Spectral behavior and computational studies of fuchsin in various solvents

Spectral behavior and computational studies of fuchsin in various solvents

Journal of Molecular Liquids 238 (2017) 193–197 Contents lists available at ScienceDirect Journal of Molecular Liquids journal homepage: www.elsevie...

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Journal of Molecular Liquids 238 (2017) 193–197

Contents lists available at ScienceDirect

Journal of Molecular Liquids journal homepage: www.elsevier.com/locate/molliq

Spectral behavior and computational studies of fuchsin in various solvents J.P. Graham a,⁎, M.A. Rauf b, S. Hisaindee b, A. Alzamly b a b

Department of Environmental Science, Sligo Institute of Technology, Sligo, Ireland Department of Chemistry, PO Box 15551, UAE University, Al-Ain, UAE

a r t i c l e

i n f o

Article history: Received 27 February 2017 Received in revised form 26 April 2017 Accepted 30 April 2017 Available online 04 May 2017 Keywords: Fuchsin Spectroscopy UV/Vis Multivariate analysis DFT

a b s t r a c t Absorption spectra of fuchsin were measured in various solvents. Two solvent-dependent absorption maxima were observed between 511 and 538 nm and 552–567 nm. Time-dependent density functional theoretical calculations assigned the transitions between the 510–540 nm and 540–557 nm to π-π* transitions between the HOMO-1 to LUMO and HOMO to LUMO respectively. The absorption data were analyzed using the KamletAboud-Taft, Catalan and Katritzky models of solvatochromic behavior. The Catalan model was found to provide the best correlation with the experimental absorption maxima, followed by the Katritzky model. Both the Catalan and Katritzky models suggest that polarizability of the solvent is the primary factor affecting the transition energy. © 2017 Elsevier B.V. All rights reserved.

1. Introduction The presence of solute in a given solvent environment can give rise to various interactions which may be intra or intermolecular in nature. These interactions play an important role in many fields of chemistry such as organic and biochemical reactions, supramolecular chemistry, solution chemistry and drug interactions. These interactions are the basis of understanding the various aspects of physical, chemical and biological processes including formation of aggregates and micelles. The physico-chemical nature and the degree of intermolecular interactions are highly dependent on the type of the solvent which interacts with the solute. This results in various types of solute-solute and solute-solvent interactions such as donor-acceptor, dipole-dipole, H-bonding and other cohesive forces. These interactions induce changes in the electronic transitions of a solute in a given solution (commonly known as solvatochromism). Spectroscopic studies of compounds in various solvents can provide important information towards understanding solvation interactions and photophysical behavior. A shift in absorption wavelength of a probe molecule in various solvents reveals information about the solute–solvent interactions [1–6]. The spectral shifts in various solvents originate from either nonspecific (dielectric enrichment) or specific (e.g. hydrogen-bonding) solute–solvent interactions, and are known as solvatochromism. The electronic structure of the probe and solvent

⁎ Corresponding author. E-mail address: [email protected] (J.P. Graham).

http://dx.doi.org/10.1016/j.molliq.2017.04.133 0167-7322/© 2017 Elsevier B.V. All rights reserved.

molecules contributes to the intermolecular solute–solvent interactions in the ground and the first excited states. Positive or negative shifts in λmax may be observed, which depends on the relative stabilization of the ground and excited states. Spectroscopic methods based on absorption spectra give valuable information on the contribution of different types of solute–solvent interactions using multi-parameter solvent polarity scales [7–10]. These changes have been used to understand various physical-organic reactions of probe molecules, which are important in different fields of pure and applied chemistry [11–15]. Fuchsin, also known as Magenta II, is a triaminotriphenylmethane dye. The structure of fuchsin is shown in Fig.1. The molecule is biologically active and a suspected carcinogen [16]. Fuchsin is used as a dye in the textiles industry and also has applications in chemical analysis [17] and as a microbiological stain [18]. Fuchsin's derivative acid fuchsin, which is synthesized by the addition of sulfonic groups, is used in histology as a stain for distinguishing different tissue types [19]. Recently, the degradation and removal of fuchsin from aqueous solutions has been a topic of considerable interest [20–23]. In this work, spectral features of fuchsin in different solvents were studied in order to understand the effect of specific and non-specific interactions on solvation of this molecule. Spectral data were analyzed using three different models and the suitability of each model to describing the behavior of fuchsin in various solvents is assessed. Recently, computational methods such as Density Functional Theory (DFT) calculations [11,24,25] have been used as tools to support experimental studies of structure, intermolecular interactions and spectra. In this work, DFT calculations are used to optimize the structure of fuchsin. Time-Dependent DFT calculations on the optimized structure are then


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Fig. 2. Absorption spectra of fuchsin in various solvents. Fig. 1. Molecular structure of fuchsin.

