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May 30, 2017 - Excited-State Dynamics of 2-(2′-Hydroxyphenyl)benzothiazole: Ultrafast Proton Transfer and Internal Conversion. Shiela Pijeau†, Don...
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Excited-State Dynamics of 2‑(2′-Hydroxyphenyl)benzothiazole: Ultrafast Proton Transfer and Internal Conversion Shiela Pijeau,† Donneille Foster,† and Edward G. Hohenstein*,†,‡ †

Department of Chemistry and Biochemistry, The City College of New York, New York, New York 10031, United States Ph.D. Program in Chemistry, The Graduate Center of the City University of New York, New York, New York 10016, United States

‡

S Supporting Information *

ABSTRACT: One of the most widely studied model systems for excited-state proton transfer (ESPT) is the 2-(2′hydroxyphenyl)benzothiazole (HBT) molecule. This compound undergoes ultrafast ESPT followed by internal conversion to return to the ground state. In the present work, we simulate the nonadiabatic photochemistry of HBT using ab initio multiple spawning (AIMS) nuclear dynamics and a complete active space configuration interaction (CASCI) method in conjunction with wave function-in-DFT embedding to obtain ground- and excited-state potential surfaces on-the-fly. Our simulation predicts ultrafast ESPT with a time constant of 48−54 fs and an excited-state lifetime of 1.7−1.8 ps. Following proton transfer, HBT becomes trapped in a metastable keto structure on the S1 state. Eventually, the molecule begins to twist and proceeds toward a seam of intersection with the ground state where internal conversion is highly efficient.

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INTRODUCTION Excited-state intramolecular proton transfer (ESIPT) reactions are fundamental and ubiquitous photochemical reactions. ESIPT is one of the fastest known chemical reactions with proton transfer within 15 fs of photoexcitation reported for certain molecules.1 Subsequent to ESIPT, both fluorescence and internal conversion are commonly observed. The structure of a particular molecule determines the nature of the excitedstate dynamics that follow ESIPT. There are several unique properties commonly associated with these photoreactions. For example, ESIPT processes are typically accompanied by a large Stokes shift and are often easily reversible on the ground state. The Stokes shift associated with ESIPT can be harnessed in photochromic materials and photoswitchable dyes.2−7 The combination of Stokes shift and reversibility often imparts remarkable photostability on molecules that undergo ESIPT. As a result, many naturally occurring dyes and pigments contain ESIPT pathways;8−13 similarly, ESIPT is present in many common photostabilizers and sunscreens.14−17 In these cases, the ESIPT reaction provides access to an efficient internal conversion pathway. It is essential for effective photoprotectants to absorb UV light and to quench the resulting excited state quickly and reversibly. Insight into the dynamics of these processes aids in the design and characterization of new compounds that can exploit the ESIPT reaction. Of present interest is the ESIPT reaction and subsequent internal conversion that occurs in 2-(2′-hydroxyphenyl)benzothiazole (HBT) following photoexcitation.18 This molecule undergoes an enol to keto phototautomerization and then it is believed that twisting about its central carbon−carbon bond quenches the excited-state.19 There are a large number of © 2017 American Chemical Society

molecules with photochemistries similar to that of HBT; for example, 10-hydroxybenzo[h]quinoline (HBQ) is a rigid molecule that exhibits strong fluorescence from its keto tautomer,20−24 2-(2′-hydroxy-5′-methylphenyl)benzotriazole (known commercially as Tinuvin P) is a photostabilizer that undergoes rapid ESIPT and internal conversion,16,25−27 and Nsalicylideneaniline is a model compound for aromatic Schiff bases that lacks the sulfur atom and fused ring systems of HBT.28−30 HBT is of particular interest due to the large number of high-quality experimental studies of this compound that have been conducted over the last 35 years.1,18,19,31−45 Some of the most recent measurements of the proton transfer rate were obtained by Joo and co-workers via time-resolved fluorescence spectroscopy and estimate the proton transfer time to be 62 fs (in cyclohexane).1 The transient absorption measurements of Schriever et al. predict a slightly shorter proton transfer time of 50 fs.44 Of particular importance to the present work are the gas-phase transient absorption measurements of the excited-state lifetime by Barbatti et al.; they report the lifetime to be 2.6 ps.19 The fluorescence lifetime of HBT shows a strong dependence on the polarity and viscosity of the solvent.18 For example, the intrinsic 2.6 ps lifetime is extended to 15 ps in acetonitrile and 100 ps in cyclohexane.43 In the present work, we will focus on the photochemistry of HBT in the gas phase. In addition to the experiments on HBT, there have also been a number of theoretical studies of the photochemistry of Received: February 7, 2017 Revised: April 26, 2017 Published: May 30, 2017 4595

