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Bustamante CM, Todorov T, Gadea ED, Tarasi F, Stella L, Horsfield A, Scherlis DA. Modeling the electroluminescence of atomic wires from quantum dynamics simulations. J Chem Phys 2024; 160:214102. [PMID: 38828814 DOI: 10.1063/5.0201447] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/30/2024] [Accepted: 05/14/2024] [Indexed: 06/05/2024] Open
Abstract
Static and time-dependent quantum-mechanical approaches have been employed in the literature to characterize the physics of light-emitting molecules and nanostructures. However, the electromagnetic emission induced by an input current has remained beyond the realm of molecular simulations. This is the challenge addressed here with the help of an equation of motion for the density matrix coupled to a photon bath based on a Redfield formulation. This equation is evolved within the framework of the driven-Liouville von Neumann approach, which incorporates open boundaries by introducing an applied bias and a circulating current. The dissipated electromagnetic power can be computed in this context from the time derivative of the energy. This scheme is applied in combination with a self-consistent tight-binding Hamiltonian to investigate the effects of bias and molecular size on the electroluminescence of metallic and semiconducting chains. For the latter, a complex interplay between bias and molecular length is observed: there is an optimal number of atoms that maximizes the emitted power at high voltages but not at low ones. This unanticipated behavior can be understood in terms of the band bending produced along the semiconducting chain, a phenomenon that is captured by the self-consistency of the method. A simple analytical model is proposed that explains the main features revealed by the simulations. The methodology, applied here at a self-consistent tight-binding level but extendable to more sophisticated Hamiltonians such as density functional tight binding and time dependent density functional theory, promises to be helpful for quantifying the power and quantum efficiency of nanoscale electroluminescent devices.
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Affiliation(s)
- Carlos M Bustamante
- Max Planck Institute for the Structure and Dynamics of Matter, Hamburg 22761, Germany
| | - Tchavdar Todorov
- Centre for Quantum Materials and Technologies, School of Mathematics and Physics, Queen's University Belfast, Belfast BT7 1NN, United Kingdom
| | - Esteban D Gadea
- Departamento de Química Inorgánica, Analítica y Química Física/INQUIMAE, Facultad de Ciencias Exactas y Naturales, Universidad de Buenos Aires, Buenos Aires, Argentina
| | - Facundo Tarasi
- Departamento de Química Inorgánica, Analítica y Química Física/INQUIMAE, Facultad de Ciencias Exactas y Naturales, Universidad de Buenos Aires, Buenos Aires, Argentina
| | - Lorenzo Stella
- Centre for Light-Matter Interactions, School of Mathematics and Physics, Queen's University Belfast, Belfast BT7 1NN, United Kingdom
| | - Andrew Horsfield
- Department of Materials, Thomas Young Centre, Imperial College London, South Kensington Campus, London SW7 2AZ, United Kingdom
| | - Damián A Scherlis
- Departamento de Química Inorgánica, Analítica y Química Física/INQUIMAE, Facultad de Ciencias Exactas y Naturales, Universidad de Buenos Aires, Buenos Aires, Argentina
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2
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Oz A, Nitzan A, Hod O, Peralta JE. Electron Dynamics in Open Quantum Systems: The Driven Liouville-von Neumann Methodology within Time-Dependent Density Functional Theory. J Chem Theory Comput 2023; 19:7496-7504. [PMID: 37852250 PMCID: PMC10653109 DOI: 10.1021/acs.jctc.3c00311] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/17/2023] [Indexed: 10/20/2023]
Abstract
A first-principles approach to describe electron dynamics in open quantum systems driven far from equilibrium via external time-dependent stimuli is introduced. Within this approach, the driven Liouville-von Neumann methodology is used to impose open boundary conditions on finite model systems whose dynamics is described using time-dependent density functional theory. As a proof of concept, the developed methodology is applied to simple spin-compensated model systems, including a hydrogen chain and a graphitic molecular junction. Good agreement between steady-state total currents obtained via direct propagation and those obtained from the self-consistent solution of the corresponding Sylvester equation indicates the validity of the implementation. The capability of the new computational approach to analyze, from first principles, non-equilibrium dynamics of open quantum systems in terms of temporally and spatially resolved current densities is demonstrated. Future extensions of the approach toward the description of dynamical magnetization and decoherence effects are briefly discussed.
