Theoretical Studies for the Rates and Kinetic Isotope Effects of the

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Theoretical Studies for the Rates and Kinetic Isotope Effects of the Excited-State Double Proton Transfer in the 1:1 7-Azaindole:H2O Complex Using Variational Transition State Theory Including Multidimensional Tunneling My Phu Thi Duong and Yongho Kim* Department of Chemistry, Kyung Hee UniVersity, 1 Seochun-dong, Giheung-Gu, Yongin-si, Gyeonggi-do, 449-701, Korea ReceiVed: NoVember 4, 2009; ReVised Manuscript ReceiVed: January 22, 2010

Variational transition state theory calculations including multidimensional tunneling (VTST/MT) for excitedstate tautomerization in the 1:1 7-azaindole:H2O complex were performed. Electronic structures and energies for reactant, product, transition state, and potential energy curves along the reaction coordinate were computed at the CASSCF(10,9)/6-31G(d,p) level of theory. The potential energies were corrected by second-order multireference perturbation theory to take the dynamic electron correlation into consideration. The final potential energy curves along the reaction coordinate were generated at the MRPT2//CASSCF(10,9)/6-31G(d,p) level. Two protons in the excited-state tautomerization are transferred concertedly, albeit asynchronously. The position of the variational transition state is very different from the conventional transition state, and is highly dependent on isotopic substitution. Rate constants were calculated using VTST/MT, and were on the order of 10-6 s-1 at room temperature. The HH/DD kinetic isotope effects are consistent with experimental observations; consideration of both tunneling and variational effects was essential to predict the experimental values correctly. I. Introduction Proton transfer is one of the primary processes involved in numerous chemical and biological reactions. In particular, tautomerization through bridging hydrogen bonds in the 7-azaindole (7AI) system is an interesting biological model that has been studied extensively both experimentally and theoretically. Kasha and co-workers studied 7AI as a model for hydrogen bonding in DNA base pairs.1 Petrich and co-workers2-4 have shown that 7-azatryptophan is a novel in situ optical probe of protein structure and dynamics, with 7AI functioning as a key chromophore. 7AI has an N-H bond and a heteroaromatic N atom as hydrogen bond donor and acceptor site, respectively, and the normal form becomes unstable with respect to the tautomer form in the S1 state.5,6 The monomer species of 7AI is capable of excited-state double proton transfer (ESDPT) from the five-membered ring (donor site) to the six-membered ring (acceptor site) in a variety of environments, including gas phase as well as solvent clusters when assisted by solvent molecules. Huang et al.7 studied the 1:1 7AI:water complex in the first excited state in cold beams and reported a fluorescence lifetime of 8 ns, which implies that the tautomerization rate constant of ESDPT cannot be larger than approximately 107 s-1. However, no direct observation of ESDPT in this complex has yet been made. The tautomerization in 7AI has also been studied in the condensed phase in alcohol or water solutions.8-11 The tautomerization of 7AI in alcohols has been discussed in terms of a two-step process.12-15 The first step involves solvent reorganization to form a cyclic hydrogen-bonded 7AI-alcohol complex; the second step, intrinsic double proton transfer. Arrhenius activation energies of tautomerization were very similar to those associated with the solvent viscosity,14 which implies that solvent motion controls the reaction. If this motion was rate-limiting, no * To whom correspondence should be addressed. E-mail: [email protected]. Phone: +82-31-201-2456. Fax: +82-31-203-5773.

significant kinetic isotope effect (KIE) would be expected. However, KIEs for excited-state tautomerization were observed in the 7AI complexes with various alcohols.9,12,14 Moogs et al.14 suggested that both solvent reorganization and the intrinsic proton transfer step determine the reaction rate, and Chen et al.9 suggested that two protons are transferred concertedly in the intrinsic double proton transfer step based on the observed rates and KIEs satisfying the rule of geometric mean. However, the mechanism of ESDPT in water remains unclear. Chou et al.16 measured rates and KIEs for ESDPT of the 1:1 3-cyano7AI:water complex to clarify the mechanism of 7AI in water. These authors and others8,13,16,17 suggested that fast excited-state equilibrium between the 1:1 cyclic hydrogen-bonded complex and randomly hydrated complexes is established and followed by ESDPT that may be governed by a tunneling mechanism. Chen et al.9 observed the breakdown of the rule of the geometric mean in water and suggested the stepwise ESDPT mechanism. The rate constants in water are on the order of 109 s-1, and the HH/DD KIEs are in the range 3.4-3.9 at room temperature.8,9,16 These small KIEs might also be supportive for the stepwise mechanism. However, theoretical studies in the gas phase suggested the concerted mechanism. In early theoretical calculations, Chaban and co-workers5,6 investigated the ground- and excited-state tautomerization processes in 7AI with and without mediating solvent using ab initio calculations. They used a CASSCF procedure with multireference second-order perturbation theory (MCQDPT2) to include dynamic electron correlation