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The Journal of Physical Chemistry A HBT.19,43,46−53 Most of the recent theoretical work applies some flavor of time-dependent density functional theory (TDDFT).54,55 TDDFT can be expected to describe ESIPT in HBT reasonably well, because the ESIPT reaction proceeds adiabatically along the first excited singlet state.19,49,51 However, it is well-known that TDDFT fails to describe conical intersections between the ground and first-excited state.56 Therefore, it cannot be applied to the internal conversion process that is likely mediated by a seam of conical intersections. As a result, studies that leverage static calculations to describe the photochemistry of HBT typically use TDDFT for the ESIPT reaction and include separate computations with multiconfigurational wave functions near the intersections. Studies of the excited-state dynamics of HBT have been limited, largely, to classical simulations of the ESIPT process using TDDFT.51,53 The one exception is the work of Barbatti et al.;19 they extend their classical dynamics simulations to longer times and find that HBT twists and rapidly approaches a conical intersection. Because these simulations were performed with TDDFT, it was not possible to predict the excited-state lifetimes, directly. Obviously, it would be ideal to perform the excited-state dynamics simulations with a more reliable method, for example, multistate complete active space second-order perturbation theory (MS-CASPT2).57,58 However, due to the size of the HBT molecule, the time scale of the process, and the computational demands of highly correlated multireference methods, it remains infeasible to simulate the nonadiabatic dynamics of HBT with such a method. We leverage nonadiabatic dynamics simulations to determine the structural changes that lead to internal conversion, which will aid in the understanding of similar photochemical processes. We consider the excited-state dynamics of HBT from photoexcitation to the internal conversion back to the ground state. Foremost, our goal is to definitively identify the quenching mechanism of HBT and understand the structural features of HBT that give rise to this behavior. In our simulation, the electronic structure of HBT is described by a new method we have developed that uses density functional theory (DFT) to correct complete active space configuration interaction (CASCI) via wave function-in-DFT embedding.59 Our secondary goal is to demonstrate that this approach can be successfully applied in simulations of internal conversion processes. We improve on the existing theoretical studies of the excited-state dynamics of HBT in two regards. First, the method we apply is capable of describing both the ESIPT and internal conversion processes. Second, due to the efficiency of the method, we are able to perform an ab initio multiple spawning (AIMS)60,61 simulation of the nonadiabatic excitedstate dynamics to directly access the excited-state lifetime and the precise quenching mechanism.

Figure 1. Active molecular orbitals used in the FOMO-CASCI active space at several geometries of HBT. (a, b) π and π* orbitals at the Franck−Condon point. (c, d) π and π* orbitals at the keto geometry optimized on the S1 state. (e, f) π and π* orbitals at the “down” MECI geometry. (g, h) π and π* orbitals at the “up” MECI geometry.

CASCI wave function, we use a wave function-in-DFT embedding approach64 where the core (inactive) electrons are treated with DFT, the active electrons are treated with CASCI, and a mean-field embedding potential is applied.59 The range-separated hybrid ωPBE functional is used for the DFT portion of the computation with a range separation parameter 65 of 0.3 a−1 All FOMO-CASCI computations use a 6-31G* 0 . basis set (an analysis of the basis set dependence of this method is provided in the Supporting Information). The fractional occupation number Hartree−Fock orbitals are obtained with Gaussian broadening of the orbital energy levels and a temperature parameter of β = 0.075 au. These computations are performed using our quadratic-scaling, 6(N 2), implementation of this method within the graphical processing unit (GPU) accelerated quantum chemistry package, TeraChem.66−70 The nonadiabatic dynamics of HBT are simulated using the ab initio multiple spawning (AIMS) approach, which has been described in detail elsewhere.60,61 The AIMS simulation is initialized within the independent-first-generation approximation from 200 nuclear basis functions.71 The initial positions and momenta of the basis functions were sampled from a Wigner distribution of the ground-state vibrational wave function of HBT where the geometry and vibrational frequencies were obtained at the B3LYP/6-31G** level of theory. Here, B3LYP is applied due to its typically excellent performance in the prediction of geometries and vibrational frequencies for simple organic molecules. Throughout this work, we will refer to the time evolution of a single initial basis function and any basis functions spawned from this initial function (or its descendants) as an AIMS trajectory. All nuclear basis functions within a trajectory are fully coupled, but basis functions in separate trajectories are not coupled. The dynamics were followed for 4 ps or until the population of the first excited state fell below 0.01. The AIMS equations of motion were integrated using a time step of 25 au (∼0.6 fs). The

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COMPUTATIONAL DETAILS The electronic structure of the ground and first excited state of HBT is described using a floating occupation molecular orbital complete active space configuration interaction (FOMOCASCI) wave function62,63 with a minimal 2/2 active space consisting of the highest-lying π orbital and the lowest-lying π* orbital (Figure 1). This active space is sufficiently flexible to describe the regions of the S1 potential surface that are of interest in the present work. A discussion of the active space selection and computations using larger active spaces can be found in the Supporting Information. To account for some of the neglected dynamic electron correlation in the FOMO4596

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The Journal of Physical Chemistry A required gradients and nonadiabatic coupling elements were evaluated analytically.72,73

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RESULTS AND DISCUSSION Excited-State Proton Transfer. The first step in the photochemistry of HBT is excited-state proton transfer. The most recent experimental evidence suggests that proton transfer occurs approximately 50−62 fs following excitation to the S1 state.1,44 The proton transfer reaction is a phototautomerization from the enol form of HBT that is favored on the ground state to the keto form that is more stable on the S1 state. The time evolution of the nuclear density along the proton transfer coordinate is shown in Figure 2. The proton transfer coordinate

Figure 3. Definition of several geometric parameters relevant to the photochemistry of HBT. (a) The proton transfer coordinate is defined as the difference between the NH distance and the OH distance. (b) The bond alternation coordinate is taken to be a difference between a sum of bond lengths that increase after excitation (R1 and R3) and the central carbon−carbon bond that shortens after excitation (R2). (c) The pyramidalization angle is supplementary to the angle formed between the centroid of the phenyl group, the 2-carbon of the benzothiazole, and the centroid of the benzothiazole. (d) The dihedral angle is between best fit planes through the six carbon atoms (blue) of the phenyl group and the nine non-hydrogen atoms of the benzothiazole moiety (red).

