophores. Herein, we aim to understand the optical behavior of a wellknown pH indicator, bromophenol blue (3′,3″,5′,5″-tetrabromophenolsulfonaphthalein) (BPB)10−13 and attempt to find out which particular forms of this molecule are responsible for its absorption spectra obtained at low and high pH. Also, by calculating the first hyperpolarizability of the aforesaid molecule, we will comment on its pH-dependent nonlinear optical behavior as well. Experimentally, BPB10−13 has been studied extensively in buffers of varying pH and it has been found that it can change its characteristic spectra within the narrow pH range 3.0−4.6. It is yellow at pH 3.0 and changes to purple at pH 4.6 and does not show any characteristic color change beyond this limit. At low pH, it strongly absorbs in the UV-blue region and appears as yellow, whereas, at high pH, it absorbs in the red region and emits at blue. In this context, Henari et al.13 have recently measured the absorption of BPB at different pH values, ranging from 2.0 to 9.0, and found two characteristic peaks at 453 and 591 nm, respectively. The peak at 453 nm corresponds to lower pH, and the intensity of this peak decreases by increasing the pH of the solution while a new peak appears at 591 nm at higher pH, and the intensity of this peak increases with increasing pH of the solution. The same author12 also measured the nonlinear absorption coefficient and nonlinear refractive index of BPB by using a continuous wave laser of 488 and 514 nm and reported that it has reverse saturation absorption and self-defocusing property. In another work Wei et al.10 have investigated the interaction of BPB with bovine serum albumin and γ-globulin in acidic solution. Also, Ferreira et al.19 in another work developed pH sensitive materials using polypyrrole film doped with BPB. It is noteworthy that some properties of BPB10−13 have been investigated by several groups so far but none of them have focused on exploring those properties correlating with the different structural forms of BPB or as a function of pH. The pH effect on the structure is usually modeled using differently protonated molecular forms.20 The molecular form that is stable or dominates the population in the given pH range is responsible for the observed properties in that pH range. Recently, the integrated approaches are becoming increasingly popular and are shown to be successful in modeling the linear, nonlinear, and magnetic properties of molecules at finite temperature in the presence of solvent.1,2,4−6 In the current study, we have adopted such an approach to study the structure and optical properties of different protonated forms of BPB. There are two hydroxyl groups in BPB,10−13 and it can exist in three different possible forms, namely, neutral, anionic, and dianionic. It is worth mentioning here that depending on the

Figure 1. Schematic representations of (a) closed and (b) open forms of BPB. The color schemes for different types of atoms are as below: Red for oxygen, yellow for sulfur, cyan for carbon, maroon for bromine, and white for hydrogen.

considered for computing the one-photon absorption (OPA) properties within the static approach. However, due to the computational demand posed by the integrated approach, this set of calculations were carried out only for the most relevant forms, namely, closed neutral, open neutral (refer to Figure 1), open anionic, and open dianionic forms (refer to Figure 2) of

Figure 2. Schematic representation of (a) anionic and (b) dianionic forms of BPB. The coloring schemes for different types of atoms are as below: Red for oxygen, yellow for sulfur, cyan for carbon, maroon for bromine, and white for hydrogen.

BPB. Moreover, the open anionic and open dianionic forms were found to be stable by 10.4 and 17.6 kcal/mol when compared to the closed forms (computed with PCM description for water solvent), which suggests that these open molecular forms are of importance. Within the integrated approach, we employed a molecular dynamics (MD) for structure modeling and TD-DFT/MM approach for modeling the optical properties of BPB. With the set of calculations including solvents explicitly, we here intend to address the question: How the one-photon absorption property of different forms of BPB is altered in the presence of a protic solvent such as water. In other words, the change in absorption properties can be attributed either to the difference in the molecular forms in terms of their protonation states or to the relative stabilization of ground states of different forms due to solvation. Naturally, the charged forms are more stabilized due to solvation by polar solvent than their neutral counterparts. It can be proposed that the protonated forms dominate 7176