10.1021/jp910533m  2010 American Chemical Society Published on Web 02/18/2010

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and calculate energetics and intrinsic reaction coordinates for the hydrogen transfer process in the ground and first excited states of the 7AI and the 7AI-H2O complexes. They demonstrated that the dynamic electron correlation and additional water molecule dramatically reduced the activation barrier. Furthermore, they showed that the ESDPT in the 7AI-H2O complex occurs via a concerted process. Tautomerization involves transfer of a light (H) atom between heavy (N and O) atoms, so quantum mechanical tunneling is expected to have a significant impact on the reaction rate. However, the HH/DD KIEs in aqueous solution8,9 do not provide clear evidence for significant tunneling. To interpret these KIE values correctly, accurate potential energy surfaces for the excited state and a dynamics theory that can handle multidimensional tunneling in large molecular systems are required. However, prior to this study, no accurate multidimensional potential energy surfaces along the reaction coordinate for the excited-state proton transfer reactions were generated. Fernańdez-Ramos et al.18 calculated the rate constants for excited-state tautomerization of 7AI complexes with water, represented by discrete water molecules with or without a dielectric continuum, using the approximate instanton method (AIM). They concluded that tautomerization occurs via a quantum mechanical tunneling process and the classical contribution to the rate constants is negligible or very small. However, their transition state (TS) structures, which were calculated at the CASSCF(8,8)/6-31D(d) level, were very different from those obtained from previous higher level calculations.5 For example, the activation barrier of double proton transfer in the 1:1 complex, at the CASSCF(8,8)/ 6-31D(d) level, was 20.6 kcal/mol, whereas the barrier at the CASSCF(10,9)/DZP level was 18.2 kcal/mol.5 The zero-point energy (ZPE) corrections increased the CASSCF(8,8)/6-31G(d) barrier by 1.5 kcal/mol18 but reduced the CASSCF(10,9)/DZP barrier by 3.5 kcal/mol.5 It is very unusual that the ZPE correction increases the barrier height. At the CASSCF(10,9)/ DZP level, the N-H bond in the five-membered ring moves first toward a water molecule in the TS of the 1:1 complex, while the O-H bond is nearly unchanged, whereas, at the CASSCF(8,8)/6-31G(d) level, the O-H bond moves first toward the six-membered ring, while the N-H bond in the fivemembered ring is nearly unchanged. The order of proton in flight was reversed. As a result, the CASSCF(10,9)/DZP and CASSCF(8,8)/6-31G(d) levels predicted an H3O+-like moiety and an OH--like moiety in the TS, respectively. Recent experimental results showed that 7AI becomes acidic in the S1 state upon the π-π* electronic excitation so that the N-H bond would be broken easily;19 therefore, it will be more plausible that an H3O+-like moiety is formed in the TS. These results suggest that the TS used in the AIM study18 was inappropriate, because it was not on the intrinsic reaction coordinate, but probably on a higher energy reaction path that is relatively unimportant. Tautermann et al.20 pointed out that the instanton method might sometimes work due to error compensation. In AIM, the reaction coordinate is not the minimum energy path (MEP), but the imaginary frequency mode in the TS, and the tunneling distance between the two equilibrium positions of the hydrogen atom is measured along this reaction coordinate; i.e., the energies and structures of the reactants, products, and TS, and the force fields of three stationary points were used to generate the appropriate potential energy surface. However, this method can not consider a real MEP with an arbitrary shape, and the curvature of the reaction path, which needs to be taken into account when considering tunneling.

Duong and Kim Very recently, Kina et al.21 performed ab initio molecular dynamics (AIMD) simulations for the 7AI-H2O complex; they showed that the ESDPT occurs at t ) ∼50 fs after the photoexcitation in the gas phase via a concerted and asynchronous process. They also presented the AIMD simulation including the surrounding water molecules by effective fragment potential and suggested that the ESDPT takes places asynchronously in both the gas phase and in solution. It is interesting to note that the mechanism was not altered by the solvent effect. In the trajectory of the AIMD simulations, the O-H proton moves first to the six-membered ring followed by the N-H proton from the five-membered ring to water. However, the TS structures obtained by Chaban et al.5 and Kina et al.21 suggest that the N-H proton from the five-membered ring moves first, and the water proton follows, as described above. The AIMD trajectory was far from the intrinsic reaction coordinate, which might be one of the high-energy reaction paths; thus, further investigation is required. Asynchronous multiple proton transfers in other reactions have been reported previously.22-27 An accurate estimate of the potential energy surface is required to investigate the asynchronicity of double proton transfer and reaction dynamics in detail. However, it is extremely difficult to obtain high-level potential energy surfaces including dynamic electron correlation for excited-state reactions. Therefore, theoretical studies of excited-state reaction dynamics, including quantum mechanical tunneling, are very rare. Variational transition state theory including multidimensional tunneling (VTST/MT) has been successfully used to study multiple proton transfer reactions.24,28-30 To apply transition state theory in excited-state reactions, the excited species should be thermally equilibrated with the environment during the reactive processes. In solution, this equilibrium is reached by solvent relaxation. If the solvent relaxation is slower than the reactive process so that the equilibrium condition cannot be maintained, transition state theory may not be applied. Jiminez et al.31 measured ultrafast solvation dynamics of water, which is faster than 50 fs, using a coumarin probe. Horng et al.32 measured time scales of solvation dynamics in organic solvents and reported a few ps of the solvation time in methyl alcohol. The rate constants of ESDPT in water are on the order of 109 s-1. Furthermore, the temperature dependence of the ESDPT rate was measured, and linear Arrhenius plots of ln kPT vs 1/T were observed both in water and in methyl alcohol.8,14 These results mean that the solvent relaxation in water is much faster than the excited-state tautomerization reaction, and confirm that transition state theory can be used to study the ESDPT in water. In this study, we present high-level potential energy surfaces along the minimum energy path (MEP) for the ESDPT in the 7AI-H2O complex. These calculations were performed in the gas phase, because it is practically impossible to include the solvent effect on the high-level excited-state potential energy surfaces. However, the vibrational modes orthogonal to the reaction coordinate are in general less sensitive to the solvent effect, and so are the KIEs. Therefore, appropriate prediction of KIE based on the gas phase reaction dynamics calculations could provide reasonable insight for the condensed phase reaction dynamics unless the overall mechanism is changed greatly due to the solvent effect. Rate constants and KIEs are calculated to investigate the detailed mechanism of excited-state tautomerization using VTST/MT, and compared with experimental results. The detailed reaction mechanism of the ESDPT will be discussed.

