Theoretical Studies for Excited-State Tautomerization in the 7

ARTICLE pubs.acs.org/JPCA

Theoretical Studies for Excited-State Tautomerization in the 7-Azaindole(CH3OH)n (n = 1 and 2) Complexes in the Gas Phase Hua Fang and Yongho Kim* Department of Applied Chemistry, Kyung Hee University, 1 Seochun-Dong, Giheung-Gu, Yongin-Si, Gyeonggi-Do 446-701, Korea ABSTRACT: The excited-state tautomerization of 7-azaindole (7AI) complexes bonded with either one or two methanol molecule(s) was studied by systematic quantum mechanical calculations in the gas phases. Electronic structures and energies for the reactant, transition state (TS), and product were computed at the complete active space self-consistent field (CASSCF) levels with the second-order multireference perturbation theory (MRPT2) to consider the dynamic electron correlation. The time-dependent density functional theory (TDDFT) was also used for comparison. The excited-state double proton transfer (ESDPT) in 7AICH3OH occurs in a concerted but asynchronous mechanism. Similarly, such paths are also found in the two transition states during the excited-state triple proton transfer (ESTPT) of the 7AI(CH3OH)2 complex. In the first TS, the pyrrole ring proton first migrated to methanol, while in the second the methanol proton moved first to the pyridine ring. The CASSCF level with the MRPT2 correction showed that the former path was much preferable to the latter, and the ESDPT is much slower than the ESTPT. Additionally, the vibrationalmode enhanced tautomerization in the 7AI(CH3OH)2 complex was also studied. We found that the excitation of the lowfrequency mode shortens the reaction path to increase the tautomerization rate. Overall, most TDDFT methods used in this study predicted different TS structures and barriers from the CASSCF methods with MRPT2 corrections.

1. INTRODUCTION Proton and hydrogen-atom transfer is of key importance to the redox (oxidationreduction) reactions in many chemical and biological processes, to the proton transport via membranespanning proteins, and to the proton relay system in enzymes, of which prototropic tautomerisms of DNA base-pairs have attracted much interest for many years,15 since they are related to the gene mutation under UV light. However, it is difficult to monitor the proton transfer in real DNA base-pairs because of their conformational complexities and poor spectroscopic properties. Therefore, 7-azaindole (7AI) is utilized as a model compound to resemble the DNA base pair, and the proton transfer in 7AI dimer has been extensively studied. 7AI contains a hydrogen bond donor site (NH) and an acceptor site (dN —) and displays simple hydrogen-bonding structures upon dimerization and complexation with water and/or alcohols. Proton transfer in the cyclic hydrogen-bonded complexes of amphoteric aromatic molecules with water and/or alcohols, such as 7AI or 7-hydroxyquinoline (7HQ), has also been studied extensively,616 since it can mimic the proton relay system in enzyme and proton transport in membrane.17 Consequently a detailed understanding of the multiple proton transfer mechanism at the molecular level might provide insight into these complicated chemical and biological processes.18,19 A large number of proton transfer reactions in hydrogenbonded complexes of 7AI with water have been studied in the gas phase as well as in the condensed phase. Chaban and Gordon20 r 2011 American Chemical Society

have calculated the structures and energetics of the proton transfer in the 7AIH2O complex for the first excited state (S1). Compared to the isolated 7AI, the energy barriers of tautomerization in the 7AIH2O complex were dramatically decreased. Duong and Kim21,22 studied the 7AIH2O complex at the CASSCF(10,9)/6-31G(d,p) level and presented that the geometries of reactant, product, and the TS were in good agreement with previous studies at the CASSCF(10,9)/DZP level.20 They also reported that the excited-state double proton transfer (ESDPT) occurs via a concerted, albeit asynchronous, mechanism, and the bond order of the hydrogen atom in flight was not conserved along the reaction coordinate. Recently, Kina et al.23 conducted ab initio QM/MM molecular dynamics simulations for the excited-state full tautomerization process in 7AI(H2O)n (n = 1, 2) complexes, and they found that the ESDPT takes place asynchronously in both the gas and solution phases. Very recently, Sakota et al.24 investigated the excitedstate multiple-proton transfer reactions of 7AI water clusters, 7AI(H2O)n (n = 2, 3), in the gas phase by combining electronic spectroscopy and quantum chemical calculations. They suggested that tautomerization occurs via excited-state triple proton transfer in the cyclic 7AI(H2O)2 complex although no excitedstate tautomerization was observed for the 7AIH2O complex in Received: August 11, 2011 Revised: October 14, 2011 Published: October 19, 2011 13743