Figure 2. AIMS nuclear density on the S1 state evolving along the proton transfer coordinate as a function of time for the first 150 fs following excitation. The density is averaged over 200 AIMS trajectories. The innermost (red) isolines correspond to a density of 0.15 and the outermost (blue) isolines correspond to a density of 0.01.

is defined in Figure 3a as the difference between the nitrogen− hydrogen bond length and the oxygen−hydrogen bond length: RPT = R OH − RNH (1) The density is initially localized at negative values of the proton transfer coordinate corresponding to the S1 enol state. Progress along the proton transfer coordinate is almost immediate; our simulation suggests that the proton transfer reaction in HBT begins 10 fs after photoexcitation. The reaction is nearly complete within 100 fs. However, we do observe some residual population in the S1 enol state for several hundred femtoseconds; this appears to be a result of the back proton transfer reaction, which, although unfavorable, does occasionally occur. To make a quantitative comparison with the experimental time constants of the proton transfer reaction, we obtain a population corresponding to the S1 enol state. We define the enol state to be any geometry of HBT with a negative value of the proton transfer coordinate, RPT (as shown in Figure 3a). In this way, the population of the enol state may be obtained as the integrated AIMS nuclear density on the S1 state with negative values of the proton transfer coordinate. The population in the S1 enol state is shown in Figure 4. To obtain the time constant associated with the proton transfer reaction, we fit exponential functions to the population decay. There is some ambiguity with regard to the functional form of the exponential for comparison with experiment (the experimental rates were obtained from fitting time-resolved spectroscopic data). We have obtained time constants with the preexponential factor fixed and while treating the pre-exponential

Figure 4. Time evolution of the population in the S1 enol state averaged over 200 AIMS trajectories. We extract the proton transfer time by modeling the decay of the S1 enol state with exponential functions. We estimate the proton transfer time to be in the range 48− 54 fs. Here, the S1 enol population is defined by integrating the nuclear wave function on the S1 state with negative values of the proton transfer coordinate.

factor as a free parameter. We obtain values of 54 and 48 fs, respectively, for the proton transfer time; the root-mean-square (RMS) of the residuals for these two functions is 0.065 and 0.053, respectively, in units of population. The results presented here were obtained by fitting the S1 enol population for the first 150 fs following excitation. The time constants are relatively insensitive to the length of time considered, provided that the length of time is greater than 100 fs. The values we obtain are in excellent agreement with experiment and are within the error bars of both recent measurements.1,44 These experiments use pump pulses in the 350−360 nm range and should directly 4597

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Figure 5. Snapshots of the AIMS nuclear density on the S1 state projected onto the proton transfer and bond alternation coordinates (as defined in Figure 3) and averaged over 200 trajectories. The horizontal line denotes the value of the bond alternation coordinate at the Franck−Condon point: 1.28 Å.

access the S1 excited state; therefore, the experimental proton transfer rates should be directly comparable to our theoretical result obtained from simulations that begin exclusively on the S1 state. Although the proton transfer reaction in HBT certainly qualifies as ultrafast, it is still four or five times slower than other excited-state proton transfer reactions in related molecules.1 This has been attributed to a bond rearrangement that precedes proton transfer and effectively “gates” the reaction (passive proton transfer).1,74 In Figure 5, we consider a bond alternation coordinate (see Figure 3b for the definition) as the source of this behavior. After excitation, the central carbon−carbon bond connecting the two ring systems of HBT shortens (R2 in Figure 3b), while the adjacent carbon−carbon bond (R1) and carbon−nitrogen bond (R3) lengthen. The bond alternation occurs immediately following photoexcitation; proton transfer follows shortly thereafter. We find that proton transfer occurs exclusively after progress has been made along the bond alternation coordinate; this implies that there is an apparent barrier to the reaction that exists until bond alternation occurs. The S1 keto state begins to appear within 10 fs; the enol and keto states have roughly equal population 50 fs after excitation. The result of the bond rearrangement is a change from an sp2-like nitrogen to an sp3-like nitrogen atom; this change in electronic structure is the primary driving force behind the proton transfer reaction. We note that there is no significant change in the atomic charge of the hydrogen atom that is transferred. In both the ground and excited state it has a charge of approximately 0.5e that oscillates by no more than ±0.1e during the proton transfer reaction (where the charges

are obtained by Mulliken analysis). This reaction (and related reactions) are sometimes labeled as excited-state hydrogen transfer. In the present work, we use the term proton transfer generically to avoid making the distinction between hydrogen and proton transfer. Internal Conversion. In the gas phase, transient absorption experiments find HBT to have an excited-state lifetime of 2.6 ps.19 These experiments used a pump pulse of 325 nm to access the ππ* state (S1). We model this experiment by also starting our simulations on the S1 ππ* state. In Figure 6, the population of the S1 state of HBT obtained from our AIMS simulation is shown for the first 4 ps following excitation. In an AIMS simulation, the nuclear wave function, χI, corresponding to the Ith adiabatic electronic state, NI

