1
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Richardson JO. Nonadiabatic Tunneling in Chemical Reactions. J Phys Chem Lett 2024; 15:7387-7397. [PMID: 38995660 DOI: 10.1021/acs.jpclett.4c01098] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 07/13/2024]
Abstract
Quantum tunneling can have a dramatic effect on chemical reaction rates. In nonadiabatic reactions such as electron transfers or spin crossovers, nuclear tunneling effects can be even stronger than for adiabatic proton transfers. Ring-polymer instanton theory enables molecular simulations of tunneling in full dimensionality and has been shown to be far more reliable than commonly used separable approximations. First-principles instanton calculations predict significant nonadiabatic tunneling of heavy atoms even at room temperature and give excellent agreement with experimental measurements for the intersystem crossing of two nitrenes in cryogenic matrix isolation, the spin-forbidden relaxation of photoexcited thiophosgene in the gas phase, and singlet oxygen deactivation in water at ambient conditions. Finally, an outlook of further theoretical developments is discussed.
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Affiliation(s)
- Jeremy O Richardson
- Department of Chemistry and Applied Biosciences, ETH Zurich, 8093 Zurich, Switzerland
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2
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Fay TP. Extending non-adiabatic rate theory to strong electronic couplings in the Marcus inverted regime. J Chem Phys 2024; 161:014101. [PMID: 38949594 DOI: 10.1063/5.0218653] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/13/2024] [Accepted: 06/12/2024] [Indexed: 07/02/2024] Open
Abstract
Electron transfer reactions play an essential role in many chemical and biological processes. Fermi's golden rule (GR), which assumes that the coupling between electronic states is small, has formed the foundation of electron transfer rate theory; however, in short range electron/energy transfer reactions, this coupling can become very large, and, therefore, Fermi's GR fails to make even qualitatively accurate rate predictions. In this paper, I present a simple modified GR theory to describe electron transfer in the Marcus inverted regime at arbitrarily large electronic coupling strengths. This theory is based on an optimal global rotation of the diabatic states, which makes it compatible with existing methods for calculating GR rates that can account for nuclear quantum effects with anharmonic potentials. Furthermore, the optimal GR (OGR) theory can also be combined with analytic theories for non-adiabatic rates, such as Marcus theory and Marcus-Levich-Jortner theory, offering clear physical insights into strong electronic coupling effects in non-adiabatic processes. OGR theory is also tested on a large set of spin-boson models and an anharmonic model against exact quantum dynamics calculations, where it performs well, correctly predicting rate turnover at large coupling strengths. Finally, an example application to a boron-dipyrromethane-anthracene photosensitizer reveals that strong coupling effects inhibit excited state charge recombination in this system, reducing the rate of this process by a factor of 4. Overall, OGR theory offers a new approach to calculating electron transfer rates at strong couplings, offering new physical insights into a range of non-adiabatic processes.
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Affiliation(s)
- Thomas P Fay
- Institut de Chimie Radicalaire, Aix-Marseille Université, Campus de Saint-Jérôme, Av. Esc. Normandie Niemen, 13397 Marseille, France
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3
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Lawrence JE, Mannouch JR, Richardson JO. A size-consistent multi-state mapping approach to surface hopping. J Chem Phys 2024; 160:244112. [PMID: 38940540 DOI: 10.1063/5.0208575] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/15/2024] [Accepted: 06/05/2024] [Indexed: 06/29/2024] Open
Abstract
We develop a multi-state generalization of the recently proposed mapping approach to surface hopping (MASH) for the simulation of electronically nonadiabatic dynamics. This new approach extends the original MASH method to be able to treat systems with more than two electronic states. It differs from previous approaches in that it is size consistent and rigorously recovers the original two-state MASH in the appropriate limits. We demonstrate the accuracy of the method by applying it to a series of model systems for which exact benchmark results are available, and we find that the method is well suited to the simulation of photochemical relaxation processes.
