TD-DFT Study of the Excited-State Potential Energy Surfaces of 2-(2

Feb 25, 2010 - ... Norimitsu Tohnai , Tomoyuki Akutagawa , Ken-ichi Sakai , Shu Seki .... Kazuki Furukawa , Norifumi Yamamoto , Takakazu Nakabayashi ...
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J. Phys. Chem. A 2010, 114, 4065–4079

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TD-DFT Study of the Excited-State Potential Energy Surfaces of 2-(2′-Hydroxyphenyl)benzimidazole and its Amino Derivatives Hui-Hsu Gavin Tsai,* Hui-Lun Sara Sun, and Chun-Jui Tan Department of Chemistry, National Central UniVersity, Jhong-Li City, Tao-Yuan County 32001, Taiwan ReceiVed: January 2, 2010; ReVised Manuscript ReceiVed: January 21, 2010

In this study, we used TD-PBE0 calculations to investigate the first singlet excited state (S1) behavior of 2-(2′-hydroxyphenyl)benzimidazole (HBI) and its amino derivatives. We employed the potential energy surfaces (PESs) at the S1 state covering the normal syn, tautomeric (S1-Tsyn), and intramolecular charge-transfer (S1-TICT) states in ethanol and cyclohexane to investigate the reaction mechanisms, including excited-state intramolecular proton transfer (ESIPT) and intramolecular charge-transfer (ICT) processes. Two new S1-TICT states, stable in ethanol and cyclohexane, were found for HBI and its amino derivatives; they are twisted and pyramidalized. The flat PES of the ICT process makes the S1-TICT states accessible. The S1-TICT state is effective for radiationless relaxation, which is responsible for quenching the fluorescence of the S1-Tsyn state. In contrast to the situation encountered conventionally, the S1-TICT state does not possess a critically larger dipole moment than its precursor, S1-Tsyn state; hence, it is not particularly stable in polar solvents. On the basis of the detailed PESs, we rationalize various experimental observations complementing previous studies and provide insight to understand the excited-state reaction mechanisms of HBI and its amino derivatives. Introduction In recent years, there has been an increasing interest in excited-state intramolecular proton transfer (ESIPT)1-11 because of its wide applications to such systems as laser dyes,12 fluorescence sensors,13-17 UV-light polymer stabilizers,18 and molecular switches.17,19,20 ESIPT is a photoinduced process in which a proton “hops” from a protic acid group to a basic one; it is generally observed for molecules featuring both a protic acid group and a basic site within a suitable conformation (e.g., one that forms an intramolecular hydrogen bond). For successful ESIPT, the acidity and/or basicity of these groups must increase upon photoexcitation.21 The excited-state behavior of a particular class of hydroxyphenylbenzazole (HBA) derivativessincluding 2-(2′-hydroxyphenyl)benzimidazole (HBI),22-25 2-(2′-hydroxyphenyl)benzoxazole (HBO),25-27 2-(2′-hydroxyphenyl)benzothiazole (HBT),25,28 and their derivativesshas attracted much attention. HBA derivatives have applications as fluorescent probes29,30 (for the labeling of proteins and DNA) and as model base pairs31 (for studying the environments within the major and minor grooves of DNA duplexes). In the ground state (S0), an HBI molecule exists in an equilibrium between several different conformers arising from tautomerism and rotamerism (Figure 1).32 The normal planar syn form (denoted S0-Nsyn)33 features an intramolecular hydrogen bond between the acidic hydroxyl (OH) group and the basic nitrogen atom. The S0-Nsyn conformer can undergo proton transfer (PT) to form its tautomer (denoted S0-Tsyn). These two conformers undergo rotamerization to form their nonplanar anti forms (denoted S0-Nanti and S0-Tanti, respectively). The S0-Nanti form (chemical structure not shown in Figure 1) has its OH group rotated to the opposite side, relative to that of the planar * To whom correspondence should be addressed. E-mail: hhtsai@ cc.ncu.edu.tw.

form. In a protic solvent, the S0-Nanti conformer can form hydrogen bonds with solvent molecules, but it cannot undergo ESIPT. Upon excitation to the first singlet excited state (S1), the OH group of HBI becomes more acidic and/or the nitrogen atom becomes more basic, relative to those in its ground state, thereby inducing ESIPT. In the S1 state, the S1-Tsyn form may become more stable than its tautomer S1-Nsyn. The S1-Tsyn form may return to its ground state (S0-Tsyn) accompanied by fluorescence emission. In some cases, dual fluorescence is observed in polar protic solvents; in addition to fluorescence from the S1-Tsyn form, the S1-Nsyn form (hydrogen-bonded with the solvent) can also exhibit weak-intensity and normal Stokes-shifted fluorescence. Solvent molecules can affect not only the structural equilibrium between these species but also their absorption and fluorescence spectra. The ESIPT process produces the tautomeric form and can be coupled with the formation of other states, such as the intramolecular charge transfer (ICT) state,32 which can form via intramolecular charge transfer with a rotational interannular bond to produce a nonplanar configuration of the two rings. The ICT state can be deactivated back to its ground state via radiationless relaxation. The coupling of ESIPT and ICT is crucial for many important biological processes, including photosynthesis and vision. Although many experimental studies and theoretical calculations34-40 have been performed in this field, the details of these processes at the molecular level have remained poorly understood. Moreover, relatively less research effort has been devoted to understanding the properties of ICT states. Recently, Rodrı´guez-Prieto, Rodrı´guez, and co-workers performed a series of detailed studies, using UV-vis absorption spectroscopy and steady state and time-resolved fluorescence spectroscopy, to investigate the solvent- and temperaturedependence of the rotamerization, tautomerization, and ESIPT processes of HBI and its amino derivatives.25,32 Their studies provide valuable information relating to the excited-state reaction

10.1021/jp100022y  2010 American Chemical Society Published on Web 02/25/2010

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Figure 1. Structures of various HBI species in the ESIPT and ICT processes. From the TD-DFT results, the o-quinoid structures are presented for the tautomeric and ICT forms. The structures displayed here are only one of each of the Lewis structures, which do not present detailed structural and bonding characteristics. For details of the geometrical parameters and bonding, please see the main text.

mechanism of HBI and its amino derivatives. They found that the fluorescence quantum yield (φΤ) of the HBI S1-Tsyn state is independent of the temperature, dielectric permittivity, and viscosity of the solvent. The behavior of 2-(4′-N,N-diethylamino2′-hydroxyphenyl)benzimidazole (denoted HBI-NEt2) is completely different: its value of φΤ decreases strongly when the temperature is increased and is dependent on the solvent’s viscosity. In other words, the excited tautomer of HBI-NEt2 experiences a solvent-dependent radiationless deactivation process, which may not occur for HBI. This process may be associated with a large-amplitude conformational change, such as the formation of internal-rotated ICT states. Nevertheless, the properties of the ICT state have remained unclear.25,32 In this study, we employed time-dependent density functional theory (TD-DFT) to investigate the first singlet excited state behavior of HBI and its amino derivatives, 2-(4′-amino-2′hydroxyphenyl)benzimidazole (denoted HBI-NH2) and HBINEt2. Our main objectives were (1) to locate the stationary structures of the S1-Nsyn, S1-Tsyn, and S1-TICT states (particularly the latter); (2) to understand the structural transformation of the ESIPT and ICT processes upon photoexcitation; (3) to delineate the detailed potential energy surfaces (PESs) of the ESIPT and ICT processes; and (4) to complement experimental observations25,32 on the basis of our theoretical results. All calculations were performed with polar (ethanol) and nonpolar (cyclohexane) solvents to examine the solvent-dependency of these processes. The PESs give valuable information to understand the reaction mechanism of the S1 state in detail. We found that HBI, HBI-NH2, and HBI-NEt2 have two S1-TICT states which are stable in both ethanol and cyclohexane. The existence of nonfluorescent S1-TICT states provides a fluorescence quenching pathway for the S1-Tsyn state-particularly for HBI. Our theoretical findings allowed us to interpret the experimental behavior (e.g., fluorescence quantum yield; temperature- and solvent-dependent fluorescence quantum yield) of the S1-Tsyn states and to determine the reaction mechanisms of the S1 states of HBI and its amino derivatives. Computational Methods All calculations were performed using density functional theory (DFT) within the Turbomole V5.1041 suite of programs on a PC cluster. Energy-minimum structures were searched for the S0 ground states in ethanol and cyclohexane, using a hybrid function, PBE042 with SVP basis set.43 The solvation effect was