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limitations29 of the PCM model21 while describing the hydrogen bonding and charge transfer interactions between solute and polar solvent molecules. One should also note that the static approach discards the contributions from solute vibrations, flexibility in solvent degrees of freedom, and the finite temperature and pressure effects. Within this static approach, we have calculated the OPA parameters for the lowest six excited states of all different forms of BPB using both hybrid B3LYP30,31 and range separated CAM-B3LYP32 functionals (see Table 1) with the 6-311+G(d,p) basis set.33 In

the equilibrium at lower pH than the unprotonated forms. At higher pH rather, anionic and dianionic forms may dominate. We have computed the one-photon absorption (OPA) of different molecular forms of BPB in the presence of water solvent by employing both static and integrated approaches and then compared the absorption spectra from the experiments.13

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COMPUTATIONAL METHODS Herein, we briefly explain the details of excitation energy calculations by employing both static and integrated approaches.1,2,4−6 The latter one uses configurations for different forms of BPB in water solvent as obtained from molecular dynamics simulations. Molecular Dynamics Simulations. The molecular geometries of the neutral (both open and closed), anionic, and dianionic forms of BPB were optimized at the B3LYP/6311+G(d,p) level in the presence of water solvent using the polarizable continuum model (PCM)21 as implemented in Gaussian09.22 We have used the “United atom for Hartree− Fock” (UAHF) model23 to build the cavity and used the spheres, located on heavy elements of BPB molecule to construct the van der Waals (vdW) surface. The additional partial charges for the different protonated forms of BPB were obtained by fitting the molecular electrostatic potential (ESP) using the CHELPG procedure24 as implemented in Gaussian09.22 These ESP charges and the optimized molecular geometries of BPB were used as inputs for subsequent MD simulations. The MD simulations were carried out in an isothermal−isobaric (NPT) ensemble and within an orthorhombic simulation box of dimensions 74, 76, and 66 Å using the Amber1225 computational package. We have used the general amber force field26 for BPB and the TIP3P force field for water. Each of the different forms of BPB molecules were solvated by almost 12000 water solvent molecules, and neutralization (in the case of anionic and dianionic forms) was achieved by adding positively charged sodium ions. The simulations at ambient temperature and pressure followed a standard protocol where the first step was the minimization runs to remove any hot spot from the system, if present. Followed by the minimization run, we have carried out a molecular dynamics simulation in an isothermal−isobaric ensemble where the system temperature and pressure were controlled with a Langevin thermostat27 and a Berendsen barostat.28 The relaxation time of 2 ps and collision frequency of 1 ps−1 were used. The time scale chosen for integration of the equation of motion was 2 fs, and the equilibration runs were carried out until the density and energy of the solute− solvent system converged successfully. The total simulation time scale for the production run was approximately 10 ns. Finally, we have picked up 100 configurations at regular intervals from the trajectory corresponding to the production run to carry out the TD-DFT/MM calculation for subsequent optical property calculations. We would like to add that, independent of initial geometry, the structure and dynamics of the whole solute−solvent system are dictated by the employed force field. Absorption Spectra from a Static Approach. The Gaussian0922 optimized geometries of different forms of BPB10−13 were used to calculate the excitation energies using the TD-DFT method. Both the geometry optimization and excitation energy calculations have been done in water solvent, which is described using the PCM model21 as implemented in Gaussian09.22 It has been quite well-known that there are

Table 1. Excitation Wavelength and the Oscillator Strength for the Lowest Three Excited States of Neutral (for both closed and open forms), Anion, and Dianion BPB Computed Using Both B3LYP30,31 and CAM-B3LYP32 Functionals within the TD-DFT Level of Theory (static approach) Excitation wavelength in nm (oscillator strength in parentheses) BPB Closed-neutral Closed-anion Closed-dianion Open-neutral Open-anion Open-dianion Expt19

