Theoretical Study on Water-Mediated Excited-State Multiple Proton

Oct 8, 2012 - Andrés M. Durantini , R. Darío Falcone , Jorge D. Anunziata , Juana J. Silber ... Rathawat Daengngern , Supa Hannongbua , Mario Barbat...
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Theoretical Study on Water-Mediated Excited-State Multiple Proton Transfer in 7‑Azaindole: Significance of Hydrogen Bond Rearrangement Xue-fang Yu,† Shohei Yamazaki, and Tetsuya Taketsugu* Department of Chemistry, Faculty of Science, Hokkaido University, Sapporo 060-0810, Japan S Supporting Information *

ABSTRACT: Excited-state multiple proton transfer (ESMPT) in the cluster of 7-azaindole with three water molecules [7-azaindole(H2O)3] is theoretically investigated by the TDDFT, CASPT2, and CC2 methods. Examination of the potential energy surface in the first excited state indicates that ESMPT in 7-azaindole(H2O)3 proceeds initially with the rearrangement of hydrogen bond structure of water molecules from a bridged-planar isomer to a cyclic-nonplanar isomer, followed by triple proton transfer in the latter. This reaction is found to be energetically more favorable than quadruple proton transfer in the bridged-planar isomer without hydrogen bond reorganization. It is also shown that all proton-transfer processes follow a concerted mechanism rather than a stepwise mechanism. The computational results show good consistency with the unexpected experimental observations as to the electronic spectra and excited-state lifetime. In particular, the barrier of the hydrogen bond rearrangement is found to be less than 1 kcal/mol, consistent with the missing vibronic bands for 7azaindole(H2O)3 with an excess energy of more than 200 cm−1 in the S1 state.

1. INTRODUCTION Proton transfer reactions play important roles in a variety of chemical and biological processes1,2 such as keto−enol tautomerism and proton relay in enzyme reaction. 7-Azaindole (7AI) as a prototype, which contains both a proton donor and acceptor, has received particular attention in experimental and theoretical studies. The tautomerization process of 7AI via the excited-state multiple proton transfer (ESMPT) from the fivemembered ring to the six-membered ring has been extensively studied for the homodimer,3−11 heterodimer,12−17 and cluster with a small number of molecules18−37 in the gas phase and in the condensed phase. For the 7AI homodimer and heterodimer, it has been controversial whether ESMPT follows a concerted mechanism or a stepwise mechanism. In the concerted mechanism, two protons are transferred simultaneously in a single step, while in the stepwise mechanism, two protons are transferred sequentially with more than one step, where a stable intermediate compound is formed on the way. Recently, we reported high-level calculations of potential energy surfaces for the ESMPT processes in the 7AI homodimer and (3-methyl7AI)-7AI heterodimer using the multireference second-order perturbation theory (CASPT2), an ab initio method taking account of dynamic electron correlation, as well as the timedependent density functional theory (TDDFT) with long-range correction which improves the prediction of charge-transfer excitation energy.10,17 The theoretical results led us to conclude that the concerted mechanism is more favorable in these dimers and that the two protons are transferred asynchronously. Our © 2012 American Chemical Society

results also suggest that systematic improvement of the electronic structure method is critical for a qualitative description of the ESMPT mechanism in both ab initio and TDDFT calculations. Ando et al. carried out quantum dynamics calculations for the 7AI homodimer based on potential energy surfaces at the multireference second-order Møller−Plesset perturbation theory (MRMP2) level and also proposed the asynchronous concerted mechanism.11 As to ESMPT in the cluster of 7AI with water molecules, Chaban and Gordon theoretically revealed that cooperation of a single water molecule considerably decreases the energy barrier for the tautomerization of 7AI from normal cluster to tautomer cluster in both the ground and excited states.18,20 This picture of “water-assisted proton transfer” provides a significant insight into the mechanism of enzyme reactions.1 Sakota et al. reinvestigated ESMPT of 7AI(H2O)2 in the gas phase by using electronic spectroscopy and quantum chemical calculations33 and suggested that the ESMPT follows the concerted mechanism. Several theoretical studies proposed the asynchronous concerted mechanism for ESMPT of 7AI−solvent clusters in the gas phase.21,29,32,34,36,37 Moreover, vibrational-mode specificity was reported for ESMPT in 7AI(H2O)2 and 7AI(CH3OH)2;28,33 the ESMPT was found to be promoted by the excitation of a specific vibrational mode corresponding to the cooperative motion of the hydrogen bond network. Received: August 28, 2012 Revised: October 5, 2012 Published: October 8, 2012 10566

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Figure 1. Molecular structures of 7AI(H2O)3: (a) bridged-planar isomer and (b) cyclic-nonplanar isomer.