ESDPT in the 1:1 7-Azaindole:H2O Complex

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kCVT/SCT(T) ) κSCT(T)kCVT(T)

II. Computational Methods The geometries of the reactant complex, product complex, and TS in the excited electronic state were optimized at the CASSCF(10,9)/6-31G(d,p) level using the Gaussian 03 quantum mechanical package.33 Single point energy calculations were also performed using second-order multireference perturbation theory for stationary points. The minimum energy paths (MEPs) were initially obtained in the mass-scaled coordinate by 1 amu at the CASSCF(10,9)/6-31G(d,p) level using the Euler steepest descent method and the reoriented generalized-transition-statetheory dividing surface algorithm34 with a step size of 0.01 amu1/2 bohr. The quality of the CASSCF calculations strongly depends on the choice of the active space and basis sets. The CASSCF(10,9)/DZP level was the highest level reported in the literature for the 1:1 7AI:H2O complex.5 At a nonstationary point of the excited-state MEP, these CASSCF calculations sometimes failed to reach SCF convergence, so we chose the CASSCF(10,9)/ 6-31G(d,p) level in this study. Frequencies along the MEP were calculated at the same level and scaled by 0.9. The small step size in the MEP calculations was required to ensure well-defined frequencies at a nonstationary point on the MEP. The interpolated VTST by mapping35 (IVTST-M) algorithm was used to construct the potential and vibrationally adiabatic energy curves in the excited state with 31 Hessian and 310 gradient points, denoted as IVTST-M-31/310. This potential energy curve in the S1 electronic state was corrected by 31 interpolated single point energies (ISPEs)36 along the MEP using second-order multireference perturbation theory (MRPT2)37-42 so that the interpolation could generate the high-level potential energy surface points required for the rate calculations. These nonstationary Hessian and high level energy points were chosen every 0.1 bohr between -2.3 and 0.8 b along the MEP. Therefore, the final excited-state potential energy curves along the MEP in this study were obtained at the dual level, namely, the interpolated MRPT2//CASSCF(10,9)/6-31G(d,p). All MRPT2 calculations were performed using the GAMESS program.43 We performed polarizable continuum model calculations using the integral equation formalism (IEFPCM)44-46 for cyclic and noncyclic reactant complexes and TS at the CASSCF level to elucidate the mechanism of ESDPT in water. The Gaussian 09 program47 was used for the solvent effect calculations. Rate calculations were carried out with VTST including multidimensional semiclassical tunneling approximations. The Born-Oppenheimer potential on the MEP is called VMEP(s), where s is the reaction coordinate parameter and the canonical VTST rate constant is given by

kGT(T, s) kCVT(T) ) min s ) σ

kBT QGT(T, sCVT) * exp[-βVMEP(sCVT)] h * ΦR

(1) The superscript GT denotes the generalized transition state theory; β is 1/kBT; kB is the Boltzmann constant; h is Planck’s constant; s/CVT is the value of s at which kGT is minimum, that is, the location of the canonical variational transition state (CVT); σ is the symmetry factor; and QGT and ΦR are partition functions for the generalized transition state (GTS) and reactants, respectively. To include the tunneling effect, the calculated rate constant kCVT(T) is multiplied by a transmission coefficient, κSCT

(2)