χI =

∑ cnIχnI n

(2)

is expressed as a sum of NI frozen Gaussian functions, χIn, with complex amplitude, cIn. The population of a particular adiabat is calculated as the norm of the amplitude associated with that electronic state. More detailed descriptions of the AIMS method can be found elsewhere.60,61,75 To model the population decay, we fit a delayed exponential function; this functional form describes the decay seen in our simulation quite well. We find an onset time of 710 fs followed by exponential decay with a time constant of 1050 ps (the error in this fit was a 0.026 RMS of the residuals in units of population). We take the sum of these two quantities to be the predicted excited-state lifetime of 1.7−1.8 ps. Other choices for modeling the population dynamics do not describe the result of the 4598

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Figure 6. Population of the S1 state of HBT averaged over 200 AIMS trajectories. We model the population on S1 as delayed exponential decay. Taking the excited-state lifetime to be the sum of the onset time and the decay constant, we find predict an excited-state lifetime of 1.7−1.8 ps.

simulation quite as well. Exponential decay functions with and without pre-exponential factors treated as free parameters lead to time constants of 1.5 and 1.9 ps, respectively (with 0.081 RMS with a pre-exponential factor and 0.119 RMS without); the description of the population decay is somewhat better described with a Gaussian function where σ = 1.3 ps (0.044 RMS). None of these other choices performs as well as the delayed exponential function, and therefore, we believe that the best estimate of the excited-state lifetime consistent with our results is in the range 1.7−1.8 ps. Our simulation predicts a lifetime that is somewhat shorter than what is obtained from experiment. This level of agreement is sufficient to inspire confidence that the overall mechanistic details of the internal conversion process will be correct, but it also suggests that some of the finer details may not agree quantitatively with experiment (we will discuss possible sources of error in the simulations, later). The primary motion associated with the internal conversion process is a twisting about the central carbon−carbon bond that links the phenyl group and the benzothiazole. To quantify this motion, we define a dihedral angle as the angle formed between best fit planes through the non-hydrogen atoms of the phenyl ring and the benzothiazole system (Figure 3). We have identified two S1/S0 minimum energy conical intersection (MECI) geometries with dihedral angles between 80° and 90° (meaning that the two rings lie in planes that are nearly perpendicular). In Figure 7, we show the evolution of the nuclear density in terms of the proton transfer coordinate and the dihedral angle described above. HBT remains planar until the proton transfer process has completed. After proton transfer, HBT is trapped in the metastable S1 keto state until twisting begins. Whereas the dynamics that occur shortly after photoexcitation (roughly, 250 fs) are dominated by the proton transfer reaction, the dynamics at longer times consist primarily of molecules in the S1 keto state twisting until they reach the intersection seam and decay back to the ground state. Our dynamics simulation suggests the existence of a small barrier to twisting; however, a barrierless pathway from the S1 keto geometry to the “down” MECI exists (Supporting Information). The potential energy surface is very flat along this pathway in the vicinity of the S1 keto geometry; the lack of a significant driving force traps the wavepacket in the S1 keto

Figure 7. Snapshots of the AIMS nuclear density on the S1 state projected onto the proton transfer coordinate and dihedral angle (as defined in Figure 3) and averaged over 200 trajectories.

state following proton transfer. Upon leaving this flat region of the potential energy surface, trajectories proceed rapidly toward one of the two MECIs. In addition to the twist about the central carbon−carbon bond, both MECIs that we have located also show significant pyramidalization about the 2-carbon of the benzothiazole moiety (Figure 3); both MECIs have similar pyramidalization angles that are between 46° and 47°. To determine the role of pyramidalization in the internal conversion process, we have projected the nuclear density onto the twisting and pyramidalization coordinates (shown in Figure 8). Until the proton transfer is complete, little progress is made along either the twisting or pyramidalization coordinate. Subsequent to proton transfer, the molecule begins to twist and pyramidalize. We find that the twisting motion allows HBT to leave the planar S1 keto state; once a trajectory has left the S1 keto state, pyramidalization and further twisting occur until one of the two MECIs is reached. We never observe significant pyramidalization to precede twisting. Further, it appears that twisting in the absence of pyramidalization is disfavored; this can be inferred from the lack of nuclear density with large dihedral and small pyramidalization angles. Immediately following proton transfer, 4599

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Figure 9. Following proton transfer, twisting about the central carbon−carbon bond takes HBT from the S1 keto geometry (a) to one of two MECIs. Some spawning geometries representative of the “down” MECI (b) and “up” MECI (c) are shown. A total of 86% of the population transfer is mediated by the “down” MECI, and the remainder decays via the “up” MECI.