2. COMPUTATIONAL DETAILS Equilibrium geometries of 7AI(H2O)3 in the ground state were determined by the MP2 method and the DFT method with the B3LYP38 functional, while geometries of minima and transition states in the first-excited state were determined by the TDDFT method with B3LYP (TD-B3LYP). All minima and transition states in S0 and S1 states were confirmed by normal-mode analysis at the respective computational levels. Zero-point energy (ZPE) was also calculated for the S1 stationary points with the TD-B3LYP method. The reaction path in the S1 state was determined by intrinsic reaction coordinate (IRC) calculations at the TD-B3LYP level, starting from the respective transition states. For the geometry optimization in S1, we also tested the coulomb attenuated B3LYP (CAM-B3LYP) functional,39 which includes the long-range correction. However, the resulting energies are found to be very similar to the TDB3LYP ones (see the Supporting Information), indicating that the effect of long-range correction is small for 7AI(H2O)3. In particular, the charge-transfer excited state is not likely involved in the ESMPT of this cluster. For the S0 state, the accuracy of the B3LYP functional was checked by single-point energy calculations at the MP2 level as well as the DFT level using the ωB97X-D functional,40 which includes both atom−atom dispersion correction and long-range correction. The ωB97X-D functional was also used for TDDFT single-point energy calculations of S1 stationary points located at the TD-B3LYP level to assess the effect of dispersion correction on the excited-state potential energy profiles. Geometry optimization at the TD-ωB97X-D level was also carried out for a few S1 minima, but optimization of other structures including transition states could not be completed because of much larger computational cost than TD-B3LYP. For comparison, single-point energy calculations in the S1 state were also carried out with the CASPT241 (single-state CASPT2) and CC242 (second-order approximate coupled cluster) methods, which are ab initio multireference and singlereference methods, respectively, taking into account the dynamic electron correlation effect. In CASPT2 calculations, the reference complete-active-space self-consistent field (CASSCF) wave function was constructed with the active space of 10 electrons distributed in 9 π orbitals of the 7AI

Very recently, Pino et al. proposed that rearrangement of hydrogen bond structure plays a crucial role in the ESMPT reaction of 7AI(H2O)3.35 For this cluster, they found an unexpected internal energy dependence in the resonance enhanced multiphoton ionization (REMPI) and fluorescence excitation (FE) spectra. They also showed that the decay time of the vibronic states was very different between 7AI(H2O)2 and 7AI(H2O)3 and that the vibrational-mode specificity was lacking in the latter. Drastic decrease in the excited-state lifetime was found for 7AI(H2O)3 with vibrational energy increased, which is likely to correlate with the unusual red shift of the dispersed fluorescence (DF) spectrum previously reported.26 Based on theoretical calculations, these remarkable observations were attributed to the isomerization of hydrogen bond network in 7AI(H2O)3, followed by ESMPT.35 Figure 1 shows typical structures of the two isomers, referred to as the bridged-planar and cyclic-nonplanar isomers following ref 35. In the bridged-planar isomer (Figure 1a), three water molecules form a chain-like hydrogen bond structure linking the NH and N groups of 7AI, where each water molecule has one OH bond free from a hydrogen bond. In the cyclic-nonplanar isomer (Figure 1b), both OH bonds of the water molecule linked to the NH group of 7AI are hydrogen-bonded to the other water molecules. It was also suggested that the cyclic-nonplanar isomer is energetically more stable than the bridged-planar isomer in the ground and excited states of 7AI(H2O)3. The detailed processes in the excited state were, however, not adequately examined. In this paper we theoretically address several questions that have arisen as to ESMPT in 7AI(H2O)3: (1) What isomer is the energetically most stable in the S0 and S1 states? (2) Does the isomerization of hydrogen bond network occur in the S1 state with a modest energy barrier? (3) Which mechanism is likely to be followed in the proton transfer reaction, concerted or stepwise? To answer these questions, we perform considerable theoretical calculations at the ab initio and TDDFT levels. In particular, the present work gives the first theoretical evidence that the hydrogen bond rearrangement provides efficient reaction path for the excited-state tautomerization of 7AI(H2O)3. 10567