The transmission coefficient is defined as the ratio of the thermally averaged quantal ground-state transmission probability, P(E), to the thermally averaged classical transmission probability for the effective potential along the reaction coordinate. When the reaction path curvature is small, tunneling is assumed to occur on a path defined by the classical turning points on the concave side of the MEP. This is an example of corner-cutting tunneling.48-50 The centrifugal-dominant smallcurvature semiclassical adiabatic ground state (CD-SCSAG) tunneling approximation48,49,51 is used to calculate P(E). The CD-SCSAG method is referred to as “small-curvature tunneling” (SCT). All rate calculations were carried out by direct dynamics52-54 using the IVTST-M35 algorithm and interpolated single point energies (ISPE) along the MEP obtained using the GAUSSRATE55 program, which is an interface of the GAUSSIAN33 and POLYRATE56 dynamics programs. III. Results and Discussion A. Electronic Structures. The optimized geometries for the reactant (normal form), product (tautomer form), and the transition state in the excited state at the CASSCF(10,9)/631G(d,p) level are illustrated in Figure 1. The geometries of reactant, product, and the conventional TS where the potential energy is maximum are in good agreement with previous studies.5,21 The O16-H18 distance at the TS is 1.086 Å, which is only 0.134 Å greater than its value at the reactant, whereas the N1-H10 bond distance is 0.259 Å greater than its reactant value. The H10 moved more than halfway from N1 toward the O16 atom, but the H18 atom moved very little, which generates a H3O-like moiety in part of the TS. Chaban and Gordon5 reported the TS structure in the ground state, where the H18 atom moved all the way to the N7 atom but the H10 moved only 0.14 Å, producing a OH-like moiety. These results suggest that 7AI, which is a base in the ground state, becomes acidic in the excited state, so that the N1-H10 bond in the excited state becomes weak and is easily broken. Sakota and Sekiya19 recently showed that the N-H bond strength becomes weaker in the S1 state than in the S0 state upon π-π* electronic excitation. Barrier heights and reaction energies based on theoretical levels are given in Table 1. Chaban and Gordon5 calculated that the barrier heights at the CASSCF(10,9)/DZP and MCQDPT2 levels were 18.20 and 9.80 kcal/mol, respectively. They found that a water molecule bridging the nitrogen atoms in 7AI greatly reduces the barrier. The CIS and CASSCF methods tend to overestimate the energy barriers of the excited state, which suggests that dynamic electron correlation should be taken into consideration. In this paper, we used CASSCF(10,9)/6-31G(d,p) followed by single-point MRPT2 level calculations. The MRPT2 barrier heights were 9.72 and 6.39 kcal/mol without and with zero-point energy (ZPE) corrections, respectively; these values agree very well with the corresponding MCQDPT2 values.5 The energetics and geometric parameters obtained from calculations using the DZP and 6-31G(d,p) basis sets are consistent with one another. Time-dependent density functional theory, however, slightly underestimates the barrier height. B. Potential Energy Surfaces. The potential energy curves for the MEP of the ESDPT at the CASSCF and MRPT2// CASSCF levels are depicted in Figure 2. The single-level calculations for the potential energy curve at the MRPT2 level were practically impossible, which have never been performed before, and so forth for the MRPT2 frequencies. Therefore, the MRPT2 level in this study means dual level, i.e., MRPT2//

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Figure 2. Potential energy curves along the MEP for the ESDPT calculated at the CASSCF(10,9)/6-31G(d) and MRPT2//CASSCF(10,9)/ 6-31G(d) levels.

Figure 1. Excited-state CASSCF(10,9)/6-31G(d,p) structures of reactant, product, and the TS for the double proton transfer in the 1:1 7-azaindole:H2O complex. Values in parentheses are from the CASSCF(10,9)/DZP calculations. Bond distances are in Å.

TABLE 1: Reaction Energies and Barrier Heights for the Double Proton Transfer in the Excited State at Various Levels of Theorya computational method b

CIS/6-31G(d) CIS/6-31G(d,p) CIS/6-31+G(d,p) TD-B3LYP//CIS /6-31G(d)b CASSCF(8,8)/6-31G(d)c CASSCF(10,9)/sDZPd CASSCF(10,9)/DZP(d,p)e CASSCF(10,9)/6-31G(d,p) MCQDPT2//CASSCF(10,9)/DZPe MRPT2//CASSCF(10,9)/6-31G(d,p) b

∆V (kcal/mol) ∆E (kcal/mol) 26.94 25.19 27.15 6.42 20.64 (22.07) 16.90 (13.5) 18.20 (14.7) 18.08 (14.39) 9.80 (6.3) 9.72 (6.39)

-18.15 -17.67 -15.58 -21.47 -33.19 -32.20 (-31.7) -31.80 (-31.2) -28.56 (-27.92) -18.00 (-17.4) -18.95 (-18.31)

a The numbers in parentheses include zero-point energies. Reference 65. c Reference 18. d Reference 21. e Reference 5.

