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Mejía L, Kleinekathöfer U, Franco I. Coherent and incoherent contributions to molecular electron transport. J Chem Phys 2022; 156:094302. [DOI: 10.1063/5.0079708] [Citation(s) in RCA: 3] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
We numerically isolate the limits of validity of the Landauer approximation to describe charge transport along molecular junctions in condensed phase environments. To do so, we contrast Landauer with exact time-dependent non-equilibrium Green’s function quantum transport computations in a two-site molecular junction subject to exponentially correlated noise. Under resonant transport conditions, we find Landauer accuracy to critically depend on intramolecular interactions. By contrast, under nonresonant conditions, the emergence of incoherent transport routes that go beyond Landauer depends on charging and discharging processes at the electrode–molecule interface. In both cases, decreasing the rate of charge exchange between the electrodes and molecule and increasing the interaction strength with the thermal environment cause Landauer to become less accurate. The results are interpreted from a time-dependent perspective where the noise prevents the junction from achieving steady-state and from a fully quantum perspective where the environment introduces dephasing in the dynamics. Using these results, we analyze why the Landauer approach is so useful to understand experiments, isolate regimes where it fails, and propose schemes to chemically manipulate the degree of transport coherence.
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Affiliation(s)
- Leopoldo Mejía
- Department of Chemistry, University of Rochester, Rochester, New York 14627-0216, USA
| | - Ulrich Kleinekathöfer
- Department of Physics and Earth Sciences, Jacobs University Bremen, 28759 Bremen, Germany
| | - Ignacio Franco
- Department of Chemistry, University of Rochester, Rochester, New York 14627-0216, USA
- Department of Physics, University of Rochester, Rochester, New York 14627-0216, USA
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2
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Quantum Phonon Transport in Nanomaterials: Combining Atomistic with Non-Equilibrium Green's Function Techniques. ENTROPY 2019; 21:e21080735. [PMID: 33267449 PMCID: PMC7515264 DOI: 10.3390/e21080735] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Received: 07/01/2019] [Revised: 07/23/2019] [Accepted: 07/25/2019] [Indexed: 11/16/2022]
Abstract
A crucial goal for increasing thermal energy harvesting will be to progress towards atomistic design strategies for smart nanodevices and nanomaterials. This requires the combination of computationally efficient atomistic methodologies with quantum transport based approaches. Here, we review our recent work on this problem, by presenting selected applications of the PHONON tool to the description of phonon transport in nanostructured materials. The PHONON tool is a module developed as part of the Density-Functional Tight-Binding (DFTB) software platform. We discuss the anisotropic phonon band structure of selected puckered two-dimensional materials, helical and horizontal doping effects in the phonon thermal conductivity of boron nitride-carbon heteronanotubes, phonon filtering in molecular junctions, and a novel computational methodology to investigate time-dependent phonon transport at the atomistic level. These examples illustrate the versatility of our implementation of phonon transport in combination with density functional-based methods to address specific nanoscale functionalities, thus potentially allowing for designing novel thermal devices.
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3
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Rahman H, Kleinekathöfer U. Non-equilibrium Green’s function transport theory for molecular junctions with general molecule-lead coupling and temperatures. J Chem Phys 2018; 149:234108. [DOI: 10.1063/1.5054312] [Citation(s) in RCA: 7] [Impact Index Per Article: 1.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- Hasan Rahman
- Department of Physics and Earth Sciences, Jacobs University Bremen, Campus Ring 1, 28759 Bremen, Germany
| | - Ulrich Kleinekathöfer
- Department of Physics and Earth Sciences, Jacobs University Bremen, Campus Ring 1, 28759 Bremen, Germany
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5
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Schmaltz T, Gothe B, Krause A, Leitherer S, Steinrück HG, Thoss M, Clark T, Halik M. Effect of Structure and Disorder on the Charge Transport in Defined Self-Assembled Monolayers of Organic Semiconductors. ACS NANO 2017; 11:8747-8757. [PMID: 28813143 DOI: 10.1021/acsnano.7b02394] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/07/2023]
Abstract
Self-assembled monolayer field-effect transistors (SAMFETs) are not only a promising type of organic electronic device but also allow detailed analyses of structure-property correlations. The influence of the morphology on the charge transport is particularly pronounced, due to the confined monolayer of 2D-π-stacked organic semiconductor molecules. The morphology, in turn, is governed by relatively weak van-der-Waals interactions and is thus prone to dynamic structural fluctuations. Accordingly, combining electronic and physical characterization and time-averaged X-ray analyses with the dynamic information available at atomic resolution from simulations allows us to characterize self-assembled monolayer (SAM) based devices in great detail. For this purpose, we have constructed transistors based on SAMs of two molecules that consist of the organic p-type semiconductor benzothieno[3,2-b][1]benzothiophene (BTBT), linked to a C11 or C12 alkylphosphonic acid. Both molecules form ordered SAMs; however, our experiments show that the size of the crystalline domains and the charge-transport properties vary considerably in the two systems. These findings were confirmed by molecular dynamics (MD) simulations and semiempirical molecular-orbital electronic-structure calculations, performed on snapshots from the MD simulations at different times, revealing, in atomistic detail, how the charge transport in organic semiconductors is influenced and limited by dynamic disorder.