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respectively (see Figure 1 for the atom labeling). Two structures (labeled as a and b) are found for each type, which exhibit different directions of a free OH bond of water molecules. The MP2/aug-cc-pVDZ calculation predicts that the bridged-planar structure NCS0‑Ba is the energetically more stable than the other five isomers in the ground state. Table 1

molecule, with averaging the lowest three electronic states with equal weights, and a level shift of 0.343 was applied to avoid the intruder state problems (the IPEA shift was not used). Levelshift values in the range of 0.2−0.3 give very similar relative energies of S 1 stationary points (see the Supporting Information), while CASPT2 calculations with smaller values failed due to intruder states. In CC2 calculations, the resolution-of-the-identity (RI) approximation was employed.44 In this study, cc-pVDZ, aug-cc-pVDZ, and aug-cc-pVTZ basis sets45,46 were used. In MP2 and DFT calculations of the S0 state, we examined a basis set superposition error (BSSE) through a counterpoise scheme.47,48 MP2 and (TD-)ωB97X-D calculations were performed in Gaussian 09, 49 while (TD-)B3LYP and (TD-)CAM-B3LYP calculations were performed with GAMESS.50 CASPT2 and CC2 calculations were performed with MOLPRO 2008.151 and TURBOMOLE 6.3,52 respectively.

Table 1. Relative Energies (in kcal/mol) of Equilibrium Structures in the Ground State, where Energy of NCS0‑Ba is Set To Be Zeroa NCS0‑Bb

NCS0‑cyc1a

NCS0‑cyc1b

0.74 (0.66) 0.72 (0.67)

−0.93 (2.47) −0.86 (1.63) 0.79 (0.77) 0.88 (0.88)

0.80 (0.82) 0.74 (0.75)

1.69 (1.79) 0.71 (0.78)

MP2/cc-pVDZ B3LYP/cc-pVDZ MP2/aug-ccpVDZ

3. RESULTS AND DISCUSSION 3.1. Equilibrium Geometries in the Ground and Excited States. For normal cluster (NC) of 7AI(H2O)3 in the ground state, six equilibrium structures were located at the MP2/aug-cc-pVDZ level, labeled as NCS0. Figure 2 shows the

MP2/aug-ccpVTZ// MP2/ aug-cc-pVDZ B3LYP/aug-ccpVDZ ωB97X-D/aug-ccpVDZ// B3LYP/aug-ccpVDZ a

NCS0‑cyc2a

NCS0‑cyc2b

−0.42 (1.28) −0.56 (1.67) 0.92 (0.93) 1.02 (1.02)

1.07 (1.67) 1.56 (1.78)

0.14 (3.46) 1.90 (4.64) 1.28 (1.80) 1.72 (1.96)

1.88 (1.97) 0.87 (0.97)

3.86 (3.99) 1.47 (1.62)

4.17 (4.28) 1.79 (1.94)

Numbers in parentheses denote the values corrected for BSSE.

summarizes calculated energies of the equilibrium structures. The energies relative to NCS0‑Ba are calculated to be 0.74, 0.79, 0.92, 1.07, and 1.28 kcal/mol for NCS0‑Bb, NCS0‑cyc1a, NCS0‑cyc1b, NCS0‑cyc2a, and NCS0‑cyc2b, respectively. The order of energy in these six isomers is unchanged when BSSE correction is added. We also verify that the relative energies at the MP2/aug-ccpVDZ level do not so change at the MP2/aug-cc-pVTZ level. Both B3LYP/aug-cc-pVDZ and ωB97X-D/aug-cc-pVDZ calculations also predict that NCS0‑Ba is the lowest-energy isomer. The DFT/aug-cc-pVDZ relative energies are little affected by BSSE correction. For cyclic-nonplanar isomers, B3LYP relative energies are larger than MP2 and ωB97X-D values by up to a few kcal/mol, presumably because of the underestimation of noncovalent interaction energy by the lack of dispersion correction in the B3LYP functional. Compared to calculations with aug-cc-pVXZ (X = D, T) basis sets, both MP2 and B3LYP calculations with the cc-pVDZ basis set predict that the cyclic-nonplanar isomers NCS0‑cyc1a and NCS0‑cyc1b are more stable than the bridged-planar isomer NCS0‑Ba and no existence of NCS0‑Bb and NCS0‑cyc2a isomers. A similar result was also reported in DFT and CC2 calculations with cc-pVDZ basis set by Pino et al.35 However, when BSSE correction is added in MP2/cc-pVDZ and B3LYP/cc-pVDZ calculations, NCS0‑Ba becomes the most stable isomer again, as shown in Table 1. These findings suggest that the cc-pVDZ basis set seriously overestimates the intermolecular interaction energy of 7AI(H2O)3 due to large BSSE and that the overstabilization is larger for cyclic-nonplanar isomers than for bridged-planar isomers. It is worth noting that the former isomers have a large number of intermolecular hydrogen bonds than the latter (5 and 4, respectively), which may lead to larger overestimation of hydrogen-bond interaction. The results of BSSE correction shown in Table 1 strongly indicates the significance of inclusion of diffuse functions in the