CASSCF, from now on. The MRPT2 corrections for dynamic correlation did not change the overall shape of the excited-state potential energy curve along the MEP, with the exception of the height of the curve. The conventional TS at the CASSCF level remained the same at the dual-level MRPT2 calculations,

Figure 3. Zero-point energy curves along the MEP for the ESDPT calculated at the CASSCF(10,9)/6-31G(d,p) level. The solid and dashed lines represent the points at the conventional TS (s ) 0 bohr) and where the adiabatic energy is maximum (s ) -0.79 bohr), respectively.

and the CASSCF potential energy curve was reduced smoothly without making any irregularity, which suggests the validity of the dual level calculations. Chaban et al.5 observed the same behavior in their intrinsic reaction coordinate calculations, although they used a very large step size of 0.3 amu1/2 bohr. The potential energy decreased rapidly as the reaction proceeded from the TS to the product side (tautomer form), and decreased extremely slowly in the reactant side (normal form). However, the ZPE increased very rapidly in the reactant side, and rather slowly in the product side, as shown in Figure 3. This ZPE change is attributed to the change in vibrational modes involved in the proton transfer, i.e., the stretching and bending modes of N · · · H · · · O. As the elongated N-H or O-H bonds at the TS become equilibrium bonds at reactant or product again, the stretching and bending frequencies become larger and smaller, respectively. Because the magnitude of the stretching frequency is much larger than that of the bending frequencies, the ZPE usually increases as the reaction goes to reactant or product from TS. It is interesting to note that the minimum in the ZPE is not at the conventional TS but rather located at a point where the reaction proceeds further toward product (tautomer form). In a usual single proton transfer reaction, the increased stretching frequency is larger than the decreased bending frequencies when


J. Phys. Chem. A, Vol. 114, No. 10, 2010 3407 TABLE 2: Some Geometric Parameters of Variational TSs at 0 K for the ESDPTa r(N1-H10) r(O16-H10) r(N7-H18) r(O16-H18) r(C8-O16)

s ) -0.79 bohrb

s ) -0.14 bohrc

1.033 1.564 1.590 0.987 2.826

1.196 1.286 1.475 1.057 2.797

a

Bond lengths are in Å. b The highest point in the adiabatic energy curve of HH transfer. c The highest point in the adiabatic energy curve of DD transfer.

Figure 4. (A) The adiabatic energy barriers for the ESDPT at the MRPT2//CASSCF(10,9)/6-31G(d,p) level depending on the isotopic substitution, where the first and second H atoms represent the H10 and H18 in Figure 1, respectively. The numbers in parentheses represent the s values where the adiabatic energy curve is maximum. The dashed and solid lines represent the variational TS at 0 K and conventional TS for HH, respectively. (B) Relative bond distances in Å along the reaction coordinate for the ESDPT.

the reaction proceeds from the TS to either reactant or product, and the minimum of ZPE appears at the conventional TS. In double or multiple transfer reactions, if all transferring protons move in unison, the minimum of ZPE is still at the conventional TS. Therefore, the shift in the minimum point of the ZPE toward the product side indicates that protons may move asynchronously. It is also important to note that the ZPE in the reactant side reaches its maximum plateau near s ) -1.0 bohr and varies very little, which means that the hydrogenic motions are nearly finished at this point. C. Adiabatic Energy Surfaces and the Variational Effect. The vibrationally adiabatic energy (sum of the ZPE and the potential energy) curves for the double hydrogen and deuterium transfer in the excited state are shown in Figure 4A. The first and second Hs in this figure represent H10 and H18, respectively. The decrease in the potential energy and the increase in the ZPE are not necessarily the same; particularly, when the ZPE increases faster than the potential energy decreases, the maximum in the vibrationally adiabatic energy curve does not match the maximum of the potential energy curve. This phenomena has been reported and discussed previously with respect to the hydride transfer reaction of NAD+ analogues in solution.57 The change in the ZPE along the MEP depends largely on the N-H and O-H frequencies, and the CASSCF level overestimates these frequencies,58 so we scaled all frequencies along the MEP by 0.9. No adiabatic curve has its maximum at s ) 0 bohr, and the shape of the curve is quite different from the potential energy curve shown in Figure 2. When we calculated the adiabatic energy curve for the DD transfer, we used the complex that all hydroxyl protons were exchanged to mimic the reaction in the D2O solution; i.e., the secondary hydrogen on oxygen was also deuterated. It is interesting to note that the maximum points of vibrationally adiabatic energy curves for the HH and DD transfer (which is the variational TS at 0 K) appear at very different