dx.doi.org/10.1021/jp207701r | J. Phys. Chem. A 2011, 115, 13743–13752

The Journal of Physical Chemistry A the gas phase, which agreed very well with the recent study using high level quantum mechanical calculations.25 Sekiya et. al9,10 have studied the excited-state triple proton transfer (ESTPT) of 7AI(CH3OH)n, n = 13, in the gas phase. No evidence of tautomer formation has been obtained for 7AI(CH3OH)n, n = 1, 3. This could be attributed to the tautomerization rate that is too slow for the tautomeric forms to be observed in the visible fluorescence spectrum. In contrast, the ESTPT was observed in the S1 state of 7AI(CH3OH)2. It was shown that the in-phase cooperative stretching motion of the whole hydrogen-bonded network enhances ESTPT in 7AI(CH3OH)2.10 This is so because the rate of ESTPT was remarkably enhanced by exciting the in-phase intermolecular stretching vibration of the cyclically hydrogen-bonded network, in the low internal energy region (0600 cm1) of S1. However, no additional vibrationalmode enhanced ESTPT appeared in the high internal energy region, and such behavior was ascribed to the competition effect arising from ESTPT with the intramolecular vibrational energy redistribution. Therefore, it will be very interesting to see whether this vibrational mode is related to the heavy-atom motions that enhance proton tunneling in the hydrogen-bonded clusters, which can be used as a model to mimic the similar activity in an enzyme. It was postulated that the role of the heavy-atom motions in a multiple proton transfer process may provide insight into the catalytic mechanism of enzymes. The multiple-proton transfer in 7AI complexes bound with alcohol in the gas phase and in solution was thoroughly studied in order to reveal the proton transfer dynamics in complicated molecular systems such as enzymes and proteins with water molecules bonded. In the condensed phase, the only ESDPT was observed in the 7AICH3OH complex; however, in the gas phase, the tautomerization was observed only in the 7AI (CH3OH)2 complex. Thus, a systematic theoretical study is required to rationalize these results whereas very few theoretical studies have been performed for the excited-state tautomerization in 7AI(CH3OH)n (n = 1, 2) complexes. In the present paper, we report high level quantum mechanical studies on the tautomerization of the biologically interesting 7AICH3OH and 7AI(CH3OH)2 complexes using the CASSCF methods including dynamic electron correlation. The structures and energetics of the reactant, TS, and product were calculated and compared with the experimental results. The vibrational frequencies in the S1 state were also computed to rationalize the vibration assisted tunneling in terms of the vibrational mode specific enhancement of the ESTPT. The TDDFT methods have recently been used successfully to study excited-states for many systems; however, most of the studies were focused on the spectroscopic properties. To understand reaction dynamics in the excited-state, detailed information about structures, energies, and vibrational frequencies of reactants and transition states is essential. However, the TDDFT calculations for excited-state reaction barriers have rarely been performed. Naturally, the TDDFT functionals retain all the problems of the groundstate functionals and, importantly, fail to describe charge-transfer excited states26,27 or polarizabilities in conjugated systems,28 which are sensitive to the virtual orbitals and the long-range behavior of the functionals. Thus, there is great interest in learning which functionals are most successful for studying excited-state reactions. In this study, five TDDFT methods, which contained a hybrid functional, long-range correction (LC), and empirical dispersion functionals, were used to systematically investigate excited-state tautomerization reactions in the gas phase.

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Figure 1. Reactant, product, and the transition state of the ESDPT in the 7AICH3OH complex at the CASSCF(10,9)/6-311G(d,p) level.

2. COMPUTATIONAL DETAILS The reactant, product, and TS geometries of the excited-state proton transfer reaction in the 7AI(CH3OH)n (n = 1, 2) complexes were fully optimized at the TDDFT and CASSCF levels with 6-31G(d,p), 6-311G(d,p), and 6-311+G(d,p) basis sets using the Gaussian 09 program29 in the gas phase. At the CASSCF level, the active space, which is an essential component of the calculation, includes four π bonds, four corresponding antibonding orbitals, and one nitrogen lone pair, resulting in an active space of 10 electrons in 9 orbitals, which was denoted as CASSCF(10,9). Vibrational frequencies were also calculated via a similar procedure. Single point energy calculations were performed using the second-order multireference perturbation theory (MRPT2) for stationary points. All MRPT2 calculations were performed using the GAMESS program.30 Analytic TDDFT gradients were calculated using the variational TDDFT formulation of Furche and Ahlrichs.31 Several different exchange-correlation DFT potentials were used in the systems. These include Becke’s three-parameter LeeYangParr hybrid functional32 (B3LYP), Handy and co-workers’ long-range corrected version of B3LYP using the Coulomb-attenuating method33 (CAM-B3LYP), the long-range-corrected version of BLYP34 (LC-BLYP), the hybrid functional of Truhlar and Zhao35 (M06-2X), and the latest functional from Head-Gordon and co-workers, which included empirical dispersion34 (WB97XD). 3. RESULTS AND DISCUSSION 3.1. 7AICH3OH Complex. Structures of the stationary points in the 7AICH3OH complex optimized at the CASSCF(10,9)/ 13744

dx.doi.org/10.1021/jp207701r |J. Phys. Chem. A 2011, 115, 13743–13752

The Journal of Physical Chemistry A

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Table 1. Geometric Parameters of Reactant, Product, and Transition States for Excited-State Proton Transfer in 7AICH3OH Complexesa reactant

product

computational method

r(H10O16)

r(H17N6)

r(N1H10)

r(O16H17)

CASSCF(10,9)/6-31G(d,p)

2.147

2.112

2.182

2.177

CASSCF(10,9)/6-311G(d,p)

2.154

2.127

2.199

2.187

B3LYP/6-31G(d,p) B3LYP/6-311+G(d,p)

1.838 1.871

1.804 1.837

1.952 1.975

1.994 2.028

CAM-B3LYP/6-31G(d,p)

1.808

1.793

1.945

1.962

CAM-B3LYP/6-311+G(d,p)

1.840

1.827

1.963

1.988

LC-BLYP/6-31G(d,p)

1.787

1.784

1.930

1.922

LC-BLYP/6-311+G(d,p)

