Theoretical Investigation of Excited State Proton Transfer Process in

Jan 11, 2013 - ABSTRACT: Excited state reaction coordinate and the consequent energy profiles of a new Schiff base, N-salicylidene-2-bromoethylamine, ...
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Theoretical Investigation of Excited State Proton Transfer Process in the N‑Salicylidene-2-bromoethylamine Ahmad J. Moghadam, Reza Omidyan,* Valiollah Mirkhani, and Gholamhasan Azimi Department of Chemistry, University of Isfahan, 81746-73441 Isfahan, Iran S Supporting Information *

ABSTRACT: Excited state reaction coordinate and the consequent energy profiles of a new Schiff base, N-salicylidene-2-bromoethylamine, have been investigated at the CC2 level of theory. The electron-driven proton transfer and torsional deformation have been identified as the most important photochemical reaction coordinates. In contrast to the ground state, the excited state potential energy profile shows a barrierless dissociation pattern along the O−H stretching coordinate, which verifies the proton transfer reaction along the O−H coordinate at the S1 state. The calculations showed that the PT is electron driven and that the S1 transition has charge transfer character. The keto-type S1 state attained by barrierless proton transfer is found to be unstable via a torsional motion, which provides fast access to a S1−S0 conical intersection. From the conical intersection, a barrierless reaction path directs the system back to the enol-type minimum of the S0 potential energy surface, thus closing the photocycle. Tanak45 and Pyta et al.46 established that intramolecularhydrogen bond has an effective role to stabilize the enol form of Schiff base compounds at the ground state. Recently, Jankowska and co-workers investigated the photophysics of the salicylidene methylamine (SMA) by the aim of CC2, TDDFT, and CASPT2 theoretical methods. Their calculations indicate two S1/S0 conical intersections, which provide nonadiabatic gates for a radiationless decay to the ground state of SMA. Also, they concluded that the photochromic species of SMA are only formed as a result of cooperation between the ESIPT process and the photoinduced rotation around the double bond.47 Very rare reports are devoted to experimental study of ESIPT process in Schiff bases. Chudoba et al. using a pump− probe experimental study on the 2-(2′-hydroxy-5-methylphenyl)-benzotriazole48 concluded that the S1-state decays within 120 fs. The ESIPT process of 2-(2′-8-hydroxyphenyl) benzothiazole (HBT) was investigated by Lochbrunner et al.49 On the basis of the experimental results of this work, it was concluded that the proton takes 60 fs to arrive at its S1 equilibrium position. Later, Schriever et al.50 confirmed the time scale of 30−50 fs for ESIPT and gave a detailed picture of structural and mechanistic aspects of that process. Finally, the subsequent intersystem crossing after the ESIPT was the subject of a joint experimental and theoretical study of HBT, which was performed by Mario Barbatti et al.51 Their results demonstrated a lifetime of 2.6 ps for isolated molecule of HBT in the gas phase.

1. INTRODUCTION Aromatic Schiff bases and their metal complexes have recently attracted considerable attention because of their interesting and important properties such as biological activities,1 antiinflammatory,2 antibacterial,3 fluorescent chemodosimeter,4 molecular tweezers, 5,6 photochemical behavior, 7 ionophores,8−10 catalytic activities,11 and pH-responsive.12 According to significances of proton transfer and tautomerism processes in Schiff bases, so far, they have been the subject of numerous studies.13−19 The photochromism and tautomerism features make extensive applications for Schiff bases in the laser dyes, molecular switches, nonlinear optical properties, and molecular electronic devices.20−25 The photochromic process in Schiff base compounds is associated with the ability to undergo proton-tautomerism reaction between the enol and keto forms of them. This is well-known that photoexcitation of such molecules is usually followed by a rapid excited state intramolecular proton transfer (ESIPT) reaction.26−29 Despite their importance, the photophysical properties of only a few number of aromatic Schiff bases were studied.30−39 Zgierski40,41 and Ortiz-Sánchez42,43 investigated the electronic structure of some simple aromatic Schiff-base derivatives such as salicylidene aniline (SA), with the aim of theoretical methods.40 They showed that the stable enol form of SA is twisted in the ground electronic state, and at the first singlet excited state of enol form, the SA is stabilized by an nπ* twisted structure, which can be in competition with the proton transfer process in ππ* planar structure. However, in the keto form, this minimum corresponds to a planar (ππ*) state, which leads to a photochromic process in the SA molecule. Zgierski also concluded that structural flexibility of twisted S1 (nπ*) state is essential for photochromic activity of Schiff bases.44 Also, © 2013 American Chemical Society