Functional

first

second

B3LYP 274 (0.02) CAM-B3LYP 252 (0.06) B3LYP 390 (0.01) CAM-B3LYP 297 (0.14) B3LYP 382 (0.02) CAM-B3LYP 295 (0.05) B3LYP 545 (0.01) CAM-B3LYP 426 (0.72) B3LYP 436 (0.73) CAM-B3LYP 392 (0.96) B3LYP 504(0.89) CAM-B3LYP 482 (1.03) first excited wavelength at pH = 2 453 nm

third

271 (0.02) 270 (0.01) 250 (0.05) 240 (0.00) 367 (0.04) 345 (0.04) 292 (0.01) 276 (0.08) 375 (0.01) 357 (0.02) 292 (0.05) 292 (0.09) 488 (0.02) 475 (0.45) 386 (0.11) 380 (0.03) 408 (0.01) 387 (0.01) 327 (0.01) 325 (0.00) 377(0.00) 374 (0.04) 313 (0.00) 311 (0.21) first excited wavelength at pH = 9 591 nm

addition, the full absorption spectra for all six molecular forms of BPB as obtained by convoluting the peaks corresponding to six low energy excitations are shown in Figure 3a and 3b, respectively. The broadening parameter used for each of the bands is set to the default value as in the Molden software.34 Absorption Spectra from a Dynamic Approach. In the next step we have carried out calculations for the important molecular forms of BPB by employing the linear response TDDFT/MM approach.3,35 Herein, we used 100 configurations for each form of BPB, which we picked up from MD simulations. Keeping in mind that it is optimal to include a limited number of solvent molecules in the MM region, we included around 400 water molecules as solvent, in particular those appearing within 15 Å distance from the center of mass of solute BPB. It is worth noting here that this approach treats the solute molecules by density functional theory and the solvent molecules by polarizable force-field, namely Åhlstrom,36 and an effective Hamiltonian is used to describe the interactions between QM and MM subsystems. Usually, van der Waals, electrostatic, and polarization interactions are included, and depending upon the property of interest, one or more terms can be added or removed in the Hamiltonian. The modeling of structural properties majorly require inclusion of van der Waals and electrostatic interactions37 while polarization interactions may not be dominantly contributing. However, when it comes to modeling the electronic properties using DFT/MM 7177

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Figure 4. Plot of one-photon absorption spectra for closed neutral, open neutral, anionic and dianionic forms of BPB. (a) Based on TDB3LYP level calculations on the coordinates of dye molecule only (b) Based on the TD-DFT/MM calculations with B3LYP functional carried out for BPB-solvent system where solvents are described as MM subsystem (c) Based on the TD-DFT/MM calculations with CAM-B3LYP functional carried out for BPB-solvent system where solvents are described as MM subsystem.

Figure 3. Absorption spectra of various forms of BPB obtained using the TD-DFT/PCM approach by employing the B3LYP and CAMB3LYP functionals with 6-311+G(d,p) basis sets. In particular, panel (a) refers to results from B3LYP and (b) refers to the CAM-B3LYP functional.

approaches, the van der Waals terms are excluded, as it is usually assumed that these interactions only contribute to the total energy and do not alter the electron density of the QM subsystem. Moreover, the DFT/MM implementation in Dalton38,39 uses two different schemes, namely electrostatic and polarizable electrostatic embedding.3,35 In the former one, only the QM subsystem is polarized by the charges of the MM environment while the latter accounts for mutual polarization of both QM and MM subsystems and requires a polarizable force-field to describe the MM subsystem. For this reason, we have employed the Åhlstrom force-field to describe water, which places charges and isotropic polarizability on each of its atomic sites. The excitation energies were calculated using the TD-DFT/MM approach by employing both B3LYP and CAMB3LYP functionals and the TZVP basis set40 for all atoms in the QM region. We have calculated the six lowest excitation energies of all different forms of BPB, both by explicitly including solvent molecules. One more set of calculations without including solvents but just using the geometry of the BPB dye from the molecular dynamics trajectory were carried out at the B3LYP/TZVP level. The absorption spectra obtained by convoluting all computed excitations have been presented in Figure 4. The broadening parameters used for each of the bands were based on the standard deviation values in excitation energies, and the approach is discussed in our earlier works.20,41 The standard deviation in excitation energies for each of the excitations was in the range 0.10−0.18 eV. Comparison between Figure 4a and 4b shows the importance of including the solvent contribution in determining the optical behavior of the BPB molecule while the comparison of Figure 4b and 4c shows the relative performance of the B3LYP and CAM-B3LYP functionals in reproducing the optical response of BPB dye. The average excitation energies as obtained from the TD-DFT/ MM approach corresponding to the bands associated with larger oscillator strengths are provided in Table 2. Hyperpolarizability Calculations Using Static and Dynamic Approaches. We have also computed the static hyperpolarizability for the aforementioned four important molecular forms of BPB using Gaussian09 software. The optimized molecular geometries in water solvent have been used in these calculations. We employed the B3LYP/6-