Figure 2. Minimum-energy geometries of 7AI(H2O)3 in the S0 state optimized at the MP2/aug-cc-pVDZ level: (a) NCS0−Ba, (b) NCS0‑Bb, (c) NCS0‑cyc1a, (d) NCS0‑cyc1b, (e) NCS0‑cyc2a, and (f) NCS0‑cyc2b. Bond lengths are in Å.

optimized structures. These six isomers can be classified into three types, referred to as NCS0−B, NCS0‑cyc1, and NCS0‑cyc2, according to the structure of the hydrogen bond network. NCS0−B is the bridged-planar structure, while NCS0‑cyc1 and NCS0‑cyc2 are the cyclic-nonplanar structure. In NCS0‑cyc1 and NCS0‑cyc2, a bifurcated hydrogen bond is formed at the O3 atom of a water molecule and the N2 atom of the 7AI molecule, 10568

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reaction. Other two equilibrium structures of cyclic-nonplanar normal clusters in the S1 state, corresponding to NCS0‑cyc1b and NCS0‑cyc2b in the S0 state, are also located (NCcyc1b and NCcyc2b, see the Supporting Information). The electronic structure for all NCn and TCn isomers is characterized by the 1La excitation53 of the 7AI molecule from the highest occupied molecular orbital (HOMO) to the lowest unoccupied molecular orbital (LUMO); see the Supporting Information for the orbitals. Meanwhile, lengths of intermolecular hydrogen bonds are significantly shorter at NCn than at NCS0‑Cn. This result suggests that the strength of these hydrogen bonds is enhanced upon excitation, which may facilitate the proton transfer in the excited state. At the TD-B3LYP level, NCB is the lowest-energy isomer among normal clusters, with NCcyc1 and NCcyc2 lying 0.9 and 0.3 kcal/mol higher than NCB, respectively, while at the TDωB97X-D, CASPT2, and CC2 levels, NCcyc2 exhibits lower energy than other normal clusters (see Table 2). Taking into account the difference between TD-B3LYP and TD-ωB97X-D methods, the inclusion of the dispersion correction is crucial for correct prediction of the energetics in the excited state. The energies of tautomer clusters, TCB, TCcyc1, and TCcyc2, are calculated to be −14.5, −11.9, and −9.8 kcal/mol, respectively, relative to NCB at the TD-B3LYP level, indicating that tautomerization from NCn to TCn is exothermic. The order in energy for TCn is unchanged at the TD-ωB97X-D, CASPT2, and CC2 levels. The adiabatic excitation energy for the NCB structure of 7AI(H2O)3 is calculated to be 3.80 eV at the TD-B3LYP/augcc-pVDZ level. For 7AI(H2O)2, the corresponding excitation energy is estimated as 3.81 eV. The energy lowering by 0.01 eV (81 cm−1) from 7AI(H2O)2 to 7AI(H2O)3 is consistent with the red shift of 78 cm−1 in the 0−0 band of the rotationally resolved LIF spectrum.19 3.2. Reaction Paths in the Excited State. Next, we discuss reaction pathways connecting equilibrium geometries in the first-excited state. Transition state (TS) geometries were optimized for (1) the excited-state quadruple proton transfer (ESQPT) of the bridged-planar isomer from NCB to TCB, (2) the hydrogen bond rearrangement (HBR) in the S1 state from NCB to NCcyc1 and from NCcyc1 to NCcyc2, and (3) the excitedstate triple proton transfer (ESTPT) of the cyclic-nonplanar isomer from NCcyc1 to TCcyc1 and from NCcyc2 to TCcyc2, followed by the IRC calculations at the TD-B3LYP/aug-ccpVDZ level. These structures are labeled as TSQPT, TSHBR1, TSHBR2, TSTPT1, and TSTPT2, respectively. For QPT and TPT, each IRC reaction path from NC to TC exhibits only one TS structure with no intermediate minimum, indicating that the