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Affiliation(s)
- Joseph E Lawrence
- Department of Chemistry and Applied Biosciences, ETH Zurich, 8093 Zurich, Switzerland
- Simons Center for Computational Physical Chemistry, New York University, New York, New York 10003, USA
- Department of Chemistry, New York University, New York, New York 10003, USA
| | - Jonathan R Mannouch
- Hamburg Center for Ultrafast Imaging, Universität Hamburg and the Max Planck Institute for the Structure and Dynamics of Matter, Luruper Chaussee 149, 22761 Hamburg, Germany
| | - Jeremy O Richardson
- Department of Chemistry and Applied Biosciences, ETH Zurich, 8093 Zurich, Switzerland
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4
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Ansari IM, Heller ER, Trenins G, Richardson JO. Heavy-atom tunnelling in singlet oxygen deactivation predicted by instanton theory with branch-point singularities. Nat Commun 2024; 15:4335. [PMID: 38773078 DOI: 10.1038/s41467-024-48463-2] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/13/2023] [Accepted: 04/29/2024] [Indexed: 05/23/2024] Open
Abstract
The reactive singlet state of oxygen (O2) can decay to the triplet ground state nonradiatively in the presence of a solvent. There is a controversy about whether tunnelling is involved in this nonadiabatic spin-crossover process. Semiclassical instanton theory provides a reliable and practical computational method for elucidating the reaction mechanism and can account for nuclear quantum effects such as zero-point energy and multidimensional tunnelling. However, the previously developed instanton theory is not directly applicable to this system because of a branch-point singularity which appears in the flux correlation function. Here we derive a new instanton theory for cases dominated by the singularity, leading to a new picture of tunnelling in nonadiabatic processes. Together with multireference electronic-structure theory, this provides a rigorous framework based on first principles that we apply to calculate the decay rate of singlet oxygen in water. The results indicate a new reaction mechanism that is 27 orders of magnitude faster at room temperature than the classical process through the minimum-energy crossing point. We find significant heavy-atom tunnelling contributions as well as a large temperature-dependent H2O/D2O kinetic isotope effect of approximately 20, in excellent agreement with experiment.
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Affiliation(s)
- Imaad M Ansari
- Department of Chemistry and Applied Biosciences, ETH Zürich, 8093, Zürich, Switzerland
| | - Eric R Heller
- Department of Chemistry and Applied Biosciences, ETH Zürich, 8093, Zürich, Switzerland
- Department of Chemistry, University of California, Berkeley, 94720, Berkeley, USA
| | - George Trenins
- Department of Chemistry and Applied Biosciences, ETH Zürich, 8093, Zürich, Switzerland
- MPI for the Structure and Dynamics of Matter, Luruper Chaussee 149, 22761, Hamburg, Germany
| | - Jeremy O Richardson
- Department of Chemistry and Applied Biosciences, ETH Zürich, 8093, Zürich, Switzerland.
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5
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Fay TP, Limmer DT. Unraveling the mechanisms of triplet state formation in a heavy-atom free photosensitizer. Chem Sci 2024; 15:6726-6737. [PMID: 38725521 PMCID: PMC11077524 DOI: 10.1039/d4sc01369g] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/27/2024] [Accepted: 03/29/2024] [Indexed: 05/12/2024] Open
Abstract
Triplet excited state generation plays a pivotal role in photosensitizers, however the reliance on transition metals and heavy atoms can limit the utility of these systems. In this study, we demonstrate that an interplay of competing quantum effects controls the high triplet quantum yield in a prototypical boron dipyrromethene-anthracene (BD-An) donor-acceptor dyad photosensitizer, which is only captured by an accurate treatment of both inner and outer sphere reorganization energies. Our ab initio-derived model provides excellent agreement with experimentally measured spectra, triplet yields and excited state kinetic data, including the triplet lifetime. We find that rapid triplet state formation occurs primarily via high-energy triplet states through both spin-orbit coupled charge transfer and El-Sayed's rule breaking intersystem crossing, rather than direct spin-orbit coupled charge transfer to the lowest lying triplet state. Our calculations also reveal that competing effects of nuclear tunneling, electronic state recrossing, and electronic polarizability dictate the rate of non-productive ground state recombination. This study sheds light on the quantum effects driving efficient triplet formation in the BD-An system, and offers a promising simulation methodology for diverse photochemical systems.
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Affiliation(s)
- Thomas P Fay
- Department of Chemistry, University of California Berkeley CA 94720 USA
| | - David T Limmer
- Department of Chemistry, University of California Berkeley CA 94720 USA
- Kavli Energy Nanoscience Institute Berkeley CA 94720 USA
- Chemical Science Division Lawrence Berkeley National Laboratory Berkeley CA 94720 USA
- Material Science Division Lawrence Berkeley National Laboratory Berkeley CA 94720 USA
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6
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Lawrence JE, Mannouch JR, Richardson JO. Recovering Marcus Theory Rates and Beyond without the Need for Decoherence Corrections: The Mapping Approach to Surface Hopping. J Phys Chem Lett 2024; 15:707-716. [PMID: 38214476 PMCID: PMC10823533 DOI: 10.1021/acs.jpclett.3c03197] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/14/2023] [Revised: 12/22/2023] [Accepted: 01/05/2024] [Indexed: 01/13/2024]
Abstract
It is well-known that fewest-switches surface hopping (FSSH) fails to correctly capture the quadratic scaling of rate constants with diabatic coupling in the weak-coupling limit, as expected from Fermi's golden rule and Marcus theory. To address this deficiency, the most widely used approach is to introduce a "decoherence correction", which removes the inconsistency between the wave function coefficients and the active state. Here we investigate the behavior of a new nonadiabatic trajectory method, called the mapping approach to surface hopping (MASH), on systems that exhibit an incoherent rate behavior. Unlike FSSH, MASH hops between active surfaces deterministically and can never have an inconsistency between the wave function coefficients and the active state. We show that MASH not only can describe rates for intermediate and strong diabatic coupling but also can accurately reproduce the results of Marcus theory in the golden-rule limit, without the need for a decoherence correction. MASH is therefore a significant improvement over FSSH in the simulation of nonadiabatic reactions.