Received: October 23, 2012 Revised: January 10, 2013 Published: January 11, 2013 718

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In this work, we have investigated the photophysical properties of the recently synthesized and characterized Nsalicylidene-2-bromoethylamine Schiff base (SBEA).52 The CC2 method was employed to explore the photophysical dynamics of entitled compound after the photoexcitation to the S1 (ππ*) electronic state. The reaction pathway in which the excited molecules decays to the ground state via a low-lying conical intersection between the S1/S0 is being analyzed.

2. COMPUTATIONAL DETAILS The ab initio and DFT calculations have been performed with the TURBOMOLE program package.53,54 The Resolution-ofidentity Møller−Plesset perturbation theory55 to second-order (RI-MP2)56,57 calculations were performed to obtain the equilibrium geometry of the titled compound at the ground electronic state. Excitation energies and equilibrium geometry of the lowest excited singlet states have been determined at the resolution-of-identity second-order approximate coupled-cluster (RI-CC2)58−60 method and time-dependent density functional theory (TD-DFT).61,62 The calculations were performed with the correlation-consistent polarized valence double-ζ (cc-pVDZ) and the augmented cc-pVDZ63 basis sets. The charge distribution calculations were performed based on the Natural Population Analysis algorithm (NPA)64 implemented in the TURBOMOLE program package. In order to optimize the excited state geometries, the MP2 optimized geometries have been chosen as the starting point of the calculations. Regarding the electronic states and PES interpretations, we have preferred the familiar nomenclature in the literature, mostly used by A. L. Sobolewski and W. Domcke.65−68 Furthermore, the abbreviations of SBEA and E are being used, respectively, as alternatives of N-salicylidene-2-bromoethylamine and the most stable configuration for the enol form of that.

Figure 1. Optimized geometries and numbering pattern: (a) the most stable configuration of the enol form of SBEA (calculated at the MP2/ aug-cc-pVDZ level of theory); (b) the S1 optimized structure of cisketo form of SBEA (determined at the CC2/aug-cc-pVDZ geometry optimization of the E form); (c) the optimized geometry structure of trans-keto form of SBEA obtained at the MP2/cc-pVDZ level of theory; (d) geometry of the S1−S0 conical intersection of SBEA.

Table 1. Optimized Geometry and Relative Ground State Energy of Several Rotamers of SBEAa

3. RESULTS 3.1. Ground State Structures. One can predict several conformers for the enol form of SBEA, corresponding to different orientations of ethylamine with respect to the benzene ring or OH group. Thus, the first step of this study is to look for the most stable structure of the enol form of this molecule. Therefore, almost all of the conformers have been considered in the S0 geometry optimization at the MP2/cc-pVDZ or augcc-pVDZ level of theory. Figure 1 shows the most stable conformer of SBEA in its enol form. Other configurations can be obtained either by rotation of C8−C9 around the C8−N or by rotation of C9−Br around the C8−C9 bond. The energetic ground state level of these configurations with respect to the most stable structure of enol form of SBEA (namely, the E rotamer) is presented in Table 1. For every orientation of the C7−N1-C8−C9, there is two alternatives for locating the O1−H8 bond; it either settles in the same side with the C7−N1−C8−C9 (producing the d-type rotamers in Table 1) or stays in front of this moiety (producing the u-types in Table 1). As shown, the energetic level of isomers, which consist of intramolecular Hbond, is lower than the others. For instance, the 1d isomer is 0.56 eV more stable than the 1u, due to its strong hydrogen bonding. As expected, the keto tautomer associated with E structure of SBEA does not represent a stable minimum at the MP2/ccpVDZ level of theory. Any attempt for optimization of this

a

The values in parentheses (in eV) represent the difference between the internal energy associated with each rotamer and the most stable configuration of SBEA (E form). The calculations have been done at the MP2/cc-pVDZ level of theory.