1.814

1.811

1.936

1.940

M06-2X/6-31G(d,p)

1.838

1.826

2.021

1.980

M06-2X/6-311+G(d,p)

1.857

1.851

2.025

2.017

WB97XD/6-31G(d,p) WB97XD/6-311+G(d,p)

1.834 1.863

1.832 1.842

1.979 1.981

1.974 2.011

transition state

a

r(N1H10)

r(H10O16)

r(O16H17)

r(H17N6)

CASSCF(10,9)/6-31G(d,p)

1.288

1.187

1.035

1.557

CASSCF(10,9)/6-311G(d,p)

1.299

1.174

1.019

1.605

B3LYP/6-31G(d,p)

1.233

1.282

1.151

1.376

B3LYP/6-311+G(d,p)

1.246

1.266

1.154

1.373


1.234

1.270

1.129

1.398

CAM-B3LYP/6-311+G(d,p) LC-BLYP/6-31G(d,p)

1.254 1.235

1.247 1.262

1.127 1.117

1.404 1.408


1.255

1.239

1.120

1.408

M06-2X/6-31G(d,p)

1.238

1.267

1.100

1.445

M06-2X/6-311+G(d,p)

1.260

1.238

1.092

1.461

WB97XD/6-31G(d,p)

1.241

1.259

1.126

1.398

WB97XD/6-311+G(d,p)

1.261

1.234

1.117

1.412

Bond distances are in Å.

6-311G(d,p) level are shown in Figure 1. Some geometrical parameters at various levels of theory were listed in Table 1, from which the general trend observed is that larger basis sets tend to increase the H-bond distances in the reactants and products. The H10O16 and H17N6 distances in the reactant at all the TDDFT calculations using the 6-31G(d,p) basis sets in this work were 0.310.36 Å and 0.280.33 Å shorter, respectively, than those at the CASSCF level. The long-range corrected functionals (CAM-B3LYP and LC-BLYP) and the WB97XD functional that included empirical dispersion underestimated all four H-bond distances. Noticeably, the long-range corrected CAM-B3LYP functional did not show better agreement with the CASSCF results than the B3LYP itself. On comparison, the LC-BLYP method predicts the shortest H-bond distances. The shorter the H-bond length, the higher the H-bond energy; therefore, the LC-BLYP level overestimated the H-bond strength greatly compared to the CASSCF results. The hybrid M06-2X gave the smallest total error for four H-bond distances in the reactant and product compared with the corresponding values obtained at the CASSCF level. Although the larger 6-311+G(d,p) basis set increased H-bond distances at all TDDFT levels, their values are still shorter than the CASSCF values.

TS geometries for the excited-state proton transfer reaction in 7AICH3OH were fully optimized and confirmed by frequency calculations, and some of the geometric parameters were also listed in Table 1. In the TS, it is observed that the double proton transfer occurred in a concerted but asynchronous way, where the H10 atom migrated first followed by the H17 atom. When the CASSCF/6-31G(d,p) level was applied, the H10 atom moved more than halfway along the reaction coordinate toward O16, whereas the H17 atom rarely moved. However, at all TDDFT levels using the same basis sets, the H10 atom moved slightly less than halfway and the H17 atom moved slightly further than at the CASSCF level. All the TS structures at these TDDFT levels seemed to satisfy Hammond’s postulate that the TS of the exothermic reaction resembles the reactant structure (denoted as an early TS), although the positions of the two H atoms at the TS were not completely synchronized. However, when the 6-311+G(d,p) basis set was applied, all the TDDFT methods except TD-B3LYP predicted similar TS structures to the CASSCF calculation, in which the H10 atom moved more than halfway toward O16, whereas the H17 atom moved slightly less than halfway. Very recently, the structures, energetics, and rate constants of the excited-state tautomerization in 7AIwater complexes were 13745



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Table 2. Mulliken Partial Charges of Selected Atoms in the TS Calculated at the CASSCF(10,9)/6-311G(d,p) Level 7AIH2O

7AICH3OH

N1

0.41

0.42

N6 O16

0.73 0.54

0.74 0.47

H3O+

0.52

CH3OH2+

0.57

calculated at the CASSCF level, including dynamic electron correlation.21,25 Compared to the corresponding geometric parameters of the TS in the 7AIH2O complex obtained at the CASSCF/6-311G(d,p) level,25 the N1H10 and N6H17 distances of the TS in the 7AICH3OH complex were increased 0.022 and 0.126 Å, respectively, whereas the H10O16 and O16H17 distances decreased 0.024 and 0.048 Å, respectively. These geometrical changes of the TS were probably attributed to the electron-donating methyl group that made the basicity (gasphase proton affinity) of methanol bigger than that of water.36 A methyl group can stabilize the positive charge, so the partial charges of the CH3OH2+ moiety in part of the 7AICH3OH TS is larger than that of the H3O+ moiety in the TS of the 7AIH2O complex, as listed in Table 2. Interestingly, the partial charges of N1 and N6 were nearly the same, and only the oxygen charges were varied upon the methyl substitution. The replacement of a proton with a methyl group changed the TS structures to increase its ion-pair character; however, the overall mechanism of double proton transfer remained the same. A correlation between the hydrogen bond length and the proton transfer coordinate is plotted in Figure 2. Limbach et al.3739 defined the hydrogen bond coordinates q1 = 1/2(rAH rBH) and q2 = rAH + rBH to represent the correlation between rAH and rBH in many hydrogen-bonded complexes (AH 3 3 3 B). For a linear H-bond, q1 represents the distance of H from the H-bond center and q2 represents the distance between atoms A and B. A strong H-bond results in short rBH and slightly elongated rAH distances. The bond distance depends on bond energy and bond order. In the AH 3 3 3 B complexes, the rAH and rBH distances depend on each other, leading to allowed rAH and rBH values based on the following Pauling equations under the assumption that the sum of two bond orders is conserved, nAH + nBH = 1: ° nAH ¼ expf ðrAH rAH Þ=bAH g