4. Results and discussion employed to investigate the nature of the visible-region electronic transitions of fuchsin.

Absorption spectra of fuchsin were recorded in various solvents of different polarity at room temperature (25 ± 2 °C) and are shown in Fig. 2. The difference in spectral behavior indicates an interaction between the probe molecule and the solvent environment. These changes were correlated with various solvent parameters and analyzed by the Kamlet-Abboud-Taft, Catalan and Katritzky models.

2. Experimental All the solvents used in this work, namely, dimethyl formamide, dimethyl sulfoxide, 1,2-dimethoxy ethane, acetone, acetonitrile, ethanol, methanol, 2-propanol, dioxane and ethyl acetate were purchased from Aldrich and were of analytical grade. Prior to use, they were dried over 4 Å molecular sieves for a week. The working solutions in a given solvent were prepared by dilution from the stock solutions of fuchsin. The final concentration of the solutions was maintained at 70 μM in all cases. CARY 50 UV/Vis spectrophotometer was used to obtain the absorption spectrum of each solution using a 1 cm quartz cell. The absorption values were ascertained to fall in the linear range of Lambert-Beer's law. Absorption maxima for the two low energy transitions were resolved by fitting Gaussian functions to the experimental spectra using the Origin 9.0 program (Table 1). Multivariate regression using MSExcel was performed to fit observed absorption spectra to the KamletAboud-Taft, Catalan and Katritzky models of solvatochromic behavior.

4.1. DFT calculations Time Dependent DFT calculations using the CAM-B3LYP functional performed in the gas phase and using the PCM model of solvation overestimate the transition energy for fuchsin. The experimentally observed absorption in the region 543–562 nm is assigned to the HOMO → LUMO transition which is calculated to occur between 405 and 410 nm using the PCM model for the solvents studied. The transition is π → π* in nature as illustrated by the isosurfaces for the HOMO and LUMO given in Fig. 3. No significant correlation for solvent effects between experimental absorption maxima and those calculated using the PCM model for various solvents was observed. The calculated dipole moment for fuchsin in the ground state is 7.05 D and that for the first excited state is 8.71 D. The higher energy transition observed between 511 and 538 nm is assigned to the HOMO-1 → LUMO transition, which is calculated to occur between 314 and 326 nm. The calculations indicate this transition should have an oscillator strength of approximately 0.43, compared to 1.06 for the HOMO → LUMO transition, consistent with the experimental spectra. The dipole moment of this second excited state is calculated to be 14.3 D. This large increase in dipole moment indicates significant charge transfer character and is consistent with the difference in spatial distribution of the LUMO and HOMO-1 orbital isosurfaces (Fig. 4).

3. Computational details All calculations were performed using the Gaussian 09 program [26]. The structure of fuchsin was optimized without symmetry constraints using the B3LYP functional and 6–311 + G(d,p) basis set [27]. The optimized structure was confirmed to be energy minimum through vibrational frequency calculations. The electronic spectrum of fuchsin was calculated by TDDFT using the CAM-B3LYP functional and 6–311 + G(d,p) basis set [28]. Solvent effects were modeled using the PCM model with the default solvent parameters of Gaussian 09 [29].

Table 1 Experimental absorption data of fuchsin along with solvent parameters of the Katritzky model. Solvent

λabs (1) (nm)

νabs (1) (cm−1)

λabs (2) (nm)

νabs (2) (cm−1)




Dimethyl formamide 1,2-Dimethoxy ethane 2-Propanol Acetone Ethyl acetate Methanol Ethanol Dioxane Acetonitrile Dimethyl sulfoxide

562.4 557.5 556.5 551.5 556.0 552.8 554.9 558.7 546.2 566.6

17,780.9 17,937.2 17,969.5 18,132.4 17,985.6 18,089.7 18,021.3 17,898.7 18,308.3 17,649.1

534.7 525.6 522.2 516.4 517.0 519.6 522.2 524.4 511.0 538.5

18,702.1 19,025.9 19,149.8 19,364.8 19,342.4 19,245.6 19,149.8 19,069.4 19,569.5 18,570.1

36.7 7.2 17.9 20.7 6.02 32.7 24.5 2.25 37.5 46.7

1.431 1.354 1.377 1.359 1.372 1.326 1.359 1.422 1.344 1.476

43.2 51.7 48.4 42.2 38.1 55.4 51.9 36 45.6 45.1

J.P. Graham et al. / Journal of Molecular Liquids 238 (2017) 193–197


Fig. 3. Calculated HOMO and LUMO isosurfaces of fuchsin.