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Affiliation(s)
- Annabelle Oz
- Department
of Physical Chemistry, School of Chemistry, the Raymond and Beverly
Sackler Faculty of Exact Sciences, and the Sackler Center for Computational
Molecular and Materials Science, Tel Aviv
University, Tel Aviv, 6997801, Israel
| | - Abraham Nitzan
- Department
of Physical Chemistry, School of Chemistry, the Raymond and Beverly
Sackler Faculty of Exact Sciences, and the Sackler Center for Computational
Molecular and Materials Science, Tel Aviv
University, Tel Aviv, 6997801, Israel
- Department
of Chemistry, University of Pennsylvania, Philadelphia, Pennsylvania 19103, United States
| | - Oded Hod
- Department
of Physical Chemistry, School of Chemistry, the Raymond and Beverly
Sackler Faculty of Exact Sciences, and the Sackler Center for Computational
Molecular and Materials Science, Tel Aviv
University, Tel Aviv, 6997801, Israel
| | - Juan E. Peralta
- Department
of Physics, Central Michigan University, Mount Pleasant, Michigan 48859, United States
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3
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Bustamante CM, Scherlis DA. Doping and coupling strength in molecular conductors: polyacetylene as a case study. Phys Chem Chem Phys 2021; 23:26974-26980. [PMID: 34842869 DOI: 10.1039/d1cp04728k] [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
The doping mechanisms responsible for elevating the currents up to eleven orders of magnitude in semiconducting polymer films are today well characterized. Doping can also improve the performance of nanoscale devices or single molecule conductors, but the mechanism in this case appears to be different, with theoretical studies suggesting that the dopant affects the electronic properties of the junctions. In the present report, multiscale time-dependent DFT transport simulations help clarify the way in which n-type doping can raise the current flowing through a polymer chain connected to a pair of electrodes, with the focus on polyacetylene. In particular, our multiscale methodology offers control over the magnitude of the chemical coupling between the molecule and the electrodes, which allows us to analyze the effect of doping in low and strong coupling regimes. Interestingly, our results establish that the impact of dopants is the highest in weakly coupled devices, while their presence tends to be irrelevant in low-resistance junctions. Our calculations point out that both the equalization of the frontier orbitals with the Fermi level and a small gap between the HOMO and the LUMO must result from doping in order to observe any significant increase of the currents.
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Affiliation(s)
- Carlos M Bustamante
- Departamento de Química Inorgánica, Analítica y Química Física/INQUIMAE, Facultad de Ciencias Exactas y Naturales, Universidad de Buenos Aires, Buenos Aires (C1428EHA), Argentina.
| | - Damián A Scherlis
- Departamento de Química Inorgánica, Analítica y Química Física/INQUIMAE, Facultad de Ciencias Exactas y Naturales, Universidad de Buenos Aires, Buenos Aires (C1428EHA), Argentina.
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4
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Elenewski JE, Wójtowicz G, Rams MM, Zwolak M. Performance of reservoir discretizations in quantum transport simulations. J Chem Phys 2021; 155:124117. [PMID: 34598565 DOI: 10.1063/5.0065799] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/21/2022] Open
Abstract
Quantum transport simulations often use explicit, yet finite, electronic reservoirs. These should converge to the correct continuum limit, albeit with a trade-off between discretization and computational cost. Here, we study this interplay for extended reservoir simulations, where relaxation maintains a bias or temperature drop across the system. Our analysis begins in the non-interacting limit, where we parameterize different discretizations to compare them on an even footing. For many-body systems, we develop a method to estimate the relaxation that best approximates the continuum by controlling virtual transitions in Kramers turnover for the current. While some discretizations are more efficient for calculating currents, there is little benefit with regard to the overall state of the system. Any gains become marginal for many-body, tensor network simulations, where the relative performance of discretizations varies when sweeping other numerical controls. These results indicate that typical reservoir discretizations have little impact on numerical costs for certain computational tools. The choice of a relaxation parameter is nonetheless crucial, and the method we develop provides a reliable estimate of the optimal relaxation for finite reservoirs.