also determine the amount of population transfer facilitated by each of the MECIs. We find that the majority of the population (85%) is transferred via the “down” MECI. This MECI is slightly higher in energy (by about 0.1 eV) than the “up” MECI. However, we have also found a nonsymmetric S1 keto minimum that is distorted in the direction of the “down” MECI. Our simulation suggests that after proton transfer occurs, HBT becomes trapped in a metastable S1 keto state that is slightly distorted in the direction of the “down” MECI; as a result, when the molecule begins to twist and leaves the S1 keto minimum, it will, most probably, proceed toward the “down” MECI. There is a small barrier (about 1 kcal mol−1) to twisting in the direction of the “up” MECI; although the molecule has sufficient energy to overcome this barrier, it is sufficient to push most of the trajectories in the direction of the “down” MECI. We also find that once a trajectory reaches the vicinity of an MECI, the population transfer is rapid and complete (where complete is taken to mean that more than 99% of the S1 population transfers to S0). We do not observe any trajectories to reach the vicinity of an MECI, fail to transfer more than 99% of its population, and subsequently return to the S1 keto minimum. Critical Analysis. We believe that the primary sources of error in our simulation are deficiencies in the electronic structure method. We have used a wave function-in-DFT embedding approach where a FOMO-CASCI wave function (with a minimal active space) is embedded in DFT with a mean-field potential. We have previously validated this approach for excited-state proton transfer reactions and its ability to properly describe multiple electronic states.59 This is the first application of the method in a simulation of nonadiabatic dynamics. The idea behind this approach is to use a small active space CASCI wave function to describe the qualitative feature of the electronic structure. Much of the neglected dynamic electron correlation, often required for quantitative agreement with experiment, is captured with a DFT treatment of the inactive electrons. The advantage of this method is that it is highly stable in the vicinity of intersections between ground and excited electronic states, the DFT treatment of the inactive electrons offers significant improvement over the usual CASCI method, and finally, this approach is computationally efficient, our implementation scales as 6(N 2) with system size. To assess the quality of the potential

Figure 8. Snapshots of the AIMS nuclear density on the S1 state projected onto the pyramidalization and dihedral angles (as defined in Figure 3) and averaged over 200 trajectories.

HBT exists in the S1 keto state with relatively small dihedral (less than 30°) and pyramidalization angles (less than 20°). Once HBT leaves this metastable state, it simultaneously twists and pyramidalizes until one of the two MECIs is reached and it can decay to the S0 state. In the absence of a pyramidalization angle, twisting in a clockwise or counterclockwise direction would be equivalent. In the present case, however, there is significant pyramidalization and the two twisting directions are distinct. The twisting directions lead to different MECIs that we have labeled “up” and “down”. If the benzothiazole is placed in a plane and the central carbon−carbon bond points upward from the plane, then the MECI geometries are named on the basis of the position of the oxygen atom. Because our definition of the twisting angle does not distinguish between the two MECIs, we analyze the spawning geometries from the AIMS simulation (Figure 9). These are geometries at which additional nuclear basis functions are created (spawned) on the S0 state; these structures indicate where population transfer between the S1 and S0 states occurs in our simulation. Further, by analyzing the norm of the wave function coefficients associated with these spawned basis functions at the end of the simulation, we may 4600

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scale of the internal conversion process (our primary interest in this study) should be most sensitive to the relative energetics of these intersections. There is a similar level of agreement between FOMO-CASCI and SA-CASSCF using a (10,10) active space; the energies of the “up” and “down” MECIs agree to about 0.19 and 0.11 eV, respectively. In this case, the SACASSCF predict the intersections occur at lower energies than does FOMO-CASCI. Another difference is that the SACASSCF computations predict a lesser degree of pyramidalization in the MECI geometries. This appears to be a result of the optimization of the orbitals rather than an effect of the larger active space; SA-CASSCF with a minimal (2,2) active space also shows somewhat reduced pyramidalization. As a result, it is likely that the motion along the pyramidalization coordinate is exaggerated in our simulations. The extent to which this affects the time scale associated with internal conversion is unclear. We hesitate to simply assign the underestimated excited-state lifetime to this effect alone. We note that a simulation of the excited-state dynamics of HBT with SA-CASSCF and a (10,10) active space would not be an improvement over our present approach, because an energetic barrier exists on the ESIPT reaction coordinate. These results motivate the development of analytic gradients and nonadiabatic couplings for SA-CASSCF including a DFT correction so that other choices of molecular orbitals may be considered. Although the overestimation of the vertical excitation energy at the Franck−Condon point is certainly troubling, it does not directly manifest in our simulation of the excited-state dynamics. It does, however, limit some of the predictions that can be made. Quantitative predictions of the absorption spectrum (static or transient), time-resolved fluorescence spectrum, or the Stokes shift cannot be extracted from our simulation. It might be possible to postprocess the trajectories with a method more suitable for describing the vertical excitation energies, although we have not pursued that possibility. The overestimation of the proton transfer reaction energy (the difference between the Franck−Condon point and the S1 keto minimum) may accelerate the excited-state dynamics. First, the proton transfer reaction itself might occur more quickly on this potential energy surface due to the exaggerated driving force. However, it is possible that the rate of the proton transfer process is relatively unaffected by this inaccuracy in our potential energy surface, because the proton transfer reaction is gated by bond rearrangement (as discussed previously). After proton transfer, the excess kinetic energy may increase the rate at which trajectories escape the S1 keto minimum. Although the relative energies of the two MECIs show good agreement between CC2 and FOMOCASCI, FOMO-CASCI might be somewhat biased toward the “down” structure, which is slightly overstabilized. The errors in the FOMO-CASCI potential energy surface appear to be consistent with the underestimation of the excited-state lifetime observed in our simulation. The focus of our present simulation is the excited-state dynamics of HBT, in particular, the dynamics that lead to the quenching of the excited state. We do not consider the subsequent ground-state dynamics including the reverse proton transfer and possible generation of the less stable rotameric form of HBT. Although the recovery process may be of future interest, there are several barriers preventing its immediate study. Foremost is the computational expense. The simulation is initialized with 200 nuclear basis functions on the first excited state; when the simulation is complete, approximately 1000

energy surface, we employ in the dynamics, we compare the relative energies of several geometries that are important to the photochemistry of HBT to those computed with CC2; this comparison is shown in Figure 10. We have chosen CC2 as a