The PCM model was employed to calculate solvent effects on the absorption energy for both transitions. It was found that the model did not give a strong correlation between experimental and calculated absorption wavelengths. A plot of calculated vs. experimental absorption maxima results in an R2 value of 0.58 for the HOMO → LUMO transition and only 0.02 for the HOMO-1 → LUMO transition. The PCM model relies heavily on solvent polarity as an indication of solute-solvent interactions and does not account for specific interactions. As discussed below, the principal factor in determining the observed solvatochromic shifts appears not to be solvent polarity, but polarizability of the solvent, and to a lesser extent specific interactions arising from solvent basicity. As such, it is not surprising that the PCM model did not accurately reproduce the observed spectral shifts.

Fig. 4. Calculated HOMO-1 isosurface of fuchsin.

4.2. Multiparamater solvatochromic models Contributions of different specific and non-specific interactions towards the solute stabilization were analyzed by multiparameter solvent polarity scales. In this regard, Kamlet–Abboud–Taft multilinear analysis was initially used which is expressed in the equation form as follows [30]. ~ a Þ0 þ aα þ bβ þ sπ  ~ a ¼ ðν ν


where ṽ is the absorption energy in cm−1, α is the hydrogen-bond donating ability (HBD), β is the hydrogen-bond accepting ability (HBA) of the solvent, π* is an index of the solvent polarity dipolarity/polarizability of the solvent, which reflects the ability of the solvent to stabilize a dissolved charge or dipole (values listed in Table 2). The values s, a, b are independent constants whose magnitudes and sign provide a measure of the influence of the corresponding solute–solvent interactions on the absorption maximum wavenumber. Multivariate regression resulted in the following Eqs. (5) and (6) for the HOMO-1 → LUMO and HOMO → LUMO transitions respectively: ~ 2 ¼ 19900:5ð351:6Þ ν þ 475:1ð272:5Þα−1172:9ð462:9Þβ−353:1ð518:4Þπ


~ 1 ¼ 18309:4ð206:4Þ þ 403:7ð159:9Þα−820:7ð271:7Þβ ν þ 48:7ð304:3Þπ


Plots of the experimental transition energies vs. calculated transition energies using Eqs. (2) and (3) for the HOMO-1 → LUMO and HOMO → LUMO transitions are given in Supplementary Figs. S1 and S2 respectively. Relatively poor correlations were obtained with R2 values of 0.679 and 0.655 respectively. The large negative coefficient of β in both equations appears to suggest that hydrogen-bond acceptance by the solvent is the most important factor in stabilizing the excited state of fuchsin. However, due to the relatively poor fit of the data to the Kamlet-Abboud-Taft model, these coefficients cannot be considered reliable. The standard deviation for the coefficients of π* in both equations exceed the coefficient values and indicate no correlation. Other models, discussed below, suggest that hydrogen-bond acceptance or basicity is not the most important factor, but rather solvent polarizability. An improvement to the Kamlet-Abboud-Taft model was suggested by Catalan [31]. According to this model, two parameters for specific


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hydrogen bonded solvents. The (n2 – 1/2n2 + 1) parameter, a function of refractive index n, accounts for solvent polarizability effects. The equation in its applied form is written below [33].