treated using a conductor-like screening model (COSMO).44 The  values of cyclohexane and ethanol were set to 2.20 and 24.55, respectively, to model nonpolar and polar environments, respectively. The energy-minimum structure and constrained PES for the S1 state in ethanol and cyclohexane were calculated using TD-DFT with the PBE0 functional and SVP basis set. Vibration frequency calculations were performed to validate that the found energy-minima and transition states corresponded to the stationary states and first-order transition states, respectively. The eigenvectors of the imaginary vibration mode for the first-order transition states were examined visually to validate that they connected the reactant and product properly. TD-DFT methods have been used previously to calculate the ESIPT PESs for a series of ESIPT-allowed molecules, including HBI analogues and HBT, with satisfactory accuracy at comparably moderate computing cost; these methods appear to be appropriate for the description of the ESIPT PES.45,46 In particular, the TD-PBE0 method provide electronic spectra that are in very good agreement with the available experimental results.47 Figure 2a presents the chemical structures (with atom labeling) of HBI, HBI-NH2, and HBI-NEt2. The pyramidalization angle (R) centered at the C1 atom was defined as the angle between the vector of the C1-C2 bond and the plane defined by the three atoms C1, N6, and N (Figure 2b). A similar definition was applied to calculate the pyramidalization angle (R) centered at the N18 atom. Results Energies of Stationary Points in S0 and S1 States. Determining the stationary points of HBI, HBI-NH2, and HBI-NEt2 in the S0 and S1 states and their relative energies gave us the first idea of how the ESIPT and ICT processes occur (Figure 1). We searched the stationary points of the Nsyn, Tsyn, and TICT forms of HBI, HBI-NH2, and HBI-NEt2 in their S0 and S1 states in ethanol and cyclohexane using the PBE0/SVP theoretical method with the COSMO solvent model; we did not search the anti forms because they are not involved in the ESIPT process. Table 1 lists the relative energies of the stationary Nsyn, Tsyn, and TICT forms of HBI, HBI-NH2, and HBI-NEt2 in the S0 and S1 states in cyclohexane and ethanol. These stationary structures were validated in terms of their vibrational frequency calculations with all positive values.

PES of 2-(2′-Hydroxyphenyl)benzimidazole

Figure 2. (a) Chemical structures and atom labels of HBI, HBI-NH2, and HBI-NEt2. The nitrogen atom of the NH2/NEt2 group is labeled N18. (b) Pyramidalization angle (R) centered at the C1 atom, defined as the angle between the vector of the C1-C2 bond and the plane defined by the three atoms C1, N6, and N. (c) Pyramidalization angle (R) centered at the N18 atoms of the NH2 and NEt2 groups, defined as the angle between the vector of the N18-C16 bond and the plane defined by the N18 atom and its two bonded atoms (not C16).

For the S0 state, we found the stationary points of the Nsyn forms for HBI, HBI-NH2, and HBI-NEt2 in ethanol and cyclohexane. In contrast, we did not find the stationary points of the S0-TICT forms, with twisted structures, for any of the three studied molecules, either in ethanol or in cyclohexane. The stationary points of the Tsyn forms of the three studied molecules were stable only in ethanol; we did not find them in cyclohexane. In ethanol, the S0-Nsyn forms of HBI, HBI-NH2, and HBI-NEt2 were ca. 5.6-5.8 kcal/mol more stable in energy than their corresponding S0-Tsyn forms. These results indicate that HBI, HBI-NH2, and HBI-NEt2 mainly adopt normal syn conformations, with an intramolecular hydrogen bond in the S0 state. In the S1 state, we found the stationary points of the S1-Nsyn, S1-Tsyn, and S1-TICT forms of HBI-NH2 and HBI-NEt2 in ethanol and cyclohexane. For HBI, we also located the stationary points of the S1-Tsyn and S1-TICT forms in ethanol and in cyclohexane, but we could not locate the stationary point of its S1-Nsyn form in either solvent. The normal syn structure of HBI was converted to its tautomeric form during the geometry optimization, due to its barrierless PES for ESIPT (vide infra). Interestingly, we found two stationary ICT states (denoted S1-TICT-1 and S1-TICT-2) for HBI, HBI-NH2, and HBI-NEt2 in the ethanol and cyclohexane. The structures of these two S1-TICT forms exhibited twisting between the two rings and pyramidalization at C1 atoms. More interestingly, for all three systems in ethanol, the two S1-TICT forms and the S1-Tsyn form had similar energies; in contrast, in cyclohexane, the two S1-TICT forms were ca. 6-7 kcal/mol more stable in energy than the corresponding S1-Tsyn form. Structure and Structural Change Involved During Reactions. The equilibrium geometries of the stationary points and their differences provided us with the basis to understand how the molecular structure transformed upon photoexcitation, ESIPT, and ICT. Figure 3 displays the important bond lengths (C1-C2, C2-C3, N6-C1, C3-O4) of the S0-Nsyn, S1-Nsyn, and S1-Tsyn states of HBI, HBI-NH2, and HBI-NEt2 in ethanol and cyclohexane. For the S0-Nsyn f S1-Nsyn and S1-Nsyn f S1-Tsyn processes, these bond lengths changed significantly with