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Affiliation(s)
- Joseph E. Lawrence
- Department
of Chemistry and Applied Biosciences, ETH
Zurich, 8093 Zurich, Switzerland
| | - Jonathan R. Mannouch
- Hamburg
Center for Ultrafast Imaging, Universität
Hamburg and Max Planck Institute for the Structure and Dynamics of
Matter, Luruper Chaussee 149, 22761 Hamburg, Germany
| | - Jeremy O. Richardson
- Department
of Chemistry and Applied Biosciences, ETH
Zurich, 8093 Zurich, Switzerland
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7
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Upadhyayula S, Pollak E. Uniform Semiclassical Instanton Rate Theory. J Phys Chem Lett 2023; 14:9892-9899. [PMID: 37906954 PMCID: PMC10641875 DOI: 10.1021/acs.jpclett.3c02779] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/06/2023] [Revised: 10/17/2023] [Accepted: 10/19/2023] [Indexed: 11/02/2023]
Abstract
The instanton expression for the thermal transmission probability through a one-dimensional barrier is derived by using the uniform semiclassical energy-dependent transmission coefficient of Kemble. The resulting theory does not diverge at the "crossover temperature" but changes smoothly. The temperature-dependent energy of the instanton is the same as the barrier height when ℏβω‡ = π and not 2π as in the "standard" instanton theory. The concept of a crossover temperature between tunneling and thermal activation, based on the divergence of the instanton rate, is obsolete. The theory is improved by assuring that at high energy when the energy-dependent transmission coefficient approaches unity the integrand decays exponentially as dictated by the Boltzmann factor and not as a Gaussian. This ensures that at sufficiently high temperatures the uniform theory reduces to the classical. Application to Eckart barriers demonstrates that the uniform theory provides a good estimate of the numerically exact result over the whole temperature range.
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Affiliation(s)
- Sameernandan Upadhyayula
- Chemical and Biological Physics
Department Weizmann Institute of Science, Rehovoth 76100, Israel
| | - Eli Pollak
- Chemical and Biological Physics
Department Weizmann Institute of Science, Rehovoth 76100, Israel
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8
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Mulvihill CR, Georgievskii Y, Klippenstein SJ. Quantum and anharmonic effects in non-adiabatic transition state theory. J Chem Phys 2023; 159:174104. [PMID: 37916591 DOI: 10.1063/5.0168612] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/19/2023] [Accepted: 09/25/2023] [Indexed: 11/03/2023] Open
Abstract
Quantitative descriptions of non-adiabatic transition rates at intermediate temperatures are challenging due to the simultaneous importance of quantum and anharmonic effects. In this paper, the interplay between quantum effects-for motion across or along the seam of crossing-and anharmonicity in the seam potential is considered within the weak coupling limit. The well-known expression for quantized 1-D motion across the seam (i.e., tunneling) in the linear terms approximation is derived in the thermal domain using the Lagrangian formalism, which is then applied to the case when tunneling is distributed along the seam of crossing (treating motion along the seam classically). For high-frequency quantum modes, a vibrationally adiabatic (VA) approach is developed that introduces to the non-adiabatic rate constant a factor associated with high-frequency wavefunction overlap; this approach treats the high-frequency motion along the seam quantum mechanically. To test these methodologies, the reaction N2O ↔ N2 + O(3P) was chosen. CCSD(T)-F12b/cc-pVTZ-F12 explorations of the 3A'-1A' seam of N2O revealed that seam anharmonicity has a strong effect on the rate constant (a factor of ∼20 at 2000 K). Several quantum effects were found to be significant at intermediate/lower temperatures, including the quantum N-N vibration that was coupled with seam anharmonicity using the VA approach. Finally, a 1-D approximation to non-adiabatic instanton theory is presented to estimate the validity limit of the linear terms model at low temperatures (∼250 K for N2O). We recommend that the assumptions built into many statistical theories for non-adiabatic reactions-harmonic behavior, classical motion, linear terms, and weak coupling-should be verified on a case-by-case basis.