form at the higher levels (using bigger basis sets such as aug-ccpVDZ and TZVP) restored to the enol minimum. Hence, we could not determine a local minimum for the cis-keto form at the MP2 level. In contrast to the cis-keto, the MP2 calculation shows that the trans-keto is stable at the ground state. Nevertheless, its energetic level is significantly higher (0.84 eV) than the origin minimum of the most stable enol configuration (see Figure 1c). Similar to the enol form of SBEA, various rotamers for the trans-keto structure could be considered. 719

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Concerning our main goal in this work, for focusing on the photophysical properties of the most stable enol form, we neglected to investigate the structural properties of trans-keto and other configurations for enol form. The MP2 optimized geometric parameters of the most stable structure of enol form of SBEA are presented in Table 2. As shown, the parameters

Table 3. Vertical Energy Gap (eV) and Oscillator Strength ( f) of the E and trans-Keto Rotamers, Calculated at the Crucial Points of Ground State Potential Energy Surface with the CC2 and TD-DFT Methods, Using cc-pVDZ and aug-cc-pVDZ Basis Sets CC2

Table 2. Selected Bonds Lengths (Å), Bond Angles, and Dihedral Angles (deg) of the S0 and S1 Geometry Optimized of SBEA (Enol and Keto Forms)

state

S0 (most stable enol form, E) S1 (cis-keto)a

MP2 parameter

ccpVDZ

C1−C6 C5−C6 C4−C5 C1−O1 C1−C2 C2−C3 C2−C7 O1−H8 N1−H8 C9−Br1

1.410 1.400 1.410 1.347 1.425 1.415 1.461 0.995 1.726 1.948

H1−O1−C1 C2−C1−O1 C2−C1−C6 C1−C2−C3 C2−C3−C4 C5−C4−C3 C1−C6−C5 C6−C5−C4 C2−C7−N1 C7−N1−C8

105.4 122.5 118.8 119.6 121.0 119.0 120.7 120.7 122.1 117.0

C7−N1−C8− C9 C1−C2−C7− N1

180.0 0.100

aug-ccpVDZ

exptb

Bond Lengths (Å) 1.410 1.398 1.402 1.382 1.412 1.379 1.357 1.355 1.425 1.403 1.417 1.393 1.460 1.462 0.996 0.825 1.740 1.840 1.955 1.955 Bond Angles (deg) 106.4 107.66 122.126 121.433 119.378 120.000 119.462 118.890 120.859 121.086 119.243 119.302 120.280 119.444 120.778 121.265 122.212 122.400 117.322 119.200 Dihedral Angles (deg) 114.814 123.216 0.400

0.000

cc-pVDZ

aug-ccpVDZ

1.380 1.437 1.387 1.415 1.439 1.409 1.437 1.863 1.031 1.957

1.380 1.438 1.391 1.429 1.436 1.413 1.437 1.926 1.028 1.964

118.676 122.008 117.152 121.387 119.996 119.485 119.890 121.643 118.628

118.470 123.000 116.727 121.298 120.228 119.003 119.787 121.498 118.593

72.400

71.962

23.300

24.300

TD-DFT

ccpVDZ

aug-ccpVDZ

S1 S2 S3 S4

(ππ*) (nπ*) (ππ*) (ππ*)

4.10 5.08 5.30 6.09

4.03 4.95 5.09 5.51

S1 S2 S3 S4

(nπ*) (ππ*) (ππ*) (πσ*)

3.01 3.30 4.88 5.70

2.89 3.07 4.37 4.62

f

Enol (E Form) 0.125 0.001 0.255 0.004 trans-Keto 0.002 0.320 0.006 0.172

ccpVDZ

aug-ccpVDZ

f

3.88 4.68 4.85 5.23

3.85 4.63 4.47 5.11

0.107 0.015 0.355 0.000

2.88 3.12 4.44 4.48

2.87 2.98 4.01 4.33

0.003 0.208 0.001 0.219

the ππ* state. Specially, one electron excitations that contribute to this transition are ∼58% (H−1)−L and 26% H−(L+1). However, the weakest transition is S2−S0, which has the nπ* character corresponding to the electronic transition of (H−4)− L with the oscillator strengths of 0.001. The S4−S0 (ππ*) electronic transition consists of the contributions of ∼49% H− (L+1) and 30% (H−1)−L and is too weak (see Tables 3 and 4). Table 4. Frontier Molecular Orbitals of (a) the Most Stable Conformation of Enol and (b) trans-Keto Forms of the SBEA

a

The CC2 optimization from of the S1 excited state has been done on the MP2/aug-cc-pVDZ optimized geometry. bThe experimental values were taken from ref 52.