ð1Þ

° nBH ¼ expf ðrBH rBH Þ=bBH g

ð2Þ

where r°AH and r°BH are the equilibrium lengths of the free AH and BH bonds, and bAH and bBH are the parameters describing the decrease of the AH and the HB unit bond valences with the corresponding distances. This type of correlation, i.e., the “bond energy bond order method”, has been used for many years to study hydrogen atom transfer.40,41 When H is transferred from A to B in the AH 3 3 3 B complex, q1 increases from negative to positive values and q2 goes through a minimum, which is located at q1 = 0. Limbach et al.3739 suggested that both proton transfer and hydrogen-bonding coordinates could be combined into the same correlation. This correlation can be used to study the characteristics of the transition state, such as earliness or lateness, tightness or looseness, bond order, and asynchronicity. The negative or positive q1 value corresponds to early or late TS, respectively, and the small

Figure 2. Correlation of the H-bond distances, q2 = r1 + r2, with the proton transfer coordinate, q1= 1/2(r1 r2), for the 7AICH3OH complex in the gas phase. All points are for the transition states in S1 optimized at the CASSCF/6-311G(d,p) and TD-DFT/6-311+G(d,p) levels. The solid lines designate the correlation that satisfies conservation of the bond order. The parameters for Pauling equations were from the literature.38 The regions above and below the black line are where the sums of bond orders are smaller and larger than unity, respectively.

or large q2 value corresponds to tight or loose TS, respectively. In addition, the two q1 values of two protons in the TS of double proton transfer should be very similar and different in the synchronous and asynchronous mechanism, respectively. The correlations between N1H10 and H10O16 distances (H10 transfer), and N6H17 and H17O16 distances (H17 transfer) in the TS of the 7AICH3OH complex are presented in Figure 2. It is interesting that correlation points at the CASSCF and most TDDFT levels were slightly below and above the solid line satisfying the conservation of bond order, which stands for a slightly increased and decreased total bond order at the TS, respectively. In the synchronous double proton transfer, two q1 values at the TS of double proton transfers should be approximately the same. However, the q1 value of H10 transfer at the CASSCF/6-311G(d,p) level was slightly positive but for H17 it was very negative, resulting from a highly asynchronous TS (slightly late TS for H10 but very early for H17 transfers). Fernandez-Ramos et al.42 calculated the rate constants of double proton transfer in the complex of acetic acid with methanol, and compared them with the NMR experimental results obtained by Gerritzen and Limbach.43 They also observed a highly asynchronous TS that would give different q1 values for two transferring protons. The position of the transferring proton between two end atoms at the TS depends on the relative acidity and basicity of the hydrogen-bond donor and acceptor. The asynchronous TS of the energetically symmetric double proton 13746



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Table 3. Geometric Parameters of Reactant, Product. and Transition States for Excited-State Proton Transfer in 7AI(CH3OH)2 Complexesa reactant

product

computational method

r(H10-O16)

r(O22H17)

r(H23N6)

r(N1H10)

r(O16H17)

r(O22H23)

CASSCF(10,9)/6-31G(d,p)

1.789

1.815

1.878

2.065

1.917

2.017

CASSCF(10,9)/6-311G(d,p)

1.789

1.827

1.896

2.079

1.931

2.021

B3LYP/6-31G(d,p) B3LYP/6-311+G(d,p)

1.652 1.695

1.632 1.675

1.672 1.717

1.818 1.846

1.726 1.760

1.808 1.843


1.619

1.606

1.657

1.808

1.705

1.782


1.665

1.648

1.702

1.832

1.733

1.814

LC-BLYP/6-31G(d,p)

1.585

1.571

1.636

1.784

1.670

1.744


1.638

1.616

1.681

1.803

1.694

1.774

M062X/6-31G(d,p)

1.560

1.609

1.643

1.869

1.753

1.790

M062X/6-311+G(d,p)

1.633

1.689

1.706

1.901

1.813

1.823

WB97XD/6-31G(d,p) WB97XD/6-311+G(d,p)

1.639 1.670

1.677 1.673

1.700 1.711

1.850 1.833

1.756 1.753

1.792 1.806

Transition State

a

r(N1H10)

r(H10-O16)

r(O16H17)

r(H17O22)

r(O22H23)

r(H23N6)

CASSCF(10,9)/6-31G(d,p)TS1

1.480

1.054

1.042

1.400

1.015

1.586


1.548

1.027

1.045

1.385

1.009

1.599


1.072

1.514

1.029

1.429

1.381

1.121


1.067

1.526

1.018

1.451

1.416

1.103

B3LYP/6-31G(d,p)

1.193

1.306

1.133

1.288

1.199

1.287

B3LYP/6-311+G(d,p) CAM-B3LYP/6-31G(d,p)