basis sets. The following discussions are based on the results calculated with the aug-cc-pVDZ basis set. The effect of BSSE is expected to be small for TDDFT/aug-cc-pVDZ potential energy profiles in the excited state. According to the present calculations of the ground state, the lowest-energy structure NCS0‑Ba can be assigned to the isomer observed in laser-induced fluorescence (LIF) and IR-dip spectroscopy of 7AI(H2O)3 in a supersonic jet expansion.19,22 Furthermore, our results support that NCS0‑Ba is likely to be detected in the electronic spectra by Pino et al., such as REMPI and FE.35 Thus, their observations for photoexcited 7AI(H2O)3 are likely to be relevant to the excited-state reactions starting with the bridged-planar isomer. The equilibrium structures in the first-excited state are determined by TD-B3LYP/aug-cc-pVDZ calculations. Figure 3

Figure 3. Minimum-energy geometries of 7AI(H2O)3 in the S1 state optimized at the TD-B3LYP/aug-cc-pVDZ level: (a) NCB, (b) TCB, (c) NCcyc1, (d) TCcyc1, (e) NCcyc2, and (f) TCcyc2. Bond lengths are in Å.

shows the normal clusters NCn (n = B, cyc1, and cyc2) corresponding to NCS0‑na in the ground state and tautomer clusters TCn, which can be formed from NCn by the ESMPT

Table 2. Relative Energies (in kcal/mol) of Stationary Points in the First Excited State where aug-cc-pVDZ Basis Set is Employed and Energy of NCB is Set To Be Zeroa TD-B3LYP TD-ωB97X-D CASPT2 CC2

a

TSQPT

TCB

TSHBR1

NCcyc1

TSTPT1

TCcyc1

TSHBR2

NCcyc2

TSTPT2

TCcyc2

8.6 (3.6) 10.6 (5.6) 10.2 (5.2) 8.3 (3.3)

−14.5 (−14.1) −15.7 (−15.3) −16.8 (−16.4) −18.6 (−18.2)

1.1 (1.1) 0.3 (0.2) 0.2 (0.2) 0.1 (0.1)

0.9 (0.9) −0.2 (−0.2) −0.3 (−0.2) −0.4 (−0.3)

4.8 (2.1) 5.0 (2.3) 4.1 (1.4) 2.1 (−0.7)

−11.9 (−11.3) −14.0 (−13.4) −15.4 (−14.8) −17.3 (−16.7)

2.1 (2.3) −0.5 (−0.2) −0.4 (−0.1) −0.8 (−0.5)

0.3 (0.7) −2.0 (−1.6) −2.7 (−2.3) −3.5 (−3.1)

9.6 (6.2) 7.5 (4.1) 4.8 (1.4) 1.0 (−2.4)

−9.8 (−9.3) −13.1 (−12.6) −14.8 (−14.3) −17.0 (−16.5)

Values in parentheses include zero-point energy correction at the TD-B3LYP/aug-cc-pVDZ level. 10569

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ESMPT reaction in 7AI(H2O)3 follows the concerted mechanism rather than the stepwise mechanism for both the bridged-planar and cyclic-nonplanar isomers. Figure 4 shows the energy diagram for ESMPT processes in the 7AI(H2O)3 cluster at the CASPT2/aug-cc-pVDZ//TD-

Figure 4. Potential energy profiles of ESMPT in 7AI(H2O)3 cluster obtained at the CASPT2/aug-cc-pVDZ, where minimum and transition-state geometries are determined with the TD-B3LYP/augcc-pVDZ method. Figure 5. Structural changes along excited-state reaction routes of 7AI(H2O)3. Geometries of minima and transition states in the S1 state are optimized at the TD-B3LYP/aug-cc-pVDZ level.