obtained by the present MP2 calculations are quite in agreement with the experimental values. The poorest agreement is related to the C7−N1−C8−C9 dihedral angle. The calculated value for this angle at the MP2/cc-pVDZ is very far from experiment (180°). However, using the augmented basis set (aug-cc-pVDZ), the calculated value becomes closer to the experimental value (114.8°). 3.2. Excited State: Geometry and Electronic Properties. The vertical electronic transition energies of the most stable enol form of SBEA (E) are presented in Table 3. The vertical excitation energy at the CC2/aug-cc-pVDZ level on the S0 geometry of the E identifies two strong electronic transitions: The S1−S0 transition at 4.03 eV (370.7 nm) can be described as the ππ* (H−L) excitation, (H and L indicate to HOMO and LUMO, respectively). The oscillator strength of this transition is 0.125. The S3−S0 lies at 5.09 eV (244 nm) with the oscillator strength of 0.255, and can be described as

The vertical excitation energies at the same level of theory on the MP2 ground state optimized geometry of trans-keto tautomer indicate two strong electronic transitions; the S2−S0 transition at the 3.07 eV (404.56 nm) can be described as the ππ* (H−L) excitation (see Table 4). The oscillator strength of this transition is 0.320. The S4−S0 transition also lies at 4.62 eV (268.8 nm) with the oscillator strength of 0.17 and can be described as the πσ* since there is one electron excitation of H−(L+1). At the CC2 level, the weakest transition is the S1− S0, which has the nπ* character corresponding to the electronic transition of (H−2)−L with the oscillator strength of 0.002. 720

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The S3−S0 (ππ*) electronic transition is also very weak. The one electron excitation contributing to the S3−S0 is only (H− 1)−L. At the same geometries, the TD-B3LYP calculations determined smaller values for the vertical transition energies of S1 to S4 associated with the enol or trans-keto form of SBEA (see Table 3). The excited state proton transfer (ESPT) is mainly achieved after the S1 geometry optimization of the E form at the CC2 level. This effect transfers the E structure to a cis-keto form, which is shown in Figure 1b. The H8 moves from oxygen toward nitrogen during the excited state geometry optimization. The cis-keto structure is not stable in the ground state. It converts to the E form at the MP2 optimization because of the back proton transfer from nitrogen to oxygen. Furthermore, all of the geometric parameters of the cis-keto are more or less different with respect to corresponding S0 optimized values of the enol (E) form. The geometric parameters are presented in Table 2. As shown, the most important geometric alteration in the enol-keto tuatomerization is related to the dihedral angles. The C7−N1−C8−C9 decreases from 114.8° to 71.96°, and the C1−C2−C7−N1 increases from 0° to 24.3°. With respect to the values in the ground state, the C2−C1−O1 and C1−C2−C3 angles decrease by roughly 3.7° and 2.7°, respectively. The C2−C1−C6 is increased by around 3.6°, more or less; other angles stay without significant changes. The S1 optimization elongates the C5−C6, C1−C2, and C7− N1 bonds to 0.04, 0.02, and 0.09 Å, respectively. Furthermore, the C−C−C bond angles of the benzene ring increased by around 3°. The most important change in the dihedral angles is related to the C7−N1−C8−C9, which decreased by about 43°. Also, the C1−C2−C7−N1 increased from 0 to 23.4° .The other dihedral angles stay without a significant change. The calculated charge distributions at the ground and S1 excited state of E show an important charge transfer character along with the S1−S0 excitation. The total charge transferred from the phenolic part of the SBEA toward the rest is −0.17q (see Table SM3 in the Supporting Information). These calculations may verify that the ESIPT is consequently electron driven. 3.3. Potential Energy Profiles and Internal Conversion. The potential energy profile calculated along the minimum energy paths (MEP) for rotation of the ethylbromid group of E around the N1−C7 bond (dihedral angle of θ(C9− C8−N1−C7)) is depicted in Figure 2. The energetic values have been determined at the MP2/cc-pVDZ level of theory. The minimum energy path was obtained by freezing the θ(C9−C8− N1−C7) dihedral angle, and all of the other geometry parameters were free to be optimized in the ground state. The PES verifies that the most stable structure for the E form of the conformation is the one where θ(C9−C8−N1−C7) is 114.8°. When θ lies around 180° (i.e., the C9−C8−N1−C7 stays in the same plane with the benzene ring; see rotamer 1d in Table 1), the energetic level of the corresponding configuration is 0.13 eV higher than the most stable structure of SBEA. Although the adjustment of θ(C9−C8−N1−C7) from 0° to 114.8° is favored by considering the PE curve, there is a small barrier around 0.02 eV corresponding to the θ = 40° in the potential energy profile. The potential energy profiles calculated along the minimum energy paths (MEP) for hydrogen (or proton) transfer of the enol form of SBEA together with torsion of the ethylamine group (C1−C2−C7−N1 dihedral angle) in the keto structure of SBEA in the S0 and S1 states are shown in Figure 3a,b,