1.152 1.213

1.372 1.271

1.126 1.124

1.298 1.287

1.277 1.160

1.214 1.324


1.192

1.301

1.125

1.286

1.214

1.263

LC-BLYP/6-31G(d,p)

1.223

1.252

1.117

1.285

1.134

1.352


1.219

1.257

1.125

1.271

1.166

1.311

M062X/6-31G(d,p)

1.244

1.233

1.106

1.310

1.106

1.398

M062X/6-311+G(d,p)

1.282

1.197

1.107

1.308

1.099

1.409

WB97XD/6-31G(d,p)

1.225

1.253

1.125

1.287

1.161

1.316

WB97XD/6-311+G(d,p)

1.200

1.286

1.120

1.288

1.209

1.260

Bond distances are in Å.

transfer in the acetic acid complex with methanol resulted from their relative acidity and basicity. The H10 position at the TS of the 7AICH3OH complex is similar to that of the acetic acidmethanol complex. The q1 value of H10 at the TS was 0.063 at the CASSCF(10,9)/6-311G(d,p) level, and that of the corresponding proton in the acetic acidmethanol complex was 0.096 at the QCISD level.42 Considering that the ESDPT in the 7AICH3OH complex was highly exothermic to give an early TS based on the Hammond’s postulate and that different computational levels were used, the q1 values of transferring protons in two complexes agreed well with each other. These results suggest that the acidity of the pyrrolic proton in 7AI, which becomes larger upon excitation,44 might be similar to that of acetic acid. The TDDFT/6-311+G(d,p) levels also predicted an asynchronous TS for the double proton transfer, but their asynchronicity was smaller; the q1 values of H10 transfer were very close to zero, and those of H17 transfer were less negative than that of the CASSCF level. All the correlation points from the TDDFT methods were further from those of the CASSCF level. On comparison, the TDDFT methods with a long-range correction and empirical dispersion functional gave slightly better agreement

with the CASSCF results than the B3LYP. Overall, the M06-2X method exhibited the best agreement among the DFT methods used in this study. 3.2. 7AI(CH3OH)2 Complex. The optimized structural parameters of the reactant, product, and TS for the 7AI(CH3OH)2 complex are listed in Table 3, and their structures at the CASSCF(10,9)/6-311G(d,p) level are depicted in Figure 3. Interestingly, all H-bond distances in the 7AI(CH3OH)2 complex were shorter than those in the 7AICH3OH complex, due to the strengthened linear H-bonds as shown in Figure 3. Particularly, all TDDFT methods using the 6-31G(d,p) basis set predicted very short H-bonds for the reactant. The H10O16, H17O22, and H23N6 distances in the reactant at the LC-BLYP level were 0.204, 0.244, and 0.242 Å shorter than the corresponding CASSCF values, respectively. The long-range corrected CAM-B3LYP method predicted slightly shorter H-bond distances than those from the uncorrected method. The M06-2X and WB97XD methods also produced shorter H-bonds compared with the CASSCF results. These results suggested that all TDDFT methods used in this study overestimated the H-bond strength in the excited state. When the 6-311+G(d,p) basis set 13747



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Figure 3. Reactant, product, and two transition states (TS1 and TS2) of the ESTPT in the 7AI(CH3OH)2 complex at the CASSCF(10,9)/6311G(d,p) level.

was used, all TDDFT distances were slightly increased but still smaller than the CASSCF values. The WB97XD method generated the smallest total error for six H-bond distances from reactant and product compared with the values at the CASSCF level. The geometries of the TS were fully optimized at the TDDFT and CASSCF levels and confirmed by frequency calculations. Surprisingly, two TS structures at the CASSCF level were found as shown in Figure 3. In the first TS (denoted as TS1), the H10 moved more than halfway from the N1 to O16 atom with the H17 and H23 barely moving, which generated a CH3OH2+-like moiety in a portion of the TS (at O16). However, in the second TS (denoted as TS2), the H23 moved more than halfway from the O22 to N6 atom, but the H10 and H17 stayed, resulting in a CH3O-like moiety as a part of the TS (at O22). Considering only one proton migrated substantially while the other two barely moved, a stepwise mechanism with a possible intermediate can be anticipated. However, all calculations to find this intermediate ended up with either the reactant or the product. Thus, these results suggest that there are potentially two concerted but asynchronous processes in the ESTPT. At all TDDFT levels used in this study, we were unable to find two TSs despite of all the efforts. The correlations between N1H10 and H10O16 distances (H10 transfer), O16H17 and H17O22 distances (H17 transfer), and N6H23 and H23O22 distances (H23 transfer) at the TSs of the ESTPT in the 7AI(CH3OH)2 complex are depicted in Figure 4. For the TS1 at the CASSCF level, the q1 values of H10 and H23 were very positive and negative, respectively, whereas those for the TS2 were opposite. The opposite signs of the q1 values

Figure 4. Correlation of the H-bond distances, q2 = r1 + r2, with the proton transfer coordinate, q1 = 1/2(r1 r2), for the 7AI(CH3OH)2 complex in the gas phase. All points are for the transition states in S1 optimized at the CASSCF/6-311G(d,p) and TD-DFT/6-311+G(d,p) levels. The correlation for the normal mode vibration of 182 cm1 is depicted in a solid line with red open circles; the numbers 0, 1, 2, 3, and 4 represent the turning points of the zero-point, first, second, third, and fourth vibrational levels, respectively.

