Article pubs.acs.org/JPCB
Linear Energy Relationships in Ground State Proton Transfer and Excited State Proton-Coupled Electron Transfer Ana P. Gamiz-Hernandez,† Artiom Magomedov,† Gerhard Hummer,‡ and Ville R. I. Kaila*,† †
Department Chemie, Technische Universität München (TUM) Lichtenbergstraße 4, D-85747 Garching, Germany Department of Theoretical Biophysics, Max Planck Institute of Biophysics, Max-von-Laue-Straße 3, 60438 Frankfurt am Main, Germany
‡
S Supporting Information *
ABSTRACT: Proton-coupled electron transfer (PCET) processes are elementary chemical reactions involved in a broad range of radical and redox reactions. Elucidating fundamental PCET reaction mechanisms are thus of central importance for chemical and biochemical research. Here we use quantum chemical density functional theory (DFT), time-dependent density functional theory (TDDFT), and the algebraic diagrammatic-construction through second-order (ADC(2)) to study the mechanism, thermodynamic driving force effects, and reaction barriers of both ground state proton transfer (pT) and photoinduced proton-coupled electron transfer (PCET) between nitrosylated phenyl-phenol compounds and hydrogen-bonded t-butylamine as an external base. We show that the obtained reaction barriers for the ground state pT reactions depend linearly on the thermodynamic driving force, with a Brønsted slope of 1 or 0. Photoexcitation leads to a PCET reaction, for which we find that the excited state reaction barrier depends on the thermodynamic driving force with a Brønsted slope of 1/2. To support the mechanistic picture arising from the static potential energy surfaces, we perform additional molecular dynamics simulations on the excited state energy surface, in which we observe a spontaneous PCET between the donor and the acceptor groups. Our findings suggest that a Brønsted analysis may distinguish the ground state pT and excited state PCET processes.
1. INTRODUCTION Proton-coupled electron transfer (PCET) is the stepwise or concerted transfer of two elementary particles, an electron (e−) and a proton (H+).1−6 PCET is involved in many fundamental chemical and biological processes. In biological energy transduction, it forms key catalytic steps in cell respiration and photosynthesis;7,8 in organic chemistry, it is the basic mechanism of many radical reactions.1−6 Understanding the fundamental principles of PCET is also of particular importance for designing new biomimetic energy technology, such as water-oxidizing molecular catalysts.9,10 Recently, Westlake et al.11 studied photoinduced PCET between p-nitrophenyl-phenol and t-butylamine in 1,2dichloroethane solvent using ultrafast time-resolved pump− probe spectroscopy. The photoexcitation was shown to lead to an instantaneous intramolecular charge transfer (ICT) in pnitrophenyl-phenol followed by a picosecond proton transfer (pT) to the base. Moreover, intersystem crossing to an excited triplet state was suggested to result in a concerted PCET processes between the phenol and the base. Ko et al.12 studied p-nitrophenyl-phenol/t-methylamine using TDDFT and ab initio calculations and suggested that the experimentally observed states correspond to the excited S1 and S2 states, with ππ* and nπ* characters, respectively. They further found that while the ππ* potential energy surface has two minima © XXXX American Chemical Society
corresponding to the protonated donor and acceptor groups, separated by a low barrier, only a single energy minimum, corresponding to the protonated donor group, was identified on the nπ* surface. Inspired by these findings and the interesting properties of the system as a general chemical model system for PCET,11,13 we employ here the p-nitrophenyl-phenol/t-butylamine dimer, and chemically modified versions thereof (Figure 1), to study ground and excited state reaction barriers and transfer mechanisms using electronic structure theory. We exploit the effect of chemical substitutions to explore reaction mechanisms in a way amenable to experiment.14,15 In previous studies of the simple model system of hydrogenbonded water-wires connecting proton donating and accepting groups, we found that the reaction barrier for a proton transfer (pT) process responds linearly to perturbations in the thermodynamic driving force. More specifically, we observed Brønsted slopes of 0 and 1 when the proton accepting or Special Issue: Photoinduced Proton Transfer in Chemistry and Biology Symposium Received: August 30, 2014 Revised: December 6, 2014
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processes, we provide a physical rationale for these distinct differences between pT and PCET.
2. MODELS AND METHODS The molecular structure of p-nitrophenyl-phenol hydrogen bonded to t-butylamine was optimized using Becke’s three parameter functional, B3LYP18,19 and the Karlsruhe triple-basis set extended with two polarization functions, def2-TZVPP.20 Reaction profiles for the ground state proton transfer process were obtained by constrained ground state optimizations, in which the phenolic proton was stepwise transferred to tbutylamine. The nonadiabatic reaction profile for the excited state was obtained by vertical excitations from the ground state surface, using linear-response time-dependent density functional theory (TDDFT)21 at the B3LYP/def2-TZVPP level of theory. The respective structures along the proton transfer coordinates as well as the dihedral bond between the phenyl groups were also relaxed on the excited state surface at the BHLYP19/def2-SVP level of theory, that is, the half-and-half functional with the exact Hartree−Fock exchange increased to 50% due to its suggested better performance in treating charge transfer states at the TDDFT level.22,23 Solvation effects were studied using the COSMO model24 with a dielectric constant set to 10.42, corresponding to the dielectric screening of 1,2dichloroethane (DCE).25 The thermodynamic driving force was increased by stepwise nitrosylation of the phenyl ring (Figure 1), followed by the same optimization procedure. In addition to BHLYP calculations,19,22,23 TDDFT charge transfer problems were also studied by employing the range-corrected functional CAM-B3LYP,26 and the algebraic diagrammatic construction through second order method, ADC(2),27,28 with def2-TZVPP basis sets. We also computed ground and excited state electrostatic potential (ESP) charges and charge density differences to analyze charge redistribution effects. We did not observe triplet or other instabilities29−31 in our benchmarking calculations of the model system, suggesting that the electronic ground state has a proper singlet reference state, in agreement with the experimental data.11 To study the dynamics of the proton transfer process, we performed first-principles molecular dynamics at the B3LYP/def2-SVP level18,32,33 on the ground state and first excited state energy surfaces using an integration step of 1 fs, and initial velocities obtained from a random Maxwell−Boltzmann distribution with T = 298.15 K. The firstprinciples molecular dynamics simulations on the isolated systems were performed in the gas-phase. To investigate explicit solvent effects, we also performed first-principles molecular dynamics simulation in the ground state and first excited state of the p-nitrophenyl-phenol/t-butylamine with six DCE solvent molecules explicitly considered using DFT cluster calculations and hybrid QM/MM simulations at the B3LYP/ def2-SVP level. Starting structures were obtained from a 1 ns equilibrated classical MD simulation of the system at T = 300 K with N = 500 DCE molecules using a simulation box with dimensions 40 × 40 × 40 Å. p-Nitrophenyl-phenol/tbutylamine was fixed in its optimized ground state geometry during the classical equilibration. Interactions with the DCE solvent were modeled using electrostatic potential (ESP) charges determined at the B3LYP/def2-TZVP level of theory and Lennard-Jones parameters obtained from the CHARMM36 force field.34 Parameters for DCE were also obtained from the CHARMM36 parameters for 1,1-dichloroethane.35 The calculations were performed using TURBOMOLE versions 6.3− 6.6,36 and Q-Chem v4.1 for the CAM-B3LYP calculations,37
Figure 1. Hydrogen-bonded nitrophenyl-phenol/t-butylamine dimer models (M0−M5) used for studying proton transfer in the ground and excited states: (A) phenyl-phenol (M0), (B) 4-nitrophenyl-phenol (M1), (C) 3,5-dinitrophenyl-phenol (M2), (D) 2,4,6-trinitrophenylphenol (M3), (E) 2,3,4,5,6-pentanitrophenyl-phenol (M5). The molecule shown in B (M1) corresponds to the system studied experimentally by Westlake et al.11
donating groups, respectively, were chemically modified.16 In a tyrosine/tyrosyl radical dimer of the enzyme ribonucleotide reductase (RNR), we further showed that the barrier for a direct PCET process without mediating water responds to changes in the thermodynamic driving force with a Brønsted slope of 1/2.17 We show here that both effects occur within the pnitrophenyl-phenol/t-butylamine dimer; on the ground state potential energy surface, we observe a pT process, with ideal Brønsted slopes of 0 and 1, whereas photoexcitation leads to PCET processes, characterized by a perfectly mixed Brønsted slope of 1/2. By analyzing electronic structure changes in these B
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Figure 2. Energetics of the pT and PCET reactions (in eV) between nitro-substituted phenyl-phenol and t-butylamine as a function of the proton transfer reaction coordinate (in Å), r1(O−H)−r2(N−H) on the electronic ground state (A, B), and nonadiabatic excited state potential energy surfaces (C,D) obtained at the (A) B3LYP, (B) MP2, (C) TDDFT/B3LYP, (D) ADC(2) levels of theory with def2-TZVPP basis sets and ε = 10.42. Color-coding: phenyl-phenol (red), 4-nitrophenyl-phenol (black), 3,5-dinitrophenyl-phenol (yellow), 2,4,6-trinitrophenyl-phenol (green), 2,3,4,5,6pentanitrophenyl-phenol (blue).