Figure 2. Energy profile of the S0 state of the E form of SBEA as a function of the C9−C8−N1−C7 dihedral angle computed at the MP2/ cc-pVDZ level of theory.

Figure 3. Potential energy curves of the S0 state (squares) and the S1(ππ*) state (circles), determined at the CC2/cc-pVDZ level as the functions of hydrogen transfer reaction path in the enol form of SBEA (a) and torsional reaction path in the keto form of SBEA (b). The energy origin is the energy of minimum enol in the ground state. The full lines represent the energy profiles of reaction paths determined in the same electronic state, and the dashed lines show the energy profiles of reaction paths determined in the complementary electronic state. The sun shape denotes the area where the CC2 geometry optimization fails to converge.

respectively (full curves). The coordinate-driven minimumenergy paths for PT have been obtained by fixing the protontransfer coordinates (O−H8) and optimizing the lowest 1ππ* state with respect to all other coordinates. The geometry optimizations have been performed with the CC2 method. The energies at the optimized geometries have been calculated at the CC2/cc-pVDZ level. Figure 3a shows the resulting PE profile of the 1ππ* state of E as a function of O−H, (solid lines with the filled circles). The PE profiles of the S0 state, calculated at the 1ππ*-optimized geometries (dashed lines with hollow squares) and at the S0-optimized geometries, determined with the MP2 method (solid lines with filled squares), are also shown. 721

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eV) and relative intensities of 3:2, respectively. Thus, by comparison with the present calculations, the 320 nm band can readily be assigned to excitation of SBEA from the S0 to the S1 state. The calculated vertical transition energy of 4.03 eV compares very favorably with the experimental band maximum of 3.76 eV. An interpretation of the 265 nm band is in fact an assignment of the transition to the optically allowed S3 state. The fact that the geometry of the S1 and S3 states in the Franck−Condon region is very different from its minimum structure can explain the difference between the higher-lying vertical transition energy and the adiabatic transition energy. Thus, the calculated vertical transition energy may overestimate the experimentally observed band center. Furthermore, the CC2 level in general tends to fairly overestimate the excitation energies, which may also partly explain the discrepancy between the experimental and calculated spectrum in Figure 4.