for H10 and H23 were a clear indication of the large asynchronicity in the concerted multiple proton transfer (via TS1 and TS2) and also revealed the opposite order of H10 and H23 transfers. It is worth noting that the correlation points for both TSs were under the solid line as described in Figure 4, which postulated that the total bond orders are slightly increased. This is probably due to the formation of CH3OH2+-like moiety at TS1 and a CH3Olike moiety at TS2 that induces Coulomb interactions to increase the bond strength. In the TS structures at the TDDFT levels, the position of H10 was closer to the center of two end atoms (N1 and O16) compared with those of two TSs (TS1 and TS2) at the CASSCF level. So were the positions of H17 and H23. Therefore, the q1 values of these protons were closer to zero, as shown in Figure 4, 13748



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Table 4. Tautomerization Energies, Barrier Heights, and Dipole Moment for Proton Transfer in 7AICH3OH and 7AI(CH3OH)2 in the S1 State at Various Levels of Theory a 7AICH3OH

7AI(CH3OH)2 μ (D)

computational method CASSCF(10,9)/6-31G(d,p)

ΔV‡

ΔE

17.1(13.7)

31.9(31.3)

R 1.55

TS 4.87

μ (D) ΔV‡

P 1.75

ΔE b

13.5(10.6)

32.3(31.9)

R 4.94

14.4(10.2)c CASSCF(10,9)/6-311G(d,p) MRPT2/CASSCF(10,9)/6-31G(d,p)

16.4(13.5) 8.71(5.31)

32.3(31.5)

1.46

5.20

1.71

19.22(18.6)

13.7(11.5)b 15.7(12.1)c 4.95(2.06)b

TS

P b

6.15

1.87

6.86c 31.8(31.4)

5.00

6.39b 7.03c

1.91

19.6(19.2)

7.37(3.14)c MRPT2/CASSCF(10,9)/6-311G(d,p)

7.90(4.97)

18.6(17.9)

3.98(1.81)b

18.9(18.5)

10.2(6.55)c

a

B3LYP/6-31G(d,p)

6.59(2.55)

18.1(17.5)

4.25

2.98

1.49

4.60(0.79)

15.3(14.4)

3.76

3.24

1.45


6.00(2.19)

19.7(18.8)

4.13

3.26

1.61

3.87(1.30)

16.5(15.4)

3.67

3.20

1.72

LC-BLYP/6-31G(d,p) M062X/6-31G(d,p)

5.57(2.03) 4.67(1.54)

19.3(18.1) 20.4(19.3)

3.64 4.31

3.28 3.39

1.80 1.76

2.85(1.76) 1.99(2.20)

15.9(14.5) 16.7(15.5)

3.19 3.68

3.04 3.15

2.04 2.30

WB97XD/6-31G(d,p)

7.29(3.44)

20.0(19.1)

4.27

3.28

1.75

5.43(0.49)

16.9(15.8)

3.85

3.24

2.31

B3LYP/6-311+G(d,p)

8.90(4.73)

17.5(16.9)

4.06

3.01

1.13

6.73(1.11)

15.2(14.4)

3.84

3.96

1.17


8.49(4.70)

18.7(17.8)

3.88

3.37

1.36

6.31(0.49)

16.1(15.1)

3.72

3.49

1.53


8.40(4.89)

17.8(16.7)

3.25

3.39

1.65

5.46(0.05)

15.2(13.9)

3.21

3.09

1.89

M062X/6-311+G(d,p)

6.84(3.68)

19.1(17.9)

3.88

3.56

1.82

3.64(0.76)

16.2(15.2)

3.41

3.36

2.21

WB97XD/6-311+G(d,p)

9.20(5.53)

18.9(18.0)

4.06

3.41

1.64

7.29(1.42)

16.2(15.0)

3.73

3.54

1.51

The numbers in parentheses include zero-point energies. Energies are in kcal/mol. b TS1. c TS2.

which indicates smaller asynchronicity. All q1 values were negative, except the ones for H10 and H23 at the M06-2X and B3LYP levels, respectively. Among the TDDFT levels used in this study, the M06-2X and B3LYP levels produced the closest correlation points (for H10 and H23) to those of TS1 and TS2 at the CASSCF level, respectively. Although the geometrical parameters are quite different, the TSs at the M06-2X and B3LYP levels are qualitatively similar to TS1 and TS2 at the CASSCF levels, respectively. However, neither of these methods predicted two TSs for the ESTPT. 3.3. Energetics of Excited-State Proton Transfer. Barrier heights (ΔV‡), excited-state tautomerization energies (ΔE), and dipole moments (μ) for the 7AICH3OH and 7AI(CH3OH)2 complexes are listed in Table 4. Tautomerization energies and barrier heights are highly dependent on the dynamic electron correlation. The ΔE values of 7AICH3OH and 7AI(CH3OH)2 complexes using 6-311G(d,p) basis sets were 17.9 and 18.5 kcal/mol, respectively, including zero-point energies. The tautomerization energies of the 7AICH3OH and 7AI(CH3OH)2 complexes agreed very well with each other, within 1 kcal/mol, which suggests that the relative formation energies of cyclic H-bonds with 7AI and the tautomer are approximately the same for the one and two methanol complexes. The ΔV‡ values of the ESDPT in the 7AICH3OH complex were 8.7 and 7.9 kcal/mol at the MRPT2 level using the 6-31G(d,p) and 6-311G(d,p) basis sets without ZPE corrections, respectively, and 5.3 and 5.0 kcal/mol including the ZPE corrections, respectively. For the ESTPT in the 7AI(CH3OH)2 complex, two TSs were predicted at the CASSCF level, and the ΔV‡ values of TS1 and TS2 with the MRPT2 correction were 4.0 and 10.2 kcal/mol, respectively, when using the 6-311G(d,p) basis set. The barrier of TS2 was 6.2 kcal/mol higher in energy than that of TS1. These results indicated that