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Affiliation(s)
- Thomas Schmaltz
- Organic Materials & Devices (OMD), Dept. of Materials Science, Friedrich-Alexander-Universität Erlangen-Nürnberg (FAU) , Martensstraße 7, 91058 Erlangen, Germany
| | - Bastian Gothe
- Organic Materials & Devices (OMD), Dept. of Materials Science, Friedrich-Alexander-Universität Erlangen-Nürnberg (FAU) , Martensstraße 7, 91058 Erlangen, Germany
| | - Andreas Krause
- Computer-Chemie-Centrum and Interdisciplinary Center for Molecular Materials, FAU , Nägelsbachstraße 25, 91052 Erlangen, Germany
| | - Susanne Leitherer
- Institute for Theoretical Physics and Interdisciplinary Center for Molecular Materials (ICMM), FAU , Staudtstrasse 7/B2, 91058 Erlangen, Germany
| | - Hans-Georg Steinrück
- SSRL Materials Science Division, SLAC National Accelerator Laboratory , Menlo Park, California 94025, United States
| | - Michael Thoss
- Institute for Theoretical Physics and Interdisciplinary Center for Molecular Materials (ICMM), FAU , Staudtstrasse 7/B2, 91058 Erlangen, Germany
| | - Timothy Clark
- Computer-Chemie-Centrum and Interdisciplinary Center for Molecular Materials, FAU , Nägelsbachstraße 25, 91052 Erlangen, Germany
| | - Marcus Halik
- Organic Materials & Devices (OMD), Dept. of Materials Science, Friedrich-Alexander-Universität Erlangen-Nürnberg (FAU) , Martensstraße 7, 91058 Erlangen, Germany
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6
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Feliciano GT, Sanz-Navarro C, Coutinho-Neto MD, Ordejón P, Scheicher RH, Rocha AR. Addressing the Environment Electrostatic Effect on Ballistic Electron Transport in Large Systems: A QM/MM-NEGF Approach. J Phys Chem B 2017; 122:485-492. [DOI: 10.1021/acs.jpcb.7b03475] [Citation(s) in RCA: 16] [Impact Index Per Article: 2.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Affiliation(s)
- Gustavo T. Feliciano
- Instituto
de Química, Departamento de Fisico-Química, Universidade Estadual Paulista (UNESP), 14800-060, Araraquara, SP, Brazil
| | - Carlos Sanz-Navarro
- Catalan Institute
of Nanoscience and Nanotechnology (ICN2), CSIC, and The Barcelona
Institute of Science and Technology, Campus UAB, Bellaterra, 08193 Barcelona, Spain
| | | | - Pablo Ordejón
- Catalan Institute
of Nanoscience and Nanotechnology (ICN2), CSIC, and The Barcelona
Institute of Science and Technology, Campus UAB, Bellaterra, 08193 Barcelona, Spain
| | - Ralph H. Scheicher
- Division
of Materials Theory, Department of Physics and Astronomy, Uppsala University, SE-751 20, Uppsala, Sweden
| | - Alexandre Reily Rocha
- Instituto
de Fı́sica Teorica, Universidade Estadual Paulista (UNESP), 01140-070, São Paulo, SP, Brazil
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7
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Carey R, Chen L, Gu B, Franco I. When can time-dependent currents be reproduced by the Landauer steady-state approximation? J Chem Phys 2017; 146:174101. [DOI: 10.1063/1.4981915] [Citation(s) in RCA: 16] [Impact Index Per Article: 2.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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Kubař T, Elstner M, Popescu B, Kleinekathöfer U. Polaron Effects on Charge Transport through Molecular Wires: A Multiscale Approach. J Chem Theory Comput 2016; 13:286-296. [DOI: 10.1021/acs.jctc.6b00879] [Citation(s) in RCA: 15] [Impact Index Per Article: 1.9] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 02/07/2023]
Affiliation(s)
- Tomáš Kubař
- Institute of Physical Chemistry & Center for Functional Nanostructures, Karlsruhe Institute of Technology, 76131 Karlsruhe, Germany
| | - Marcus Elstner
- Institute
of Physical Chemistry, Karlsruhe Institute of Technology, 76131 Karlsruhe, Germany
| | - Bogdan Popescu
- Department
of Physics and Earth Sciences, Jacobs University Bremen, Campus Ring 1, 28759 Bremen, Germany
| | - Ulrich Kleinekathöfer
- Department
of Physics and Earth Sciences, Jacobs University Bremen, Campus Ring 1, 28759 Bremen, Germany