Figure 10. Comparison of FOMO-CASCI/6-31G* energies (in bold), SA-CAS(10,10)SCF/6-31G* (in italics), and CC2/cc-pVDZ energies in electronvolts for several geometries of HBT relevant to its photochemistry. Arrows denote vertical excitation energies; experimental excitation energies are shown in parentheses.37 The relative energy of each geometry on the S1 state is also shown. Geometries on the S1 state are optimized at the FOMO-CASCI/6-31G* and SACAS(10,10)SCF/6-31G* levels of theory. CC2 energies are computed using the FOMO-CASCI/6-31G* geometries; at the MECI geometries, the CC2 S1/S0 energy gap is 0.33 and 0.03 eV for the “down” and “up” geometries, respectively. The relative energies of the MECIs are computed as an average of ground- and excited-state energies.

reference due to its success in the description of excited-state proton transfer processes;49 further, recent work has shown CC2 to be surprisingly stable in the vicinity of intersections between ground and excited states, it seems to be able to correctly describe the topology of the electronic states in the vicinity of the intersection.76 At the Franck−Condon point, we see that our FOMOCASCI wave function grossly overestimates the vertical excitation energy relative to CC2 (and experiment). Systematically overestimated vertical excitation energies are a wellknown deficiency of compact CASCI wave functions; however, it is often the case that the artifacts resulting from this overestimation are more pronounced on the ground-state potential surface than on the excited state. Indeed, this can be seen in numerous studies of excited-state processes that successfully employ CASCI-type wave functions with modest active spaces.77−83 In the present case, we find that both FOMO-CASCI and CC2 predict barrierless proton transfer pathways; however, FOMO-CASCI overestimates the reaction energy by about 0.4 eV. In the context of the internal conversion of HBT, perhaps the most important features of the potential energy surface are the energies of the two twisted MECIs relative to the S1 keto geometry. These relative energies show excellent agreement between FOMO-CASCI and CC2. The relative energies of the “up” and “down” MECIs agree to about 0.02 and 0.17 eV, respectively. We speculate that the overstabilization of the “down” MECI relative to CC2 may be related to the degree of charge transfer present at each geometry. Again, we have chosen our point of reference for these comparisons to be the S1 keto geometry because the time 4601

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ps, let alone 2.6 ps. This 500 fs time scale is shorter than the onset time for quenching obtained in our simulation (710 fs). We note that the experimental lifetime comes from transient absorption measurements with a probe pulse consistent with the S1 keto structure of HBT. We suspect that the decay in the transient absorption signal occurs as HBT leaves the S1 keto minimum and before HBT reaches the vicinity of the S1/S0 seam. If the rapid twisting observed in the TDDFT dynamics is correct, this would imply that the population transfer near the S1/S0 seam is highly inefficient. Perhaps the repeated twisting of HBT to the intersection and back to the planar S1 keto geometry could be consistent with both the experimental results and the TDDFT dynamics. Simulation at a more reliable level of theory will be needed to verify if this is the case, or if our simpler picture of a delayed twisting motion followed by rapid, efficient internal conversion is correct.

basis functions have been spawned on the ground state. Propagating these 1000 basis functions to study the return to S0 enol geometries would be extremely computationally demanding. Additionally, the errors in the FOMO-CASCI potential surface that result from the overestimated vertical excitation energies are not problematic on the S1 surface; however, it is likely that they will affect the treatment of S0. For example, the excited-state proton transfer reaction is overstabilized by about 0.4 eV; the reverse reaction is overstabilized by 1.5 eV on the ground state. The errors that are hidden in the excited-state dynamics will likely manifest in the subsequent ground-state dynamics. Finally, our FOMO-CASCI approach becomes problematic when the ground-state dynamics are considered. The electronic structure of the first excited state can be reasonably described with the compact (2/2) active space including the π and π* orbitals. During the excited-state dynamics, the FOMO-CASCI wave function is remarkably stable; no issues with energy conservation resulting from a discontinuous potential energy surface were observed in the dynamics simulation. The ground state, however, is well described by a single Slater determinant. As a result, the physics that stabilizes the active orbitals in the excited state is not present on the ground state. This leads to discontinuities in the potential surface resulting from orbital rotations that would be redundant in a single determinant wave function but are not in our CASCI wave function (i.e., occupied-occupied rotations). This issue could possibly be avoided by choosing the molecular orbitals differently (perhaps using state-averaged complete active space self-consistent field (SA-CASSCF) orbitals would avoid this issue). It might also be possible to introduce a penalty function into the FON-HF orbital optimization to bias the solution against these orbital rotations. Prior to this work, the most complete study of the excitedstate dynamics of HBT was due to Barbatti et al. applying timedependent density functional theory (TDDFT), using the B3YLP functional, in a classical simulation of the dynamics.19 They reported an excited-state proton transfer time of 30−50 fs, which is in good agreement with experiment and our theoretical results. However, the excited-state lifetime could not be extracted directly from their simulations; this is a deficiency of standard TDDFT methods, which cannot describe conical intersections between the ground and excited state. In addition, the TDDFT computations become unstable at the twisted geometries of HBT. As Barbatti et al. state,19 . . . thirty trajectories were computed at the TD-DFT(B3LYP)/SV(P) level for a maximum of 500 fs. Most of trajectories (25) run at least 400 fs, but only six of them completed 500 fs without nishing due to an error in the TDDFT section of the calculation. This error was a consequence of the fact that the multireference character becomes important between 400 fs and 500 fs and it was not possible to continue the simulation using TD-DFT. They report that HBT had twisted and reached the S1/S0 intersection when these errors occurred. As a result of this failure of TDDFT, only a lower bound of 400−500 fs could be placed on the excited-state lifetime. This is significantly shorter than the experimental lifetime (2.6 ps) and the result we obtain from our simulations (1.7−1.8 ps). Although Barbatti et al. claim that their result is consistent with the experimental excited-state lifetime, we have found internal conversion to be extremely efficient near the twisted MECIs. It would seem highly unlikely that trajectories reaching the intersection seam within 500 fs could be consistent with a lifetime greater than 1