J. Phys. Chem. A, Vol. 114, No. 12, 2010 4067 the same trend for three studied molecules. Detailed geometric parameters of the found stationary points of HBI, HBI-NH2, and HBI-NEt2 and their geometric changes after photoexcitation and reactions are provided in the Supporting Information. In the S0 state, the S0-Nsyn structures of HBI, HBI-NH2, and HBI-NEt2 were planar in both ethanol and cyclohexane, as indicated by their near-zero torsion angles τ(N6-C1-C2-C3) associated with the phenol and benzimidazole rings. After photoexcitation (S0-Nsyn f S1-Nsyn), the S1-Nsyn structures of HBI, HBI-NH2, and HBI-NEt2 remained planar in both solvents, with the bond angles effectively unchanged;48 some of the bond lengths, however, were affected: the C1-C2 bond shortened and the C2-C3 and N6-C1 bonds elongated significantly (Figure 3). These changes in bond length resulted from the π-electron density transition from the highest occupied molecular orbital (HOMO) to the lowest unoccupied molecular orbital (LUMO) in S0-Nsyn (Figures 4a and 4b). After the HOMO to LUMO transition, the π-bond character of the C2-C3 and N6-C1 bonds decreased; therefore, these bonds were elongated. In contrast, the π-bond character of the C1-C2 bond increased, thereby shortening the C1-C2 bond and, consequently, decreasing the H5 · · · N6 distance, which was advantageous for ESIPT. Moreover, the excitation also increased the electron density on the O4 atom, thereby enhancing the acidity of the OH group, which also promoted ESIPT. During the ESIPT process (S1-Nsyn f S1-Tsyn), the O-H bond broke and the N-H bond formed, leading to rearrangement of the electron density and molecular geometry, causing the C3-O4 bond to shorten. For example, for HBI-NH2 in ethanol, the C3-O4 bond shortened by 0.05 Å (from 1.323 Å in S1-Nsyn to 1.273 Å in S1-Tsyn), giving it more carbonyl character. Interestingly, the central C1-C2 bond elongated moderately, thereby decreasing its partial double bond character (e.g., for HBI-NH2 in ethanol, it increased by 0.025 Å from 1.417 Å in S1-Nsyn to 1.442 Å in S1-Tsyn). This elongation of the central C1-C2 bond and the breaking of the hydrogen-bonded chelated ring in S1-Tsyn may lead to the inter-rotation of the quinoid and benzimidazole rings. Inter-rotation of the two rings of the planar S1-Tsyn state, driven by thermal energy, will lead to the formation of twisted intermolecular CT states.49,50 We found two nonplanar ICT states (denoted S1-TICT-1 and S1-TICT-2). More interestingly, they are not only twisted, but also pyramidalized at the C1 atom of the benzimidazole ring. Figure 5 displays the structures of the two ICT states of HBI in ethanol. The direction of pyramidalization is opposite for the S1-TICT-1 and S1-TICT-2 states. For the S1-TICT-1 state of HBI in ethanol, the pyramidalization angle was 41.5° and the C3-C2-C1-N6 torsion angle was 117.2°; for the S1-TICT-2 state of HBI in ethanol, these angles were -32.6° and 67.6°, respectively. The pyramidalization of the S1-TICT-1 and S1-TICT-2 states can be understood by considering the HOMO and LUMO orbitals of the S0-Tsyn form. As indicated in Figures 4c and 4d, after the S0 f S1 transition of the S0-Tsyn form, the electron density located at the C1 atom increased, thereby repelling the atoms connected to the C1 atom and resulting in a pyramidal structure. Potential Energy Curve of ESIPT. We calculated the potential energy curves of HBI connecting the Nsyn and Tsyn states as a function of O4 · · · H5 distance to describe the ESIPT process in the S0 and S1 states in cyclohexane and ethanol (Figure 6). Apart from constraining the O4 · · · H5 distance, we relaxed all other degrees of freedom without imposing any symmetry constraints during the geometry optimization. For the ground state, the potential energy of HBI in cyclohexane

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TABLE 1: Relative Energies (kcal/mol) of the Stationary Nsyn, Tsyn, and TICT States of HBI, HBI-NH2 and HBI-NEt2 in the Ground State (S0) and First Singlet Excited State (S1) in Ethanol and Cyclohexanea in ethanolb state-conformer

HBI

S0-Nsyn S0-Tsync S0-TICTc S1-Nsyn (FC)d S1-Nsync S1-Tsyn S1-TICT-1 S1-TICT-2

0.00 5.83

0.00 5.62

0.00 5.82

0.00

0.00

0.00

12.92

8.43 5.41 0.00 -1.74 -2.05

4.85 2.54 0.00 -1.36 -1.61

12.21

10.67 7.54 0.00 -7.09 -6.52

7.98 5.40 0.00 -5.89 -5.33

0.00 0.45 0.03

HBI-NH2

in cyclohexaneb HBI-NEt2

HBI

0.00 -6.68 -6.19

HBI-NH2

HBI-NEt2

a All calculations were performed at the PBE0/SVP level with the COSMO solvent model. b The relative energies were calculated for the same electronic state and in the same solvent; in the S0 state, the energy of the S0-Nsyn form was used as the reference; in the S1 state, the energy of the S1-Tsyn form was chosen as the reference. c A dash indicates that the energy-minimum structure was not found. d The energy was calculated at its Franck-Condon (FC) state.

Figure 3. Bond lengths (C1-C2, C2-C3, N6-C1, C3-O4) of the S0-Nsyn, S1-Nsyn, and S1-Tsyn states of HBI, HBI-NH2, and HBI-NEt2 in ethanol and cyclohexane. Because the stationary S1-Nsyn form of HBI was not found, we calculated the geometry of the S1-Nsyn form of HBI with its O-H distance constrained at 1.026 Å, the optimized distance for HBI-NH2.

increased upon increasing the O4 · · · H5 distance; hence, the S0-Tsyn state was not stabilized in cyclohexane. In ethanol, the potential energy of HBI converged to a minimum upon increasing the O4 · · · H5 distance, resulting in a stationary S0-Tsyn state, which was ca. 5.8 kcal/mol less stable than its corresponding S0-Nsyn state. Following the potential energy curves for the HBI S1 state in cyclohexane and ethanol from shorter O4 · · · H5 distances to longer ones, we observed no energy minimum in the region of the S1-Nsyn state. Therefore, the ESIPT process for HBI is barrierless and the S1-Tsyn state is more stable than the S1-Nsynlike state. Thus, the ESIPT of HBI is a barrierless, spontaneous,

exothermic process in both ethanol and cyclohexane. More interestingly, the potential energy curves for these processes in cyclohexane and ethanol nearly overlapped, indicating that the ESIPT process for HBI is insensitive to the polarity of the solvent. Figure 7 displays potential energy curves for the PT processes of HBI-NH2 in ethanol and cyclohexane. In the S0 state, the PT behavior of HBI-NH2 is similar to that of HBI: the S0-Tsyn state is stabilized in ethanol, but not in cyclohexane. In the S1 state, there is a barrier separating the S1-Nsyn and S1-Tsyn states of HBI-NH2-a different situation with respect to the barrierless ESIPT process for HBI. This barrier was 2.08 kcal/mol in

PES of 2-(2′-Hydroxyphenyl)benzimidazole

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Figure 4. HOMO and LUMO orbitals of the (a, b) S0-Nsyn and (c, d) S0-Tsyn forms, calculated at the PBE0/SVP level in the gas phase. The geometry of the S0-Tsyn form was optimized with the N6-H5 distance constrained at 1.05 Å because its true stationary point was not found. The chemical structure and some atom labels of HBI are provided for convenience.

ethanol (O4 · · · H5 distance: 1.20 Å) and 1.34 kcal/mol in cyclohexane (O4 · · · H5 distance: 1.20 Å). These barrier heights are slightly lower than the energies of their corresponding S1-Nsyn Franck-Condon states. A barrier has also been observed for the ESIPT process of HBO, calculated at the CIS/ TDDFT level in the gas phase.51 Figure 8 displays the potential energy curves for the PT processes of HBI-NEt2 in ethanol and cyclohexane. In the S0 state, the PT behavior of HBI-NEt2 is similar to those of HBI and HBI-NH2. In the S1 state, the PT behavior of HBI-NEt2 is similar to that of HBI-NH2: an energy barrier exists between the S1-Nsyn and S1-Tsyn states and the ESIPT process is exothermic; this barrier is 3.36 kcal/mol in ethanol (O4 · · · H5 distance: 1.30 Å) and 3.03 kcal/mol in cyclohexane (O4 · · · H5 distance: 1.25 Å). These barrier heights are comparable with (slightly lower than) those of their corresponding Franck-Condon states. Unlike the similar ESIPT behavior of HBI in ethanol and cyclohexane, HBI-NH2 and HBI-NEt2 are more stable in cyclohexane than in ethanol after crossing the ESIPT barrier. Upon photoexcitation, the reaction starts from the FranckCondon point S1-Nsyn (FC), with the geometry of the S0-Nsyn state; it passes through the S1-Nsyn state with geometric rearrangement from the S1-Nsyn (FC) state, with the molecule gaining a certain amount of kinetic energy. For HBI, the ESIPT occurs spontaneously and quickly because it is a barrierless reaction. For HBI-NH2 and HBI-NEt2, the Franck-Condon

Figure 5. Structures of the ICT states of HBI calculated at the PBE0/ SVP level in ethanol: (a) S1-TICT-1 and (b) S1-TICT-2.