and the hybrid QM/MM simulations were performed using the CHARMM-TURBOMOLE interface.38
3. RESULTS AND DISCUSSION 3.1. Energetics and Reactions Barriers for Proton Transfer in the Electronic Ground and Excited States. Potential energy surfaces for the ground state (S0) and first excited state (S1) pT between the nitro-substituted phenylphenol compounds and t-butylamine are shown in Figure 2. The ground state pT process is endergonic by 0.1−0.5 eV (2− 12 kcal mol−1) at the B3LYP level of theory, with reaction barriers of 0.4−0.7 eV (9−16 kcal mol−1), which agree well with the respective reaction energetics and barriers obtained at the MP2/def2-TZVPP level (Figure 2B). Vertical photoexcitation to the nonadiabatic S1 potential energy surfaces that would be expected to arise upon instantaneous photoexcitation prior to nuclear rearrangement, leads to exergonic proton transfer reactions by −0.2 to −0.6 eV (−5 to −14 kcal mol−1) in all systems, with lower reaction barriers of 0.05−0.3 eV (1−7 kcal mol−1; Figure 2C). Relaxation of the pnitrophenyl-phenol/t-butlyamine structure on the excited state surfaces further reduces the reaction barriers to 0.011 eV at BHLYP/def2-TZVP level of theory (Figure 3). For the singly substituted nitro-phenyl system, our driving force and
Figure 3. Energetics of the PCET reactions (in eV) between 4nitrophenyl-phenol and t-butylamine as a function of the proton transfer reaction coordinate (in Å) on the relaxed excited state BHLYP/def2-TZVPP/ε = 10.42 surface, showing a small pT barrier of 0.011 eV.
nonadiabatic reaction barrier are thus qualitatively similar to the values obtained by Ko et al.12 for their adiabatic S1 profile on C
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Figure 4. (A) Barrier of proton transfer between nitro-substituted phenyl-phenol and t-butylamine (in eV) in the ground state (A) and excited state (B) as a function of the thermodynamic driving force (in eV) obtained using B3LYP (blue squares), BHLYP (open black circles), CAM-B3LYP (orange triangle), MP2/ADC(2) (closed red circles) with def2-TZVPP basis sets and ε =10.42. Barriers for the relaxed excited state (ad BHLYP) are shown as blue open squares. The barrier for the ground state pT process depends linearly on the thermodynamic driving force with a Brønsted slope of α = 1 or 0, for the pT from D → A and A → D, respectively, with chemically modified D groups. In contrast, the Brønsted slope changes to α = 1/ 2 in the electronic excited state. (C) Physical interpretation of Brønsted slopes. Top: chemical modification of D in the electronic ground state (GS) perturbs only its own energy level, leaving the energy levels of the transition state (TS) and A unperturbed. Below: In the electronic excited state (ES), the energy levels of both D and TS are perturbed as a result of chemical modification on D.
driving force is changed over a range of 0.8 eV (18 kcal mol−1). For chemical substitutions on the phenyl-phenol moiety, the pT barrier from the phenyl group to t-butylamine responds with a linear slope of 1 to changes in the thermodynamic driving force. In contrast, the pT barrier from the t-butylamine to the phenyl-group is insensitive to modifications of the distal phenyl group, suggesting that chemical modifications stabilize or destabilize only the ground state but do not significantly affect the energy of the transition state (Figure 4C). This mechanism is consistent with our earlier observations on linear energy relationships obtained for pT in short water chains.16 The barrier for the nonadiabatic excited state pT processes also depends linearly on modifications of the thermodynamic driving force over a range of 1.2 eV (28 kcal mol−1), but in contrast to the ground state pT process, we observe a slope of 1/2 for the excited state PCET process. A Brønsted slope of 1/ 2 was previously observed for a direct PCET process in the stacked tyrosine dimer of ribonucleotide reductase (RNR).17 This picture would be expected to arise from a situation where chemical modifications of the electron-accepting group in the S1 state perturb the energy of both the proton donor and the transition state (Figure 4C). When the acceptor energy levels (the amine side) are aligned, only the proton donor level (phenol) moves in the electronic ground state, while both the donor level and transition states are perturbed in the electronic excited state (Supporting Information, Figure 2). To explore possible problems associated with charge-transfer states in TDDFT, we performed additional calculations using the BHLYP functional, in which the exact Hartree−Fock
the similar p-nitrophenyl-phenol/t-methylamine system, showing two minima and a low pT barrier. Consistent with the nonadiabatic S1 surface at the B3LYP level, we obtain similar nonadiabatic S1 potential energy surfaces at the CAM-B3LYP level (SI Figure 1) and by using ADC(2)/def2-TZVPP (Figure 1D), indicating that the profiles along the calculated proton reaction coordinates are robust with respect to the electronic structure methodology. The reaction barriers obtained at the BHLYP level are somewhat larger, and are also shown in Supporting Information, Figure 1. We observe that the dielectric medium, modeled here using the conductor-like screening model (COSMO), has a significant effect in stabilizing the product state of the pT processes; the dielectric screening by 1,2-dichloroethane, which corresponds to ε = 10.42,25 increases the exergonicity of the reactions by 0.5−0.6 eV (12−14 kcal mol−1). The obtained reaction profiles suggest that the transition state moves toward the acceptor side with increasing endergonicity in the electronic ground state, while in the electronic excited state, the transition state moves closer to the proton donating phenol group with increasing exergonicity, consistent with Hammond’s postulate.39 This behavior is likely to be linked to the increase in the equilibrium O−H bond length and decrease in the H···N hydrogen bond length with increasing acidity of the substituted phenyl rings. 3.2. Linear Energy Relationships. Figure 4 shows the reaction barriers as a function of the chemical driving force for the electronic ground state and the nonadiabatic excited state processes. At the electronic ground state, we obtain a linear dependence on the reaction barrier when the thermodynamic D
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Figure 6. Electron density difference between the ground and excited states when the proton is associated with 4-nitrophenyl-phenol (system M1, top), t-butylamine (bottom), and at the transition state (middle). Electron density differences are shown with an isocontour surface of ±0.002 e/Å3. The red and blue isocontour surfaces indicate increased and decreased electron density, respectively, in the excited state relative to the ground state. The electron density difference distributions suggest that the photoexcitation leads to a ππ* transitions, with an internal charge transfer between the proton donating phenol and the nitrosylated distal phenyl groups. In addition, there is a partial charge transfer toward the amine nitrogen from the proton donating phenol side, resembling an electron driven proton transfer process (see text).41 VMD was used for visualization.48
Figure 5. Total ESP charge of the proton donating phenol in the ground state (top), and electronic excited state (bottom). The photoexcitation leads to an instantaneous oxidation of the proton donating phenol, which increases the total ESP charge in the excited state. The pT polarizes the phenol group 0.3−0.4e more negative. Color-coding: phenyl-phenol (red), 4-nitrophenyl-phenol (black), 3,5dinitrophenyl-phenol (yellow), 2,4,6-trinitrophenyl-phenol (green), 2,3,4,5,6-pentanitrophenyl-phenol (blue).