B3LYP/aug-cc-pVDZ level. Table 2 shows a summary of the energies calculated with TD-B3LYP, TD-ωB97X-D, CASPT2, and CC2 methods using aug-cc-pVDZ, where the energy of NCB is set as zero for reference at each computational level. We have found three reaction routes from NCB:

H12 bond, followed by rocking of the O1−H8 bond. At the TS structure of the second HBR (TSHBR2, see Figure 5), the imaginary-frequency mode exhibits the rotation of the O2−H9, O2−H10, and O3−H12 bonds, which leads to the formation of hydrogen bond between the H10 and N2 atoms and the breaking of the hydrogen bond between H9 and O3 atoms. The reaction paths through TSHBR1 and TSHBR2 indicate that an essential step of HBR is the hydrogen bond formation of a free OH group in a water molecule with another water or the 7AI molecule. For TSHBR2, in particular, it is worth noting that both OH bonds of the O2−H9−H10 water molecule are temporally hydrogen-bonded through rotational motion. The HBR via molecular rotation seems to be specific to the cluster with water molecules and is less likely to be observed for the cluster with methanol or ethanol, which has only one OH group per molecule. We have found that the barrier for HBR is much lower than the QPT reaction, see Figure 4. This finding suggests that routes II and III are more likely to be accessed than route I. For the first HBR from NCB to NCcyc1, the relative energy of the transition state TSHBR1 is calculated to be in the range of 0.1− 1.1 kcal/mol depending on the computational method. These values are almost unchanged when including the ZPE correction. For the second HBR, the barrier height is calculated to be 1.2 kcal/mol relative to NCcyc1 at the TD-B3LYP level (1.4 kcal/mol with the ZPE correction), but the energies of TSHBR2 become lower than NCcyc1 at the TD-ωB97X-D, CASPT2, and CC2 levels. This result implies that HBR may proceed directly from NCB to NCcyc2 without forming an intermediate of NCcyc1. To examine this possibility, we carried

route I: NCB → TSQPT → TCB route II: NCB → TSHBR1 → NCcyc1 → TSTPT1 → TCcyc1

route III: NCB → TSHBR1 → NCcyc1 → TSHBR2 → NCcyc2 → TSTPT2 → TCcyc2

Figure 5 shows geometries of minima and TS along the respective reaction routes. Route I is the reaction path for the concerted ESQPT process from NCB to TCB without HBR. The barrier height of TSQPT is estimated to be 8.6, 10.6, 10.2, and 8.3 kcal/mol from NCB at the TD-B3LYP, TD-ωB97X-D, CASPT2, and CC2 levels, respectively. Being corrected with ZPE calculated at the TD-B3LYP level, these values become 3.6, 5.6, 5.2, and 3.3 kcal/mol, respectively. At TSQPT, all four transferred protons (H1, H7, H9, and H11) are located in the middle of the respective hydrogen bonds. Routes II and III accompany HBR from the bridged-planar to cyclic-nonplanar structure, followed by the ESTPT reaction. In both routes, HBR from NCB to NCcyc1 occurs as the first step, and then, the second HBR from NCcyc1 to NCcyc2 follows in route III. In the first HBR, the TS structure (TSHBR1, see Figure 5) exhibits the imaginary-frequency mode of simultaneous rocking of the O1− H8 and O3−H12 bonds, which are free from hydrogen bond at the NCB structure. Thus, the IRC path from NCB to NCcyc1 shows the formation of a hydrogen bond between the H8 and the O3 atoms. It is noted that the IRC path first passes through an unstable structure similar to NCS0‑Bb by rocking of the O3− 10570

