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Erpenbeck A, Ke Y, Peskin U, Thoss M. How an electrical current can stabilize a molecular nanojunction. NANOSCALE 2023; 15:16333-16343. [PMID: 37766513 DOI: 10.1039/d3nr02176a] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 09/29/2023]
Abstract
The stability of molecular junctions under transport is of the utmost importance for the field of molecular electronics. This question is often addressed within the paradigm of current-induced heating of nuclear degrees of freedom or current-induced forces acting upon the nuclei. At the same time, an essential characteristic of the failure of a molecular electronic device is its changing conductance - typically from a finite value for the intact device to zero for a device that lost its functionality. In this publication, we focus on the current-induced changes in the molecular conductance, which are inherent to molecular junctions at the limit of mechanical stability. We employ a numerically exact framework based on the hierarchical equations of motion approach, which treats both electronic and nuclear degrees of freedom on an equal footing and does not impose additional assumptions. Studying generic model systems for molecular junctions with dissociative potentials for a wide range of parameters spanning the adiabatic and the nonadiabatic regime, we find that molecular junctions that exhibit a decrease in conductance upon dissociation are more stable than junctions that are more conducting in their dissociated state. This represents a new mechanism that stabilizes molecular junctions under current. Moreover, we identify characteristic signatures in the current of breaking junctions related to the interplay between changes in the conductance and the nuclear configuration and show how these are related to properties of the leads rather than characteristics of the molecule itself.
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Affiliation(s)
- André Erpenbeck
- Department of Physics, University of Michigan, Ann Arbor, Michigan 48109, USA.
| | - Yaling Ke
- Institute of Physics, University of Freiburg, Hermann-Herder-Strasse 3, 79104 Freiburg, Germany
| | - Uri Peskin
- Schulich Faculty of Chemistry, Technion-Israel Institute of Technology, Haifa 32000, Israel
| | - Michael Thoss
- Institute of Physics, University of Freiburg, Hermann-Herder-Strasse 3, 79104 Freiburg, Germany
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Gardner J, Habershon S, Maurer RJ. Assessing Mixed Quantum-Classical Molecular Dynamics Methods for Nonadiabatic Dynamics of Molecules on Metal Surfaces. THE JOURNAL OF PHYSICAL CHEMISTRY. C, NANOMATERIALS AND INTERFACES 2023; 127:15257-15270. [PMID: 37583439 PMCID: PMC10424245 DOI: 10.1021/acs.jpcc.3c03591] [Citation(s) in RCA: 4] [Impact Index Per Article: 4.0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Figures] [Subscribe] [Scholar Register] [Received: 05/27/2023] [Revised: 06/30/2023] [Indexed: 08/17/2023]
Abstract
Mixed quantum-classical (MQC) methods for simulating the dynamics of molecules at metal surfaces have the potential to accurately and efficiently provide mechanistic insight into reactive processes. Here, we introduce simple two-dimensional models for the scattering of diatomic molecules at metal surfaces based on recently published electronic structure data. We apply several MQC methods to investigate their ability to capture how nonadiabatic effects influence molecule-metal energy transfer during the scattering process. Specifically, we compare molecular dynamics with electronic friction, Ehrenfest dynamics, independent electron surface hopping, and the broadened classical master equation approach. In the case of independent electron surface hopping, we implement a simple decoherence correction approach and assess its impact on vibrationally inelastic scattering. Our results show that simple, low-dimensional models can be used to qualitatively capture experimentally observed vibrational energy transfer and provide insight into the relative performance of different MQC schemes. We observe that all approaches predict similar kinetic energy dependence but return different vibrational energy distributions. Finally, by varying the molecule-metal coupling, we can assess the coupling regime in which some MQC methods become unsuitable.