exchange is increased to 50%,19 and by using the rangeseparated functional CAM-B3LYP,26 which employs 19% shortrange Hartree−Fock exchange and 65% long-range Hartree− Fock exchange to more closely follow the expected 1/r distance dependence for the charge transfer state. We also calculated the profiles at the correlated ab initio level using the algebraic diagrammatic construction through second-order ADC(2). We find the qualitative behavior obtained at the B3LYP level of theory to be unchanged with the CAM-B3LYP and BHLYPfunctionals and at the MP2/ADC(2) level of theory, with Brønsted slopes of 1 and 0 in the ground-state, and 1/2 in the excited state (Figure 4). These results suggest that the change in Brønsted slopes is unlikely to arise from DFT charge transfer problems. We find that the adiabatic potential energy surface for M1 (Figure 3) also supports the Brønsted slope of 1/2, applying in the limit where nuclear relaxation is fast compared to pT. Nevertheless, due to the limited accuracy of TDDFT, it is not currently possible to unambiguously confirm this kinetic behavior, which would most likely require simulations of the full dynamics and excited state optimization at correlated ab initio levels. 3.3. Physical Rationale for the Brønsted Slopes. To gain insight into the origin of the observed differences in Brønsted slopes, we studied density differences in the electronic structure that arise upon the photoexcitation and analyzed the electrostatic potential (ESP) charges in the ground and excited
states. The data in Figures 5 and 6 indicate that the photoexcitation indeed couples to a charge transfer of 0.5e from the proton-donating phenol-moiety to the nitrosylated phenyl ring, facilitating the proton transfer by decreasing the electrostatic attraction between the proton and the phenol ring. We find that the photoexcited S1 state has a ππ* character, consistent with results recently obtained by Ko et al.12 The charge seems to be instantaneously transferred upon the photoexcitation in the singly substituted p-nitrophenyl-phenol system, leading to a large increase in the dipole moment. This suggests that the pT process is likely to take place after the photoinduced electron transfer process, consistent with the picture suggested by Westlake et al.11 Interestingly, in both the ground and excited states, the pT polarizes the donating groups by 0.4e, whereas the total effective charge of the t-butylamine group remains nearly unchanged in both the ground and excited states. Nevertheless, the O−H bond pointing toward the nitrogen of the external base is strongly polarized in the electronic excited state (Figure 6), with excess electron density transferred from the proton donating side toward the proton accepting side. We also find that the charge transfer to the amine group becomes stronger with increasing thermodynamic driving force (Supporting Information, Figure 3), for which the density differences around the nitrogen, proton, and oxygen involved in the transfer process become more polarized. E
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Figure 7. Two-dimensional relaxed excited state potential energy surface (PES, in eV) for the proton transfer and dihedral twist of the phenyl planes on the TDDFT/B3LYP/def2-TZVPP (left) and TDDFT/BHLYP/def2-TZVPP (right) levels of theory. Bottom panels: projection of the dihedral twist coordinate. Relaxed excited state structures were obtained on the TDDFT/BHLYP/def2-SVP level of theory. Both surfaces suggest that the ±90° twisted conformation is located in an energy minimum, together with minima predicted near ±30° at the BHLYP level. A 4 ps excited state first-principle molecular dynamics trajectory is projected on the B3LYP surface, suggesting that a dihedral twist couples to the pT process. The dihedral angles below −90° (see Figure 8) were projected to the positive side (0−90°) for visualization of the complete trajectory.
the BHLYP level further suggest that the potential energy landscape for the dihedral rotation is rather flat, with local minima also observed near ±30°, close to the ground state energy minimum. To further probe the transfer mechanism arising from these static potential energy surfaces, we performed first-principle molecular dynamics simulations on the first excited state. A resulting trajectory, projected on the B3LYP surface and shown in Figure 8A, suggest that the pT process is likely to be preceded by a dihedral rotation, consistent with the PES. In this trajectory, the dihedral bond rotation begins at about 0.1 ps, whereas the first proton transfer to the base follows after 0.2 ps. Our MD simulations further suggest that several pT attempts occur in the excited state between 0.2 and 1.5 ps, after which the proton is stabilized on the amine, comparable to the experimentally observed timescales.11 To explicitly study solvent effects, we performed additional first-principles molecular dynamics simulations on a microsolvated p-nitrophenyl-phenol/t-butylamine using both QM cluster calculations and hybrid QM/MM simulations. In both simulation setups, shown in Figure 8B, we observe a qualitatively similar PCET process as for the isolated systems. However, the dihedral rotation of the phenol rings seems to be somewhat delayed relative to the isolated system, due to coupled solvent motions. Moreover, in contrast to the isolated system with a stepwise dihedral rotation and pT process, the condensed phase models suggest a more concerted reaction mechanism. For the more nitrosylated systems, we obtain a similar qualitative picture with the dihedral coupled to the proton transfer, but observe more rapid proton transfer to the base (Supporting Information, Figure 4). Our preliminary nonadiabatic surface hopping simulations suggest that the ground and excited state become more rapidly degenerate with increasing thermodynamic driving force, which result in conical
Interestingly, the nonsubstituted phenyl system (M0) is likely to have a lower electron affinity relative to the nitrosylated phenyl. Indeed, our calculations suggest that the approaching proton makes the amine group the dominant electron acceptor instead of the distal phenyl group, suggesting that the pT is coupled to an intermolecular electron transfer (Supporting Information, Figure 3). Such proton-driven electron transfer processes play a central role in the coupled proton and electron transfer process in the respiratory enzyme cytochrome c oxidase.7 The polarization of the N−H bond in all chemically modified phenyl-phenol systems studied here, may result in the perturbed transition state energies for the excited state pT process, in contrast to the ground state process where chemical modifications affect only the relative energy of the proton donor. 3.4. Coupling of Rotational Degrees of Freedom to the Excited State PCET Process. To study the coupling of the pT reaction with other degrees of freedom, we performed a two-dimensional excited state potential energy surface optimization of the pT coordinate as a function of the dihedral angle between the phenyl planes. Figure 7 shows the relaxed excited state 2D surface of the pT process as a function of the dihedral angle obtained using B3LYP and BHLYP. Both computational levels suggest that the deprotonated phenol has a local energy minimum at the ±90° twisted conformation, suggesting that a dihedral rotation of the phenyl-phenol bond might be involved in the excited state pT process, as also suggested by Hammes-Schiffer.13 Ko et al.12 observe from a rigid dihedral scan a minimum located at 94° using a state specific polarizable continuum model, whereas the linear response-type polarizable continuum model predicted minima at 15 and 22°, suggesting that the dihedral coordinate might be sensitive to the description of the solvent. Our calculations at F
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Figure 8. First-principles molecular dynamics simulations and hybrid QM/MM molecular dynamics simulation of the isolated 4-nitrophenyl-phenol/ t-butyl amine system (panel A) and the 4-nitrophenyl-phenol/t-butyl amine solvated with six DCE solvent molecules in the QM region (panel B). The QM/MM systems were additionally solvated with N = 494 classical DCE molecules. The ground state simulations are shown in black for the isolated system and QM cluster models, and in green for the QM/MM simulations. The excited state simulations are shown in red for the isolated system and the QM cluster models, and in blue for the QM/MM simulations. For the isolated system, shown in panel A, a dihedral twist starts at about 0.1 ps and couples to the proton transfer process at about 0.2 ps. Several pT attempts occur in the excited state between 0.2 and 1.5 ps, after which the proton is stabilized on the amine. For the condensed phase simulations, shown in panel B, the pT starts at about 0.1 ps and couples to the dihedral twist nearly concertedly with the pT process. The condensed phase simulations suggest that the DCE solvent molecules rearrange around the phenol rings, and slow down the dihedral rotation, indicating that solvent motion might be coupled to the PCET process. The MD trajectory for the M3 system is shown in Supporting Information, Figure 4.
intersection and relaxation pathways back to the ground state, but which are usually poorly dealt with in TDDFT.40 3.5. Connection to Electron Driven Proton Transfer in Hydrogen Bonded Systems. A mechanistic picture that has arisen from studies of several hydrogen-bonded systems41−46 suggest that photoexcitations generally lead to an excited state hydrogen atom transfer process, in which the conical intersection between the ground and excited state becomes easily accessible, and results in an ultrafast photophysical relaxation pathway to the electronic ground state. Such electron-driven proton transfer (EDPT) processes are likely to play an important role in, for example, the photostability of organic and biological molecules.47 The excited state proton transfer process in phenyl-phenol systems are clearly also driven by a photoinduced electron transfer process, but in contrast to many of the previously studied hydrogen bonded systems, the main driving force is likely to arise from the electron transfer to the distal nitrosylated phenyl group that
functions as an electron sink. Nevertheless, as indicated by the charge density differences between the ground and excited states (Figure 6, Supporting Information, Movie 1), the pT process also seems to be coupled to a partial electron redistribution between the donor and acceptor groups, similar to that described for excited state EDPT processes. Our findings support the recently suggested ππ*-like character of the S1 state with charge transfer character both between the phenyl rings and between the proton donating ring and the amine. This effect becomes more prominent with increasing thermodynamic driving force, which suggest that this possible local partial EDPT process, may lead to the observed linear energy dependence of the barrier on the thermodynamic driving force with a slope of 1/2 that was previously suggested to be characteristic for coupled proton−electron transfer processes.17 In contrast, a pure pT process from a photooxidized protonated phenol radical (Ph−OH•/+) to the amine G
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the Leibniz Supercomputing Centre, LRZ (http://www.lrz.de/) are acknowledged for computer time.