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Affiliation(s)
- Justin E Elenewski
- Biophysical and Biomedical Measurement Group, Microsystems and Nanotechnology Division, Physical Measurement Laboratory, National Institute of Standards and Technology, Gaithersburg, Maryland 20899, USA
| | - Gabriela Wójtowicz
- Jagiellonian University, Institute of Theoretical Physics, Łojasiewicza 11, 30-348 Kraków, Poland
| | - Marek M Rams
- Jagiellonian University, Institute of Theoretical Physics, Łojasiewicza 11, 30-348 Kraków, Poland
| | - Michael Zwolak
- Biophysical and Biomedical Measurement Group, Microsystems and Nanotechnology Division, Physical Measurement Laboratory, National Institute of Standards and Technology, Gaithersburg, Maryland 20899, USA
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5
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Bustamante CM, Gadea ED, Horsfield A, Todorov TN, González Lebrero MC, Scherlis DA. Dissipative Equation of Motion for Electromagnetic Radiation in Quantum Dynamics. PHYSICAL REVIEW LETTERS 2021; 126:087401. [PMID: 33709735 DOI: 10.1103/physrevlett.126.087401] [Citation(s) in RCA: 3] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/07/2020] [Accepted: 01/19/2021] [Indexed: 06/12/2023]
Abstract
The dynamical description of the radiative decay of an electronically excited state in realistic many-particle systems is an unresolved challenge. In the present investigation electromagnetic radiation of the charge density is approximated as the power dissipated by a classical dipole, to cast the emission in closed form as a unitary single-electron theory. This results in a formalism of unprecedented efficiency, critical for ab initio modeling, which exhibits at the same time remarkable properties: it quantitatively predicts decay rates, natural broadening, and absorption intensities. Exquisitely accurate excitation lifetimes are obtained from time-dependent DFT simulations for C^{2+}, B^{+}, and Be, of 0.565, 0.831, and 1.97 ns, respectively, in accord with experimental values of 0.57±0.02, 0.86±0.07, and 1.77-2.5 ns. Hence, the present development expands the frontiers of quantum dynamics, bringing within reach first-principles simulations of a wealth of photophysical phenomena, from fluorescence to time-resolved spectroscopies.
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Affiliation(s)
- Carlos M Bustamante
- Departamento de Química Inorgánica, Analítica y Química Física/INQUIMAE, Facultad de Ciencias Exactas y Naturales, Universidad de Buenos Aires, Buenos Aires (C1428EHA), Argentina
| | - Esteban D Gadea
- Departamento de Química Inorgánica, Analítica y Química Física/INQUIMAE, Facultad de Ciencias Exactas y Naturales, Universidad de Buenos Aires, Buenos Aires (C1428EHA), Argentina
| | - Andrew Horsfield
- Department of Materials, Thomas Young Centre, Imperial College London, South Kensington Campus, London SW7 2AZ, United Kingdom
| | - Tchavdar N Todorov
- Atomistic Simulation Centre, School of Mathematics and Physics, Queen's University Belfast, Belfast BT7 1NN, United Kingdom
| | - Mariano C González Lebrero
- Departamento de Química Inorgánica, Analítica y Química Física/INQUIMAE, Facultad de Ciencias Exactas y Naturales, Universidad de Buenos Aires, Buenos Aires (C1428EHA), Argentina
| | - Damián A Scherlis
- Departamento de Química Inorgánica, Analítica y Química Física/INQUIMAE, Facultad de Ciencias Exactas y Naturales, Universidad de Buenos Aires, Buenos Aires (C1428EHA), Argentina
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6
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Bustamante CM, Todorov TN, Sánchez CG, Horsfield A, Scherlis DA. A simple approximation to the electron-phonon interaction in population dynamics. J Chem Phys 2020; 153:234108. [PMID: 33353325 DOI: 10.1063/5.0031766] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
The modeling of coupled electron-ion dynamics including a quantum description of the nuclear degrees of freedom has remained a costly and technically difficult practice. The kinetic model for electron-phonon interaction provides an efficient approach to this problem, for systems evolving with low amplitude fluctuations, in a quasi-stationary state. In this work, we propose an extension of the kinetic model to include the effect of coherences, which are absent in the original approach. The new scheme, referred to as Liouville-von Neumann + Kinetic Equation (or LvN + KE), is implemented here in the context of a tight-binding Hamiltonian and employed to model the broadening, caused by the nuclear vibrations, of the electronic absorption bands of an atomic wire. The results, which show close agreement with the predictions given by Fermi's golden rule (FGR), serve as a validation of the methodology. Thereafter, the method is applied to the electron-phonon interaction in transport simulations, adopting to this end the driven Liouville-von Neumann equation to model open quantum boundaries. In this case, the LvN + KE model qualitatively captures the Joule heating effect and Ohm's law. It, however, exhibits numerical discrepancies with respect to the results based on FGR, attributable to the fact that the quasi-stationary state is defined taking into consideration the eigenstates of the closed system rather than those of the open boundary system. The simplicity and numerical efficiency of this approach and its ability to capture the essential physics of the electron-phonon coupling make it an attractive route to first-principles electron-ion dynamics.