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Affiliation(s)
- Clayton R Mulvihill
- Chemical Sciences and Engineering Division, Argonne National Laboratory, Lemont, Illinois 60439, USA
| | - Yuri Georgievskii
- Chemical Sciences and Engineering Division, Argonne National Laboratory, Lemont, Illinois 60439, USA
| | - Stephen J Klippenstein
- Chemical Sciences and Engineering Division, Argonne National Laboratory, Lemont, Illinois 60439, USA
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9
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Fang W, Heller ER, Richardson JO. Competing quantum effects in heavy-atom tunnelling through conical intersections. Chem Sci 2023; 14:10777-10785. [PMID: 37829019 PMCID: PMC10566476 DOI: 10.1039/d3sc03706a] [Citation(s) in RCA: 1] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/18/2023] [Accepted: 09/07/2023] [Indexed: 10/14/2023] Open
Abstract
Thermally activated chemical reactions are typically understood in terms of overcoming potential-energy barriers. However, standard rate theories break down in the presence of a conical intersection (CI) because these processes are inherently nonadiabatic, invalidating the Born-Oppenheimer approximation. Moreover, CIs give rise to intricate nuclear quantum effects such as tunnelling and the geometric phase, which are neglected by standard trajectory-based simulations and remain largely unexplored in complex molecular systems. We present new semiclassical transition-state theories based on an extension of golden-rule instanton theory to describe nonadiabatic tunnelling through CIs and thus provide an intuitive picture for the reaction mechanism. We apply the method in conjunction with first-principles electronic-structure calculations to the electron transfer in the bis(methylene)-adamantyl cation. Our study reveals a strong competition between heavy-atom tunnelling and geometric-phase effects.
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Affiliation(s)
- Wei Fang
- Department of Chemistry, Fudan University Shanghai 200438 P. R. China
- Department of Chemistry and Applied Biosciences, ETH Zürich 8093 Zürich Switzerland
| | - Eric R Heller
- Department of Chemistry and Applied Biosciences, ETH Zürich 8093 Zürich Switzerland
| | - Jeremy O Richardson
- Department of Chemistry and Applied Biosciences, ETH Zürich 8093 Zürich Switzerland
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10
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Rivlin T, Pollak E. Nonadiabatic Couplings Can Speed Up Quantum Tunneling Transition Path Times. J Phys Chem Lett 2022; 13:10558-10566. [PMID: 36342976 PMCID: PMC9677498 DOI: 10.1021/acs.jpclett.2c03008] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/02/2022] [Accepted: 11/02/2022] [Indexed: 06/16/2023]
Abstract
Quantum tunneling is known to play an important role in the dynamics of systems with nonadiabatic couplings. However, until recently, the time-domain properties of nonadiabatic scattering have been severely under-explored. Using numerically exact quantum methods, we study the impact that nonadiabatic couplings have on the time it takes to tunnel through a barrier. We find that the Wigner phase time is the appropriate measure to use when determining the tunneling flight time also when considering nonadiabatic systems. The central result of the present study is that in an avoided crossing system in one dimension, the nonadiabatic couplings speed up the tunneling event, relative to the adiabatic case in which all nonadiabatic coupling is ignored. This has implications for both the study of quantum tunneling times and for the field of nonadiabatic scattering and chemistry.
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11
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Anderson MC, Schile AJ, Limmer DT. Nonadiabatic transition paths from quantum jump trajectories. J Chem Phys 2022; 157:164105. [DOI: 10.1063/5.0102891] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
We present a means of studying rare reactive pathways in open quantum systems using transition path theory and ensembles of quantum jump trajectories. This approach allows for the elucidation of reactive paths for dissipative, nonadiabatic dynamics when the system is embedded in a Markovian environment. We detail the dominant pathways and rates of thermally activated processes and the relaxation pathways and photoyields following vertical excitation in a minimal model of a conical intersection. We find that the geometry of the conical intersection affects the electronic character of the transition state as defined through a generalization of a committor function for a thermal barrier crossing event. Similarly, the geometry changes the mechanism of relaxation following a vertical excitation. Relaxation in models resulting from small diabatic coupling proceeds through pathways dominated by pure dephasing, while those with large diabatic coupling proceed through pathways limited by dissipation. The perspective introduced here for the nonadiabatic dynamics of open quantum systems generalizes classical notions of reactive paths to fundamentally quantum mechanical processes.
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Affiliation(s)
- Michelle C. Anderson
- Department of Chemistry, University of California, Berkeley, California 94720, USA
| | - Addison J. Schile
- Department of Chemistry, University of California, Berkeley, California 94720, USA
| | - David T. Limmer
- Department of Chemistry, University of California, Berkeley, California 94720, USA
- Kavli Energy NanoSciences Institute, University of California, Berkeley, California 94720, USA
- Chemical Sciences Division, Lawrence Berkeley National Laboratory, Berkeley, California 94720, USA
- Materials Sciences Division, Lawrence Berkeley National Laboratory, Berkeley, California 94720, USA
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12
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Heller ER, Richardson JO. Heavy‐Atom Quantum Tunnelling in Spin Crossovers of Nitrenes**. Angew Chem Int Ed Engl 2022; 61:e202206314. [PMID: 35698730 PMCID: PMC9540336 DOI: 10.1002/anie.202206314] [Citation(s) in RCA: 7] [Impact Index Per Article: 3.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/03/2022] [Indexed: 01/01/2023]
Abstract
We simulate two recent matrix‐isolation experiments at cryogenic temperatures, in which a nitrene undergoes spin crossover from its triplet state to a singlet state via quantum tunnelling. We detail the failure of the commonly applied weak‐coupling method (based on a linear approximation of the potentials) in describing these deep‐tunnelling reactions. The more rigorous approach of semiclassical golden‐rule instanton theory in conjunction with double‐hybrid density‐functional theory and multireference perturbation theory does, however, provide rate constants and kinetic isotope effects in good agreement with experiment. In addition, these calculations locate the optimal tunnelling pathways, which provide a molecular picture of the reaction mechanism. The reactions involve substantial heavy‐atom quantum tunnelling of carbon, nitrogen and oxygen atoms, which unexpectedly even continues to play a role at room temperature.