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Figure 6. Potential energy curves of HBI as a function of the O4 · · · H5 distance (in Å): (a) in the ground state in cyclohexane and ethanol; (b) in the first singlet excited state in cyclohexane and ethanol. Calculations were performed at the TD-PBE0/SVP level with the COSMO solvent model. The stationary point of the S0-Tsyn state in cyclohexane was not located; for comparison, it is represented by S0-Tsyn*, with an O4 · · · H5 distance of 1.6 Å. In the first singlet excited state, the stationary point of the S1-Nsyn state was not found in cyclohexane or ethanol; the Franck-Condon states are denoted in the graph by S1-Nsyn (FC).

Figure 7. Potential energy curves of HBI-NH2 as a function of the O4 · · · H5 distance (in Å): (a) in the ground state in cyclohexane and ethanol; (b) in the first singlet excited state in cyclohexane and ethanol. Calculations were performed at the TD-PBE0/SVP level with the COSMO solvent model. The stationary point of the S0-Tsyn state in cyclohexane was not located; for comparison, it is denoted by S0-Tsyn*, with an O4 · · · H5 distance of 1.6 Å. In the first singlet excited state, the Franck-Condon states are denoted in the graph by S1-Nsyn (FC).

states have larger kinetic energies, which will drive the molecules to overcome the energy-comparable barriers between the S1-Nsyn and S1-Tsyn states; the existence of energy barriers will, however, retard the formation of the S1-Tsyn states and reduce the yields of the S1-Tsyn states. PES of Excited-State ICT Reaction. In addition to the formation of the S1-Tsyn state, the ESIPT process can also produce excited-state ICT states. We calculated the PESs of S1-Tsyn f S1-TICT reactions to understand their thermodynamics and kinetics. Relative to the structure of the S1-Tsyn state, the two largest structural differences in the excited-state ICT states are found in the torsion angle between the two rings and the pyramidalization angle centered at the C1 atom. The other coordinates remained nearly constant or were dependent on only these two coordinates during the S1-Tsyn f S1-TICT processes. Therefore, we used the N6-C1-C2-C3 dihedral angle and pyramidalization angle centered at the C1 atom to calculate the three-dimensional PES. This approach has been used previously to describe the PES of the electrocyclic ring-opening of cyclohexadiene.52 Figures 9-11 display the 3D PESs of the S1-Tsyn f S1-TICT processes for HBI, HBI-NH2, and HBINEt2 in ethanol and cyclohexane in terms of the N6-C1-C2-C3 torsion angle and the pyramidalization angle centered at the C1 atom. The presented ranges of dihedral and pyramidalization angles cover the stationary points of the S1-Tsyn and S1-TICT

states. The dihedral and pyramidalization angle were scanned every 10° and 5°, respectively. Determining the minimum-energy pathway (MEP) connecting the S1-Tsyn and S1-TICT states allowed us to understand the mechanism of this reaction. We established the MEP by considering the PESs as lattices. Starting from the S1-Tsyn state, we searched the lowest point of all its nearest neighbors, including the diagonal point. To avoid recursion and to let the reaction move toward the product, any new accepted step will move to a point having a dihedral and/or pyramidalization angle closer to those of the products. For example, for the S1-Tsyn f S1-TICT-1 reaction, the intermediates move to attain a larger dihedral and/or larger pyramidalization angle. The MEPs of the S1-Tsyn f S1-TICT-1 and S1-Tsyn f S1-TICT-2 reactions are labeled with arrows on the surfaces. In ethanol, the three studied molecules have similar PESs: there are three lower-energy valleys existing on the surfaces corresponding to the S1-Tsyn and two S1-TICT states; these three states are nearly isoenergetic, as discussed above. There is an energy ridge separating the reactant (S1-Tsyn) and the two products (S1-TICT-1 and S1-TICT-2). The MEPs of the S1-Tsyn f S1-TICT-1 reactions of the three studied molecules in ethanol have similar characteristics: before reaching the transition state (TS) region, the reaction occurred through a zigzag pathway by changing the N6-C1-C2-C3

PES of 2-(2′-Hydroxyphenyl)benzimidazole

Figure 8. Potential energy curves of HBI-NEt2 as a function of the O4 · · · H5 distance (in Å): (a) in the ground state in cyclohexane and ethanol; (b) in the first singlet excited state in cyclohexane and ethanol. Calculations were performed at the TD-PBE0/SVP level with the COSMO solvent model. The stationary point of the S0-Tsyn state in cyclohexane was not located; for comparison, it is denoted by S0-Tsyn*, with an O4 · · · H5 distance of 1.6 Å. In the first singlet excited state, the Franck-Condon states are denoted in the graph by S1-Nsyn (FC).

dihedral angle and the pyramidalization angle alternatively; once the molecules were close to the TS region, the reaction followed the MEP pathway of increasing torsion angle only (i.e., the pyramidalization angle remains unchanged). The TS structures of HBI, HBI-NH2, and HBI-NEt2 were similar, each having a pyramidalization angle of ca. 25°. The TS structure of HBI had an N6-C1-C2-C3 dihedral angle of 70° and an activation energy of 2.22 kcal/mol; for HBI-NH2, these values were 70° and 2.15 kcal/mol, respectively; for HBI-NEt2, they were 60° and 2.79 kcal/mol, respectively i.e., slightly higher than those of HBI and HBI-NH2. For the S1-Tsyn f S1-TICT-2 reaction in ethanol, the TS structures for all three studied molecules had the same N6-C1C2-C3 dihedral angle of 40° and a pyramidalization angle of -10°. The activation energies for HBI, HBI-NH2, and HBINEt2 were 2.81, 2.82, and 3.25 kcal/mol, respectively somewhat higher than those of their corresponding S1-Tsyn f S1-TICT-2 reactions. The PESs for HBI, HBI-NH2, and HBI-NEt2 in cyclohexane were different from those in ethanol. In cyclohexane, there were two lower-energy valleys existing on the surfaces, corresponding to the two S1-TICT states, with the valley of the S1-Tsyn state being less obvious. For all three studied molecules, the TS energies for the S1-Tsyn f S1-TICT reactions in cyclohexane were lower than their corresponding values in ethanol. For the