would be expected to result in Brønsted slopes of 1 or 0, similar to those observed for the ground state pT process.16
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4. CONCLUSIONS We show here using density functional theory (DFT), linearresponse time dependent density functional theory (TDDFT)21 and correlated ab inito (ADC(2)) calculations,27,28 that a kinetic Brønsted analysis may help distinguish an excited state proton-coupled transfer (PCET) process from a ground state proton transfer (pT). Using the experimentally studied hydrogen-bonded p-nitrophenyl-phenol/t-butylamine dimer, and chemically modified versions thereof, we show that changes in the thermodynamic driving force by chemical substitutions, perturb the energy level of the proton donating group and leave the energy of the transition state unchanged, which results in linear energy relations with Brønsted slopes of 1 or 0. Such behavior is expected to arise if chemical substations affect the energy level of the proton donor/acceptor group but not the transition state. In contrast, for the excited state PCET process, the transition state energy is also perturbed by electronic polarization of the chemical bond between the proton donor and acceptor, which is a likely factor in the shift to a linear energy relation with a Brønsted slope of 1/2. Lowering of the kinetic barrier for PCET results from a diminished electrostatic attraction between the proton and the proton-donating group by photoinduced charge redistribution. The ground and excited state proton transfer process between nitro-substituted phenyl-phenol and t-butylamine represents an attractive model system for elucidating underlying energetics and reaction rate theories for general proton transfer and proton-coupled electron transfer processes. An interesting complication is that relaxation of the nuclear degrees of freedom on the excited-state surface can significantly lower the barrier for proton transfer. Since the barrier-lowering dihedral rotation of the phenyl planes found here would likely displace solvent molecules, the overall transfer process should thus also become coupled to solvent motions, as indicated by our explicit condensed phase simulations. Despite these complicating factors, the present findings on linear energy relationships may provide an experimental way to distinguish proton transfer from PCET processes in complex chemical and biological systems.
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(1) Reece, S. Y.; Nocera, D. G. Proton-Coupled Electron Transfer in Biology: Results from Synergistic Studies in Natural and Model Systems. Annu. Rev. Biochem. 2009, 78, 673−699. (2) Cukier, R. I.; Nocera, D. G. Proton-Coupled Electron Transfer. Annu. Rev. Phys. Chem. 1998, 49, 337−369. (3) Hammes-Schiffer, S.; Stuchebrukhov, A. A. Theory of Coupled Electron and Proton Transfer Reactions. Chem. Rev. 2010, 110, 6939− 6960. (4) Mayer, J. M. Understanding Hydrogen Atom Transfer: from Bond Strengths to Marcus Theory. Acc. Chem. Res. 2010, 44 (1), 36− 46. (5) Huynh, M. H. V.; Meyer, T. J. Proton-Coupled Electron Transfer. Chem. Rev. 2007, 107, 5004−5064. (6) Bonin, J.; Costentin, C.; Louault, C.; Robert, M.; Savéant, J. M. Water (in Water) as an Intrinsically Efficient Proton Acceptor in Concerted Proton Electron Transfers. J. Am. Chem. Soc. 2011, 133, 6668−6674. (7) Kaila, V. R. I.; Verkhovsky, M. I.; Wikström, M. Proton-Coupled Electron Transfer in Cytochrome Oxidase. Chem. Rev. 2010, 110, 7062−7081. (8) Tommos, C.; Babcock, G. T. Proton and Hydrogen Currents in Photosynthetic Water Oxidation. Biochim. Biophys. Acta, Bioenerg. 2000, 1458, 199−219. (9) Kanan, M. W.; Nocera, D. G. In Situ Formation of an OxygenEvolving Catalyst in Neutral Water Containing Phosphate and Co2+. Science 2008, 321, 1072−1075. (10) Duan, L.; Bozoglian, F.; Mandal, S.; Stewart, B.; Privalov, T.; Llobet, A.; Sun, L. A Molecular Ruthenium Catalyst with WaterOxidation Activity Comparable to that of Photosystem II. Nat. Chem. 2012, 4, 418−423. (11) Westlake, B. C.; Brennaman, M. K.; Concepcion, J. J.; Paul, J. J.; Bettis, S. E.; Hampton, S. D.; Miller, S. A.; Lebedeva, N. V.; Forbes, M. D.; Moran, A. M.; Meyer, T. J.; Papanikolas, J. M. Concerted ElectronProton Transfer in the Optical Excitation of Hydrogen-Bonded Dyes. Proc. Natl. Acad. Sci. U.S.A. 2011, 108, 8554−8558. (12) Ko, J.; Solis, B. H.; Soudackov, A. V.; Hammes-Schiffer, S. Photoinduced Proton-Coupled Electron Transfer of HydrogenBonded p-Nitrophenylphenol−Methylamine Complex in Solution. J. Phys. Chem. B 2013, 117, 316−325. (13) Hammes-Schiffer, S. When Electrons and Protons Get Excited. Proc. Natl. Acad. Sci. U.S.A. 2011, 108 (21), 8531−8532. (14) Yokoyama, K.; Uhlin, U.; Stubbe, J. Site-Specific Incorporation of 3-Nitrotyrosine as a Probe of pKa Perturbation of Redox-Active Tyrosines in Ribonucleotide Reductase. J. Am. Chem. Soc. 2010, 132 (24), 8385−8397. (15) Yokoyama, K.; Uhlin, U.; Stubbe, J. A Hot Oxidant, 3-NO2Y122 Radical, Unmasks Conformational Gating in Ribonucleotide Reductase. J. Am. Chem. Soc. 2010, 132 (43), 15368−15379. (16) Kaila, V. R. I.; Hummer, G. Energetics and Dynamics of Proton Transfer Reactions along Short Water Wires. Phys. Chem. Chem. Phys. 2011, 13, 13207−13215. (17) Kaila, V. R. I.; Hummer, G. Energetics of Direct and WaterMediated Proton-Coupled Electron Transfer. J. Am. Chem. Soc. 2011, 133, 19040−19043. (18) Lee, C.; Yang, W.; Parr, R. G. Development of the Colle-Salvetti Correlation-Energy Formula into a Functional of the Electron Density. Phys. Rev. B 1988, 37, 785−789. (19) Becke, A. D. Density-Functional Thermochemistry. III. The Role of Exact Exchange. J. Chem. Phys. 1993, 98, 5648−5652. (20) Weigend, F.; Ahlrichs, R. Balanced Basis Sets of Split Valence, Triple Zeta Valence and Quadruple Zeta Valence Quality for H to Rn: Design and Assessment of Accuracy. Phys. Chem. Chem. Phys. 2005, 7 (18), 3297−3305.
ASSOCIATED CONTENT
* Supporting Information S
Additional supporting figures. This material is available free of charge via the Internet at http://pubs.acs.org.
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REFERENCES
AUTHOR INFORMATION
Corresponding Author
*E-mail: [email protected]. Tel.: (+) 49 89 289 13612. Fax: (+) 49 89 289 13622. Notes
The authors declare no competing financial interest.
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ACKNOWLEDGMENTS V.R.I.K. acknowledges Prof. Wolfgang Domcke for insightful discussion. This research was supported by the Jane and Aatos Erkko Foundation (V.R.I.K.) and the Max Planck Society (G.H.). The Biowulf cluster at NIH (http://biowulf.nih.gov/), the CSC - IT Center for Science Ltd. (http://www.csc.fi/), and H
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Chemistry 17; Domcke, W., Yarkony, D. R., Köppel, H., Eds.; World Scientific Publishing Co.: Singapore, 2011. (43) Mališ, M.; Loquais, Y.; Gloaguen, E.; Biswal, H. S.; Piuzzi, F.; Tardivel, B.; Brenner, V.; Broquier, M.; Jouvet, C.; Mons, M.; Došlić, N.; Ljubić, I. Unraveling the Mechanisms of Nonradiative Deactivation in Model Peptides Following Photoexcitation of a Phenylalanine Residue. J. Am. Chem. Soc. 2012, 134 (50), 20340−20351. (44) Groenhof, G.; Bouxin-Cademartory, M.; Hess, B.; De Visser, S. P.; Berendsen, H. J.; Olivucci, M.; Mark, A. E.; Robb, M. A. Photoactivation of the Photoactive Yellow Protein: Why Photon Absorption Triggers a Trans-to-Cis Isomerization of the Chromophore in the Protein. J. Am. Chem. Soc. 2004, 126 (13), 4228−4233. (45) Houari, Y.; Charaf-Eddin, A.; Laurent, A. D.; Massue, J.; Ziessel, R.; Ulrich, G.; Jacquemin, D. Modeling Optical Signatures and Excited-State Reactivities of Substituted Hydroxyphenylbenzoxazole (Hbo) ESIPT Dyes. Phys. Chem. Chem. Phys. 2014, 16, 1319−1321. (46) Laurent, A. D.; Houari, Y.; Carvalho, P. H. P. R.; Neto, B. A. D.; Jacquemin, D. ESIPT or Not ESIPT? Revisiting Recent Results on 2,1,3-Benzothiadiazole under the TD-DFT Light. RSC Adv. 2014, 4, 14189−14192. (47) Sobolewski, A. L.; Domcke, W. The Chemical Physics of the Photostability of Life. Europhys. News 2006, 37, 20−23. (48) Humphrey, W.; Dalke, A.; Schulten, K. Vmd: Visual Molecular Dynamics. J. Mol. Graphics 1996, 14, 33−38.