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Affiliation(s)
- James Gardner
- Department
of Chemistry, University of Warwick, Gibbet Hill Road, Coventry CV4 7AL, United Kingdom
| | - Scott Habershon
- Department
of Chemistry, University of Warwick, Gibbet Hill Road, Coventry CV4 7AL, United Kingdom
| | - Reinhard J. Maurer
- Department
of Chemistry, University of Warwick, Gibbet Hill Road, Coventry CV4 7AL, United Kingdom
- Department
of Physics, University of Warwick, Gibbet Hill Road, Coventry CV4 7AL, United Kingdom
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3
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Ke Y, Kaspar C, Erpenbeck A, Peskin U, Thoss M. Nonequilibrium reaction rate theory: Formulation and implementation within the hierarchical equations of motion approach. J Chem Phys 2022; 157:034103. [DOI: 10.1063/5.0098545] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022] Open
Abstract
The study of chemical reactions in environments under nonequilibrium conditions has been of interest recently in a variety of contexts, including current-induced reactions in molecular junctions and scanning tunneling microscopy experiments. In this work, we outline a fully quantum mechanical, numerically exact approach to describe chemical reaction rates in such nonequilibrium situations. The approach is based on an extension of the flux correlation function formalism to nonequilibrium conditions and uses a mixed real and imaginary time hierarchical equations of motion approach for the calculation of rate constants. As a specific example, we investigate current-induced intramolecular proton transfer reactions in a molecular junction for different applied bias voltages and molecule-lead coupling strengths.
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Affiliation(s)
- Yaling Ke
- Institute of Physics, Albert-Ludwigs-Universität Freiburg, Germany
| | | | | | - Uri Peskin
- Chemistry, Technion Israel Institute of Technology, Israel
| | - Michael Thoss
- University of Freiburg Institute of Physics, Germany
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Bian X, Qiu T, Chen J, Subotnik JE. On the meaning of Berry force for unrestricted systems treated with mean-field electronic structure. J Chem Phys 2022; 156:234107. [PMID: 35732536 DOI: 10.1063/5.0093092] [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 show that the Berry force as computed by an approximate, mean-field electronic structure can be meaningful if properly interpreted. In particular, for a model Hamiltonian representing a molecular system with an even number of electrons interacting via a two-body (Hubbard) interaction and a spin-orbit coupling, we show that a meaningful nonzero Berry force emerges whenever there is spin unrestriction-even though the Hamiltonian is real-valued and formally the on-diagonal single-surface Berry force must be zero. Moreover, if properly applied, this mean-field Berry force yields roughly the correct asymptotic motion for scattering through an avoided crossing. That being said, within the context of a ground-state calculation, several nuances do arise as far interpreting the Berry force correctly, and as a practical matter, the Berry force diverges near the Coulson-Fischer point (which can lead to numerical instabilities). We do not address magnetic fields here.
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Affiliation(s)
- Xuezhi Bian
- Department of Chemistry, University of Pennsylvania, Philadelphia, Pennsylvania 19104, USA
| | - Tian Qiu
- Department of Chemistry, University of Pennsylvania, Philadelphia, Pennsylvania 19104, USA
| | - Junhan Chen
- Department of Chemistry, University of Pennsylvania, Philadelphia, Pennsylvania 19104, USA
| | - Joseph E Subotnik
- Department of Chemistry, University of Pennsylvania, Philadelphia, Pennsylvania 19104, USA
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Abstract
Dynamics at molecule-metal interfaces are a subject of intense current interest and come in many different flavors of experiments: gas-phase scattering, chemisorption, electrochemistry, nanojunction transport, and heterogeneous catalysis, to name a few. These dynamics involve nuclear degrees of freedom entangled with many electronic degrees of freedom (in the metal), and as such there is always the possibility for nonadiabatic phenomena to appear: the nuclei do not necessarily need to move slower than the electrons to break the Born-Oppenheimer (BO) approximation. In this Feature Article, we review a set of dynamical methods developed recently to deal with such nonadiabatic phenomena at a metal surface, methods that serve as alternatives to Tully's independent electron surface hopping (IESH) model. In the weak molecule-metal coupling regime, a classical master equation (CME) can be derived and a simple surface hopping approach is proposed to propagate nuclear and electronic dynamics stochastically. In the strong molecule-metal interaction regime, a Fokker-Planck equation can be derived for the nuclear dynamics, with electronic DoFs incorporated into the overall friction and random force. Lastly, a broadened classical master equation (BCME) can interpolate between the weak and strong molecule-metal interactions. Here, we briefly review these methods and the relevant benchmarking data, showing in particular how the methods can be used to calculate nonequilibrium transport properties. We highlight several open questions and pose several avenues for future study.