J. Phys. Chem. A, Vol. 114, No. 12, 2010 4071 S1-Tsyn f S1-TICT-1 reactions in cyclohexane, the TS energies, N6-C1-C2-C3 dihedral angles, and pyramidalization angles were 0.42 kcal/mol, 50°, and 10°, respectively, for HBI; 1.04 kcal/mol, 50°, and 15°, respectively, for HBI-NH2; and 2.13 kcal/mol, 40°, and 25°, respectively, for HBI-NEt2. For the S1-Tsyn f S1-TICT-2 reactions in cyclohexane, the TS energies, N6-C1-C2-C3 dihedral angles, and pyramidalization angles were 0.56 kcal/mol, 20°, and -10°, respectively, for HBI; 1.17 kcal/mol, 40°, and -5°, respectively, for HBI-NH2; and 1.88 kcal/mol, 40°, and -5°, respectively, for HBI-NEt2. In contrast to the S1-Tsyn state, the fluorescence of the S1-TICT states is nearly forbidden. For example, for HBI-NEt2 in ethanol, the calculated fluorescence oscillator strengths were 1.4 × 10-5 for the S1-TICT-1 state and 5.4 × 10-6 for the S1-TICT-2 state; in contrast, the fluorescence oscillator strength of the S1-Tsyn form was 0.11. Figure 12 presents the S1-S0 energy difference of tautomeric HBI-NEt2 in ethanol and cyclohexane as a function of the N6-C1-C2-C3 dihedral angle and pyramidalization angle centered at the C1 atom (corresponding to the PES of Figure 11). The two smaller S1-S0 energy gaps are observed at the ICT structural regions. In ethanol, the S1-S0 energy gap is reduced from the highest energy (70.15 kcal/mol) at the S1-Tsyn state to the lowest energy (31.36 kcal/mol) at the S1-TICT-1 region and to the lowest energy (36.74 kcal/mol) at the S1-TICT-2 region; in cyclohexane, the S1-S0 energy gap is reduced from the highest energy (64.32 kcal/mol) at the S1-Tsyn state to the lowest energy (17.59 kcal/ mol) at the S1-TICT-1 region and to the lowest energy (28.44 kcal/mol) at the S1-TICT-2 region. We observed quite similar trends for HBI and HBI-NH2 in ethanol and cyclohexane (data provided in the Supporting Information). The smaller S1-S0 energy gaps imply effective internal conversion channels for the ICT states. Effect of Amino/Diethylamino Group Rotation. To obtain a more complete understanding of the behavior of HBI-NH2 and HBI-NEt2, we searched their S1-Tsyn conformers featuring twisted terminal amino/diethylamino groups. We found no stationary S1-Tsyn conformer having a twisted terminal amino/ diethylamino group: the energies of the S1-Tsyn conformers of HBI-NH2 and HBI-NEt2 increased upon increasing the twist angle between the quinoid ring and the amino/diethylamino group. We used the torsion angles H2-N18-C16-C17 and (H2)C-N18-C16-C17 to measure the degree of amino/diethylamino group twisting for HBI-NH2 and HBI-NEt2, respectively. Pyramidalization, centered at the N18 atoms, accompanied the amino/diethylamino group twisting. Interestingly, twisting of the amino/diethylamino group did not reduce the fluorescence oscillator strength of the HBI-NH2 and HBI-NEt2 S1-Tsyn states. Moreover, the S1-S0 energy gap was not reduced significantly upon twisting of the amino/diethylamino group. These results indicate that twisting of the amino/diethylamino group does not quench the fluorescence of the HBI-NH2 and HBI-NEt2 S1-Tsyn states. The supporting material provides the relative energy, fluorescence oscillator strength, S1-S0 energy gap, and degree of pyramidalization centered at the N18 atoms as functions of the torsion angles H2-N18-C16-C17 and (H2)C-N18-C16-C17 for HBI-NH2 and HBI-NEt2, respectively, in ethanol. Discussion In the photoexcitation process, the ground states of HBI and its derivatives absorb photons and undergo a rearrangement of their electron density, which induces the ESIPT process and produces the excited state tautomeric forms. Our calculations reveal that one planar and two nonplanar excited state tautomeric

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Figure 9. PESs of the S1 state of HBI in (a) ethanol and (b) cyclohexane as a function of the N6-C1-C2-C3 torsion angle and the pyramidalization angle centered at the C1 atom. The energy of the S1-Tsyn state was chosen as the reference. The MEP from the S1-Tsyn state to the S1-TICT-1 state is depicted in red arrows; the MEP from the S1-Tsyn state to the S1-TICT-2 state is depicted in yellow arrows.

forms exist for each of HBI, HBI-NH2, and HBI-NEt2. They are all stable in polar (ethanol) and nonpolar (cyclohexane) solvents. The occurrence of these sequential processes can be understood by considering the electron density change after photoexcitation and the consequent changes in the interannular bond length. Upon excitation, the electron density of the ground state of HBI was mainly promoted from its HOMO to its LUMO. This excitation increases the π-character of the interannular C1-C2 bond, thereby shortening it, as observed for the S1-Nsyn forms of constrained-HBI,53 HBI-NH2, and HBI-NEt2 in both ethanol and cyclohexane. The shortening of the interannular C1-C2 bond decreases the N6 · · · H5 distance, thereby promoting the occurrence of the ESIPT processes.

After ESIPT, the electron density underwent rearrangement; nevertheless, the S1-Tsyn forms of HBI, HBI-NH2, and HBINEt2 remained planar and the interannular bond lengths of the S1-Tsyn forms were longer than those of the S1-Nsyn forms. A longer C-C bond implies a lower double-bond character. Hence, the energy barrier for inter-rotation of the two rings of the S1-Tsyn form is lower than that of the corresponding S1-Nsyn form. Inter-rotation of the two rings of the S1-Tsyn form, driven by thermal energy, leads to the formation of the nonplanar S1-TICT form. Moreover, the two found S1-TICT forms are pyramidalized at the C1 atom, but with opposite directions of pyramidalization. The pyramidalization of the S1-TICT form at the C1 atom can be understood by considering the large increase

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Figure 10. PESs of the S1 state of HBI-NH2 in (a) ethanol and (b) cyclohexane as a function of the N6-C1-C2-C3 torsion angle and the pyramidalization angle centered at the C1 atom. The energy of the S1-Tsyn state was chosen as the reference. The MEP from the S1-Tsyn state to the S1-TICT-1 state is depicted in red arrows; the MEP from the S1-Tsyn state to the S1-TICT-2 state is depicted in yellow arrows.

in electron density at the C1 atom of the S1-Tsyn form, which repels the atoms connected to the C1 atom. The relationship between the two S1-TICT conformations of each of the three studied molecules is comparable with umbrella-like conformational inversion. Similar pyramidalization at one of the ethylenic carbon atoms of stilbene has been suggested as a prerequisite coordinate for its cis-trans photoisomerization.54 Based on the electron density and geometrical changes, we provide an understanding of the ESIPT and ICT processes of HBI and its amino derivatives in a static fashion. To understand the chemical dynamics of ESIPT and ICT processes theoretically, one can

analyze the normal modes along the MEP51 or perform on-thefly dynamics simulations using TD-DFT.55 Our findings brought up two new questions: Why does an energy barrier exist for the ESIPT process for HBI-NH2 and HBI-NEt2, but not for HBI? Why do the energy barriers follow the order HBI (barrierless) < HBI-NH2 < HBI-NEt2? To answer these questions, we consider the interannular bond length differences among the S1-Nsyn forms of HBI, HBI-NH2, and HBI-NEt2. Because we could not find the stationary point of the HBI S1-Nsyn form, we calculated40 the geometry of the constrained HBI S1-Nsyn form for the following discussion. In ethanol, the interannular bond length