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In routes II and III, the barrier for the TPT reaction of the cyclic-nonplanar isomers is calculated to be higher than that for the preceding HBR. This finding is very consistent with the excitation energy dependence of the FE spectrum.35 At the lower excitation energy, UV emission was observed for normal cluster, while visible emission was absent for tautomer cluster. This observation indicates that the tautomerization via TPT is not likely to occur when vibrational energy is smaller than a threshold. The experimental value of this threshold is 744 cm−1, which is larger than the threshold for HBR indicated by the REMPI and DF spectra (∼200 cm−1, see above). The threshold value of 744 cm−1 (2.1 kcal/mol)35 can be compared to the energies of TSTPT1 and TSTPT2 relative to NCB (see Table 2). In particular, the CASPT2 calculations exhibit the relative energies in good agreement with the experimental value; 1.4 kcal/mol for both TSTPT1 and TSTPT2, including the ZPE correction. The isomerization through HBR is also consistent with the biexponential decay of the pump−probe signal, which was observed when the intramolecular vibrational mode of 744 cm−1 was excited.35 The faster component with the lifetime of 15 ps, which was not found for 7AI(H2O)2, is likely to be related with the HBR of 7AI(H2O)3. On the basis of the present theoretical results, the unexpected lacking of vibrational mode specificity for the excited-state lifetime of 7AI(H2O)3 can be attributed to the HBR process. When the vibrational energy is smaller than the threshold for TPT (with the experimental value of 744 cm−1), the lifetime should be associated with the rate of HBR and is therefore likely to be independent of the vibrational excitation of the specific mode, which promotes the ESQPT reaction in the bridged-planar isomer. For the NCB structure of 7AI(H2O)3, the vibrational frequencies for symmetric and asymmetric intermolecular stretching modes [referred to as σ(1) and σ(2)], which might facilitate ESQPT, are calculated to be 179.2 and 185.6 cm−1, respectively, at the TD-B3LYP/augcc-pVDZ level (see the Supporting Information). These values are consistent with the experimental frequencies of 161 and 175 cm−1.35 As shown in Figure 4 and Table 1, however, the barrier for the ESQPT reaction is considerably higher than the vibrational energies of σ(1) and σ(2), which may be the reason why this reaction is not specifically promoted by these vibrational modes. This picture is in contrast to the cases of 7AI(H2O)2 and 7AI(CH3OH)2 whose ESTPT reaction is particularly promoted by the specific vibrational excitation of symmetric intermolecular stretching corresponding to σ(1) and exhibits a moderate energy barrier.28,33 When the vibrational energy of 7AI(H2O)3 is larger than the threshold, the intracluster vibrational energy redistribution (IVR) may play a significant role for the lack of vibrational mode specificity. It should be pointed out that the specificity could not be found for 7AI(CH3OH)2 with increasing the vibrational energy, presumably because of IVR.28 Pino et al. reported that the FE spectrum of 7AI(H2O)2 exhibits the 0−0 band of the visible emission corresponding to the tautomer cluster, while the 0−0 band could not be found for 7AI(H2O)3.35 One possible explanation for this behavior is that tunneling effect on ESMPT is larger in 7AI(H2O)2 than in 7AI(H2O)3. In the latter, HBR to other isomers may lead to smaller contribution of the promoting mode for symmetric intermolecular stretching. For NCcyc2, reverse HBR to other NC structures may also contribute to the redistribution of vibrational energy.

out excited-state geometry optimization for NCcyc1 and NCcyc2 by the TD-ωB97X-D and CC2 methods with the aug-cc-pVDZ basis set. Then, the TD-ωB97X-D calculations suggest the existence of the intermediate, NCcyc1, but at the CC2 level, optimization from NCcyc1 ended up with the NCcyc2 minimum, indicating that NCB is directly transformed to NCS1‑cyc2. For the TPT reaction paths from NCcyc1 to TCcyc1 (route II) and from NCcyc2 to TCcyc2 (route III), the IRC calculations at the TD-B3LYP level suggest the concerted mechanism through a single TS structure. As shown in Figure 5, in both TSTPT1 and TSTPT2, H1, H8, and H11 atoms are moving on the way of proton transfer. It should be noticed that the O2−H9−H10 water molecule is not involved in the TPT process. In route II, the IRC path from NCcyc1 first exhibits an unstable structure similar to NCS0‑cyc1b through rotation of O2−H10 bond, followed by the TPT to TCcyc1. The energy of TSTPT1 is calculated to be in the range of 2.1− 5.0 kcal/mol relative to NCB, as shown in Table 2. Including the ZPE correction, the value becomes −0.7−2.3 kcal/mol. These energies are much lower than those of TSQPT at the respective computational levels, indicating that the (HBR + TPT) reaction is more likely to occur than the QPT reaction. The energies of TSTPT2 are also lower than the corresponding energy of TSQPT, supporting the favorability of the TPT reaction along this route. For example, the energy is calculated to be 1.4 kcal/mol from NCB at the CASPT2 level with the ZPE correction. It is noted that only the TD-B3LYP method predicts a relatively high energy for TSTPT2 (6.2 kcal/mol with the ZPE correction), owing to the lacking of dispersion correction. It is also verified that the CAM-B3LYP potential energy profiles are very similar to the TD-B3LYP results (see the Supporting Information). TPT from other cyclic-nonplanar normal clusters NCcyc1b and NCcyc2b shown in the Supporting Information might also occur if they are formed, in which the energy barrier is expected to be similar with that for TPT from NCcyc1 and NCcyc2. The calculated potential energy profiles for routes II and III are consistent with remarkable experimental observations for 7AI(H2O)3. First, the low activation barrier of less than 1 kcal/ mol for the HBR is related to the observation that the REMPI spectrum of 7AI(H2O)3 is very weak for vibrational bands more than 200 cm−1 (∼0.6 kcal/mol) above the S1 origin when measured by nanosecond laser pulses.35 This behavior can be attributed to the HBR to cyclic-nonplanar structure (NCcyc1 or NCcyc2). It is worthy to mention that the REMPI spectrum of the cyclic-nonplanar isomer is less likely to be detected than the bridged-planar isomer because of the higher ionization potential and the smaller Franck−Condon factor.35 In addition, the low barrier for HBR is also consistent with the sharp decrease of the decay time of pump−probe signal with the vibrational excitation above 200 cm−1. The formation of the cyclic-nonplanar structure in the excited state is also supported by the unusual red shift of the DF spectrum with exciting the vibronic bands of more than 160 cm−1 (∼0.5 kcal/mol).26 In our TD-B3LYP calculations, the emission energy is 3.37 eV for the bridged-planar structure NCB, while it is lowered to 3.33 and 3.17 eV for the cyclicnonplanar structures NCcyc1 and NCcyc2, respectively. This result can be compared with the DF spectrum, whose peak is red-shifted from 330 to 360 nm (3.8 to 3.4 eV) with increasing the excitation energy.26 The red shift by the isomerization is also found in the TD-ωB97X-D, CASPT2 and CC2 calculations. 10571