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Li G, Govind N, Ratner MA, Cramer CJ, Gagliardi L. Influence of Coherent Tunneling and Incoherent Hopping on the Charge Transfer Mechanism in Linear Donor-Bridge-Acceptor Systems. J Phys Chem Lett 2015; 6:4889-4897. [PMID: 26554424 DOI: 10.1021/acs.jpclett.5b02154] [Citation(s) in RCA: 18] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 06/05/2023]
Abstract
The mechanism of charge transfer has been observed to change from tunneling to hopping with increasing numbers of DNA base pairs in polynucleotides and with the length of molecular wires. The aim of this paper is to investigate this transition by examining the population dynamics using a tight-binding Hamiltonian with model parameters to describe a linear donor-bridge-acceptor (D-B-A) system. The model includes a primary vibration and an electron-vibration coupling at each site. A further coupling of the primary vibration with a secondary phonon bath allows the system to dissipate energy to the environment and reach a steady state. We apply the quantum master equation (QME) approach, based on second-order perturbation theory in a quantum dissipative system, to examine the dynamical processes involved in charge-transfer and follow the population transfer rate at the acceptor, ka, to shed light on the transition from tunneling to hopping. With a small tunneling parameter, V, the on-site population tends to localize and form polarons, and the hopping mechanism dominates the transfer process. With increasing V, the population tends to be delocalized and the tunneling mechanism dominates. The competition between incoherent hopping and coherent tunneling governs the mechanism of charge transfer. By varying V and the total number of sites, we also examine the onset of the transition from tunneling to hopping with increasing length.
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Affiliation(s)
- Guangqi Li
- Department of Chemistry, Chemical Theory Center, and Supercomputing Institute, University of Minnesota , Minneapolis, Minnesota 55455, United States
| | - Niranjan Govind
- Environmental Molecular Sciences Laboratory, Pacific Northwest National Laboratory , Richland, Washington 99352, United States
| | - Mark A Ratner
- Department of Chemistry, Northwestern University , Evanston, Illinois 60208, United States
| | - Christopher J Cramer
- Department of Chemistry, Chemical Theory Center, and Supercomputing Institute, University of Minnesota , Minneapolis, Minnesota 55455, United States
| | - Laura Gagliardi
- Department of Chemistry, Chemical Theory Center, and Supercomputing Institute, University of Minnesota , Minneapolis, Minnesota 55455, United States
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Dong B, Ding GH, Lei XL. Time-dependent quantum transport through an interacting quantum dot beyond sequential tunneling: second-order quantum rate equations. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2015; 27:205303. [PMID: 25950191 DOI: 10.1088/0953-8984/27/20/205303] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/04/2023]
Abstract
A general theoretical formulation for the effect of a strong on-site Coulomb interaction on the time-dependent electron transport through a quantum dot under the influence of arbitrary time-varying bias voltages and/or external fields is presented, based on slave bosons and the Keldysh nonequilibrium Green's function (GF) techniques. To avoid the difficulties of computing double-time GFs, we generalize the propagation scheme recently developed by Croy and Saalmann to combine the auxiliary-mode expansion with the celebrated Lacroix's decoupling approximation in dealing with the second-order correlated GFs and then establish a closed set of coupled equations of motion, called second-order quantum rate equations (SOQREs), for an exact description of transient dynamics of electron correlated tunneling. We verify that the stationary solution of our SOQREs is able to correctly describe the Kondo effect on a qualitative level. Moreover, a comparison with other methods, such as the second-order von Neumann approach and Hubbard-I approximation, is performed. As illustrations, we investigate the transient current behaviors in response to a step voltage pulse and a harmonic driving voltage, and linear admittance as well, in the cotunneling regime.