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Affiliation(s)
- Carlos M Bustamante
- Departamento de Química Inorgánica, Analítica y Química Física/INQUIMAE, Facultad de Ciencias Exactas y Naturales, Universidad de Buenos Aires, Buenos Aires C1428EHA, Argentina
| | - Tchavdar N Todorov
- Atomistic Simulation Centre, School of Mathematics and Physics, Queen's University Belfast, Belfast BT7 1NN, United Kingdom
| | - Cristián G Sánchez
- Instituto Interdisciplinario de Ciencias Básicas, Facultad de Ciencias Exactas y Naturales, Universidad Nacional de Cuyo, CONICET, Padre Jorge Contreras 1300, Mendoza M5502JMA, Argentina
| | - Andrew Horsfield
- Department of Materials, Thomas Young Centre, Imperial College London, South Kensington Campus, London SW7 2AZ, United Kingdom
| | - Damian A Scherlis
- Departamento de Química Inorgánica, Analítica y Química Física/INQUIMAE, Facultad de Ciencias Exactas y Naturales, Universidad de Buenos Aires, Buenos Aires C1428EHA, Argentina
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7
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Ramirez FF, Bustamente CM, González Lebrero MC, Scherlis DA. Transport and Spectroscopy in Conjugated Molecules: Two Properties and a Single Rationale. J Chem Theory Comput 2020; 16:2930-2940. [DOI: 10.1021/acs.jctc.9b01122] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/25/2023]
Affiliation(s)
- Francisco F. Ramirez
- Departamento de Química Inorgánica, Analítica y Química Física/INQUIMAE, Facultad de Ciencias Exactas y Naturales, Universidad de Buenos Aires, Ciudad Universitaria, Pab. II, Buenos Aires C1428EHA, Argentina
| | - Carlos M. Bustamente
- Departamento de Química Inorgánica, Analítica y Química Física/INQUIMAE, Facultad de Ciencias Exactas y Naturales, Universidad de Buenos Aires, Ciudad Universitaria, Pab. II, Buenos Aires C1428EHA, Argentina
| | - Mariano C. González Lebrero
- Departamento de Química Inorgánica, Analítica y Química Física/INQUIMAE, Facultad de Ciencias Exactas y Naturales, Universidad de Buenos Aires, Ciudad Universitaria, Pab. II, Buenos Aires C1428EHA, Argentina
| | - Damián A. Scherlis
- Departamento de Química Inorgánica, Analítica y Química Física/INQUIMAE, Facultad de Ciencias Exactas y Naturales, Universidad de Buenos Aires, Ciudad Universitaria, Pab. II, Buenos Aires C1428EHA, Argentina
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8
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Bustamante CM, Ramírez FF, Sánchez CG, Scherlis DA. Multiscale approach to electron transport dynamics. J Chem Phys 2019; 151:084105. [DOI: 10.1063/1.5112372] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- Carlos M. Bustamante
- Departamento de Química Inorgánica, Analítica y Química Física/INQUIMAE, Facultad de Ciencias Exactas y Naturales, Universidad de Buenos Aires, Ciudad Universitaria, Pab. II, Buenos Aires C1428EHA, Argentina
| | - Francisco F. Ramírez
- Departamento de Química Inorgánica, Analítica y Química Física/INQUIMAE, Facultad de Ciencias Exactas y Naturales, Universidad de Buenos Aires, Ciudad Universitaria, Pab. II, Buenos Aires C1428EHA, Argentina
| | - Cristián G. Sánchez
- Departamento de Química Teórica y Computacional, Facultad de Ciencias Químicas, Universidad Nacional de Córdoba, Ciudad Universitaria, X5000HUA, Córdoba, Argentina and CONICET & Facultad de Ciencias Exactas y Naturales, Universidad Nacional de Cuyo, Mendoza, CP5500, Argentina
| | - Damián A. Scherlis
- Departamento de Química Inorgánica, Analítica y Química Física/INQUIMAE, Facultad de Ciencias Exactas y Naturales, Universidad de Buenos Aires, Ciudad Universitaria, Pab. II, Buenos Aires C1428EHA, Argentina
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9
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Oz I, Hod O, Nitzan A. Evaluation of dynamical properties of open quantum systems using the driven Liouville-von Neumann approach: methodological considerations. Mol Phys 2019. [DOI: 10.1080/00268976.2019.1584338] [Citation(s) in RCA: 7] [Impact Index Per Article: 1.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/27/2022]
Affiliation(s)
- Inbal Oz
- Department of Physical Chemistry, School of Chemistry, The Raymond and Beverly Sackler Faculty of Exact Sciences, Tel Aviv University, Tel Aviv, IL, Israel