Table 2. One-Photon Absorption for the Lowest Three Excited States of Neutral (for both closed and open forms), Anion, and Dianion BPB Computed Using the TD-DFT/ MM Method within the Linear Response Approach and Considering MD Geometries (integrated approach)a Excitation wavelength in nm BPB Closed neutral Open neutral Anion Dianion Closed neutral Open neutral Anion Dianion

first

second

B3LYP functional 298 (0.02) 289 (0.02) 524 (0.19) 495 (0.18) 575 (0.45) 494 (0.04) 595 (0.53) 466 (0.04) CAM-B3LYP functional 256 (0.04) 253 (0.03) 492 (0.15) 462 (0.24) 523 (0.58) 397 (0.02) 547 (0.65) 385 (0.20)

third 282 465 446 436

(0.02) (0.08) (0.03) (0.12)

245 443 356 364

(0.03) (0.22) (0.07) (0.15)

a

The results for both B3LYP and CAM-B3LYP functionals are provided. The standard deviation values were in the range 0.10−0.18 eV. The standard errors are in the range 0.01−0.018, as there were 100 configurations used in the calculations.

311+G** level of theory with a solvent description using the polarizable continuum model to compute the first hyperpolarizability. Using 10 independent components (which is due to Kleinman symmetry42) of the first hyperpolarizability tensor, we have computed βtotal.43 Further, the average βtotal values for all the molecular forms were computed by using at least 30 configurations picked up from regular intervals of the molecular dynamics trajectory. The calculations were carried out by employing the quadratic response TD-DFT/MM approach as implemented in Dalton software. Similar to the case of one photon absorption calculations, the B3LYP/TZVP level of theory has been used. The βtotal values as obtained using the static approach and the average βtotal for the four molecular forms are given in Table 3. 7178