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Affiliation(s)
- Eric R. Heller
- Laboratory of Physical Chemistry ETH Zürich 8093 Zürich Switzerland
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13
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Lawrence JE, Richardson JO. Improved microcanonical instanton theory. Faraday Discuss 2022; 238:204-235. [PMID: 35929848 DOI: 10.1039/d2fd00063f] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/21/2022]
Abstract
Canonical (thermal) instanton theory is now routinely applicable to complex gas-phase reactions and allows for the accurate description of tunnelling in highly non-separable systems. Microcanonical instanton theory is by contrast far less well established. Here, we demonstrate that the best established microcanonical theory [S. Chapman, B. C. Garrett and W. H. Miller, J. Chem. Phys., 1975, 63, 2710-2716], fails to accurately describe the deep-tunnelling regime for systems where the frequencies of the orthogonal modes change rapidly along the instanton path. By taking a first principles approach to the derivation of microcanonical instanton theory, we obtain an improved method, which accurately recovers the thermal instanton rate when integrated over energy. The resulting theory also correctly recovers the separable limit and can be thought of as an instanton generalisation of Rice-Ramsperger-Kassel-Marcus (RRKM) theory. When combined with the density-of-states approach [W. Fang, P. Winter and J. O. Richardson, J. Chem. Theory Comput., 2021, 17, 40-55], this new method can be straightforwardly applied to real molecular systems.
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14
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He X, Wu B, Rivlin T, Liu J, Pollak E. Transition Path Flight Times and Nonadiabatic Electronic Transitions. J Phys Chem Lett 2022; 13:6966-6974. [PMID: 35877977 PMCID: PMC9358656 DOI: 10.1021/acs.jpclett.2c01425] [Citation(s) in RCA: 2] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/11/2022] [Accepted: 07/18/2022] [Indexed: 06/15/2023]
Abstract
Transition path flight times are studied for scattering on two electronic surfaces with a single crossing. These flight times reveal nontrivial quantum effects such as resonance lifetimes and nonclassical passage times and reveal that nonadiabatic effects often increase flight times. The flight times are computed using numerically exact time propagation and compared with results obtained from the Fewest Switches Surface Hopping (FSSH) method. Comparison of the two methods shows that the FSSH method is reliable for transition path times only when the scattering is classically allowed on the relevant adiabatic surfaces. However, where quantum effects such as tunneling and resonances dominate, the FSSH method is not adequate to accurately predict the correct times and transition probabilities. These results highlight limitations in methods which do not account for quantum interference effects, and suggest that measuring flight times is important for obtaining insights from the time-domain into quantum effects in nonadiabatic scattering.
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Affiliation(s)
- Xin He
- Beijing
National Laboratory for Molecular Sciences, Institute of Theoretical
and Computational Chemistry, College of Chemistry and Molecular Engineering, Peking University, Beijing 100871, China
| | - Baihua Wu
- Beijing
National Laboratory for Molecular Sciences, Institute of Theoretical
and Computational Chemistry, College of Chemistry and Molecular Engineering, Peking University, Beijing 100871, China
| | - Tom Rivlin
- Chemical
and Biological Physics Department, Weizmann
Institute of Science, 76100 Rehovot, Israel
| | - Jian Liu
- Beijing
National Laboratory for Molecular Sciences, Institute of Theoretical
and Computational Chemistry, College of Chemistry and Molecular Engineering, Peking University, Beijing 100871, China
| | - Eli Pollak
- Chemical
and Biological Physics Department, Weizmann
Institute of Science, 76100 Rehovot, Israel
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15
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Heller ER, Richardson JO. Heavy‐Atom Quantum Tunnelling in Spin Crossovers of Nitrenes. Angew Chem Int Ed Engl 2022. [DOI: 10.1002/ange.202206314] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/07/2022]
Affiliation(s)
- Eric R Heller
- Eidgenossische Technische Hochschule Zurich Lab. Physical Chemistry SWITZERLAND
| | - Jeremy O Richardson
- Eidgenössische Technische Hochschule Zürich Lab. Physical Chemistry Vladimir-Prelog-Weg 2 8093 Zurich SWITZERLAND
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16
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Ansari IM, Heller ER, Trenins G, Richardson JO. Instanton theory for Fermi's golden rule and beyond. PHILOSOPHICAL TRANSACTIONS. SERIES A, MATHEMATICAL, PHYSICAL, AND ENGINEERING SCIENCES 2022; 380:20200378. [PMID: 35341312 PMCID: PMC8958279 DOI: 10.1098/rsta.2020.0378] [Citation(s) in RCA: 8] [Impact Index Per Article: 4.0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/16/2021] [Accepted: 09/22/2021] [Indexed: 05/29/2023]
Abstract
Instanton theory provides a semiclassical approximation for computing quantum tunnelling effects in complex molecular systems. It is typically applied to proton-transfer reactions for which the Born-Oppenheimer approximation is valid. However, many processes in physics, chemistry and biology, such as electron transfers, are non-adiabatic and are correctly described instead using Fermi's golden rule. In this work, we discuss how instanton theory can be generalized to treat these reactions in the golden-rule limit. We then extend the theory to treat fourth-order processes such as bridge-mediated electron transfer and apply the method to simulate an electron moving through a model system of three coupled quantum dots. By comparison with benchmark quantum calculations, we demonstrate that the instanton results are much more reliable than alternative approximations based on superexchange-mediated effective coupling or a classical sequential mechanism. This article is part of the theme issue 'Chemistry without the Born-Oppenheimer approximation'.