- The Sackler Center for Computational Molecular and Materials Science, Tel Aviv University, Tel Aviv, IL, Israel
| | - Oded Hod
- Department of Physical Chemistry, School of Chemistry, The Raymond and Beverly Sackler Faculty of Exact Sciences, Tel Aviv University, Tel Aviv, IL, Israel
- The Sackler Center for Computational Molecular and Materials Science, Tel Aviv University, Tel Aviv, IL, Israel
| | - Abraham Nitzan
- Department of Physical Chemistry, School of Chemistry, The Raymond and Beverly Sackler Faculty of Exact Sciences, Tel Aviv University, Tel Aviv, IL, Israel
- The Sackler Center for Computational Molecular and Materials Science, Tel Aviv University, Tel Aviv, IL, Israel
- Department of Chemistry, University of Pennsylvania, Philadelphia, PA, USA
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10
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Zwolak M. Communication: Gibbs phenomenon and the emergence of the steady-state in quantum transport. J Chem Phys 2018; 149:241102. [PMID: 30599719 PMCID: PMC6602063 DOI: 10.1063/1.5061759] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022] Open
Abstract
Simulations are increasingly employing explicit reservoirs-internal, finite regions-to drive electronic or particle transport. This naturally occurs in simulations of transport via ultracold atomic gases. Whether the simulation is numerical or physical, these approaches rely on the rapid development of the steady state. We demonstrate that steady state formation is a manifestation of the Gibbs phenomenon well-known in signal processing and in truncated discrete Fourier expansions. Each particle separately develops into an individual steady state due to the spreading of its wave packet in energy. The rise to the steady state for an individual particle depends on the particle energy-and thus can be slow-and ringing oscillations appear due to filtering of the response through the electronic bandwidth. However, the rise to the total steady state-the one from all particles-is rapid, with time scale π/W, where W is the bandwidth. Ringing oscillations are now also filtered through the bias window, and they decay with a higher power. The Gibbs constant-the overshoot of the first ring-can appear in the simulation error. These results shed light on the formation of the steady state and support the practical use of explicit reservoirs to simulate transport at the nanoscale or using ultracold atomic lattices.
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Affiliation(s)
- Michael Zwolak
- Biophysics Group, Microsystems and Nanotechnology Division, Physical Measurement Laboratory, National Institute of Standards and Technology, Gaithersburg, MD 20899, USA
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11
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Ramírez F, Díaz Mirón G, González Lebrero MC, Scherlis DA. QM–MM Ehrenfest dynamics from first principles: photodissociation of diazirine in aqueous solution. Theor Chem Acc 2018. [DOI: 10.1007/s00214-018-2305-1] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/09/2023]
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12
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Elenewski JE, Gruss D, Zwolak M. Communication: Master equations for electron transport: The limits of the Markovian limit. J Chem Phys 2018; 147:151101. [PMID: 29055298 DOI: 10.1063/1.5000747] [Citation(s) in RCA: 21] [Impact Index Per Article: 3.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
Master equations are increasingly popular for the simulation of time-dependent electronic transport in nanoscale devices. Several recent Markovian approaches use "extended reservoirs"-explicit degrees of freedom associated with the electrodes-distinguishing them from many previous classes of master equations. Starting from a Lindblad equation, we develop a common foundation for these approaches. Due to the incorporation of explicit electrode states, these methods do not require a large bias or even "true Markovianity" of the reservoirs. Nonetheless, their predictions are only physically relevant when the Markovian relaxation is weaker than the thermal broadening and when the extended reservoirs are "sufficiently large," in a sense that we quantify. These considerations hold despite complete positivity and respect for Pauli exclusion at any relaxation strength.