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Affiliation(s)
- B Dong
- Key Laboratory of Artificial Structures and Quantum Control (Ministry of Education), Department of Physics, Shanghai Jiaotong University, 800 Dongchuan Road, Shanghai 200240, People's Republic of China
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Li G, Fainberg BD, Seideman T. Optically induced transport through semiconductor-based molecular electronics. J Chem Phys 2015; 142:154111. [PMID: 25903870 DOI: 10.1063/1.4917029] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/17/2022] Open
Abstract
A tight binding model is used to investigate photoinduced tunneling current through a molecular bridge coupled to two semiconductor electrodes. A quantum master equation is developed within a non-Markovian theory based on second-order perturbation theory with respect to the molecule-semiconductor electrode coupling. The spectral functions are generated using a one dimensional alternating bond model, and the coupling between the molecule and the electrodes is expressed through a corresponding correlation function. Since the molecular bridge orbitals are inside the bandgap between the conduction and valence bands, charge carrier tunneling is inhibited in the dark. Subject to the dipole interaction with the laser field, virtual molecular states are generated via the absorption and emission of photons, and new tunneling channels open. Interesting phenomena arising from memory are noted. Such a phenomenon could serve as a switch.
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Affiliation(s)
- Guangqi Li
- Department of Chemistry, Northwestern University, Evanston, Illinois 60208, USA
| | - Boris D Fainberg
- Faculty of Science, Holon Institute of Technology, 58102 Holon, Israel
| | - Tamar Seideman
- Department of Chemistry, Northwestern University, Evanston, Illinois 60208, USA
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Popescu B, Rahman H, Kleinekathöfer U. Using the Chebychev expansion in quantum transport calculations. J Chem Phys 2015; 142:154103. [PMID: 25903862 DOI: 10.1063/1.4917198] [Citation(s) in RCA: 14] [Impact Index Per Article: 1.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/20/2023] Open
Abstract
Irradiation by laser pulses and a fluctuating surrounding liquid environment can, for example, lead to time-dependent effects in the transport through molecular junctions. From the theoretical point of view, time-dependent theories of quantum transport are still challenging. In one of these existing transport theories, the energy-dependent coupling between molecule and leads is decomposed into Lorentzian functions. This trick has successfully been combined with quantum master approaches, hierarchical formalisms, and non-equilibrium Green's functions. The drawback of this approach is, however, its serious limitation to certain forms of the molecule-lead coupling and to higher temperatures. Tian and Chen [J. Chem. Phys. 137, 204114 (2012)] recently employed a Chebychev expansion to circumvent some of these latter problems. Here, we report on a similar approach also based on the Chebychev expansion but leading to a different set of coupled differential equations using the fact that a derivative of a zeroth-order Bessel function can again be given in terms of Bessel functions. Test calculations show the excellent numerical accuracy and stability of the presented formalism. The time span for which this Chebychev expansion scheme is valid without any restrictions on the form of the spectral density or temperature can be determined a priori.