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Affiliation(s)
| | - Eric R. Heller
- Laboratory of Physical Chemistry, ETH, Zürich, Switzerland
| | - George Trenins
- Laboratory of Physical Chemistry, ETH, Zürich, Switzerland
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17
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Trenins G, Richardson JO. Nonadiabatic instanton rate theory beyond the golden-rule limit. J Chem Phys 2022; 156:174115. [DOI: 10.1063/5.0088518] [Citation(s) in RCA: 4] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
Fermi's golden rule describes the leading-order behaviour of the reaction rate as a function of the diabatic coupling. Its asymptotic (ℏ →0) limit is the semiclassical golden-rule instanton rate theory, which rigorously approximates nuclear quantum effects, lends itself to efficient numerical computation and gives physical insight into reaction mechanisms. However the golden rule by itself becomes insufficient as the strength of the diabatic coupling increases, so higher-order terms must be additionally considered. In this work we give a first-principles derivation of the next-order term beyond the golden rule, represented as a sum of three components. Two of them lead to new instanton pathways that extend the golden-rule case and, among other factors, account for the effects of recrossing on the full rate. The remaining component derives from the equilibrium partition function and accounts for changes in potential energy around the reactant and product wells due to diabatic coupling. The new semiclassical theory demands little computational effort beyond a golden-rule instanton calculation. It makes it possible to rigorously assess the accuracy of the golden-rule approximation and sets the stage for future work on general semiclassical nonadiabatic rate theories.
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Affiliation(s)
- George Trenins
- ETH Zurich Department of Chemistry and Applied Biosciences, Switzerland
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18
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Heller ER, Richardson JO. Spin Crossover of Thiophosgene via Multidimensional Heavy-Atom Quantum Tunneling. J Am Chem Soc 2021; 143:20952-20961. [PMID: 34846871 DOI: 10.1021/jacs.1c10088] [Citation(s) in RCA: 14] [Impact Index Per Article: 4.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/24/2022]
Abstract
The spin-crossover reaction of thiophosgene has drawn broad attention from both experimenters and theoreticians as a prime example of radiationless intramolecular decay via intersystem crossing. Despite multiple attempts over 20 years, theoretical predictions have typically been orders of magnitude in error relative to the experimentally measured triplet lifetime. We address the T1 → S0 transition by the first application of semiclassical golden-rule instanton theory in conjunction with on-the-fly electronic-structure calculations based on multireference perturbation theory. Our first-principles approach provides excellent agreement with the experimental rates. This was only possible because instanton theory goes beyond previous methods by locating the optimal tunneling pathway in full dimensionality and thus captures "corner cutting" effects. Since the reaction is situated in the Marcus inverted regime, the tunneling mechanism can be interpreted in terms of two classical trajectories, one traveling forward and one backward in imaginary time, which are connected by particle-antiparticle creation and annihilation events. The calculated mechanism indicates that the spin crossover is sped up by many orders of magnitude due to multidimensional quantum tunneling of the carbon atom even at room temperature.