(21) Furche, F.; Ahlrichs, R. Time-Dependent Density Functional Methods for Excited State Properties. J. Chem. Phys. 2002, 117, 7433− 7447. (22) Dreuw, A.; Head-Gordon, M. Single-Reference Ab Initio Methods for the Calculation of Excited States of Large Molecules. Chem. Rev. 2005, 105 (11), 4009−4037. (23) Plötner, J.; Tozer, D. J.; Dreuw, A. Dependence of Excited State Potential Energy Surfaces on the Spatial Overlap of the Kohn−Sham Orbitals and the Amount of Nonlocal Hartree−Fock Exchange in Time-Dependent Density Functional Theory. J. Chem. Theory Comput. 2010, 6 (8), 2315−2324. (24) Klamt, A.; Schüürmann, G. Cosmo: A New Approach to Dielectric Screening in Solvents with Explicit Expressions for the Screening Energy and Its Gradient. J. Chem. Soc., Perkin Trans. 2 1993, 5, 799−805. (25) Haynes, W. M. Handbook of Chemistry and Physics, 91st ed.; CRC Press: New York, 2010. (26) Yanai, T.; Tew, D. P.; Handy, N. C. A New Hybrid ExchangeCorrelation Functional Using the Coulomb-Attenuating Method (Cam-B3lyp). Chem. Phys. Lett. 2004, 393, 51−57. (27) Schirmer, J. Beyond the Random-Phase Approximation: A New Approximation Scheme for the Polarization Propagator. Phys. Rev. A 1982, 26, 2395−2416. (28) Hättig, C. Structure Optimizations for Excited States with Correlated Second-Order Methods: CC2, CIS(D∞), and ADC(2). Adv. Quantum Chem. 2005, 50, 37−60. (29) Peach, M. J. G.; Williamson, M. J.; Tozer, D. J. Influence of Triplet Instabilities in TDDFT. J. Chem. Theory Comput. 2011, 7, 3578−3585. (30) Peach, M. J. G.; Tozer, D. J. Overcoming Low Orbital Overlap and Triplet Instability Problems in TDDFT. J. Phys. Chem. A 2012, 116, 9783−9789. (31) Peach, M. J. G.; Benfield, P.; Helgaker, T.; Tozer, D. J. Excitation Energies in Density Functional Theory: An Evaluation and a Diagnostic Test. J. Chem. Phys. 2008, 128, 044118. (32) Schäfer, A.; Horn, H.; Ahlrichs, R. Fully Optimized Contracted Gaussian-Basis Sets for Atoms Li to Kr. J. Chem. Phys. 1992, 97, 2571− 2577. (33) Becke, A. D. A New Mixing of Hartree-Fock and Local DensityFunctional Theories. J. Chem. Phys. 1993, 98, 1372−1377. (34) Brooks, B. R.; Brooks, C. L.; Mackerell, A. D.; Nilsson, L.; Petrella, R. J.; Roux, B.; Won, Y.; Archontis, G.; Bartels, C.; Boresch, S.; et al. Charmm: The Biomolecular Simulation Program. J. Comput. Chem. 2009, 30 (10), 1545−1614. (35) Vanommeslaeghe, K.; Hatcher, E.; Acharya, C.; Kundu, S.; Zhong, S.; Shim, J.; Darian, E.; Guvench, O.; Lopes, P.; Vorobyov, I.; Mackerell, A. D., Jr. J. Comput. Chem. 2010, 31, 671−690. (36) Ahlrichs, R.; Bär, M.; Häser, M.; Horn, H.; Kölmel, C. Electronic Structure Calculations on Workstation Computers: The Program System Turbomole. Chem. Phys. Lett. 1989, 162, 165−169. (37) Shao, Y. M. L. F.; Jung, Y.; Kussmann, J.; Ochsenfeld, C.; Brown, S. T.; Gilbert, A. T.; Slipchenko, L. V.; Levchenko, S. V.; O’Neill, D. P.; et al. Advances in Methods and Algorithms in a Modern Quantum Chemistry Program Package. Phys. Chem. Chem. Phys. 2006, 8, 3172−3191. (38) Riahi, S.; Rowley, C. N. The CHARMM−Turbomole Interface for Efficient and Accurate QM/MM Molecular Dynamics, Free Energies, and Excited State Properties. J. Comput. Chem. 2014, 35 (28), 2076−2086. (39) Hammond, G. S. A Correlation of Reaction Rates. J. Am. Chem. Soc. 1955, 77, 334−338. (40) Casida, M. E.; Huix-Rotllant, M. Progress in Time-Dependent Density-Functional Theory. Annu. Rev. Phys. Chem. 2012, 63, 287− 323. (41) Domcke, W.; Sobolewski, A. L. Computational Studies of the Photophysics of Hydrogen-Bonded Molecular Systems. J. Phys. Chem. A 2007, 111 (46), 11725−11735. (42) Domcke, W.; Sobolewski, A. L. Conical Intersection: Theory, Computations and Experiment. In Advanced Series in Physical I
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Linear Energy Relationships in Ground State Proton Transfer and Excited State Proton-Coupled Electron Transfer Ana P. Gamiz-Hernandez,† Artiom Magomedov,† Gerhard Hummer,‡ and Ville R. I. Kaila*,† †
Department Chemie, Technische Universität München (TUM) Lichtenbergstraße 4, D-85747 Garching, Germany Department of Theoretical Biophysics, Max Planck Institute of Biophysics, Max-von-Laue-Straße 3, 60438 Frankfurt am Main, Germany
‡
S Supporting Information *
ABSTRACT: Proton-coupled electron transfer (PCET) processes are elementary chemical reactions involved in a broad range of radical and redox reactions. Elucidating fundamental PCET reaction mechanisms are thus of central importance for chemical and biochemical research. Here we use quantum chemical density functional theory (DFT), time-dependent density functional theory (TDDFT), and the algebraic diagrammatic-construction through second-order (ADC(2)) to study the mechanism, thermodynamic driving force effects, and reaction barriers of both ground state proton transfer (pT) and photoinduced proton-coupled electron transfer (PCET) between nitrosylated phenyl-phenol compounds and hydrogen-bonded t-butylamine as an external base. We show that the obtained reaction barriers for the ground state pT reactions depend linearly on the thermodynamic driving force, with a Brønsted slope of 1 or 0. Photoexcitation leads to a PCET reaction, for which we find that the excited state reaction barrier depends on the thermodynamic driving force with a Brønsted slope of 1/2. To support the mechanistic picture arising from the static potential energy surfaces, we perform additional molecular dynamics simulations on the excited state energy surface, in which we observe a spontaneous PCET between the donor and the acceptor groups. Our findings suggest that a Brønsted analysis may distinguish the ground state pT and excited state PCET processes.