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Figure 11. PESs of the S1 state of HBI-NEt2 in (a) ethanol and (b) cyclohexane as a function of the N6-C1-C2-C3 torsion angle and the pyramidalization angle centered at the C1 atom. The energy of the S1-Tsyn state was chosen as the reference. The MEP from the S1-Tsyn state to the S1-TICT-1 state is depicted in red arrows; the MEP from the S1-Tsyn state to the S1-TICT-2 state is depicted in yellow arrows.

of the S1-Nsyn form increased from 1.413 Å in HBI, to 1.417 Å in HBI-NH2, to 1.421 Å in HBI-NEt2. The elongation of the interannular bond lengths of the S1-Nsyn forms of HBI-NH2 and HBI-NEt2 also increased the distance between the donor and acceptor units for the subsequent ESIPT process, thereby creating an energy barrier. TD-DFT has been used to investigate the ICT mechanism in 4-(dimethylamino)benzonitrile by calculating the minimum energy path with satisfactory accuracy.56 The results confirm the state-crossing model of dual fluorescence. In this study, we employed TD-DFT to study the ICT mechanism of HBI and

its amino derivatives. Our present TD-DFT calculations reveal that there are two excited-state tautomeric ICT forms of HBI, HBI-NH2, and HBI-NEt2 that are stable in polar (ethanol) and apolar (cyclohexane) solvents. The structures of these two ICT states (denoted S1-TICT-1 and S1-TICT-2) are nonplanar and pyramidalized. The PESs for the S1-Tsyn f S1-TICT reactions of HBI, HBI-NH2, and HBI-NEt2 are quite flat; for example, in ethanol, the activation energies of the S1-Tsyn f S1-TICT-1 reactions of HBI, HBI-NH2 and HBI-NEt2 are 2.22, 2.15, and 2.79 kcal/mol, respectively. Moreover, the corresponding activation energies in cyclohexane are even lower. These results imply

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Figure 12. S1-S0 energy differences (kcal/mol) of tautomeric HBI-NEt2 in (a) ethanol and (b) cyclohexane as a function of the N6-C1-C2-C3 torsion angle and the pyramidalization angle centered at the C1 atom.

that thermal energy can drive the formation of the S1-TICT state from the S1-Tsyn state. Interestingly, when the reaction reaches the S1-TICT state region, its S1/S0 energy gap is significantly reduced, which is effective for internal conversion. Moreover, the fluorescence ability of the S1-TICT state vanished. Taken together, formation of S1-TICT species is an effective pathway to quench the fluorescence of S1-Tsyn species for HBI, HBINH2, and HBI-NEt2. A recent study combining state-of-the-art ultrafast pump-probe experiments and theoretical calculations revealed details of the photodynamic processes of HBT,55 an analogue of HBI, with lifetimes of 2.6 ps in the gas phase and ca. 100 ps in cyclohexane. Using quantum chemical calculations based on multireference configuration interactions and on-the-

fly dynamics simulations, that study clearly demonstrated that the planar HBT S1-Tsyn state can reach a nonplanar structural region without a barrier on the S1 surface in the gas phase. This nonplanar structure of HBT is twisted with a certain degree of pyramidalization at the bridge carbon atom of the thiazole ring, similar to the S1-TICT structures that we report herein for HBI, HBI-NH2, and HBI-NEt2. This twisted and pyramidalized structure features an S0/S1 conical intersection, which is responsible for ultrafast decay. Our results for HBI, HBI-NH2, and HBI-NEt2 are consistent with the findings reported previously for HBT. Experimentally,25,32 the fluorescence quantum yield (φΤ) of the S1-Tsyn form for HBI is independent of the solvent and

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temperature. The behavior for the HBI amino derivatives is completely different. For HBI-NEt2, the value of φΤ decreases as the temperature is increased; it is also influenced by the viscosity of the solvent. In addition, the value of φΤ of HBINEt2 is much lower than that of HBI. To interpret these experimental observations for HBI and HBI-NEt2, Rodrı´guezPrieto, Rodrı´guez, and co-workers suggested that a nonfluorescent ICT state is produced by the S1-Tsyn form via a largeramplitude motion,25,32 whereas HBI does not undergo such motion to produce its nonfluorescent ICT state. The formation of the nonfluorescent ICT state for HBI-NEt2 should be temperature-dependent; it will also quench the fluorescence quantum yield. In contrast, the value of φΤ of HBI is independent of the temperature or solvent. Nevertheless, information regarding the ICT state remains unclear. In this study, we found two stationary S1-TICT structures that are stable in both ethanol and cyclohexane for each of HBI, HBI-NH2, and HBI-NEt2. These findings for HBI-NEt2 are consistent with the suggestions of Rodrı´guez-Prieto, Rodrı´guez, and co-workers.25,32 More interestingly, we also found two stationary S1-TICT states for HBIquite different from previous suggestions.25,32 As discussed above, a twisted and pyramidalized structure (an S1-TICT-like state) exists for HBT in the gas phase and in cyclohexane, effective for internal conversion, which implies that an amino group is not required to induce the S1-TICT state, even in nonpolar environments. Our calculations afforded detailed PESs connecting the S1-Nsyn, S1-Tsyn, and S1-TICT forms, thereby providing valuable kinetic and thermodynamic information regarding the excited state reactions. Therefore, below we rationalize the experimental results,25,32 based on our present findings, to complement the experimental interpretations. First, we summarize the pertinent experimental observations for HBI.25,32 (1) The value of φΤ of HBI is independent of the temperature (in 2-butanol) and solvent; (2) the value of φΤ of HBI is much higher than that of HBI-NEt2, in both polar and nonpolar solvents (e.g., in methanol, the values of φΤ for HBI and HBI-NEt2 are 0.15 and 0.07, respectively; in cyclohexane, they are 0.11 and 0.06, respectively); (3) the value of φΤ of HBI is lower in cyclohexane (φΤ ) 0.11) than in polar solvents, such as methanol (φΤ ) 0.15) and acetonitrile (φΤ ) 0.25). As discussed above, the S1-Nsyn and S1-TICT states are connected to the S1-Tsyn state, which will influence the value of φΤ: the formation of the S1-Tsyn state (e.g., from the S1-Nsyn state) will increase φΤ and the depletion of the S1-Tsyn state will decrease φΤ, such as in the formation of the S1-TICT state. HBI has two S1-TICT states connected to its S1-Tsyn state, separated by an energy barrier. Therefore, we would first expect the S1-TICT states to quench their values of φΤ and result in temperature-dependent φΤ behavior. Our theoretical results reveal, however, that the S1-TICT states of HBI will not quench their values of φΤ significantly. For HBI in ethanol, the S1-Tsyn, S1-TICT-1, and S1-TICT-2 states are nearly isoenergetic; the S1-TICT-1 state is 0.45 kcal/mol higher in energy than that of the S1-Tsyn state and the S1-TICT-2 state is 0.03 kcal/mol higher in energy than that of the S1-Tsyn state. Therefore, increasing the temperature will enhance the formation of the S1-TICT states (S1-Tsyn f S1-TICT-1); nevertheless, the thermal energy will also accelerate the backward reaction, from the S1-TICT to the S1-Tsyn state, because it has a slightly lower activation energy than that of the forward reaction. Equilibrium between the S1-Tsyn and S1-TICT states, with similar forward and backward reaction rates, leads to a temperature-independent φΤ-T profile, which can be used to interpret the experimental observations.