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Affiliation(s)
- Eric R Heller
- Laboratory of Physical Chemistry, ETH Zürich, 8093 Zürich, Switzerland
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19
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Debierre V, Lassalle E. The onset time of Fermi’s golden rule. Proc Math Phys Eng Sci 2021. [DOI: 10.1098/rspa.2020.0777] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/12/2022] Open
Abstract
Fermi’s golden rule describes the decay dynamics of unstable quantum systems coupled to a reservoir, and predicts a linear decay in time. Although it arises at relatively short times, the Fermi regime does not take hold in the earliest stages of the quantum dynamics. The standard criterion in the literature for the onset time of the Fermi regime is
t
F
∼ 1/Δ
ω
, with Δ
ω
the frequency interval around the resonant transition frequency
ω
0
of the system, over which the coupling to the reservoir does not vary appreciably. In this work, this criterion is shown to be inappropriate in general for broadband reservoirs, where the reservoir coupling spectrum takes the form
R
(
ω
) ∝
ω
η
, and for which it is found that for
η
> 1, the onset time of the Fermi regime is given by
t
F
∝ (
ω
X
/
ω
0
)
η
−1
× 1/
ω
0
where
ω
X
is the high-frequency cutoff of the reservoir. Therefore, the onset of the Fermi regime can take place at times orders of magnitude larger than those predicted by the standard criterion. This phenomenon is shown to be related to the excitation of the off-resonant frequencies of the reservoir at short times. For broadband reservoirs with
η
≤ 1, and for narrowband reservoirs, it is shown that the standard criterion is correct.
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Affiliation(s)
- V. Debierre
- Max Planck Institute for Nuclear Physics, Saupfercheckweg, 1, 69117 Heidelberg, Germany
| | - E. Lassalle
- Aix Marseille Univ, CNRS, Centrale Marseille, Institut Fresnel, Marseille, France
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20
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Lawrence JE, Manolopoulos DE. An improved path-integral method for golden-rule rates. J Chem Phys 2020; 153:154113. [PMID: 33092388 DOI: 10.1063/5.0022535] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
We present a simple method for the calculation of reaction rates in the Fermi golden-rule limit, which accurately captures the effects of tunneling and zero-point energy. The method is based on a modification of the recently proposed golden-rule quantum transition state theory (GR-QTST) of Thapa, Fang, and Richardson [J. Chem. Phys. 150, 104107 (2019)]. While GR-QTST is not size consistent, leading to the possibility of unbounded errors in the rate, our modified method has no such issue and so can be reliably applied to condensed phase systems. Both methods involve path-integral sampling in a constrained ensemble; the two methods differ, however, in the choice of constraint functional. We demonstrate numerically that our modified method is as accurate as GR-QTST for the one-dimensional model considered by Thapa and co-workers. We then study a multidimensional spin-boson model, for which our method accurately predicts the true quantum rate, while GR-QTST breaks down with an increasing number of boson modes in the discretization of the spectral density. Our method is able to accurately predict reaction rates in the Marcus inverted regime without the need for the analytic continuation required by Wolynes theory.
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Affiliation(s)
- Joseph E Lawrence
- Physical and Theoretical Chemistry Laboratory, Department of Chemistry, University of Oxford, South Parks Road, Oxford OX1 3QZ, United Kingdom
| | - David E Manolopoulos
- Physical and Theoretical Chemistry Laboratory, Department of Chemistry, University of Oxford, South Parks Road, Oxford OX1 3QZ, United Kingdom
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21
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Lawrence JE, Manolopoulos DE. Confirming the role of nuclear tunneling in aqueous ferrous–ferric electron transfer. J Chem Phys 2020; 153:154114. [DOI: 10.1063/5.0022678] [Citation(s) in RCA: 4] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 02/04/2023] Open
Affiliation(s)
- Joseph E. Lawrence
- Physical and Theoretical Chemistry Laboratory, Department of Chemistry, University of Oxford, South Parks Road, Oxford OX1 3QZ, United Kingdom
| | - David E. Manolopoulos
- Physical and Theoretical Chemistry Laboratory, Department of Chemistry, University of Oxford, South Parks Road, Oxford OX1 3QZ, United Kingdom
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22
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Ediger MD, Jensen L, Manolopoulos DE, Martinez TJ, Michaelides A, Reichman DR, Sherrill CD, Shi Q, Straub JE, Vega C, Wang LS, Brigham EC, Lian T. JCP Emerging Investigator Special Collection 2019. J Chem Phys 2020; 153:110402. [PMID: 32962387 DOI: 10.1063/5.0021946] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/28/2022] Open
Affiliation(s)
- Mark D Ediger
- Department of Chemistry, University of Wisconsin-Madison, Madison, Wisconsin 53706, USA
| | - Lasse Jensen
- Department of Chemistry, Pennsylvania State University, University Park, Pennsylvania 16802, USA
| | - David E Manolopoulos
- Physical and Theoretical Chemistry Laboratory, Department of Chemistry, University of Oxford, South Parks Road, Oxford OX1 3QZ, United Kingdom