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hybridization states of the central C atom (which belongs to the benzothiazole moiety) in two different forms. Next, it also shows that all different forms of BPB within the CAM-B3LYP functional32 always absorb in the shorter wavelength region, showing a hypsochromic shift, whereas a bathochromic shift or absorption in the longer wavelength region is observed within the B3LYP30,31 functional. Table 1 also reveals that the absorption wavelengths associated with larger oscillator strength for the closed neutral, open neutral, anionic, and dianionic forms of BPB are 274, 475, 436, and 504 nm, respectively, obtained within the B3LYP30,31 functional. Likewise, the absorption wavelengths for the same as above but based on the CAM-B3LYP32 functional are 252, 426, 392, and 482 nm, respectively. A close inspection of the OPA values in Table 1 demonstrates red-shifted absorption maxima on going from closed neutral to open neutral, closed neutral to anion, closed neutral to dianion, and anion to dianion forms of BPB, although the blue-shifted absorption maxima has been observed on going from open neutral to anionic forms of BPB. Remarkably, we have observed the same trend within both B3LYP30,31 and CAM-B3LYP32 functionals. As we found that both B3LYP30,31 and CAM-B3LYP32 follow the same trend, so it can be concluded at this point that one can expect qualitatively similar performance by other DFT functionals. Thus, as experiment shows red-shifted absorption maxima (453 to 591 nm) on going from lower pH (where the protonated form of BPB exists, e.g. neutral one) to higher pH (from pH 2 to 9), we consider only those particular conversions which are associated with such a red shift. It is not at all hard to choose them from Table 1, and these are (i) closed neutral to anionic, (ii) closed neutral to dianionic, and (iii) open neutral to dianionic conversions which show red-shifted absorption maxima on going from lower to higher pH, as like in experiment. The red-shifted absorption maxima associated with these three interconversion processes of BPB are 163, 228, and 29 nm, respectively, within the B3LYP30,31 functional and 141, 226, and 55 nm, respectively, within the CAM-B3LYP32 functional, whereas the experimentally reported value is 138 nm.13 Comparing these values with the experimental one can conclude that ”closed neutral ⇒ anionic” is the interconversion process occuring in BPB with increasing pH from lower to higher value, as this agrees quite well with the experiment. As per the CAM-B3LYP functional, even the ”open neutral ⇒ dianionic” interconversion cannot be completely excluded. Moreover, it can be suggested that the closed neutral form is responsible for acidic pH behavior while the anionic form is responsible for the basic pH behavior. The negative remark on the obtained results from the static approach is that the absorption wavelength for the acidic pH form (closed neutral) is blue-shifted to the UV visible region while in experiments the absorption maximum is at 450 nm.13 To this end, we discussed the OPA of BPB using the static approach. Now, we will discuss the optical properties of BPB, calculated using the integrated approach. Due to the computational demand, we considered only the most relevant molecular forms of BPB, namely closed neutral, open neutral, anionic, and dianionic forms. As we discussed above, two sets of TD-DFT calculations were carried out for the configurations obtained from MD. In one set of calculations, the solvent molecules and ions were stripped and only the BPB coordinates were used. In another set, solvents and ions within 15 Å from the BPB center of mass were also included. In other words, these two sets refer to results from TD-DFT and TD-DFT/MM approaches (with

Table 3. Static First Hyperpolarizability of Neutral (for Both Open and Closed Forms), Anionic, and Dianionic BPB as Obtained from Static and Dynamic Approaches

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BPB

βtotal × 10−30 esu

⟨βtotal⟩ × 10−30 esu

Closed neutral Open neutral Anion Dianion

13.6 46.6 86.8 95.7

11.2 42.6 37.7 66.4

RESULTS AND DISCUSSION Figures 1 and 2 represent the important molecular forms of BPB considered in the present study. In the closed neutral form of BPB (in Figure 1a) there are two Br substituted phenol groups and one benzothiazole moiety which form a tetrahedral geometry with a sp3 hybridized C atom. On the other hand, in the open neutral form (in Figure 1b), the C atom from the benzothiazole moiety is sp2 hybridized (as one of the C−O linkages has been broken within the ring). Figure 2a and 2b correspond to the anionic and dianionic forms of BPB, which were obtained simply by deprotonation of one (for anionic BPB) and two (for dianionic BPB) phenolic hydrogen(s) in basic medium. The central C atom of these two charged molecular forms also has the same sp2 hybridization as that of the open neutral form. The excitation wavelength and corresponding oscillator strength for the lowest three excited states of different molecular forms of BPB using the static TD-DFT approach are given in Table 1. We used water as a solvent throughout this study, mainly for two reasons. First of all, one recent experiment reported on the nonlinear properties and optical limiting performance of BPB,13 in different pH media in the presence of water solvent. Thus, we have experimental data to correlate and compare with the theory. The second reason comes from the geometrical aspects of BPB.10−13 The different deprotonated forms of BPB suggest that they should be stabilized by a polar solvent such as water, and the deprotonated forms may not exist in nonpolar solvents. In Table 1 the OPA parameters of BPB are presented which are computed using both B3LYP30,31 and CAM-B3LYP32 functionals. In particular, it is well-known that the latter functional correctly describes the long-range behavior of the exchange interaction and so is capable of explaining the charge transfer excitations accurately.32 We know that the protonated forms dominate the equilibrium in the acidic pH range. So, in the current case the neutral (we do not know whether it is open neutral or closed neutral) or the anionic forms, which are respectively diprotonated and protonated forms of dianionic, should dominate the equilibrium at lower pH. So, with increasing pH, one can propose neutral ⇒ anionic, anionic ⇒ dianionic, and neutral ⇒ dianionic as the three possible interconversion processes associated with the BPB molecule. Since the neutral BPB can also exist in open and closed forms, there are five possibilities which can occur when the pH is changed from acidic to basic medium: (i) closed neutral to anionic, (ii) open neutral to anionic, (iii) anionic to dianionic, (iv) closed neutral to dianionic, and (v) open neutral to dianionic. Now, the OPA results in Table 1 and Figure 3 provide some information about the performance of the two functionals. First, the absorption maxima of the open neutral form of BPB, using both B3LYP30,31 and CAM-B3LYP,32 are red-shifted compared to the closed form and this originates due to the different 7179