Tsai et al. Our results reveal that the formation of the S1-Tsyn state via ESIPT is barrierless for HBI in both ethanol and cyclohexane. For HBI-NEt2, there is an energy barrier separating the S1-Tsyn and S1-TICT states (e.g., 3.36 kcal/mol in ethanol). Although the momentum of the S1-Tsyn Franck-Condon state may be sufficient for HBI-NEt2 to overcome this barrier, this barrier will retard the formation of the HBI-NEt2 S1-Tsyn state, which will reduce its value of φT. In ethanol, the S1-Tsyn f S1-TICT reaction of HBI-NEt2 is exothermic. Therefore, the trend is toward the depletion of the S1-Tsyn state of HBI-NEt2. Notably, this trend is opposite that for HBI in ethanol. In addition, the calculated oscillator strength of the S1-Tsyn state is larger for HBI (0.29 in ethanol) than it is for HBI-NEt2 (0.11 in ethanol). Taking into consideration the PES of the ESIPT process, the S1-Tsyn a S1-TICT reactions, and the oscillator strength of the S1-Tsyn state, our theoretical results suggest that HBI should have a larger value of φT than that of HBI-NEt2, as observed experimentally. Interestingly, experimental studies indicate that HBI has a lower value of φT in nonpolar solvents (cyclohexane) than in polar solvents. For example, the values of φT for HBI in cyclohexane, methanol, and acetonitrile are 0.11, 0.15, and 0.25, respectively. Our calculations suggest that the oscillator strengths of the HBI S1-Tsyn forms should be similar in ethanol and cyclohexane: the calculated oscillator strengths are 0.29 in ethanol and 0.26 in cyclohexane. In addition, the energy profiles for the ESIPT processes of HBI are also similar for ethanol and cyclohexane. Nevertheless, their PESs for the S1-Tsyn f S1-TICT reaction are completely different. In cyclohexane, this reaction is exothermic (∆E ) -6.68 kcal/mol for S1-TICT-1; ∆E ) -6.19 kcal/mol for S1-TICT-2); the reaction barriers are 0.56 and 0.42 kcal/mol for S1-TICT-1 and S1-TICT-2, respectively. In contrast, in ethanol, the processes are slightly endothermic and the reaction barriers are higher (2.22 and 2.82 kcal/mol for S1-TICT-1 and S1-TICT-2, respectively). Therefore, the exothermic and lower energy barrier for the S1-Tsyn f S1-TICT reaction in cyclohexane will quench the fluorescence more extensively than that in ethanol, consistent with the experimental observations. Note that our calculations using the conductor-like screening model do not consider the effect of the solvent viscosity on the energy barrier. The effect of solvent viscosity, however, will not affect our conclusion here because methanol (η ) 0.55) and acetonitrile (η ) 0.24) have lower viscosities than cyclohexane (η ) 0.98). By considering the effect of solvent viscosity only, we would expect the S1-Tsyn f S1-TICT quenching for HBI to be more effective in methanol and acetonitrile than in cyclohexane. The value of φT of HBI is, however, quenched to a greater degree in cyclohexane than in methanol or acetonitrile; hence, the smaller value of φT of HBI in cyclohexane does not arise mainly from the effect of solvent viscosity. In contrast to the behavior of HBI in 2-butanol, HBI-NEt2 displays a temperature-dependent φΤ-T profile in diethyl ether ( ) 4.20), with its value of φΤ decreasing as the temperature is increased. Our calculations reveal that the PES for the S1-Tsyn f S1-TICT reaction of HBI-NEt2 is exothermic (5.89 and 5.33 kcal/mol for S1-TICT-1 and S1-TICT-2, respectively) in nonpolar cyclohexane ( ) 2.20). The energy barriers for the S1-Tsyn f S1-TICT-1 and S1-Tsyn f S1-TICT-2 reactions in cyclohexane are 2.13 and 1.88 kcal/mol, respectively. This PES for HBINEt2 in cyclohexane reveals that the thermodynamics and kinetics favor the formation of S1-TICT forms when the temperature is increased. Hence, its value of φΤ is temperature-

0.138 -0.138 7.42 -0.043 0.043 HBI-NEt2 in Cyclohexane 0.181 -0.037 0.144 -0.181 0.037 -0.144 6.57 6.32 0.359 -0.359 -0.178 0.178 7.99 0.210 -0.210 7.69

-0.145 0.145 6.09 0.215 -0.215 6.85

0.192 -0.192 7.10 HBI-NEt2 in Ethanol 0.274 -0.082 -0.274 0.082 6.22 0.456 -0.455 -0.182 0.181 10.04 benzimidazole ring phenyl ring dipole moment

0.198 -0.198 6.30 0.456 -0.456 -0.151 0.151 8.20

benzimidazole ring phenyl ring dipole moment

benzimidazole ring phenyl ring dipole moment

HBI-NH2 in Ethanol 0.305 -0.107 -0.305 0.107 5.66

-0.090 0.090

0.229 -0.229 5.30 -0.158 0.158 0.211 -0.211 4.97 HBI in Ethanol 0.387 -0.176 -0.387 0.176 6.52

-0.064 0.064

0.144 -0.146 6.72 -0.061 0.061 0.350 -0.350

HBI-NH2 in Cyclohexane 0.205 -0.054 0.151 -0.205 0.054 -0.151 5.49 5.63

0.167 -0.167 4.75 -0.125 0.125 HBI in Cyclohexane 0.292 -0.129 0.163 -0.292 0.129 -0.163 4.51 3.87

S1-TICT-2 S1-Tsyn f S1-TICT-2 S1-TICT-1 S1-Tsyn f S1-TICT-1 S1-Tsyn S1-Nsyn f S1-T syn S1-Nsyn S1-TICT-2 S1-Tsyn f S1-TICT-2 S1-TICT-1 S1-Tsyn f S1-TICT-1 S1-Tsyn S1-Nsyn f S1-Tsyn S1-Nsyn state