| | - Todd J Martinez
- Department of Chemistry, Stanford University, Stanford, California 94305, USA
| | - Angelos Michaelides
- Thomas Young Centre and London Centre for Nanotechnology, 17-19 Gordon Street, London WC1H 0AH, United Kingdom and Department of Physics and Astronomy, University College London, Gower Street, London WC1E 6BT, United Kingdom
| | - David R Reichman
- Department of Chemistry, Columbia University, New York, New York 10027, USA
| | - C David Sherrill
- Center for Computational Molecular Science and Technology, School of Chemistry and Biochemistry, School of Computational Science and Engineering, Georgia Institute of Technology, Atlanta, Georgia 30332-0400, USA
| | - Qiang Shi
- Beijing National Laboratory for Molecular Sciences, State Key Laboratory for Structural Chemistry of Unstable and Stable Species, Institute of Chemistry, Chinese Academy of Sciences, Zhongguancun, Beijing 100190, China; University of Chinese Academy of Sciences, Beijing 100049, China; and Physical Science Laboratory, Huairou National Comprehensive Science Center, Beijing 101407, China
| | - John E Straub
- Department of Chemistry, Boston University, 590 Commonwealth Avenue, Boston, Massachusetts 02215, USA
| | - Carlos Vega
- Departamento de Química Física, Facultad de Ciencias Químicas, Universidad Complutense de Madrid, 28040 Madrid, Spain
| | - Lai-Sheng Wang
- Department of Chemistry, Brown University, Providence, Rhode Island 02912, USA
| | | | - Tianquan Lian
- Department of Chemistry, Emory University, Atlanta, Georgia 30322, USA
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23
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Heller ER, Richardson JO. Semiclassical instanton formulation of Marcus–Levich–Jortner theory. J Chem Phys 2020; 152:244117. [DOI: 10.1063/5.0013521] [Citation(s) in RCA: 11] [Impact Index Per Article: 2.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022] Open
Affiliation(s)
- Eric R. Heller
- Laboratory of Physical Chemistry, ETH Zürich, 8093 Zürich, Switzerland
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24
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Lawrence JE, Manolopoulos DE. A general non-adiabatic quantum instanton approximation. J Chem Phys 2020; 152:204117. [DOI: 10.1063/5.0009109] [Citation(s) in RCA: 7] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- Joseph E. Lawrence
- Department of Chemistry, University of Oxford, Physical and Theoretical Chemistry Laboratory, South Parks Road, Oxford OX1 3QZ, United Kingdom
| | - David E. Manolopoulos
- Department of Chemistry, University of Oxford, Physical and Theoretical Chemistry Laboratory, South Parks Road, Oxford OX1 3QZ, United Kingdom
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25
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Thorning F, Jensen F, Ogilby PR. Modeling the Effect of Solvents on Nonradiative Singlet Oxygen Deactivation: Going beyond Weak Coupling in Intermolecular Electronic-to-Vibrational Energy Transfer. J Phys Chem B 2020; 124:2245-2254. [DOI: 10.1021/acs.jpcb.0c00807] [Citation(s) in RCA: 15] [Impact Index Per Article: 3.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/14/2023]
Affiliation(s)
| | - Frank Jensen
- Chemistry Department, Aarhus University, DK-8000 Aarhus, Denmark
| | - Peter R. Ogilby
- Chemistry Department, Aarhus University, DK-8000 Aarhus, Denmark
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26
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Sakaushi K, Kumeda T, Hammes-Schiffer S, Melander MM, Sugino O. Advances and challenges for experiment and theory for multi-electron multi-proton transfer at electrified solid–liquid interfaces. Phys Chem Chem Phys 2020; 22:19401-19442. [DOI: 10.1039/d0cp02741c] [Citation(s) in RCA: 22] [Impact Index Per Article: 5.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/02/2023]
Abstract
Understanding microscopic mechanism of multi-electron multi-proton transfer reactions at complexed systems is important for advancing electrochemistry-oriented science in the 21st century.
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Affiliation(s)
- Ken Sakaushi
- Center for Green Research on Energy and Environmental Materials
- National Institute for Materials Science
- Ibaraki 305-0044
- Japan
| | - Tomoaki Kumeda
- Center for Green Research on Energy and Environmental Materials
- National Institute for Materials Science
- Ibaraki 305-0044
- Japan
| | | | - Marko M. Melander
- Nanoscience Center
- Department of Chemistry
- University of Jyväskylä
- Jyväskylä
- Finland
| | - Osamu Sugino
- The Institute of Solid State Physics
- the University of Tokyo
- Chiba 277-8581
- Japan
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27
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Fang W, Zarotiadis RA, Richardson JO. Revisiting nuclear tunnelling in the aqueous ferrous–ferric electron transfer. Phys Chem Chem Phys 2020; 22:10687-10698. [DOI: 10.1039/c9cp06841d] [Citation(s) in RCA: 4] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/16/2022]
Abstract
We find that golden-rule quantum transition-state theory predicts nearly an order of magnitude less tunnelling than some of the previous estimates. This may indicate that the spin-boson model of electron transfer is not valid in the quantum regime.
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Affiliation(s)
- Wei Fang
- Laboratory of Physical Chemistry
- ETH Zürich
- 8093 Zürich
- Switzerland
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