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4. CONCLUSIONS Mechanism of ESMPT in the 7AI(H2O)3 cluster in the gas phase has been studied with TDDFT and ab initio CASPT2 and CC2 calculations. The present work has provided the first theoretical evidence for the photoinduced HBR of 7AI(H2O)3 from the bridged-planar to cyclic-nonplanar isomer, followed by the TPT reaction in the latter.35 In particular, we have found that the multistep tautomerization including the HBR and TPT exhibits the lower barrier than the single-step tautomerization via the QPT reaction in the bridged-planar isomer. The calculated potential energy profiles are in good agreement with the unexpected experimental observation for 7AI(H2O)3 with respect to the excitation energy dependence of the excited-state lifetime and electronic spectra such as REMPI, FE, and DF.26,35 In particular, the barrier for HBR has been found to be less than 1 kcal/mol, consistent with the missing vibronic bands with an excess energy of more than 200 cm−1 in the REMPI spectrum measured by nanosecond laser pulses. The present MP2 calculation with diffuse basis functions predicts that the global minimum in the S0 state of 7AI(H2O)3 is a bridged-planar structure (NCS0−Ba), which should be the starting geometry for photoexcited 7AI(H2O)3. In the first excited state of the normal cluster, the cyclic-nonplanar isomer exhibits the lower energy than the bridged-planar isomer at the TD-ωB97X-D, CASPT2, and CC2 levels. The potential energy profiles show that the ESMPT reaction should follow the concerted mechanism for all reaction paths of TPT and QPT. No minimum for the intermediate component of proton transfer could be found.

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ASSOCIATED CONTENT

Potential energy profiles of ESMPT in 7AI(H2O)3 at the TDCAM-B3LYP level, additional equilibrium structures in the S1 state, molecular orbitals at excited-state minima, displacements of intermolecular vibrational modes, and Cartesian coordinates of equilibrium structures in the S0 and S1 states, and CASPT2 energies with different values of level shift. This material is available free of charge via the Internet at http://pubs.acs.org.

AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Present Address †

Department of Chemical System Engineering, School of Engineering, The University of Tokyo, Tokyo 113-8656, Japan. Notes

The authors declare no competing financial interest.

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REFERENCES

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ACKNOWLEDGMENTS

The authors sincerely thank Prof. Hiroshi Sekiya for valuable comments on the manuscript. This work was supported by a Grant-in-Aid for Scientific Research and Global COE Program (Project No. B01: Catalysis as the Basis for Innovation in Materials Science) from Monbukagakusho. The computations were performed using the Research Center for Computational Science, Okazaki, Japan. X.Y. thanks the China Scholarship Council, and S.Y. thanks the Japan Society for the Promotion of Science for Research Fellowships for Young Scientists. 10572

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