Table 2 Spectroscopic parameters used in multiparameter analysis of fuchsin. Kamlet-Abboud-Tafta










Dimethyl formamide 1,2-Dimethoxy Ethane 2-Propanol Acetone Ethyl acetate Methanol Ethanol Dioxane Acetonitrile Dimethyl sulfoxide

0.88 0.53 0.48 0.71 0.55 0.6 0.54 0.55 0.75 1.0

0 0 0.76 0.08 0 0.93 0.83 0 0.19 0.0

0.69 0.41 0.95 0.48 0.45 0.62 0.77 0.47 0.31 0.76

0.759 0.680 0.633 0.651 0.656 0.608 0.633 0.737 0.645 0.830

0.977 0.625 0.808 0.907 0.603 0.904 0.783 0.312 0.974 1.0

0.031 0.0 0.283 0.0 0.0 0.605 0.40 0.0 0.044 0.072

0.613 0.636 0.830 0.475 0.542 0.545 0.658 0.444 0.286 0.647

ET(30): C. Reichardt, Chem. Rev. 1994, 94, 2319–2358. a Values taken from Ref [22]. b Values taken from Ref [23].

and two parameters for non-specific interactions including separate consideration of solvent polarizability (SP) and dipolarity (SdP) was proposed as per follows: ~ a Þ0 þ aSA þ bSB þ cSP þ dSdP ~ a ¼ ðν ν

 ~ a Þ0 þ aðε−1=2ε þ 1Þ þ b n2 −1=2n2 þ 1 þ c:ET ð30Þ ~ a ¼ ðν ν


where, ṽa is the spectral peak position of the absorption spectra in wavenumbers (cm−1), ε is the relative permittivity and n is the index of refraction of a given solvent. Multivariate regression resulted in the following equations for the HOMO-1 → LUMO and HOMO → LUMO transitions respectively: ~ 2 ¼ 23126ð578:9Þ þ 0:217ð0:121Þ ν  ðε−1=2ε þ 1Þ−2920:4ð373:9Þ   n2 −1=2n2 þ 1 −1:3ð7:1ÞET ð30Þ


~ 1 ¼ 20299ð367:3Þ þ 0:223ð0:07Þ ν  ðε−1=2ε þ 1Þ−1854:2ð237:2Þ   n2 −1=2n2 þ 1 −15:6ð4:5ÞET ð30Þ



where SA, SB, SP and SdP signify the solvent acidity, basicity, polarizability and dipolarity of a solvent, respectively and are given in Table 2. The values a, b, c and d are regression coefficients. The value π* in the Kamlet–Abboud–Taft model comprises both the dipolarity and polarizability character of the solvent and is effectively split into two separate contributions in the Catalan model. Data fitting to the above relationship resulted in the following equations for the HOMO-1 → LUMO and HOMO → LUMO transitions respectively: ~ 2 ¼ 22340:3ð364:1Þ−330:9ð193:8ÞðSAÞ−788:2ð231:1Þ ν  ðSBÞ−3892:5ð543:5ÞðSPÞ−7:2ð147:5ÞðSdP Þ


~ 1 ¼ 19764:9ð183:2Þ−120:3ð97:6ÞðSAÞ−579:5ð116:3Þ ν  ðSBÞ−2274:9ð273:5ÞðSPÞ þ 142:9ð74:2ÞðSdP Þ


The data fit the Catalan model particularly well, with R2 values of 0.948 and 0.965 for the HOMO-1 → LUMO and HOMO → LUMO transitions respectively. Plots of experimental vs. calculated transition energies for the two transitions are given in supplementary Figs. S3 and S4. The large coefficient of SP for both transitions suggests that solvent polarizability is the primary factor contributing to the observed solvatochromic shifts. The fact that the coefficients of SP are negative suggests that the higher solvent polarizability leads to relative stabilization of the excited states. The second largest factor is the solvent basicity, suggesting that hydrogen-bond donation from fuchsin to the solvent is also a significant factor in determining the transition energy. The coefficient again is negative, suggesting increasing solvent basicity results in relative stabilization of the excited states for both transitions. The solvent acidity parameters have relatively small coefficients and do not contribute significantly to changes in the transition energy. The solvent dipolarity parameters also have small coefficients for both transitions, and in the case of the ν2, the standard deviation in the coefficient of SdP exceeds the value of the coefficient itself. The absorption data for fuchsin was also fit to the linear solvation relationship developed by Katritzky, which combines the ET(30) values with functions of dielectric constant and index of refraction (Eq. (7)). Values for the solvent parameters used in this study are given in Table 1. ET(30) values are a measure of solvent polarity derived from the reference dye pyridinium-N-phenolate, a betaine dye that exhibits strong solvatochromic behavior [32]. The equation is based on the hypothesis that the Kirkwood function, namely (ε − 1/2ε + 1) correctly signifies dipole–dipole interactions and that ET(30) values are sensitive to both dipolar interactions and the interactions between the solute and the