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Affiliation(s)
- Wenjie Dou
- Department of Chemistry , University of California, Berkeley , Berkeley , California 94720 , United States
| | - Joseph E Subotnik
- Department of Chemistry , University of Pennsylvania , Philadelphia , Pennsylvania 19104 , United States
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Erpenbeck A, Thoss M. Hierarchical quantum master equation approach to vibronic reaction dynamics at metal surfaces. J Chem Phys 2019; 151:191101. [DOI: 10.1063/1.5128206] [Citation(s) in RCA: 11] [Impact Index Per Article: 2.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- A. Erpenbeck
- Institute of Physics, Albert-Ludwig University Freiburg, Hermann-Herder-Strasse 3, 79104 Freiburg, Germany
| | - M. Thoss
- Institute of Physics, Albert-Ludwig University Freiburg, Hermann-Herder-Strasse 3, 79104 Freiburg, Germany
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Miao G, Ouyang W, Subotnik J. A comparison of surface hopping approaches for capturing metal-molecule electron transfer: A broadened classical master equation versus independent electron surface hopping. J Chem Phys 2019; 150:041711. [PMID: 30709317 DOI: 10.1063/1.5050235] [Citation(s) in RCA: 10] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
Within a generalized Anderson-Holstein model, we investigate electron transfer rates using two different surface hopping algorithms: a broadened classical master equation (BCME) and independent electron surface hopping (IESH). We find that for large enough bandwidth and density of one electron states, and in the presence of external friction, the IESH results converge to the BCME results for impurity-bath model systems, recovering both relaxation rates and equilibrium populations. Without external friction, however, the BCME and IESH results can strongly disagree, and preliminary evidence suggests that IESH does not always recover the correct equilibrium state. Finally, we also demonstrate that adding an electronic thermostat to IESH does help drive the metallic substrate to the correct equilibrium state, but this improvement can sometimes come at the cost of worse short time dynamics. Overall, our results should be of use for all computational chemists looking to model either gas phase scattering or electrochemical dynamics at a metal interface.
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Affiliation(s)
- Gaohan Miao
- Department of Chemistry, University of Pennsylvania, Philadelphia, Pennsylvania 19104, USA
| | - Wenjun Ouyang
- Department of Chemistry, University of Pennsylvania, Philadelphia, Pennsylvania 19104, USA
| | - Joseph Subotnik
- Department of Chemistry, University of Pennsylvania, Philadelphia, Pennsylvania 19104, USA
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Miao G, Dou W, Subotnik J. Vibrational relaxation at a metal surface: Electronic friction versus classical master equations. J Chem Phys 2017; 147:224105. [DOI: 10.1063/1.5000237] [Citation(s) in RCA: 13] [Impact Index Per Article: 1.9] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- Gaohan Miao
- Department of Chemistry, University of Pennsylvania, Philadelphia, Pennsylvania 19104, USA
| | - Wenjie Dou
- Department of Chemistry, University of Pennsylvania, Philadelphia, Pennsylvania 19104, USA
| | - Joseph Subotnik
- Department of Chemistry, University of Pennsylvania, Philadelphia, Pennsylvania 19104, USA
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Dou W, Subotnik JE. Electronic friction near metal surfaces: A case where molecule-metal couplings depend on nuclear coordinates. J Chem Phys 2017. [DOI: 10.1063/1.4965823] [Citation(s) in RCA: 26] [Impact Index Per Article: 3.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- Wenjie Dou
- Department of Chemistry, University of Pennsylvania, Philadelphia, Pennsylvania 19104, USA
| | - Joseph E. Subotnik
- Department of Chemistry, University of Pennsylvania, Philadelphia, Pennsylvania 19104, USA
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Jia C, Migliore A, Xin N, Huang S, Wang J, Yang Q, Wang S, Chen H, Wang D, Feng B, Liu Z, Zhang G, Qu DH, Tian H, Ratner MA, Xu HQ, Nitzan A, Guo X. Covalently bonded single-molecule junctions with stable and reversible photoswitched conductivity. Science 2016; 352:1443-5. [PMID: 27313042 DOI: 10.1126/science.aaf6298] [Citation(s) in RCA: 414] [Impact Index Per Article: 51.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/05/2016] [Accepted: 05/03/2016] [Indexed: 01/02/2023]
Abstract
Through molecular engineering, single diarylethenes were covalently sandwiched between graphene electrodes to form stable molecular conduction junctions. Our experimental and theoretical studies of these junctions consistently show and interpret reversible conductance photoswitching at room temperature and stochastic switching between different conductive states at low temperature at a single-molecule level. We demonstrate a fully reversible, two-mode, single-molecule electrical switch with unprecedented levels of accuracy (on/off ratio of ~100), stability (over a year), and reproducibility (46 devices with more than 100 cycles for photoswitching and ~10(5) to 10(6) cycles for stochastic switching).