the ESTPT might occur preferably via TS1. However, no obvious difference was found between the ΔV‡ values of TS1 and TS2 without considering the dynamic electron correlation. When ZPE corrections were included using the frequencies calculated at the CASSCF level, the ΔV‡ value of TS1 became only 1.8 kcal/ mol. The ZPE-corrected barriers of ESDPT using the 6-311G(d, p) basis set at the MRPT2 level was 3.2 kcal/mol higher. These results are consistent with the experimental observations of Sakota et al.9 that the excited-state tautomerization in the gas phase could be seen only in the 7AI(CH3OH)2 complex. Therefore, the tautomerization of the 7AICH3OH might be too slow to be measured in the fluorescence time scale. At the TDDFT level, the ΔE values for the 7AICH3OH complex agreed well with that at the MRPT2/6-311G(d,p) level (within 1.2 kcal/mol difference). However, for the 7AI (CH3OH)2 complex, they were quite different, where the maximum deviation is 4.6 kcal/mol. Unlike the case of the MRPT2 level, the TDDFT methods predicted a large difference in the ΔE values between the 7AICH3OH and 7AI(CH3OH)2 complexes. The ZPE-corrected ΔV‡ values for the 7AICH3OH complex obtained by TDDFT methods using the 6-31G(d,p) basis set were underestimated by a maximum difference of approximately 3.8 kcal/mol compared with the corresponding MRPT2 value. When the 6-311+G(d,p) basis set was used, the TDDFT barriers were in a better agreement with the MRPT2 values. Despite the excellent agreement, the TDDFT methods should be used carefully, since their TS structures are quite different from those of CASSCF. As mentioned above, only the M06-2X level gave similar correlations for the TS with CASSCF, and the ZPE-corrected barrier height using the larger basis sets was 3.7 kcal/mol, which is only 1.3 kcal/mol lower than the MRPT2 value. 13749



Figure 5. Normal mode of vibration with 182 cm1 of frequency in 7AI(CH3OH)2 at the CASSCF(10,9)/6-311G(d,p) level.

Unlike the case of the CASSCF level, only one TS structure was found for the 7AI(CH3OH)2 complex at all TDDFT levels used in this work. Figure 4 presented that the TS correlation points of H10 and H23 were in the middle of the two TS1 and TS2 points using the 6-311G(d,p) basis set. It is shown that the TS structures and barrier heights depend on the TDDFT level and the basis set size. For the 7AI(CH3OH)2 complex, all ZPEcorrected TDDFT barriers using the 6-31G(d,p) basis sets were greatly underestimated (even smaller than zero) compared with the MRPT2 value. Even with the larger basis set, the ZPEcorrected ΔV‡ values at all TDDFT levels were still smaller than the corresponding MRPT2 values, although those before applying the ZPE correction were larger. As pointed out earlier, the M06-2X and B3LYP levels predicted qualitatively similar TS structures to TS1 and TS2 at the CASSCF levels, respectively; however, they failed to reproduce the corresponding barrier heights at the MRPT2 level. The M06-2X and B3LYP levels greatly underestimated the ZPE-corrected barrier heights compared with the TS1 and TS2 barriers at the MRPT2 level, respectively. Overall, all TDDFT methods used in this study failed to predict consistent TS structures and barrier heights with the MRPT2 level for the excited-state proton transfer reactions. The dipole moments of the 7AICH3OH and 7AI(CH3OH)2 complexes were also listed in Table 4. For the 7AICH3OH complex, all TDDFT levels overestimate the dipole moments of reactant and underestimate the dipole moments of TS, compared with the CASSCF levels. For the 7AI(CH3OH)2 complex, the TDDFT levels greatly underestimate the dipole moments of TS compared with those of the CASSCF level. Most importantly, the dipole moments of TS were slightly smaller than those of reactant, which is contradictory to the CASSCF results. This quite different behavior of the dipole moment depending on the