positions in the reaction coordinates, namely, at s ) -0.79 and -0.14 bohr, respectively, which means that the variational TS50,59 depends very much on the isotopic substitution. The positions of the variational TS at 400 K for the HH and DD transfer are at s ) -0.81 and -0.15 bohr, respectively, which is not sensitive to the temperature. Some geometric parameters at the highest points of vibrationally adiabatic energies for HH and DD transfer are listed in Table 2. The bond distances of N1-H10 and O16-H18 at s ) -0.79 bohr are only 0.034 and 0.035 Å greater than those of the reactant. These bond distances at s ) -0.14 bohr are 0.197 and 0.105 Å greater than the corresponding reactant values but only 0.062 and 0.029 Å smaller than the conventional TS values. These results indicate that the variational TS structure at 0 K for HH transfer is similar to that of the reactant, except that 7AI and water molecules move closer to make shorter hydrogen bonds. However, the structure of variational TS for DD transfer is closer to the conventional TS. The variational effect for the HH transfer increases the vibrationally adiabatic barrier height by about 1.18 kcal/mol, comparing the vibrationally adiabatic energies at s ) 0 bohr. The vibrationally adiabatic energy curve for DD in the excited state is very flat over a wide range of reaction coordinates, and the change in the adiabatic energy barrier due to the variational effect is only about 0.09 kcal/mol. Because the adiabatic energy barrier of the HH transfer increases more than that of the DD transfer, the difference between these two barriers is very small, which is only 0.2 kcal/mol. This difference at the conventional TS is 1.29 kcal/mol. As a result, the difference between CVT and TST rate constants is very large for the HH transfer but small for the DD transfer. These results suggest that conventional transition state theory and other theories based on information from the conventional TS would fail to explain the rate constants and KIEs for the ESDPT in the 7AI-H2O complex properly. D. Asynchronous Double Proton Transfer. The changes in some bond distances along the reaction coordinate are shown in Figure 4B, where the relative bond distances of N1-H10 and O16-H18, ∆r(N1-H10) and ∆r(O16-H18), with respect to their equilibrium value at the reactant, and the relative O16-H10 and N7-H18 distances, ∆r(O16-H10) and ∆r(N7-H18), with respect to their product equilibrium values, are presented. As the reaction proceeds from the reactant to product, the H10 atom starts moving rapidly at about s ) -0.7 bohr from N1 in the five-membered ring to O16 and the ∆r(N1-H10) and ∆r(O10-H10) values are crossed near the conventional TS, whereas the H18 atom moves rather slowly from O16 to N7 in the six-membered ring and the ∆r(O16-H18) and ∆r(N7-H18) values are crossed at about s ) 0.5 bohr. The two protons in flight move very asynchronously. This asynchronicity results in the appearance of the minimum of the ZPE curve between these two crossing points, as shown in Figure 3. No stable intermediates are present in the potential energy curve along

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TABLE 3: Rate Constants (106 s-1) and Tunneling Coefficients for the Double Proton Transfer T (K)

TST kHH

CVT kHH

SCT κHH

CVT/SCT kHH

250 298 300 311 350

1.45 9.98 10.7 15.1 42.9

0.19 1.91 2.07 3.14 11.0

2.99 2.20 2.17 2.07 1.79

0.56 4.14 4.44 6.41 19.5

TABLE 5: Energetics in the S1 State Calculated at the CASSCF(10,9)/6-31G(d,p) Level in Water and Some Geometric Parameters at TS

TABLE 4: Rate Constants (106 s-1) and Tunneling Coefficients for the Double Deuterium Transfer

IEFPCM/UFFa

T (K)

TST kDD

CVT kDD

SCT κDD

CVT/SCT kDD

250 298 300 311 350

0.08 0.83 0.90 1.37 4.88

0.08 0.77 0.84 1.28 4.54

1.53 1.35 1.34 1.31 1.24

0.11 1.04 1.12 1.67 5.63

the reaction coordinate of the ESDPT, indicating that these two protons are transferred concertedly. It is interesting to note that the variational TS at 0 K is located where the N1-H10 and O16-H18 bonds are about to change; i.e., hydrogenic motion is about to start in the reaction coordinate. The reactive processes before this variational TS comprise mostly heavy atom motions that bring the 7AI and H2O molecules closer. Asynchronous multiproton transfers have been reported previously.22-27 Kina et al.21 studied the ESDPT in the 1:1 7-azaindole:water complex using ab initio MD simulations and reported that the two protons were transferred asynchronously and concertedly. Their results are consistent with this study, except that the order of transferring protons is opposite. The H18, N7, H10, N1, and O16 atoms correspond to the H4, N5, H2, N1, and O3 atoms in Figure 3b of ref 21, respectively. These authors reported that the H18 atom first moves from O16 to N7, followed by the H10 atom from N1 to O16. As a result, at about 50 fs of the ab initio MD trajectory as presented in ref 21, an OH-like moiety is formed because the N5-H4 bond is already formed while the N1-H2 bond is nearly unchanged. This result is inconsistent with the fact that 7AI becomes acidic in the S1 state upon π-π* electronic excitation, allowing the N-H bond to be broken easily.19 This trajectory is also very different from the TS predicted from this and other high level electronic structure calculations,5,21 which indicates that the reported ab initio MD trajectory is very different from the MEP and does not proceed via the TS. Further research is required to understand this discrepancy. It is very interesting to note that the asynchronicity of the ESDPT was not altered due to solvation, which suggests that the condensed phase reaction dynamics would be quite similar to the gas phase dynamics. E. Rate Constants and Kinetic Isotope Effects. The rate constants and tunneling coefficients calculated by VTST/MT are listed in Tables 3 and 4 for the HH and DD transfers, respectively. The CVT rate constants for the HH transfer without tunneling were about 3.9-7.6 times smaller than the TST values due to the large variational effect depending on the temperature used in this study. The differences between CVT and TST rate constants in the DD transfers are not large, because the variational TS is not very different from the conventional TS, as shown in Figure 4A. The SCT coefficients are fairly small as a consequence of the flat adiabatic energy curve. The CVT rate constants including tunneling are on the order of 106 s-1 and less at room temperature and below. Numerous studies, both experimental and theoretical, have investigated the rate constant of this reaction. Huang et. al7 studied the excited state of the 7AI-H2O complex in cold beams and reported an 8 ns lifetime