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Affiliation(s)
- Chuancheng Jia
- Beijing National Laboratory for Molecular Sciences, State Key Laboratory for Structural Chemistry of Unstable and Stable Species, College of Chemistry and Molecular Engineering, Peking University, Beijing 100871, P. R. China
| | | | - Na Xin
- Beijing National Laboratory for Molecular Sciences, State Key Laboratory for Structural Chemistry of Unstable and Stable Species, College of Chemistry and Molecular Engineering, Peking University, Beijing 100871, P. R. China
| | - Shaoyun Huang
- Department of Electronics and Key Laboratory for the Physics and Chemistry of Nanodevices, Peking University, Beijing 100871, P. R. China
| | - Jinying Wang
- Beijing National Laboratory for Molecular Sciences, State Key Laboratory for Structural Chemistry of Unstable and Stable Species, College of Chemistry and Molecular Engineering, Peking University, Beijing 100871, P. R. China
| | - Qi Yang
- Department of Electronics and Key Laboratory for the Physics and Chemistry of Nanodevices, Peking University, Beijing 100871, P. R. China
| | - Shuopei Wang
- Institute of Physics, Chinese Academy of Sciences, Beijing 100190, P. R. China
| | - Hongliang Chen
- Beijing National Laboratory for Molecular Sciences, State Key Laboratory for Structural Chemistry of Unstable and Stable Species, College of Chemistry and Molecular Engineering, Peking University, Beijing 100871, P. R. China
| | - Duoming Wang
- Institute of Physics, Chinese Academy of Sciences, Beijing 100190, P. R. China
| | - Boyong Feng
- Department of Electronics and Key Laboratory for the Physics and Chemistry of Nanodevices, Peking University, Beijing 100871, P. R. China
| | - Zhirong Liu
- Beijing National Laboratory for Molecular Sciences, State Key Laboratory for Structural Chemistry of Unstable and Stable Species, College of Chemistry and Molecular Engineering, Peking University, Beijing 100871, P. R. China
| | - Guangyu Zhang
- Institute of Physics, Chinese Academy of Sciences, Beijing 100190, P. R. China
| | - Da-Hui Qu
- Key Laboratory for Advanced Materials and Institute of Fine Chemicals, East China University of Science and Technology, Shanghai 200237, P. R. China
| | - He Tian
- Key Laboratory for Advanced Materials and Institute of Fine Chemicals, East China University of Science and Technology, Shanghai 200237, P. R. China
| | - Mark A Ratner
- Department of Chemistry, Northwestern University, Evanston, IL 60208, USA
| | - H Q Xu
- Department of Electronics and Key Laboratory for the Physics and Chemistry of Nanodevices, Peking University, Beijing 100871, P. R. China.
| | - Abraham Nitzan
- Department of Chemistry, University of Pennsylvania, Philadelphia, PA 19104-6323, USA. School of Chemistry, Tel Aviv University, Tel Aviv, 69978, Israel.
| | - Xuefeng Guo
- Beijing National Laboratory for Molecular Sciences, State Key Laboratory for Structural Chemistry of Unstable and Stable Species, College of Chemistry and Molecular Engineering, Peking University, Beijing 100871, P. R. China. Department of Materials Science and Engineering, College of Engineering, Peking University, Beijing 100871, P. R. China.
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