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level of theory, which results from the excited-state electron density, might be attributed to the different prediction of TS structures and energetics of the excited-state tautomerization. 3.4. Vibrational-Mode Enhanced Tautomerization. Sakota et al.9 reported the vibrational-mode specific nature of the ESTPT: the excitation of the 181 cm1 vibrational mode accelerated the reaction rate, and this mode disappeared in the higher energy region (g600 cm1). We have successfully reproduced this specific vibrational mode, 182 cm1, at the CASSCF(10,9)/6-311G(d,p) level. This mode is a heavy-atom breathing motion without hydrogenic motions, which brings two oxygen atoms and nitrogen atoms of 7AI closer, as shown in Figure 5. In this vibrational motion, the change of the H10, H17, and H23 positions between heavy atoms can be described in the correlation plot of q1 and q2 as shown in Figure 4, where the correlations of these H-atoms at the turning points of the normal mode vibration were depicted. It is clear that the excitation of this vibrational mode brings the correlation points of H10, H17, and H23 close to those of the transition state; that is, the vibrational excitation of this mode shortens the reaction path to reach the transition state and, hence, speeds up the reaction, probably by the enhanced tunneling. These results are consistent with the vibrational-mode specific nature of the ESTPT. Recently, the intrinsic reaction coordinate (IRC) of ESDPT in 7AIH2O was calculated at the CASSCF(10,9)/6-31G(d,p) level,21,22 which exhibited a quite different correlation from the reaction path with the conservation of bond order. The hydrogenic and the heavyatom motions in the IRC were well separated. The correlation plot of the IRC was flat at the bottom near q1 = 0, and below the solid line where the heavy-atom motion dominates the hydrogenic motion (q1 < 0.3).25 If the IRC of the 7AI (CH3OH)2 complex would be similar to that of 7AIH2O, the heavy-atom motion might couple very well with the 182 cm1 mode of vibration. The statistical nature in the higher energy region (g600 cm1) was attributed to the intramolecular vibrational energy redistribution (IVR).10 The density of the vibrational-state is small in the energy region below 600 cm1 and increases very rapidly with energy over 600 cm1, and hence the IVR rate. When a higher frequency mode is excited, where ESTPT does not occur directly, the rapid IVR may occur statistically to give some of its vibrational energy to the 182 cm1 mode, which results in the rate acceleration, the nonreactive (spectator) modes with lower frequencies, and the reaction coordinate motion to overcome the barrier. Sakota et al.10 suggested that IVR is faster than the ESTPT in the higher energy region where the statistical nature is observed. The IVR rate of the low frequency mode must be slower than the ESTPT due to the small density of state; otherwise, no vibrational-mode specific nature would be observed. It was also pointed out that there might be some energy region where IVR competes with ESTPT.10 Since the ZPE-corrected energy barrier of the ESTPT is equivalent to 640 cm1, the vibrational-mode specific nature would not be expected, because no tunneling would occur in the energy region above the barrier and the excited energy will be statistically relaxed by the fast IVR.

4. CONCLUSIONS In the present work, systematic studies of the excited-state proton transfer reactions in the gas phase were performed on 7AI(CH3OH)n (n = 1, 2) complexes using TDDFT and 13750


The Journal of Physical Chemistry A CASSCF methods. The energetics of the excited-state tautomerization depends on the dynamic electron correlation and the size of the basis sets. For the 7AI(CH3OH)2 complex, the CASSCF levels predicted two concerted but asynchronous paths of ESTPT: one where the proton moved first from the pyrrole ring of 7AI to methanol, and the other where the methanol proton moved first to the pyridine ring. No obvious difference was found between the barrier heights of the two paths without considering the dynamic electron correlation. However, the MRPT2 correction clearly showed that the former path was much preferable to the latter. The tautomerization barrier of the 7AI(CH3OH)2 complex was 1.8 kcal/mol at the MRPT2/CASSCF(10,9)/6311G(d,p) level, which is much lower than that of the 7AI CH3OH complex, supporting the hypothesis that the excitedstate tautomerization might occur via the formation of cyclic H-bonded complexes with two methanol molecules. Sufficiently larger basis sets and dynamic electron correlation were crucial to correctly predict the mechanism of the excited-state tautomerization of 7AI. The correlation plot of vibrational turning points of the 182 cm1 mode, which gives the vibrational-mode specific nature of the ESTPT, shows that the excitation of this vibrational mode shortens the reaction path to reach the transition state and, hence, to speed up the reaction. All DFT methods used in this study underestimated H-bond distances in the reactant and product by approximately 0.10.4 Å. No significant benefits, in terms of both structural and energetic prediction, were found from the DFT methods with long-range correction or empirical dispersion. At all TDDFT levels used in this study, the TS structures and barrier heights greatly depend on the basis set. Comparing TS structures and potential energy barriers, the M06-2X method exhibited the best agreement among the DFT methods used in this study, although further systematic studies would be necessary to conclude which methods can be used to correctly understand the excited-state proton transfer reactions.

’ AUTHOR INFORMATION Corresponding Author

*E-mail: [email protected].

’ ACKNOWLEDGMENT This work was supported by a grant from Kyung Hee University in 2011. We are pleased to acknowledge the support of the Center for Academic Computing at Kyung Hee University for the computing resources. ’ REFERENCES (1) L€owdin, P. O. Rev. Mod. Phys. 1963, 35, 724–732. (2) L€owdin, P. O. Adv. Quantum Chem. 1966, 2, 213–360. (3) Da) bkowska, I.; Rak, J.; Gutowski, M. Eur. Phys. J. 2005, 35, 429–435. (4) Gu, J.; Wang, J.; Rak, J.; Leszczynski, J. Angew. Chem., Int. Ed. 2007, 46, 3479–3481. (5) Guallar, V.; Douhal, A.; Moreno, M.; Lluch, J. M. J. Phys. Chem. A 1999, 103, 6251–6256. (6) McMorrow, D.; Aartsma, T. Chem. Phys. Lett. 1986, 125, 581–585. (7) Chou, P. T.; Martinez, M. L.; Cooper, W. C.; Collins, S. T.; McMarrow, D. P.; Kasha, M. J. Phys. Chem. 1992, 96, 5203–5205.

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Theoretical Studies for Excited-State Tautomerization in the 7

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