Relative Energies (kcal/mol) 0 cyclic 1:1 7AI:H2O 1.91 noncyclic 1:1 7AI:H2O TS 16.64 (16.01)c r(N1-H10) r(O16-H10) r(O16-H18) r(N7-H18)

Bond Distances (Å) at TS 1.346 1.137 1.009 1.659

IEFPCM/UA0b 0 2.20 16.78 1.364 1.126 0.999 1.719

a Atomic radii from the UFF force field scaled by 1.1. All hydrogens have individual spheres. b The united atom topological model was used for the atomic radii of the molecular cavity. Three explicit spheres were used for acidic hydrogens. c The number in parentheses includes nonelectrostatic terms.

of the fluorescence, which suggests that the tautomerization rate constant cannot be larger than about 107 s-1. This experimental observation is consistent with the rate constants predicted in this study. The SCT coefficients did not indicate the presence of a significant tunneling effect in the HH transfer. FernandezRamos et al.18 studied the water-catalyzed tautomerization of 7AI in the excited state using AIM. They reported that tautomerization occurs by tunneling and that the classical contribution to the rate is negligible. However, their study contains serious flaws in the TS structures, and the instanton approach60-63 does not use the MEP as a reaction coordinate but approximates the potential energy surface by utilizing the structures, energies, and force fields of three stationary points (reactant, product, and the conventional TS), as well as the imaginary frequency mode at the TS. Importantly, the variational effect cannot be taken into account. As Tautermannn et al.20 have pointed out previously, these AIM studies might work due to error compensation. The tautomerization of 7AI in the condensed phase has been observed experimentally.8-11 Chapman and Maroncelli8 reported that the rate constants for the tautomerization of 7AI in water were on the order of 109 s-1 at room temperature. Compared to experimental results in water, the rate constants in this study were a few hundred times smaller. To understand the difference between gas phase and solution reaction dynamics, we preformed IEFPCM calculations for cyclic and noncyclic reactant complexes, possible intermediates, and TS at the CASSCF level. Relative energies of cyclic and noncyclic 1:1 7AI:H2O complexes and TS in water were depicted in Table 5 along with some geometric parameters of TS. We checked the imaginary frequencies for all TS. The most significant geometrical change of TS due to solvation is the position of the H10 atom, which comes much closer to the O16 atom compared with that in the gas phase to make a H3O+-like moiety. The change in the hydrogen bond distance with the H10 atom is about 0.1 Å due to solvation. The N7-H18 hydrogen bond distance is also increased by about 0.2 Å. This change results in large ion-pair character in the TS, and increases the asynchronicity of the double proton transfer. If the ESDPT occurs via the stepwise mechanism, the intermediate should be an ion pair. All


J. Phys. Chem. A, Vol. 114, No. 10, 2010 3409

TABLE 6: The HH/DD KIEs and the Ratio of SCT Coefficients T (K)