1. INTRODUCTION Proton-coupled electron transfer (PCET) is the stepwise or concerted transfer of two elementary particles, an electron (e−) and a proton (H+).1−6 PCET is involved in many fundamental chemical and biological processes. In biological energy transduction, it forms key catalytic steps in cell respiration and photosynthesis;7,8 in organic chemistry, it is the basic mechanism of many radical reactions.1−6 Understanding the fundamental principles of PCET is also of particular importance for designing new biomimetic energy technology, such as water-oxidizing molecular catalysts.9,10 Recently, Westlake et al.11 studied photoinduced PCET between p-nitrophenyl-phenol and t-butylamine in 1,2dichloroethane solvent using ultrafast time-resolved pump− probe spectroscopy. The photoexcitation was shown to lead to an instantaneous intramolecular charge transfer (ICT) in pnitrophenyl-phenol followed by a picosecond proton transfer (pT) to the base. Moreover, intersystem crossing to an excited triplet state was suggested to result in a concerted PCET processes between the phenol and the base. Ko et al.12 studied p-nitrophenyl-phenol/t-methylamine using TDDFT and ab initio calculations and suggested that the experimentally observed states correspond to the excited S1 and S2 states, with ππ* and nπ* characters, respectively. They further found that while the ππ* potential energy surface has two minima © XXXX American Chemical Society
corresponding to the protonated donor and acceptor groups, separated by a low barrier, only a single energy minimum, corresponding to the protonated donor group, was identified on the nπ* surface. Inspired by these findings and the interesting properties of the system as a general chemical model system for PCET,11,13 we employ here the p-nitrophenyl-phenol/t-butylamine dimer, and chemically modified versions thereof (Figure 1), to study ground and excited state reaction barriers and transfer mechanisms using electronic structure theory. We exploit the effect of chemical substitutions to explore reaction mechanisms in a way amenable to experiment.14,15 In previous studies of the simple model system of hydrogenbonded water-wires connecting proton donating and accepting groups, we found that the reaction barrier for a proton transfer (pT) process responds linearly to perturbations in the thermodynamic driving force. More specifically, we observed Brønsted slopes of 0 and 1 when the proton accepting or Special Issue: Photoinduced Proton Transfer in Chemistry and Biology Symposium Received: August 30, 2014 Revised: December 6, 2014
A
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processes, we provide a physical rationale for these distinct differences between pT and PCET.
2. MODELS AND METHODS The molecular structure of p-nitrophenyl-phenol hydrogen bonded to t-butylamine was optimized using Becke’s three parameter functional, B3LYP18,19 and the Karlsruhe triple-basis set extended with two polarization functions, def2-TZVPP.20 Reaction profiles for the ground state proton transfer process were obtained by constrained ground state optimizations, in which the phenolic proton was stepwise transferred to tbutylamine. The nonadiabatic reaction profile for the excited state was obtained by vertical excitations from the ground state surface, using linear-response time-dependent density functional theory (TDDFT)21 at the B3LYP/def2-TZVPP level of theory. The respective structures along the proton transfer coordinates as well as the dihedral bond between the phenyl groups were also relaxed on the excited state surface at the BHLYP19/def2-SVP level of theory, that is, the half-and-half functional with the exact Hartree−Fock exchange increased to 50% due to its suggested better performance in treating charge transfer states at the TDDFT level.22,23 Solvation effects were studied using the COSMO model24 with a dielectric constant set to 10.42, corresponding to the dielectric screening of 1,2dichloroethane (DCE).25 The thermodynamic driving force was increased by stepwise nitrosylation of the phenyl ring (Figure 1), followed by the same optimization procedure. In addition to BHLYP calculations,19,22,23 TDDFT charge transfer problems were also studied by employing the range-corrected functional CAM-B3LYP,26 and the algebraic diagrammatic construction through second order method, ADC(2),27,28 with def2-TZVPP basis sets. We also computed ground and excited state electrostatic potential (ESP) charges and charge density differences to analyze charge redistribution effects. We did not observe triplet or other instabilities29−31 in our benchmarking calculations of the model system, suggesting that the electronic ground state has a proper singlet reference state, in agreement with the experimental data.11 To study the dynamics of the proton transfer process, we performed first-principles molecular dynamics at the B3LYP/def2-SVP level18,32,33 on the ground state and first excited state energy surfaces using an integration step of 1 fs, and initial velocities obtained from a random Maxwell−Boltzmann distribution with T = 298.15 K. The firstprinciples molecular dynamics simulations on the isolated systems were performed in the gas-phase. To investigate explicit solvent effects, we also performed first-principles molecular dynamics simulation in the ground state and first excited state of the p-nitrophenyl-phenol/t-butylamine with six DCE solvent molecules explicitly considered using DFT cluster calculations and hybrid QM/MM simulations at the B3LYP/ def2-SVP level. Starting structures were obtained from a 1 ns equilibrated classical MD simulation of the system at T = 300 K with N = 500 DCE molecules using a simulation box with dimensions 40 × 40 × 40 Å. p-Nitrophenyl-phenol/tbutylamine was fixed in its optimized ground state geometry during the classical equilibration. Interactions with the DCE solvent were modeled using electrostatic potential (ESP) charges determined at the B3LYP/def2-TZVP level of theory and Lennard-Jones parameters obtained from the CHARMM36 force field.34 Parameters for DCE were also obtained from the CHARMM36 parameters for 1,1-dichloroethane.35 The calculations were performed using TURBOMOLE versions 6.3− 6.6,36 and Q-Chem v4.1 for the CAM-B3LYP calculations,37
Figure 1. Hydrogen-bonded nitrophenyl-phenol/t-butylamine dimer models (M0−M5) used for studying proton transfer in the ground and excited states: (A) phenyl-phenol (M0), (B) 4-nitrophenyl-phenol (M1), (C) 3,5-dinitrophenyl-phenol (M2), (D) 2,4,6-trinitrophenylphenol (M3), (E) 2,3,4,5,6-pentanitrophenyl-phenol (M5). The molecule shown in B (M1) corresponds to the system studied experimentally by Westlake et al.11
donating groups, respectively, were chemically modified.16 In a tyrosine/tyrosyl radical dimer of the enzyme ribonucleotide reductase (RNR), we further showed that the barrier for a direct PCET process without mediating water responds to changes in the thermodynamic driving force with a Brønsted slope of 1/2.17 We show here that both effects occur within the pnitrophenyl-phenol/t-butylamine dimer; on the ground state potential energy surface, we observe a pT process, with ideal Brønsted slopes of 0 and 1, whereas photoexcitation leads to PCET processes, characterized by a perfectly mixed Brønsted slope of 1/2. By analyzing electronic structure changes in these B
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Figure 2. Energetics of the pT and PCET reactions (in eV) between nitro-substituted phenyl-phenol and t-butylamine as a function of the proton transfer reaction coordinate (in Å), r1(O−H)−r2(N−H) on the electronic ground state (A, B), and nonadiabatic excited state potential energy surfaces (C,D) obtained at the (A) B3LYP, (B) MP2, (C) TDDFT/B3LYP, (D) ADC(2) levels of theory with def2-TZVPP basis sets and ε = 10.42. Color-coding: phenyl-phenol (red), 4-nitrophenyl-phenol (black), 3,5-dinitrophenyl-phenol (yellow), 2,4,6-trinitrophenyl-phenol (green), 2,3,4,5,6pentanitrophenyl-phenol (blue).
and the hybrid QM/MM simulations were performed using the CHARMM-TURBOMOLE interface.38
3. RESULTS AND DISCUSSION 3.1. Energetics and Reactions Barriers for Proton Transfer in the Electronic Ground and Excited States. Potential energy surfaces for the ground state (S0) and first excited state (S1) pT between the nitro-substituted phenylphenol compounds and t-butylamine are shown in Figure 2. The ground state pT process is endergonic by 0.1−0.5 eV (2− 12 kcal mol−1) at the B3LYP level of theory, with reaction barriers of 0.4−0.7 eV (9−16 kcal mol−1), which agree well with the respective reaction energetics and barriers obtained at the MP2/def2-TZVPP level (Figure 2B). Vertical photoexcitation to the nonadiabatic S1 potential energy surfaces that would be expected to arise upon instantaneous photoexcitation prior to nuclear rearrangement, leads to exergonic proton transfer reactions by −0.2 to −0.6 eV (−5 to −14 kcal mol−1) in all systems, with lower reaction barriers of 0.05−0.3 eV (1−7 kcal mol−1; Figure 2C). Relaxation of the pnitrophenyl-phenol/t-butlyamine structure on the excited state surfaces further reduces the reaction barriers to 0.011 eV at BHLYP/def2-TZVP level of theory (Figure 3). For the singly substituted nitro-phenyl system, our driving force and
Figure 3. Energetics of the PCET reactions (in eV) between 4nitrophenyl-phenol and t-butylamine as a function of the proton transfer reaction coordinate (in Å) on the relaxed excited state BHLYP/def2-TZVPP/ε = 10.42 surface, showing a small pT barrier of 0.011 eV.