The R2 values for plots of experimental vs. predicted transitions energies were 0.922 and 0.928 (Supplementary Figs. S5 and S6) for the HOMO-1 → LUMO and HOMO → LUMO transitions respectively. The major contribution to solvatochromic shifts in the Katritzky equation arises from the refractive index, as indicated by the large b coefficients. As the refractive index is related to the polarizability of the solvent (by the Lorenz-Lorenz equation), the large b coefficients are consistent with the Catalan plot which suggests the polarizability parameter SP is most significant in determining the absorption shifts. The coefficients of ET(30) for both transitions are small and the standard deviation for ν2 exceeds the value of the coefficient, indicating no reliable correlation. It is noted that the magnitude of solvatochromic shifts observed for the higher energy transition are greater than those observed for the lower energy transition. This is consistent with the calculated higher change in dipole moment for the HOMO-1 → LUMO transition compared to the HOMO → LUMO transition. In summary, contributions in the Catalan model are arise primarily from solvent polarizability (SP) while the largest contributions in the Katritzky model arise from the (n2 – 1/2n2 + 1) polarizabilty parameter, consistent with the parameter coefficients discussed earlier. The poor fit of the Kamlet-Abboud-Taft model appears to arise from the treatment of dipolarity and polarizability in one parameter, while the other models studied employ a separate parameter for the dominant contributor, polarizabilty. The dipolarity related π*, SdP and ET(30) parameters in the Kamlet-Abboud-Taft, Catalan and Katrizky models respectively all had large standard deviations relative to coefficients and appear not to make a significant contribution to the solvatochromic behavior of fuchsin. 5. Conclusion Time-dependent density functional theoretical calculations assign the two visible region absorptions in fuchsin to π-π* transitions from the HOMO-1 and HOMO to the LUMO. It was calculated that the dipole moment of the molecule is increased upon excitation for both transitions. The solvatochromic behavior of the visible region absorption maxima were studied in various solvents and modeled with the Kamlet-Abboud-Taft, Catalan and Katritzky models. It was found that the Catalan and Katritzky models gave the best fit to experimental data and indicated that solvent polarizability is the most important factor in determining the solvatochromic shift. Both the Catalan and Katritzky models indicate increased stabilization of both excited states with increasing solvent polarizability, consistent with the calculated increase in dipole moments upon excitation.

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Appendix A. Supplementary data Supplementary data to this article can be found online at http://dx. doi.org/10.1016/j.molliq.2017.04.133. References [1] V.G. Machado, R.I. Stock, C. Reichardt, Chem. Rev. 114 (2014) 10429. [2] Y.X. Li, J.X. Qiu, J.L. Miao, Z.W. Zhang, X.F. Yang, G.X. Sun, J. Phys. Chem. C 119 (2015) 18602. [3] M.S. Zakerhamidi, S.G. Sorkhabi, J. Lumin. 157 (2015) 220. [4] M. Khattab, M.V. Dongen, F. Wang, A.H.A. Clayton, Spectrochim. Acta A 170 (2017) 226. [5] M. Nawaz, S. Hisaindee, J.P. Graham, M.A. Rauf, N.I. Saleh, J. Mol. Liq. 193 (2014) 51. [6] Z. Seferoglu, E. Aktan, N. Ertan, Color. Technol. 125 (2009) 342. [7] M.C. Almandoz, M.I. Sancho, P.R. Duchowicz, S.E. Blanco, Spectrochim. Acta A 129 (2014) 52. [8] I. Sidir, Y.G. Sidir, H. Berber, F. Demiray, J. Mol. Liq. 206 (2015) 56. [9] C. Marrassini, A. Idrissi, I. de Waele, K. Smail, N. Tchouar, M. Moreau, A. Mezzetti, J. Mol. Liq. 205 (2015) 2. [10] A.D.B. Yaseen, M. AlBalawi, Phys. Chem. Chem. Phys. 16 (2014) 15519. [11] M.A. Rauf, S. Hisaindee, J.P. Graham, M. Nawaz, J. Mol. Liq. 168 (2012) 102. [12] C. Niu, Y. You, L. Zhao, D. He, N. Na, J. Ouyang, Chem. Eur. J. 40 (2015) 14321. [13] C. Spies, B. Finkler, N. Acar, G. Jung, Phys. Chem. Chem. Phys. 15 (2013) 19893. [14] J.H. Choi, O.T. Kwon, H.Y. Lee, A.D. Towns, C. Yoon, Color. Technol. 126 (2010) 237. [15] Y. Kubota, Y. Sakuma, K. Funabiki, M. Matsui, J. Phys. Chem. A 118 (2014) 8717. [16] National Toxicology Program, Technical Report Series No. 285. Toxicology and Carcinogenesis Studies of C.I. Basic Red 9 Onohydrochloride (Pararosaniline) (CAS No. 56961e9) in F344/N Rats and B6C3F1 Mice (Feed Studies)(Report Date) January 1986. [17] F.P. Scaringelli, B.E. Saltzman, S.A. Frey, Anal. Chem. 39 (1967) 1709. [18] I.A. Schrijver, M. Melief, M. van Meurs, A.R. Companjen, J.D. Laman, J. Histochem. Cytochem. 48 (2000) 95.


