LETTER pubs.acs.org/JPCL
Direct Simulation of Excited-State Intramolecular Proton Transfer and Vibrational Coherence of 10-Hydroxybenzo[h]quinoline in Solution Masahiro Higashi†,§ and Shinji Saito*,†,‡ †
Department of Theoretical and Computational Molecular Science, Institute for Molecular Science, 38 Nishigo-Naka, Myodaiji, Okazaki 444-8585, Japan ‡ Department of Structural Molecular Science, School of Physical Sciences, The Graduate University for Advanced Studies, 38 Nishigo-Naka, Myodaiji, Okazaki 444-8585, Japan
bS Supporting Information ABSTRACT: We investigate an ultrafast excited-state intramolecular proton transfer (ESIPT) reaction and the subsequent coherent vibrational motion of 10-hydroxybenzo[h]quinoline in cyclohexane by the electronically embedded multiconfiguration Shepard interpolation method, which enables us to generate the potential energy surface of the reaction effectively and thus carry out a direct excited-state dynamics simulation with low computational costs. The calculated time scale of the ESIPT and the frequencies and lifetimes of coherent motions are in good agreement with the experimental results. The present study reveals that the coherent motions are caused by not only the proton transfer itself but also the backbone displacement induced by the ESIPT. We also discuss the effects of the solvent on the dynamics of the coherent vibrational modes. SECTION: Dynamics, Clusters, Excited States
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xcited-state reactions play important roles in the electronic properties and photoinduced functions of materials and biological systems, and intensive studies on excited-state reaction dynamics in the condensed phase have been performed both experimentally and theoretically.17 Experimentally, coherent vibrational motions up to ∼1000 cm1 that are caused by the ultrafast excited-state reactions are observed by time-resolved spectroscopic techniques such as pumpprobe spectroscopy. The excited-state intramolecular proton transfer (ESIPT) of 10-hydroxybenzo[h]quinoline (10-HBQ) in solution2,813 is a prototypical excited state reaction (Figure 1). The enol form of 10-HBQ is stable in the ground state, and the conversion from the enol to the keto form occurs very rapidly after excitation. Takeuchi and Tahara first measured the ESIPT rate and decay times of subsequent coherent vibrational motions of 10-HBQ in cyclohexane by pumpprobe transient absorption spectroscopy.10 They found that the ESIPT rate is ∼25 fs and that the decay time of a vibrational mode at ∼250 cm1 is faster than the decay times of higher-frequency modes. From their results, Takeuchi and Tahara proposed that the mode at ∼250 cm1 is correlated with the ESIPT reaction. Similar experimental results were obtained by Schriever et al.11 In addition to experimental analysis, they carried out normal-mode analysis, two-dimensional nuclear wavepacket dynamics, and classical dynamics simulation of 10-HBQ (without solvent) to analyze the ultrafast ESIPT, and they found that the skeletal motion at ∼250 cm1, which shortens the donoracceptor distance, is responsible for the ESIPT. In contrast to the results of the preceding studies, Joo's group proposed the involvement of r 2011 American Chemical Society
higher-frequency modes in the range of 12001600 cm1 in the ESIPT from the ultrafast rate measured by time-resolved fluorescence spectroscopy.12,13 This rate, 13 fs, is somewhat faster than the rates measured by the other groups. Very recently, Joo's group reported the absence of deuterium isotope effect on the ESIPT.13 Recent advances in computational technology have enabled us to tackle a wide variety of previously unsolved problems in chemistry. However, theoretical studies on the excited-state reaction dynamics of large systems still constitute one of the most challenging subjects, because of the high computational cost of reliable electronic structure calculations for excited states and the number of samplings required for on-the-fly quantum mechanical (QM) or combined quantum mechanical and molecular mechanical (QM/MM)14 molecular dynamics (MD) simulations. To reduce the computational costs, we employ the electronically embedded multiconfiguration Shepard interpolation1517 (EE-MCSI, which was previously called electrostatically embedded multiconfiguration molecular mechanics18), which makes it possible not only to provide an accurate potential energy surface (PES) but also to run a large number of trajectories. Although the details of the EE-MCSI15 (and its original version MCSI19,20) are described elsewhere, we describe it briefly in this Letter. The EE-MCSI can generate the PES of a reaction in Received: August 1, 2011 Accepted: August 30, 2011 Published: August 30, 2011 2366
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Figure 1. Schematic diagram of the ESIPT reaction of 10-HBQ and the calculated potential energy profiles of the ground and excited states along the reaction coordinate.