nonadiabatic reaction barrier are thus qualitatively similar to the values obtained by Ko et al.12 for their adiabatic S1 profile on C
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Figure 4. (A) Barrier of proton transfer between nitro-substituted phenyl-phenol and t-butylamine (in eV) in the ground state (A) and excited state (B) as a function of the thermodynamic driving force (in eV) obtained using B3LYP (blue squares), BHLYP (open black circles), CAM-B3LYP (orange triangle), MP2/ADC(2) (closed red circles) with def2-TZVPP basis sets and ε =10.42. Barriers for the relaxed excited state (ad BHLYP) are shown as blue open squares. The barrier for the ground state pT process depends linearly on the thermodynamic driving force with a Brønsted slope of α = 1 or 0, for the pT from D → A and A → D, respectively, with chemically modified D groups. In contrast, the Brønsted slope changes to α = 1/ 2 in the electronic excited state. (C) Physical interpretation of Brønsted slopes. Top: chemical modification of D in the electronic ground state (GS) perturbs only its own energy level, leaving the energy levels of the transition state (TS) and A unperturbed. Below: In the electronic excited state (ES), the energy levels of both D and TS are perturbed as a result of chemical modification on D.
driving force is changed over a range of 0.8 eV (18 kcal mol−1). For chemical substitutions on the phenyl-phenol moiety, the pT barrier from the phenyl group to t-butylamine responds with a linear slope of 1 to changes in the thermodynamic driving force. In contrast, the pT barrier from the t-butylamine to the phenyl-group is insensitive to modifications of the distal phenyl group, suggesting that chemical modifications stabilize or destabilize only the ground state but do not significantly affect the energy of the transition state (Figure 4C). This mechanism is consistent with our earlier observations on linear energy relationships obtained for pT in short water chains.16 The barrier for the nonadiabatic excited state pT processes also depends linearly on modifications of the thermodynamic driving force over a range of 1.2 eV (28 kcal mol−1), but in contrast to the ground state pT process, we observe a slope of 1/2 for the excited state PCET process. A Brønsted slope of 1/ 2 was previously observed for a direct PCET process in the stacked tyrosine dimer of ribonucleotide reductase (RNR).17 This picture would be expected to arise from a situation where chemical modifications of the electron-accepting group in the S1 state perturb the energy of both the proton donor and the transition state (Figure 4C). When the acceptor energy levels (the amine side) are aligned, only the proton donor level (phenol) moves in the electronic ground state, while both the donor level and transition states are perturbed in the electronic excited state (Supporting Information, Figure 2). To explore possible problems associated with charge-transfer states in TDDFT, we performed additional calculations using the BHLYP functional, in which the exact Hartree−Fock
the similar p-nitrophenyl-phenol/t-methylamine system, showing two minima and a low pT barrier. Consistent with the nonadiabatic S1 surface at the B3LYP level, we obtain similar nonadiabatic S1 potential energy surfaces at the CAM-B3LYP level (SI Figure 1) and by using ADC(2)/def2-TZVPP (Figure 1D), indicating that the profiles along the calculated proton reaction coordinates are robust with respect to the electronic structure methodology. The reaction barriers obtained at the BHLYP level are somewhat larger, and are also shown in Supporting Information, Figure 1. We observe that the dielectric medium, modeled here using the conductor-like screening model (COSMO), has a significant effect in stabilizing the product state of the pT processes; the dielectric screening by 1,2-dichloroethane, which corresponds to ε = 10.42,25 increases the exergonicity of the reactions by 0.5−0.6 eV (12−14 kcal mol−1). The obtained reaction profiles suggest that the transition state moves toward the acceptor side with increasing endergonicity in the electronic ground state, while in the electronic excited state, the transition state moves closer to the proton donating phenol group with increasing exergonicity, consistent with Hammond’s postulate.39 This behavior is likely to be linked to the increase in the equilibrium O−H bond length and decrease in the H···N hydrogen bond length with increasing acidity of the substituted phenyl rings. 3.2. Linear Energy Relationships. Figure 4 shows the reaction barriers as a function of the chemical driving force for the electronic ground state and the nonadiabatic excited state processes. At the electronic ground state, we obtain a linear dependence on the reaction barrier when the thermodynamic D
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Figure 6. Electron density difference between the ground and excited states when the proton is associated with 4-nitrophenyl-phenol (system M1, top), t-butylamine (bottom), and at the transition state (middle). Electron density differences are shown with an isocontour surface of ±0.002 e/Å3. The red and blue isocontour surfaces indicate increased and decreased electron density, respectively, in the excited state relative to the ground state. The electron density difference distributions suggest that the photoexcitation leads to a ππ* transitions, with an internal charge transfer between the proton donating phenol and the nitrosylated distal phenyl groups. In addition, there is a partial charge transfer toward the amine nitrogen from the proton donating phenol side, resembling an electron driven proton transfer process (see text).41 VMD was used for visualization.48
Figure 5. Total ESP charge of the proton donating phenol in the ground state (top), and electronic excited state (bottom). The photoexcitation leads to an instantaneous oxidation of the proton donating phenol, which increases the total ESP charge in the excited state. The pT polarizes the phenol group 0.3−0.4e more negative. Color-coding: phenyl-phenol (red), 4-nitrophenyl-phenol (black), 3,5dinitrophenyl-phenol (yellow), 2,4,6-trinitrophenyl-phenol (green), 2,3,4,5,6-pentanitrophenyl-phenol (blue).
exchange is increased to 50%,19 and by using the rangeseparated functional CAM-B3LYP,26 which employs 19% shortrange Hartree−Fock exchange and 65% long-range Hartree− Fock exchange to more closely follow the expected 1/r distance dependence for the charge transfer state. We also calculated the profiles at the correlated ab initio level using the algebraic diagrammatic construction through second-order ADC(2). We find the qualitative behavior obtained at the B3LYP level of theory to be unchanged with the CAM-B3LYP and BHLYPfunctionals and at the MP2/ADC(2) level of theory, with Brønsted slopes of 1 and 0 in the ground-state, and 1/2 in the excited state (Figure 4). These results suggest that the change in Brønsted slopes is unlikely to arise from DFT charge transfer problems. We find that the adiabatic potential energy surface for M1 (Figure 3) also supports the Brønsted slope of 1/2, applying in the limit where nuclear relaxation is fast compared to pT. Nevertheless, due to the limited accuracy of TDDFT, it is not currently possible to unambiguously confirm this kinetic behavior, which would most likely require simulations of the full dynamics and excited state optimization at correlated ab initio levels. 3.3. Physical Rationale for the Brønsted Slopes. To gain insight into the origin of the observed differences in Brønsted slopes, we studied density differences in the electronic structure that arise upon the photoexcitation and analyzed the electrostatic potential (ESP) charges in the ground and excited
states. The data in Figures 5 and 6 indicate that the photoexcitation indeed couples to a charge transfer of 0.5e from the proton-donating phenol-moiety to the nitrosylated phenyl ring, facilitating the proton transfer by decreasing the electrostatic attraction between the proton and the phenol ring. We find that the photoexcited S1 state has a ππ* character, consistent with results recently obtained by Ko et al.12 The charge seems to be instantaneously transferred upon the photoexcitation in the singly substituted p-nitrophenyl-phenol system, leading to a large increase in the dipole moment. This suggests that the pT process is likely to take place after the photoinduced electron transfer process, consistent with the picture suggested by Westlake et al.11 Interestingly, in both the ground and excited states, the pT polarizes the donating groups by 0.4e, whereas the total effective charge of the t-butylamine group remains nearly unchanged in both the ground and excited states. Nevertheless, the O−H bond pointing toward the nitrogen of the external base is strongly polarized in the electronic excited state (Figure 6), with excess electron density transferred from the proton donating side toward the proton accepting side. We also find that the charge transfer to the amine group becomes stronger with increasing thermodynamic driving force (Supporting Information, Figure 3), for which the density differences around the nitrogen, proton, and oxygen involved in the transfer process become more polarized. E
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Figure 7. Two-dimensional relaxed excited state potential energy surface (PES, in eV) for the proton transfer and dihedral twist of the phenyl planes on the TDDFT/B3LYP/def2-TZVPP (left) and TDDFT/BHLYP/def2-TZVPP (right) levels of theory. Bottom panels: projection of the dihedral twist coordinate. Relaxed excited state structures were obtained on the TDDFT/BHLYP/def2-SVP level of theory. Both surfaces suggest that the ±90° twisted conformation is located in an energy minimum, together with minima predicted near ±30° at the BHLYP level. A 4 ps excited state first-principle molecular dynamics trajectory is projected on the B3LYP surface, suggesting that a dihedral twist couples to the pT process. The dihedral angles below −90° (see Figure 8) were projected to the positive side (0−90°) for visualization of the complete trajectory.