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Finally, we have evaluated the static hyperpolarizability of different molecular forms of BPB using both static and dynamic approaches. It is evident from Table 3 that the static hyperpolarizability of BPB strongly depends on its protonation state and closed or open molecular geometry. The closed neutral BPB due to its rigid structure cannot rotate through the C−C σ bond. But in open neutral, anionic, and dianionic BPB the three benzene moieties can rotate freely through the C−C σ bond. The closed neutral BPB, due to less overlap between the interacting orbitals, has the smallest static hyperpolarizability. On the other hand, the open forms (open neutral, open anion, and dianion BPB), due to higher overlap, possess higher static hyperpolarizability than the neutral closed BPB. Hence, the closed neutral BPB possesses the lowest nonlinear optical response as compared with the other open forms of BPB (where more charge transfer interaction can occur). There are reports on a number of systems, such as spiropyranmerocyanine, where the open forms (charge separated) have larger hyperpolarizability than their neutral closed counterparts.44 Within the open molecular forms, the static approach predicts an increase in βtotal with increasing charges. However, there is no clear trend between the βtotal and the charge of the three molecular forms as predicted from the dynamic approach. We have earlier established the open neutral form dominates the equilibrium at low pH (or acidic pH) while the anionic and dianionic forms are dominant at basic pH. So, with increase in pH (i.e. with change from acidic to basic pH) there should be an increase in the nonlinear response (given that the dianionic form dominates the equilibrium in the basic pH range) which can be used as an indicator for pH sensing. The values for the β ratio dianionic are 2.05 and 1.56, respectively, from the static and