the condensed phase such as a solution or protein environment, based on the QM/MM methodology. The potential energy of the EE-MCSI is defined as the lowest eigenvalues of a 2 2 valence bond configuration interaction Hamiltonian given by ! H11 H12 H¼ ð1Þ H12 H22 Here, the diagonal elements H11 and H22, which consist of MM force fields, roughly describe the PES around the reactant and product. The off-diagonal element H12 is introduced to reproduce the energy and its first and second derivatives for some reference geometries and is interpolated among these geometries by the modified Shepard interpolation.21,22 The EE-MCSI requires much fewer electronic structure calculations to reproduce the global PES than the Shepard interpolation does when directly applied to the PES itself. The EE-MCSI method can be applied to a QM/MM system by replacing the electrostatically embedded QM energy with the EE-MCSI energy (EE-MCSI/ MM).16 In this study, we applied the EE-MCSI/MM MD simulations to the ESIPT reaction and vibrational coherence of 10-HBQ in cyclohexane. The coherent modes we study here are low frequencies and delocalized over heavy atoms, not the motion of a hydrogen atom or proton. Therefore, it is considered that nuclear quantum effects should be small and that the vibrational coherence is mainly attributed to the excitation of specific modes in ensemble average of classical trajectories. To investigate proton transfer (PT), we defined the reaction coordinate as the difference between breaking OH and forming NH bonds: z ¼ ROH RNH
ð2Þ
We constructed the EE-MCSI potential energy function by calculating the gas-phase S0 and S1 potential energy profiles along the reaction coordinate using density functional theory and time-dependent density functional theory with the LC-BOP
Figure 2. Time evolution of (a) the distribution of reaction coordinate up to 70 fs and (b) the averaged reaction coordinate up to 2 ps (figure enlarged up to 200 fs in the inset).
functional23,24 (Figure 1). As reported previously,11 the ESIPT of 10-HBQ is a barrierless reaction. A two-dimensional contour plot of the S1 PES in terms of the reaction coordinate and ON distance was also calculated (Figure S1a, Supporting Information). We found that the ON distance takes a minimum value 2.4 Å at z = 0.0. We used two sets of the EE-MCSI Hamiltonian to describe the S0 and S1 PESs of the 10-HBQ. Solvent molecules (cyclohexane) were treated with the OPLS-AA force field.25,26 We found that the gas-phase electronic structure calculations for nine geometries along the reaction coordinate (Figure S2) was enough to reproduce the S0 and S1 PESs in solution; the mean unsigned errors between the EE-MCSI and reference energies of 2200 geometries obtained from the restrained EE-MCSI/MM MD trajectories were 0.5 kcal/mol for both the S0 and S1 PESs (Table S1 and Figure S3). Notably, the EE-MCSI gradient calculation is 3 105 times faster than the direct electronic structure calculation. Prior to the nonequilibrium excited-state MD simulations, we performed ground-state equilibrium MD simulations for 10 ns. Then 10 000 excited-state MD simulations on the S1 PES were carried out for 10 ps by taking the coordinates and velocities from the ground-state equilibrium MD simulations as the initial conditions. Additional computational details are found in the Supporting Information. First we calculated the time evolution of the distribution of the reaction coordinate from the excited-state MD simulations (Figure 2a). At 10 fs, 7.8% of the trajectories show positive z values, and the product distribution can be clearly observed at 20 fs. The peak at z ∼ 0.4 Å that appears at 1050 fs results 2367
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Figure 3. (a) Time evolution of the averaged potential energy gap between the excited and ground states up to 2 ps. (figure enlarged up to 200 fs in the inset) (b) Fourier amplitude spectrum of the oscillatory component of the energy gap. Experimental data (inset) are taken from ref 10 (c); (d) Fourier amplitude spectra of the oscillatory components of the energy gap calculated from the simulations of MD-PT and MD-BD, respectively. All scales of the Fourier amplitudes are the same.