[19] Jocelyn H. Bruce-Gregorios, Histopathologic Techniques, JMC Press Inc., Quezon City, Philippines, 1974, ISBN 971-11-0853-4. [20] Ahlem Taamallah, Slimane Merouani, Oualid Hamdaoui, Desalin. Water Treat. 57 (2016) 27314. [21] Jiaojiao Kong, Lihui Huang, Qinyan Yue, Baoyu Gao, Desalin. Water Treat. 52 (2013) 2440. [22] Z.M. Abou-Gamra, Desalin. Water Treat. 57 (2015) 8809. [23] A.O. Deomartins, V.M. Canalli, C.M.N. Azevedo, M. Pires, Dyes Pigments 68 (2006) 227. [24] J. DostaniC, D. LonCarevic, M. Zlatar, F. Vlahovic, D.M. Jovanovic, J. Hazard Mat. 316 (2016) 26. [25] S.M. Shohayeb, R. GMohamed, H. Moustafa, S.M. El-Medani, J. Mol. Struc. 1119 (2016) 442. [26] M.J. Frisch, G.W. Trucks, H.B. Schlegel, G.E. Scuseria, M.A. Robb, J.R. Cheeseman, G. Scalmani, V. Barone, B. Mennucci, G.A. Petersson, H. Nakatsuji, M. Caricato, X. Li, H.P. Hratchian, A.F. Izmaylov, J. Bloino, G. Zheng, J.L. Sonnenberg, M. Hada, M. Ehara, K. Toyota, R. Fukuda, J. Hasegawa, M. Ishida, T. Nakajima, Y. Honda, O. Kitao, H. Nakai, T. Vreven, J.A. Montgomery, J.E. Peralta, F. Ogliaro, M. Bearpark, J.J. Heyd, E. Brothers, K.N. Kudin, V.N. Staroverov, R. Kobayashi, J. Normand, K. Raghavachari, A. Rendell, J.C. Burant, S.S. Iyengar, J. Tomasi, M. Cossi, N. Rega, J.M. Millam, M. Klene, J.E. Knox, J.B. Cross, V. Bakken, C. Adamo, J. Jaramillo, R. Gomperts, R.E. Stratmann, O. Yazyev, A.J. Austin, R. Cammi, C. Pomelli, J.W. Ochterski, R.L. Martin, K. Morokuma, V.G. Zakrzewski, G.A. Voth, P. Salvador, J.J. Dannenberg, S. Dapprich, A.D. Daniels, Ö. Farkas, J.B. Foresman, J.V. Ortiz, J. Cioslowski, D.J. Fox, Gaussian 09, Revision C01, Gaussian, Inc., Wallingford CT, 2009. [27] A.D. Becke, J. Chem. Phys. 98 (1993) 5648. [28] T. Yanai, D.P. Tew, N.C. Handy, Chem. Phys. Lett. 393 (2004) 51. [29] G. Scalmani, M.J. Frisch, J. Chem. Phys. 132 (2010) 114110. [30] M.J. Kamlet, J.M. Abboud, M.H. Abraham, R.W. Taft, J. Org. Chem. 48 (1983) 2877–2887. [31] J. Catalan, J. Phys. Chem. B 113 (2009) 5951. [32] ET(30), C. Reichardt, Chem. Rev. 94 (1994) 2319–2358. [33] F.W. Fowler, A.R. Katritzky, R.J.D. Rutherford, J. Chem. Soc. B (1971) 460.