As shown, in the ground state, the local minimum is in the enol side, whereas in the S1, the minimum is in the keto side. The minimum energetic level of the S1 state along the PT coordinate lies in the short distance to the long distance of OH, which corresponds to the new bond formation of H−N. In the ground state, the enol−keto transformation is not favored by considering the energy changes, but in the S1 state, the PES does not show a barrier, and this transformation will be favored by decreasing the internal energy of the system along the enol− keto transformation. Transfer of a proton between the oxygen and nitrogen atoms in the initial S1 state of enol leads to create the cis-keto in its ππ* state. The S(S0) curve in Figure 3a exhibits a barrier for proton 0 transfer in the S0 state of SBEA (E = 0.45 eV), while the energy profile of the S1 state calculated along the S1 reaction path (S(S1) 1 ) in Figure 3a indicates a barrierless reaction coordinate for proton transfer from oxygen toward the nitrogen atom. It verifies that spontaneous hydrogen transfer takes place, resulting in the formation of keto tautomer on the excited state potential energy surface. The keto-type S1 structure is estimated to lie 2.84 eV (CC2 result) above the global minimum of the ground state (see Figure 3a). Figure 3b shows the energy profiles for the MEP associated with the torsion of the amino group. In the S1 state, the MEP for amino torsion could be determined with the exception of geometries, which are very close to the S1−S0 conical intersection (CI), where the CC2 iteration cycle fails to converge. The ϕ((C1−C2−C7−N1) dihedral angle is taken as the driving coordinate, and corresponding energy profiles are represented by the full symbols in Figure 3b. It is seen that the energy profile corresponding to pure twisting of the amino group exhibits roughly flat reaction path from both sides of Figure 3b (left and right) and smoothly reach to the minimum at the middle of PES, corresponding to ϕ((C1−C2−C7−N1) around 90°. At this minimum, the S0/S1 potential energy profiles touch each other and obtain a conical intersection. While the CC2 method is not accurate for the location of the precise geometry of the conical intersection, the conical intersection structures is estimated by the intersection of the CC2 energies roughly before and after the CI point (see Figure 1d). Indeed, the CI stays roughly at the minimum in the reaction path of S1 state, which corresponds to the maximum in the S0 reaction coordinate. Actually, in the regions that the energetic levels of S1 approaches the one of the S0 state, the CC2 optimization faces a problem and ceases to converge. As shown in Figure 3b, the energy of CI is very close to the energy of the ground state minimum of the keto form on the ϕ((C1−C2−C7−N1) reaction path. This suggests that, after torsion of ϕ to 90° in the 1ππ* state, the molecule can easily decay via CI to the S0 state. After intersection point, the reaction coordinate (ϕ) increasing to 180°, leads the raising in curve up to 2.92 eV (corresponding to ϕ((C1−C2− the S(S1) 1 C7−N1) = 180°) and lowering the S(S0) curve to 0.83 eV, which 0 is the minimum-energy-point for the ground state geometry optimized for the trans-keto structure. 3.4. Comparison to Experiment. Although there are no gas-phase experimental data for SBEA, which we can compare to our calculated values, the only experimental data that we can refer to is the absorption spectrum of N-salicylidene-2bromoethylamine (SBEA) obtained in the chloroform by Grivani et al.52 Within the investigated spectral range (200− 400 nm; 3.1−6.2 eV), two absorption bands have been observed with band maxima at 320 and 260 nm (3.88 and 4.69

Figure 4. (a) Experimental UV absorption spectrum of SBEA (adapted from ref 52). (b) Simulated UV absorption spectrum assuming vertical transition energies at the equilibrium geometry of the S0 state, the corresponding oscillator strengths (Table 3), and a convolution of the stick spectra with a Gaussian function of 0.5 eV full width at half-maximum.

4. CONCLUSIONS The proton transfer is the main character of SBEA at the excited state. In contrast to the ground state, the PT process is significantly exoergic in the excited state. From the barrierless potential energy curve of the enol form at the excited state, one can conclude the fast dynamics for such ESIPT. A torsional deformation has been found that acts as the main reaction coordinate to produce the internal conversion between the S1− S0 states. The S1 keto-type conformation is unstable with respect to twisting, which breaks the O···H−N intermolecular hydrogen bond of S1 and leads on a barrierless reaction path to the S1−S0 conical intersection (see Figure 3b). At the S1−S0 conical intersection, the system switches from the S1 surface to the S0 surface via a nonadiabatic transition. It is thus possible that the global minimum structure of SBEA is restored with a probability very close to unity, which is a requirement for the function of SBEA as an effective photostabilizer. This result indicates that the photochromism of certain ESIPT systems is 722

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related to the conical intersection between the potential energy surfaces of the S0 and S1 states.



ASSOCIATED CONTENT

S Supporting Information *

Optimized geometry of the ground states; ground state xyz coordinates of the optimized geometry of 12 rotamers; charge distributions in the ground and the first excited states. This material is available free of charge via the Internet at http:// pubs.acs.org.



AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected] or [email protected]. Fax: (+98) 311 6689732. Notes

The authors declare no competing financial interest.



ACKNOWLEDGMENTS The research council of University of Isfahan is gratefully acknowledged. The calculations have been performed via the Computational Center of the Chemistry Department of University of Isfahan. We are grateful to Dr. Gholam Hossin Grivani for providing the UV absorption spectrum of SBEA.



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NOTE ADDED AFTER ASAP PUBLICATION This paper was published on the Web on January 22, 2013. The first author's name was corrected. The corrected version was reposted on January 31, 2013.

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