the BHLYP level further suggest that the potential energy landscape for the dihedral rotation is rather flat, with local minima also observed near ±30°, close to the ground state energy minimum. To further probe the transfer mechanism arising from these static potential energy surfaces, we performed first-principle molecular dynamics simulations on the first excited state. A resulting trajectory, projected on the B3LYP surface and shown in Figure 8A, suggest that the pT process is likely to be preceded by a dihedral rotation, consistent with the PES. In this trajectory, the dihedral bond rotation begins at about 0.1 ps, whereas the first proton transfer to the base follows after 0.2 ps. Our MD simulations further suggest that several pT attempts occur in the excited state between 0.2 and 1.5 ps, after which the proton is stabilized on the amine, comparable to the experimentally observed timescales.11 To explicitly study solvent effects, we performed additional first-principles molecular dynamics simulations on a microsolvated p-nitrophenyl-phenol/t-butylamine using both QM cluster calculations and hybrid QM/MM simulations. In both simulation setups, shown in Figure 8B, we observe a qualitatively similar PCET process as for the isolated systems. However, the dihedral rotation of the phenol rings seems to be somewhat delayed relative to the isolated system, due to coupled solvent motions. Moreover, in contrast to the isolated system with a stepwise dihedral rotation and pT process, the condensed phase models suggest a more concerted reaction mechanism. For the more nitrosylated systems, we obtain a similar qualitative picture with the dihedral coupled to the proton transfer, but observe more rapid proton transfer to the base (Supporting Information, Figure 4). Our preliminary nonadiabatic surface hopping simulations suggest that the ground and excited state become more rapidly degenerate with increasing thermodynamic driving force, which result in conical
Interestingly, the nonsubstituted phenyl system (M0) is likely to have a lower electron affinity relative to the nitrosylated phenyl. Indeed, our calculations suggest that the approaching proton makes the amine group the dominant electron acceptor instead of the distal phenyl group, suggesting that the pT is coupled to an intermolecular electron transfer (Supporting Information, Figure 3). Such proton-driven electron transfer processes play a central role in the coupled proton and electron transfer process in the respiratory enzyme cytochrome c oxidase.7 The polarization of the N−H bond in all chemically modified phenyl-phenol systems studied here, may result in the perturbed transition state energies for the excited state pT process, in contrast to the ground state process where chemical modifications affect only the relative energy of the proton donor. 3.4. Coupling of Rotational Degrees of Freedom to the Excited State PCET Process. To study the coupling of the pT reaction with other degrees of freedom, we performed a two-dimensional excited state potential energy surface optimization of the pT coordinate as a function of the dihedral angle between the phenyl planes. Figure 7 shows the relaxed excited state 2D surface of the pT process as a function of the dihedral angle obtained using B3LYP and BHLYP. Both computational levels suggest that the deprotonated phenol has a local energy minimum at the ±90° twisted conformation, suggesting that a dihedral rotation of the phenyl-phenol bond might be involved in the excited state pT process, as also suggested by Hammes-Schiffer.13 Ko et al.12 observe from a rigid dihedral scan a minimum located at 94° using a state specific polarizable continuum model, whereas the linear response-type polarizable continuum model predicted minima at 15 and 22°, suggesting that the dihedral coordinate might be sensitive to the description of the solvent. Our calculations at F
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Figure 8. First-principles molecular dynamics simulations and hybrid QM/MM molecular dynamics simulation of the isolated 4-nitrophenyl-phenol/ t-butyl amine system (panel A) and the 4-nitrophenyl-phenol/t-butyl amine solvated with six DCE solvent molecules in the QM region (panel B). The QM/MM systems were additionally solvated with N = 494 classical DCE molecules. The ground state simulations are shown in black for the isolated system and QM cluster models, and in green for the QM/MM simulations. The excited state simulations are shown in red for the isolated system and the QM cluster models, and in blue for the QM/MM simulations. For the isolated system, shown in panel A, a dihedral twist starts at about 0.1 ps and couples to the proton transfer process at about 0.2 ps. Several pT attempts occur in the excited state between 0.2 and 1.5 ps, after which the proton is stabilized on the amine. For the condensed phase simulations, shown in panel B, the pT starts at about 0.1 ps and couples to the dihedral twist nearly concertedly with the pT process. The condensed phase simulations suggest that the DCE solvent molecules rearrange around the phenol rings, and slow down the dihedral rotation, indicating that solvent motion might be coupled to the PCET process. The MD trajectory for the M3 system is shown in Supporting Information, Figure 4.
intersection and relaxation pathways back to the ground state, but which are usually poorly dealt with in TDDFT.40 3.5. Connection to Electron Driven Proton Transfer in Hydrogen Bonded Systems. A mechanistic picture that has arisen from studies of several hydrogen-bonded systems41−46 suggest that photoexcitations generally lead to an excited state hydrogen atom transfer process, in which the conical intersection between the ground and excited state becomes easily accessible, and results in an ultrafast photophysical relaxation pathway to the electronic ground state. Such electron-driven proton transfer (EDPT) processes are likely to play an important role in, for example, the photostability of organic and biological molecules.47 The excited state proton transfer process in phenyl-phenol systems are clearly also driven by a photoinduced electron transfer process, but in contrast to many of the previously studied hydrogen bonded systems, the main driving force is likely to arise from the electron transfer to the distal nitrosylated phenyl group that
functions as an electron sink. Nevertheless, as indicated by the charge density differences between the ground and excited states (Figure 6, Supporting Information, Movie 1), the pT process also seems to be coupled to a partial electron redistribution between the donor and acceptor groups, similar to that described for excited state EDPT processes. Our findings support the recently suggested ππ*-like character of the S1 state with charge transfer character both between the phenyl rings and between the proton donating ring and the amine. This effect becomes more prominent with increasing thermodynamic driving force, which suggest that this possible local partial EDPT process, may lead to the observed linear energy dependence of the barrier on the thermodynamic driving force with a slope of 1/2 that was previously suggested to be characteristic for coupled proton−electron transfer processes.17 In contrast, a pure pT process from a photooxidized protonated phenol radical (Ph−OH•/+) to the amine G
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the Leibniz Supercomputing Centre, LRZ (http://www.lrz.de/) are acknowledged for computer time.
would be expected to result in Brønsted slopes of 1 or 0, similar to those observed for the ground state pT process.16
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4. CONCLUSIONS We show here using density functional theory (DFT), linearresponse time dependent density functional theory (TDDFT)21 and correlated ab inito (ADC(2)) calculations,27,28 that a kinetic Brønsted analysis may help distinguish an excited state proton-coupled transfer (PCET) process from a ground state proton transfer (pT). Using the experimentally studied hydrogen-bonded p-nitrophenyl-phenol/t-butylamine dimer, and chemically modified versions thereof, we show that changes in the thermodynamic driving force by chemical substitutions, perturb the energy level of the proton donating group and leave the energy of the transition state unchanged, which results in linear energy relations with Brønsted slopes of 1 or 0. Such behavior is expected to arise if chemical substations affect the energy level of the proton donor/acceptor group but not the transition state. In contrast, for the excited state PCET process, the transition state energy is also perturbed by electronic polarization of the chemical bond between the proton donor and acceptor, which is a likely factor in the shift to a linear energy relation with a Brønsted slope of 1/2. Lowering of the kinetic barrier for PCET results from a diminished electrostatic attraction between the proton and the proton-donating group by photoinduced charge redistribution. The ground and excited state proton transfer process between nitro-substituted phenyl-phenol and t-butylamine represents an attractive model system for elucidating underlying energetics and reaction rate theories for general proton transfer and proton-coupled electron transfer processes. An interesting complication is that relaxation of the nuclear degrees of freedom on the excited-state surface can significantly lower the barrier for proton transfer. Since the barrier-lowering dihedral rotation of the phenyl planes found here would likely displace solvent molecules, the overall transfer process should thus also become coupled to solvent motions, as indicated by our explicit condensed phase simulations. Despite these complicating factors, the present findings on linear energy relationships may provide an experimental way to distinguish proton transfer from PCET processes in complex chemical and biological systems.
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ASSOCIATED CONTENT
* Supporting Information S
Additional supporting figures. This material is available free of charge via the Internet at http://pubs.acs.org.
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REFERENCES
AUTHOR INFORMATION
Corresponding Author
*E-mail: [email protected]. Tel.: (+) 49 89 289 13612. Fax: (+) 49 89 289 13622. Notes
The authors declare no competing financial interest.
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ACKNOWLEDGMENTS V.R.I.K. acknowledges Prof. Wolfgang Domcke for insightful discussion. This research was supported by the Jane and Aatos Erkko Foundation (V.R.I.K.) and the Max Planck Society (G.H.). The Biowulf cluster at NIH (http://biowulf.nih.gov/), the CSC - IT Center for Science Ltd. (http://www.csc.fi/), and H
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