dependent, decreasing as the temperature is increased, consistent with experimental observations. In general, the ICT state is regarded as having greater polarity because of charge separation between the donor and acceptor.57 It is considered to be more stable in polar solvents and less stable in nonpolar solvents than its corresponding species prior to ICT. Therefore, variation of the solvent polarity is generally used to tune the stability of ICT states experimentally. Although this point-of-view is helpful in some cases, our results reveal that it is not applicable for HBI, HBI-NH2, and HBI-NEt2. The S1-TICT states of all three of these molecules are more stable in cyclohexane than they are in ethanol, with respect to their corresponding S1-Tsyn states. To understand this behavior, we analyzed the Mulliken charge populations of the benzimidazole and phenol rings and the dipole moments of the S1-Nsyn, S1-Tsyn, and S1-TICT states of HBI, HBI-NH2, and HBI-NEt2 in ethanol and cyclohexane (Table 2). In the ESIPT process, the positively charged proton is transferred from the phenol ring to the benzimidazole ring. After ESIPT, the benzimidazole moiety of the S1-Tsyn form obviously becomes more positive with respect to the corresponding S1-Nsyn form. For example, the Mulliken charge populations of the benzimidazole moiety of HBI-NH2 in ethanol are -0.151 in its S1-Nsyn form and +0.305 in its S1-Tsyn form. The large-amplitude motion of the S1-Tsyn form generates the nonplanar S1-TICT form, inducing ICT with electron density transferred from the deprotonated phenol moiety to the protonated benzimidazole moiety. For example, for HBI-NH2 in ethanol, the S1-TICT-1 form has an electron density of 0.107 transferred from the deprotonated phenol moiety to the protonated benzimidazole moiety, with respect to that of the S1-Tsyn form. The direction of electron transfer is consistent with the suggestions of Rodrı´guez-Prieto, Rodrı´guez, and co-workers.25,32 However, this ICT process neutralizes the positive charge on the protonated benzimidazole moiety of the S1-Tsyn form; hence, it reduces the charge separation in the S1-TICT form with respect to that of the S1-Tsyn form. For example, the Mulliken charge populations of the protonated benzimidazole moiety of HBI-NH2 in ethanol are +0.305 for the S1-Tsyn form and +0.198 for the S1-TICT-1 form. Therefore, the less-charge-separated S1-TICT state does not warrant a much larger polarity than that of the S1-Tsyn form. As indicated in Table 2, the S1-TICT forms do not feature significantly larger dipole moments than those of their corresponding S1-Tsyn forms; some S1-TICT forms even have lower dipole moments. The dipole moment of a molecule is determined by both its electron distribution and geometry. Hence, the relative stability of the S1-Tsyn and S1-TICT states of HBI, HBINH2, and HBI-NEt2 in polar and nonpolar solvents is not determined solely by the occurrence of charge transfer; it is also determined by the collective properties of the optimized electronic and molecular structures and solvation. In terms of the ESIPT and ICT PESs derived from the TDDFT calculations, we well rationalize the experimental observations.25,32 Recent benchmark studies58,59 show that the generalized gradient approximation and hybrid functionals accurately reproduced the charge-transfer excitation energy for some test cases, while poorly described the charge-transfer excitation energy for many test cases, which may limit our conclusions. However, the PESs are computed by the energy difference between two isoelectronic states with different conformations, the intrinsic errors of TD-DFT for both states are likely to be canceled out for the PESs and the net error of TD-DFT will be significantly reduced for the PESs. Nevertheless, the deactivation mechanism, particularly, the proposed equilibrium between the

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TABLE 2: Mulliken Charge Populations on the Benzimidazole and Phenol Rings and Dipole Moments (in Debye) of HBI, HBI-NH2, and HBI-NEt2 in Ethanol and Cyclohexane and Their Changes for the ESIPT and ICT Processes

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S1-Tsyn and S1-TICT states of HBI, with similar forward and backward reaction rates, will need further exploration by additional experiments and/or more accurate theoretical methods. Summary We have used TD-DFT calculations to investigate the S1 state behavior of HBI, HBI-NH2, and HBI-NEt2. We searched for the stationary points of their S1-Nsyn, S1-Tsyn, and S1-TICT forms in ethanol and cyclohexane. The PESs covering these states were calculated to obtain a detailed map with which to (i) understand the reaction mechanisms of the ESIPT and ICT processes of these molecules and (ii) rationalize the experimental observations. We found two new nonfluorescent S1-TICT states for each of HBI, HBI-NH2, and HBI-NEt2, stable in polar (ethanol) and nonpolar (cyclohexane) solvents. The existence of the S1-TICT forms is particularly important because they quench the fluorescence quantum yield (φT) of the S1-Tsyn forms effectively and further influence the excited state photochemical and photophysical behavior. The S1-TICT conformations are twisted and pyramidalized. More interestingly, the S1-TICT state does not possess a critically larger dipole moment than its corresponding S1-Tsyn form. This property is different from that in most ICT states, in which a larger degree of charge separation exists relative to that of the precursorsshence, the term, charge transfer. Obviously, the ESIPT process generates positive charge density on the benzimidazole moiety, creating charge separation; interestingly, the following ICT process has the negatively electron density transferred from the phenyl to the benzimidazole moiety, partially neutralizing the positive charge density on the benzimidazole moiety; therefore, the S1-TICT states are particularly stabilized in polar solvent (ethanol), with respect to their corresponding S1-Tsyn forms. The PESs for HBI, HBI-NH2, and HBI-NEt2 determine the behavior of their fluorescence quantum yields as a function of temperature and solvent. Our calculated PES for HBI in ethanol revealed that the S1-Tsyn and S1-TICT forms have similar stabilities. In other words, the thermodynamic equilibrium and kinetics of the S1-Tsyn a S1-TICT reactions for HBI in polar solvents are temperature-insensitiVesa finding that agrees with the experimentally observed temperature-independent φT-T profile in 2-butanol. To interpret the experimental observations, a previous study25,32 suggested that HBI does not experience an S1-TICT state. Here, we propose an alternative view to explain the experimental behavior complementing previous studies, based on theoretical calculations. For HBI-NEt2 in nonpolar solvents, our calculations suggest that it experiences two S1-TICT states, which are more stable than its S1-Tsyn state in cyclohexane. Therefore, the values of φT for HBI-NEt2 in nonpolar solvents can be minimized by the presence of its S1-TICT states; these values decrease with temperature. Our results are consistent with previous suggestions.25,32 Acknowledgment. We thank the National Science Council of Taiwan (grant no: NSC96-2113-M-008-006-MY2) for financial support and the National Center for High-Performance Computing of Taiwan and the Vger computer cluster at the National Central University of Taiwan for providing computer time and facilities. Supporting Information Available: Total energies and more detailed geometric parameters of found stationary states; S1-S0 energy differences of tautomeric HBI and HBI-NH2 in ethanol and cyclohexane; properties of HBI-NH2 and HBI-NEt2 upon amino/diethyl group twisting. This material is available free of charge via the Internet at http://pubs.acs.org.

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J. Phys. Chem. A, Vol. 114, No. 12, 2010 4079 (53) Because the stationary S1-Nsyn form of HBI was not found, we calculated the geometry of the S1-Nsyn form of HBI with its O-H distance constrained at 1.026 Å, the optimized distance for HBI-NH2. In ethanol, the C1-C2 distance of HBI decreased from 1.455 Å in the S0-Nsyn form to 1.413 Å in the S1-Nsyn form; In cyclohexane, it decreased from 1.453 Å in the S0-Nsyn form to 1.416 Å in the S1-Nsyn form. (54) Quenneville, J.; Martinez, T. J. J. Phys. Chem. A 2003, 107, 829. (55) Barbatti, M.; Aquino, A. J. A.; Lischka, H.; Schriever, C.; Lochbrunner, S.; Riedle, E. Phys. Chem. Chem. Phys. 2009, 11, 1406. (56) Rappoport, D.; Furche, F. J. Am. Chem. Soc. 2004, 126, 1277. (57) Grabowski, Z. R.; Rotkiewicz, K.; Rettig, W. Chem. ReV. 2003, 103, 3899. (58) Silva-Junior, M. R.; Schreiber, M.; Sauer, S. P. A.; Thiel, W. J. Chem. Phys. 2008, 129, 104103. (59) Peach, M. J. G.; Benfield, P.; Helgaker, T.; Tozer, D. J. J. Chem. Phys. 2008, 128, 044118.

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