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CONCLUSIONS We have simulated the excited-state dynamics of HBT using a wave function-in-DFT embedding approach to the electronic structure and AIMS to treat the nuclear dynamics. Our simulations predict that HBT undergoes ESIPT within 48−54 fs of photoexcitation. Following proton transfer, HBT is trapped in a metastable keto geometry until the molecule begins to twist about its central carbon−carbon bond. Once twisting has begun, HBT proceeds rapidly toward the intersection seam between the ground and first excited electronic state by twisting further and pyramidalizing about the 2-carbon of the benzothiazole. From our simulations, we predict that HBT has an excited-state lifetime of 1.7−1.8 ps. These results are in reasonably good agreement with experiment; the ESIPT time we obtain is in excellent agreement with experiment, whereas our predicted excited-state lifetime is somewhat shorter than the experimental result. This level of agreement with experiment inspires confidence that the mechanistic understanding of the excited-state dynamics obtained from our simulation is correct. Further, our results demonstrate that using wave function-in-DFT embedding to improve the energetics of CASCI can be fruitful in the context of excited-state dynamics. Using this approach, simulations similar to the one presented here can be performed routinely due to the low observed computational scaling, 6(N 2), of the method and our implementation on graphical processing units (GPUs). Finally, we note that this method outperforms TDDFT in its ability to describe the excited-state dynamics of HBT. Methods that would clearly improve over our approach, such as multireference perturbation theory, scale as 6(N 5) or worse and, as a result, remain too computationally demanding for many applications in photochemical dynamics. Although the gas-phase excited-state lifetime of HBT is relatively short (at 2.6 ps), in solution, the excited-state lifetime can be much longer (300 ps in tetrachloroethylene) and is highly solvent dependent. There appears to be an interplay between solvent polarity, which seems to shorten the excitedstate lifetime, and solvent viscosity, which seems to lengthen the excited-state lifetime.18,43,45 The methodology validated in the present work can be used in the simulation of HBT in solution using a QM/MM description of the solvent. There are also a wide variety of molecules with structures similar to that of HBT that also undergo excited-state proton transfer. In particular, the 2-(2′-hydroxyphenyl)benzoxazole and 2-(2′hydroxyphenyl)benzimidazole molecules substitute oxygen 4602