TST TST kHH /kDD

CVT CVT kHH /kDD

SCT SCT κHH /κDD

CVT/SCT CVT/SCT kHH /kDD

250 298 300 311 350

17.7 12.0 11.8 11.0 8.80

2.51 2.47 2.47 2.46 2.43

1.95 1.63 1.62 1.57 1.44

4.90 3.98 3.96 3.83 3.46

calculations to find an intermediate using the TS structure as an initial geometry or the modified TS with a H3O+ moiety, which is an ion-pair-like structure, ended up either reactant or product. These results mean that the mechanism of the ESDPT in water is not stepwise via an ion-pair-like intermediate but concerted just as in the gas phase, which is consistent with recent studies by Kina et al.21 suggesting that the mechanism and the asynchronicity of the ESDPT were not altered due to solvation. In this case, the solution reaction dynamics would be quite similar to the gas phase, although not exactly the same, so the gas phase calculations could provide a good approximation for the reaction dynamics in solution. The cyclic hydrogen-bonded 1:1 7AI:H2O complex is about 2 kcal/mol more stable in energy than the noncyclic complex, which supports fast excited-state pre-equilibrium between them as suggested from previous studies.8,13,16,17 The barrier of the ESDPT in water including nonelectrostatic interaction is 16 kcal/ mol, which is about 2 kcal/mol smaller than the corresponding CASSCF value in the gas phase. The computational results in water depend on the atomic radii used for the molecular cavity. In fact, all theories of solvation were developed for the ground state, and applying them to excited-state reactions is still premature, so there might be some unidentified error involved in the excited-state solvation energy. If we recalculate the CVT/ SCT rate constants using this factor to include the solvent effect, although it is a very crude approximation, our rate constants agree better with experimental values.8,9 This agreement does not mean that the gas phase reaction dynamics is a direct representative of the condensed phase dynamics. The KIE depends on the vibrational modes orthogonal to the reaction coordinate, which are less sensitive to the solvent effect. Furthermore, it depends very much on the shape of the potential energy surface (PES) near the activated complex. It is very unlikely that a good agreement in KIE originates from two completely different PESs. Therefore, the KIE can be used as a criterion whether the gas phase reaction dynamics can provide a useful insight for the condensed phase reactions, at least near the activated complex. The variational TS, depending on isotopic substitutions, results in a significant change in the HH/DD KIE; i.e., the KIEs using the CVT rate constants become very different from those using TST. The calculated HH/DD KIEs are listed in Table 6. The conventional TST and CVT without tunneling correction resulted in predicted HH/DD KIEs of 12.0 and 2.47 at 298 K, respectively. The tunneling contribution to the KIE, which is the ratio of transmission coefficients of HH and DD, was calculated as 1.63 at 298 K. The HH/DD KIEs were measured in aqueous solution, which were 3.48 at 297 K and 3.79 at 293 K. The KIEs estimated using TST were too large, whereas those estimated using CVT were too small. The HH/DD KIE calculated using CVT with the SCT approximation was 3.98 at 298 K, which agrees remarkably well with the experimental value. There is no artificial adjustment made to reproduce experimental values. Therefore, both variational and tunneling effects need to be taken into account to reproduce the experi-

mental values. This suggests that the frequencies and shape of the vibrationally adiabatic energy curves near the activated complex in aqueous solution may not be very different from those in the gas phase. Interestingly, the reaction coordinate is concerted unlike the suggestion by Chen et al.9 that the ESDPT mechanism of 7AI in water is stepwise. Their suggestion was based on experimental rate constants that showed the breakdown of the rule of the geometric mean. However, it has been shown that the rule of the geometric mean was broken in a concerted reaction when two protons are transferred very asynchronously.24 Therefore, the breakdown of the rule of the geometric mean may not be used as absolute evidence of the stepwise mechanism for double proton transfer reactions. This study strongly suggests that the excited-state tautomerization of the 7AI-H2O complex in aqueous solution might also occur via a concerted and asynchronous mechanism. This study did not consider the solvent reorganization step to form a cyclic hydrogen-bonded complex that might be important in the condensed phase alcohol or water solutions. Chou et al.64 studied the ESDPT of 3-cyano7-azaindole in water and suggested that the solvent reorganization is very fast, so the overall rate of ESDPT is expressed as kPT ) (k1/k-1)kpt, where kpt is isotope dependent, and the KIE is H D H D /kPT ≈ kpt /kpt. The good agreement between expressed as kPT experimental and predicted KIEs in this study strongly supports their argument that the solvent reorganization in water is very fast so that fast excited-state equilibrium between the 1:1 cyclic hydrogen-bonded complex and randomly hydrated complexes is established. IV. Conclusions We performed a detailed ab initio reaction dynamics study of the excited-state tautomerization of the 1:1 7-azaindole:H2O complex using VTST/MT. Potential energy surfaces in the S1 electronic state were generated at the MRPT2//CASSCF(10,9) level using the IVTST-M algorithm with the interpolated single point energy correction. We demonstrated that the excited-state double proton transfer occurs via a concerted and asynchronous mechanism. The vibrationally adiabatic energy surfaces in the S1 electronic state depend largely on isotopic substitutions, resulting in a large variational effect, even at 0 K. The adiabatic energy surfaces are flat; therefore, the tunneling effect is not significantly large. The rate constants are on the order of 106 s-1 or less at room temperature or below, respectively, which is consistent with experiments. The IEFPCM calculations showed that the mechanism of the ESDPT was not altered due to solvation and the asynchronicity is increased to generate larger ion-pair character at the TS. The energy difference between cyclic and noncyclic hydrogenbonded 1:1 7AI:H2O complexes is only 2 kcal/mol, which supports the fast pre-equilibrium in the excited state. Interestingly, the HH/DD KIEs agree remarkably well with the experimental values in solution. Consideration of both variational and tunneling effects was essential to reproduce the KIEs. These results strongly suggest that excited-state tautomerization in solution occurs via a concerted and asynchronous mechanism, and fast excited-state equilibrium between the 1:1 cyclic hydrogen-bonded complex and randomly hydrated complexes is established in water solution. Acknowledgment. We thank professor D. G. Truhlar for helpful comments. We also thank Mr. Kisoo Park for his help in computation. References and Notes (1) Taylor, C. A.; El-Bayoumi, M. A.; Kasha, M. Proc. Natl. Acad. Aci. U.S.A. 1969, 63, 253.

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