from the reflection of the proton by the concave side of the reaction path at RON ∼ 2.5 Å (Figure S1a). Figure 2b shows the time dependence of the averaged reaction coordinate over 10 000 excited-state MD simulations. We can observe the ultrafast change in the reaction coordinate, i.e., PT from the oxygen atom to the nitrogen atom. The PT rate was estimated by fitting a single exponential function with an offset to the data and was found to be 29 fs, which is in good agreement with the experimental results: 25 ( 15 fs,10 2445 fs,11 and 13 ( 5 fs.12 A two-dimensional plot of the averaged trajectory in terms of the OH and ON distances (Figure S1b) shows that the shrinking of the ON distance after the excitation is followed by the PT, which is in agreement with the “semi-passive” mechanism obtained from the previous simulation.11 Figure 2b shows oscillatory behavior after the ultrafast PT. As mentioned above, the coherent vibrational motions have been previously experimentally observed.1013 We calculated the time evolution of the averaged potential energy gap between the excited and ground states, which can be compared with the experimental observations within the Condon and second-order cumulant approximations, and it again shows the oscillatory behavior as well as the ultrafast PT (Figure 3a). The Fourier amplitude spectrum of the oscillatory components up to 1000 cm1 is shown with the experimental result by Takeuchi
and Tahara10 in Figure 3b. The four experimentally observed coherent vibrational modes are well reproduced in our simulation. It is noted that, in addition to these four modes, other coherent vibrational modes are found in the frequency range between 800 and 2000 cm1 (Figure S4). Such high-frequency coherent modes have not been experimentally observed, although the contribution of high frequency modes has been suggested.12 We found that all of the coherent modes are in-plane modes, which are assigned by using the normal modes at the excited-state minimum geometry (Figure S5). It should be noted that a low-frequency coherent mode at 110150 cm1 has also been observed in some experiments.11,12 Because the spectrum of the time evolution of the S1 potential energy indeed shows the excitation of the out-of-plane mode at 110150 cm1 (Figure S6), it is considered that the observation of the mode can be attributed to the non-Condon effect, particularly one that depends on the excitation energy. We evaluated the decay times of the three lowest coherent vibrational modes by fitting the oscillatory component of the energy gap (Figure 3a) to the sum of three exponentially damped cosine functions with frequencies of ∼250, ∼400, and ∼550 cm1 (Table 1). We also examined the time evolution of the coherent modes by using the sliding-window Fourier transform analysis (Figure 4). The calculated results are quantitatively 2368
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Table 1. Calculated and Experimental Decay Times of the Coherent Vibrational Modes (in ps) present results 1
experimental results
frequency (cm )
solution
gas
ref 10
ref 11
ref 12
∼250
0.80
1.75
0.5 ( 0.1
0.480.61
0.60
∼400
1.42
1.02
a few
0.941.49
1.30
∼550
2.64
4.30
a few
1.533.98
N.A.
Figure 5. Schematic diagram of how each vibrational mode (in cm1) is excited.
Figure 4. Sliding-Fourier transform analysis of the oscillatory components of the energy gap: experiment from ref 2 (top), calculation in solution (middle), and calculation in the gas phase (bottom). A temporal window function with 0.5-ps full width at half-maximum width was employed.
in good agreement with the experimental results:1012 the intensity of the mode at ∼250 cm1 is the largest at a small delay time (