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fluorescent molecular probes and luminescent materials. Phys. Chem. Chem. Phys. 2012, 14, 8803−8817. (7) Padalkar, V. S.; Seki, S. Excited-state intramolecular protontransfer (ESIPT)-inspired solid state emitters. Chem. Soc. Rev. 2016, 45, 169−202. (8) Sengupta, P. K.; Kasha, M. Excited state proton-transfer spectroscopy of 3-hydroxyflavone and quercetin. Chem. Phys. Lett. 1979, 68, 382−385. (9) Strandjord, A. J.; Barbara, P. The Proton-Transfer Kinetics of 3Hydroxyflavone: Solvent Effects. J. Phys. Chem. 1985, 89, 2355−2361. (10) Chatterley, A. S.; Horke, D. A.; Verlet, J. R. R. On the intrinsic photophysics of indigo: a time-resolved photoelectron spectroscopy study of the indigo carmine dianion. Phys. Chem. Chem. Phys. 2012, 14, 16155−16161. (11) Simkovitch, R.; Huppert, D. Excited-State Intramolecular Proton Transfer of the Natural Product Quercetin. J. Phys. Chem. B 2015, 119, 10244−10251. (12) Baker, L. A.; Horbury, M. D.; Greenough, S. E.; Allais, F.; Walsh, P. S.; Habershon, S.; Stavros, V. G. Ultrafast Photoprotecting Sunscreens in Natural Plants. J. Phys. Chem. Lett. 2016, 7, 56−61. (13) Baker, L. A.; Greenough, S. E.; Stavros, V. G. A Perspective on the Ultrafast Photochemistry of Solution-Phase Sunscreen Molecules. J. Phys. Chem. Lett. 2016, 7, 4655−4665. (14) Flom, S. R.; Barbara, P. F. The photodynamics of 2-(2-hydroxy5-methylphenyl)-benzotriazole in low-temperature organic glasses. Chem. Phys. Lett. 1983, 94, 488. (15) Wiechmann, M.; Port, H.; Frey, W.; Lärmer, F.; Elässer, T. Time-resolved spectroscopy on ultrafast proton transfer in 2-(2′hydroxy-5′-methylphenyl)benzotriazole in liquid and polymer environments. J. Phys. Chem. 1991, 95, 1918. (16) Chudoba, C.; Riedle, E.; Pfeiffer, M.; Elsaesser, T. Vibrational coherence in ultrafast excited state proton transfer. Chem. Phys. Lett. 1996, 263, 622−628. (17) Baker, L. A.; Horbury, M. D.; Greenough, S. E.; Coulter, P. M.; Karsili, T. N. V.; Roberts, G. M.; Orr-Ewing, A. J.; Ashfold, M. N. R.; Stavros, V. G. Probing the Ultrafast Energy Dissipation Mechanism of the Sunscreen Oxybenzone after UVA Irradiation. J. Phys. Chem. Lett. 2015, 6, 1363−1368. (18) Barbara, P. F.; Brus, L. E.; Rentzepis, P. M. Intramolecular proton transfer and excited-state relaxation in 2-(2-hydroxyphenyl)benzothiazole. J. Am. Chem. Soc. 1980, 102, 5631−5635. (19) Barbatti, M.; Aquino, A. J. A.; Lischka, H.; Schriever, C.; Lochbrunner, S.; Riedle, E. Ultrafast internal conversion pathway and mechanism in 2-(2′-hydroxyphenyl)benzothiazole: a case study for excited-state intramolecular proton transfer systems. Phys. Chem. Chem. Phys. 2009, 11, 1406−1415. (20) Chou, P. T.; Chen, Y. C.; Yu, W. S.; Chou, Y. H.; Wei, C. Y.; Cheng, Y. M. Excited-State Intramolecular Proton Transfer in 10Hydroxybenzo[h]Quinoline. J. Phys. Chem. A 2001, 105, 1731. (21) Takeuchi, S.; Tahara, T. Coherent Nuclear Wavepacket Motions in Ultrafast Excited-State Intramolecular Proton Transfer: Sub-30-fs Resolved Pump-Probe Absorption Spectroscopy of 10-Hydroxybenzo[h]Quinoline in Solution. J. Phys. Chem. A 2005, 109, 10199. (22) Schriever, C.; Barbatti, M.; Stock, K.; Aquino, A. J. A.; Tunega, D.; Lochbrunner, S.; Riedle, E.; de Vivie-Riedle, R.; Lischka, H. The Interplay of Skeletal Deformations and Ultrafast Excited-State Intramolecular Proton Transfer: Experimental and Theoretical Investigation of 10-Hydroxybenzo[h]Quinoline. Chem. Phys. 2008, 347, 446. (23) Higashi, M.; Saito, S. Direct Simulation of Excited-State Intramolecular Proton Transfer and Vibrational Coherence of 10Hydroxybenzo[h]Quinoline in Solution. J. Phys. Chem. Lett. 2011, 2, 2366. (24) Lee, J.; Joo, T. Photophysical Model of 10-Hydroxybenzo[h]quinoline: Internal Conversion and Excited State Intramolecular Proton Transfer. Bull. Korean Chem. Soc. 2014, 35, 881−885. (25) Chudoba, C.; Lutgen, S.; Jentzsch, T.; Riedle, E.; Woerner, M.; Elsaesser, T. Femtosecond studies of vibrationally hot molecules

and nitrogen for the sulfur present in HBT; an important family of photostabilizers is based on the 2-(2′-hydroxyphenyl)benzotriazole framework. These related compounds should be amenable to study with the combination of wave function-inDFT embedding and AIMS dynamics applied in the present work. However, there are still a few remaining issues with our methodology. We need to couple the wave function-in-DFT embedding with a more robust orbital optimization procedure to treat the subsequent ground-state dynamics and the recovery of the S0 enol structure. Work is currently underway in our laboratory to apply SA-CASSCF in this context. We are optimistic that this will allow us to simulate the complete proton transfer cycle of HBT in the near future.

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ASSOCIATED CONTENT

S Supporting Information *

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.jpca.7b01215. Comparison of several active spaces, a test of the basis set dependence of our DFT-corrected FOMO-CASCI approach, comutations of the reaction pathway along the twisting coordinate, a discussion of the choice of method for the nuclear dynamics, and energies and optimized geometries of HBT (PDF)

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AUTHOR INFORMATION

Corresponding Author

*E. G. Hohenstein. E-mail: [email protected]. ORCID

Edward G. Hohenstein: 0000-0002-2119-2959 Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS Support for this project was provided by the Martin & Michele Cohen Fund for Science and PSC−CUNY Award #69805-00 47, jointly funded by The Professional Staff Congress and The City University of New York. Computational resources were provided through a Research Cluster Grant from Silicon Mechanics: award number SM-2015-289297.

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REFERENCES

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