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Affiliation(s)
- Bogdan Popescu
- Department of Physics and Earth Sciences, Jacobs University Bremen, Campus Ring 1, 28759 Bremen, Germany
| | - Hasan Rahman
- Department of Physics and Earth Sciences, Jacobs University Bremen, Campus Ring 1, 28759 Bremen, Germany
| | - Ulrich Kleinekathöfer
- Department of Physics and Earth Sciences, Jacobs University Bremen, Campus Ring 1, 28759 Bremen, Germany
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Aragó J, Troisi A. Dynamics of the excitonic coupling in organic crystals. PHYSICAL REVIEW LETTERS 2015; 114:026402. [PMID: 25635554 DOI: 10.1103/physrevlett.114.026402] [Citation(s) in RCA: 78] [Impact Index Per Article: 8.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/28/2014] [Indexed: 05/22/2023]
Abstract
We show that the excitonic coupling in molecular crystals undergoes a very large fluctuation at room temperature as a result of the combined thermal motions of the nuclei. This observation dramatically affects the description of exciton transport in organic crystals and any other phenomenon (like singlet fission or exciton dissociation) that originates from an exciton in a molecular crystal or thin film. This unexpected result is due to the predominance of the short-range excitonic coupling mechanisms (exchange, overlap, and charge-transfer mediated) over the Coulombic excitonic coupling for molecules in van der Waals contact. To quantify this effect we develop a procedure to evaluate accurately the short-range excitonic coupling (via a diabatization scheme) along a molecular dynamics trajectory of the representative molecular crystals of anthracene and tetracene.
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Affiliation(s)
- Juan Aragó
- Department of Chemistry and Centre for Scientific Computing, University of Warwick, Coventry CV4 7AL, United Kingdom
| | - Alessandro Troisi
- Department of Chemistry and Centre for Scientific Computing, University of Warwick, Coventry CV4 7AL, United Kingdom
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Abstract
The influence of the competition between polaron formation and population injection on exciton dissociation.
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Affiliation(s)
- Guangqi Li
- Department of Chemistry
- Northwestern University
- Evanston IL
- USA
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Leitherer S, Jäger CM, Halik M, Clark T, Thoss M. Modeling charge transport in C60-based self-assembled monolayers for applications in field-effect transistors. J Chem Phys 2014; 140:204702. [DOI: 10.1063/1.4876035] [Citation(s) in RCA: 15] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/12/2022] Open
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Abstract
The conductivity of DNA in molecular junctions is often probed experimentally under dry conditions, but it is unclear how much of the solvent remains attached to the DNA and how this impacts its structure, electronic states, and conductivity. Classical MD simulations show that DNA is unstable if the solvent is removed completely, while a micro-hydrated system with few water molecules shows similar charge transport properties as fully solvated DNA does. This surprising effect is analyzed in detail by mapping the density functional theory-based electronic structure to a tight-binding Hamiltonian, allowing for an estimate of conductivity of various DNA sequences with snapshot-averaged Landauer's approach. The characteristics of DNA charge transport turn out to be determined by the nearest hydration shell(s), and the removal of bulk solvent has little effect on the transport.
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Affiliation(s)
- Mario Wolter
- Institute of Physical Chemistry, Karlsruhe Institute of Technology, 76131 Karlsruhe, Germany
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Kubař T, Elstner M. A hybrid approach to simulation of electron transfer in complex molecular systems. J R Soc Interface 2013; 10:20130415. [PMID: 23883952 DOI: 10.1098/rsif.2013.0415] [Citation(s) in RCA: 57] [Impact Index Per Article: 5.2] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/12/2022] Open
Abstract
Electron transfer (ET) reactions in biomolecular systems represent an important class of processes at the interface of physics, chemistry and biology. The theoretical description of these reactions constitutes a huge challenge because extensive systems require a quantum-mechanical treatment and a broad range of time scales are involved. Thus, only small model systems may be investigated with the modern density functional theory techniques combined with non-adiabatic dynamics algorithms. On the other hand, model calculations based on Marcus's seminal theory describe the ET involving several assumptions that may not always be met. We review a multi-scale method that combines a non-adiabatic propagation scheme and a linear scaling quantum-chemical method with a molecular mechanics force field in such a way that an unbiased description of the dynamics of excess electron is achieved and the number of degrees of freedom is reduced effectively at the same time. ET reactions taking nanoseconds in systems with hundreds of quantum atoms can be simulated, bridging the gap between non-adiabatic ab initio simulations and model approaches such as the Marcus theory. A major recent application is hole transfer in DNA, which represents an archetypal ET reaction in a polarizable medium. Ongoing work focuses on hole transfer in proteins, peptides and organic semi-conductors.
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Affiliation(s)
- Tomáš Kubař
- Institute of Physical Chemistry, Karlsruhe Institute of Technology, 76131 Karlsruhe, Germany
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