B3LYP functional) and provide insight on the effect of the explicit solvent description on one photon spectra calculations. The OPA parameters for the lowest three excited states of all different forms of BPB in the presence of solvent molecules have been tabulated in Table 2. In the case of open neutral, only the excitations corresponding to larger oscillator strengths are included in the table.Figure 4 shows the absorption spectra obtained by convoluting the absorption peaks corresponding to the lowest six excitations for all protonated and deprotonated forms of BPB. Figure 4a demonstrates the absorption spectra of all different molecular forms of BPB in the absence of solvent whereas Figure 4b exemplifies the situation where the BPB interacts with solvent water molecules and the environment here described using the polarizable force-field. As can be seen from Table 2, there are four conversions that can be attributed to a pH induced red shift within the integrated approach, namely, (i) closed neutral ⇒ anionic, (ii) closed neutral ⇒ dianionic, (iii) open neutral ⇒ anionic, and (iv) open neutral ⇒ dianionic. The computed shifts associated with these interconversion processes are, 277, 297, 51, and 71 nm (see Table 2), respectively. Among these four interconversion processes, the first two involving the closed neutral species are associated with larger red-shifted absorption maxima when compared to experimental data and so can be excluded from the discussion. Further, the absorption intensity of the closed neutral form is much lower when compared to all other forms. The absorption wavelength for the open neutral form is blueshifted when compared to experimental spectra. The other two red-shifted absorption associated with open neutral ⇒ anionic (51 nm) and open neutral ⇒ dianionic (71 nm) interconversion processes fairly agree with the experimental pH induced red shift of 138 nm (even though the shift is underestimated significantly). Using the CAM-B3LYP functional, the obtained shifts for these two interconversion processes are respectively 61 and 85 nm (refer to Table 2). Based on these results, we would like to propose that the open neutral form is the relevant form for the acidic pH behavior while the anionic and dianionic forms are the relevant molecular forms for the basic pH behavior of this dye molecule. When it comes to spectral shift, even though both functionals perform comparably similar, the absorption maximum for the acidic pH form (open neutral) is better reproduced by the CAM-B3LYP functional while the absorption maxima for the basic pH molecular forms are better reproduced by the B3LYP functional. Thus, at the end of the discussion of the integrated approach we found that the results obtained from the static approach and the integrated approach are quite different for the acidic pH range. The closed neutral and open neutral forms are predicted to be responsible for the lower pH optical response from the static and dynamic approaches, respectively. Both approaches predict anionic and dianionic forms as the molecular forms responsible for the basic pH optical response of BPB. Thus, it can be concluded at this point that the integrated approach based modeling accounts for all the factors more accurately, and performs better than the static approach while describing the pH induced linear optical response of the BPB dye molecule. The importance of including solvent molecules for calculating the absorption spectra can be understood from Figure 4a and 4b. Except for the closed neutral form, the absorption spectra (not only the absorption maximum but also the line shapes) obtained using the TD-DFT (Figure 4a) and TD-DFT/MM (Figure 4b) approaches and those using the B3LYP functional differ significantly.

βopen neutral

dynamic approaches, which suggest that BPB can be turned into an effective nonlinear probe for pH sensing.45,46 However, for any practical application, the first hyperpolarizability value has to be improved through suitable chemical modification. The study overall reveals that BPB and its analogous molecules have the first large static hyperpolarizabilities and may have potential applications in the development of nonlinear optical materials.

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CONCLUSIONS In summary, we have analyzed the linear and nonlinear optical properties of the neutral and deprotonated forms of the BPB dye molecule. The linear optical properties have been calculated using both the static TD-DFT/PCM formalism and dynamic TD-DFT/MM. In particular, the input configurations for the dynamic approach have been obtained using force-field molecular dynamics for neutral and unprotonated forms of BPB in water solvent. We have also estimated the static hyperpolarizability to comment on the pH dependence (or protonation state dependent) of the nonlinear optical response of this molecule. The static approach predicts the closed neutral form to be responsible for the acidic pH behavior while the anionic and dianionic form are responsible for the basic pH behavior. The dynamic approach based calculations suggest that the open neutral molecular form is responsible for the acidic pH optical response of the BPB dye while the open anionic and dianionic forms are associated with the basic pH optical response. The calculations of static first hyperpolarizability reveal that the nonlinear optical properties also change for different forms of BPB, which suggests that indeed this molecule can also serve as a nonlinear optical probe for pH 7180

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The Journal of Physical Chemistry A

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sensing with suitable chemical modification. Overall, the current study reveals the molecular forms responsible for the acidic and basic pH optical behavior of BPB dye. Further, it shows that the dye molecule can also serve as a nonlinear probe for pH sensing, as it shows protonation state specific first hyperpolarizability.

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ASSOCIATED CONTENT

S Supporting Information *

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.jpca.6b07660. Full citations for refs 22, 25, and 39 (PDF)

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Phone: 0046 8 55378418. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS M.C. thanks the Alexander von Humboldt AvH Foundation for funding. The authors acknowledge support from the Swedish Foundation for Strategic Research (SSF), through the project “New imaging biomarkers in early diagnosis and treatment of Alzheimer’s disease”, and the support from SLL through the project “Biomolecular profiling for early diagnosis of Alzheimer’s disease”. This work was supported by the grants from the Swedish Infrastructure Committee (SNIC) for the project “In-silico Diagnostic Probes Design” (SNIC2015-1486).

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