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Affiliation(s)
- Justin E Elenewski
- Center for Nanoscale Science and Technology, National Institute of Standards and Technology, Gaithersburg, Maryland 20899, USA
| | - Daniel Gruss
- Center for Nanoscale Science and Technology, National Institute of Standards and Technology, Gaithersburg, Maryland 20899, USA
| | - Michael Zwolak
- Center for Nanoscale Science and Technology, National Institute of Standards and Technology, Gaithersburg, Maryland 20899, USA
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13
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Pal PP, Ramakrishna S, Seideman T. Emergence of Landauer transport from quantum dynamics: A model Hamiltonian approach. J Chem Phys 2018; 148:144707. [PMID: 29655338 DOI: 10.1063/1.5009815] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
The Landauer expression for computing current-voltage characteristics in nanoscale devices is efficient but not suited to transient phenomena and a time-dependent current because it is applicable only when the charge carriers transition into a steady flux after an external perturbation. In this article, we construct a very general expression for time-dependent current in an electrode-molecule-electrode arrangement. Utilizing a model Hamiltonian (consisting of the subsystem energy levels and their electronic coupling terms), we propagate the Schrödinger wave function equation to numerically compute the time-dependent population in the individual subsystems. The current in each electrode (defined in terms of the rate of change of the corresponding population) has two components, one due to the charges originating from the same electrode and the other due to the charges initially residing at the other electrode. We derive an analytical expression for the first component and illustrate that it agrees reasonably with its numerical counterpart at early times. Exploiting the unitary evolution of a wavefunction, we construct a more general Landauer style formula and illustrate the emergence of Landauer transport from our simulations without the assumption of time-independent charge flow. Our generalized Landauer formula is valid at all times for models beyond the wide-band limit, non-uniform electrode density of states and for time and energy-dependent electronic coupling between the subsystems. Subsequently, we investigate the ingredients in our model that regulate the onset time scale of this steady state. We compare the performance of our general current expression with the Landauer current for time-dependent electronic coupling. Finally, we comment on the applicability of the Landauer formula to compute hot-electron current arising upon plasmon decoherence.
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Affiliation(s)
- Partha Pratim Pal
- Department of Chemistry, Northwestern University, Evanston, Illinois 60608, USA
| | - S Ramakrishna
- Department of Chemistry, Northwestern University, Evanston, Illinois 60608, USA
| | - Tamar Seideman
- Department of Chemistry, Northwestern University, Evanston, Illinois 60608, USA
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14
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Prucker V, Bockstedte M, Thoss M, Coto PB. Dynamical simulation of electron transfer processes in self-assembled monolayers at metal surfaces using a density matrix approach. J Chem Phys 2018; 148:124705. [DOI: 10.1063/1.5020238] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- V. Prucker
- Institut für Theoretische Physik und Interdisziplinäres Zentrum für Molekulare Materialien, Friedrich-Alexander-Universität Erlangen-Nürnberg, Staudtstr. 7/B2, D-91058 Erlangen, Germany
| | - M. Bockstedte
- Department Chemistry and Physics of Materials, Universität Salzburg, Jakob-Haringer-Str. 2a, A-5020 Salzburg, Austria
- Lehrstuhl für Theoretische Festkörperphysik, Friedrich-Alexander-Universität Erlangen-Nürnberg, Staudtstr. 7/B2, D-91058 Erlangen, Germany
| | - M. Thoss
- Institut für Theoretische Physik und Interdisziplinäres Zentrum für Molekulare Materialien, Friedrich-Alexander-Universität Erlangen-Nürnberg, Staudtstr. 7/B2, D-91058 Erlangen, Germany
- Physikalisches Institut, Albert-Ludwigs-Universität Freiburg, Hermann-Herder-Str. 3, D-79104 Freiburg, Germany
| | - P. B. Coto
- Institut für Theoretische Physik und Interdisziplinäres Zentrum für Molekulare Materialien, Friedrich-Alexander-Universität Erlangen-Nürnberg, Staudtstr. 7/B2, D-91058 Erlangen, Germany
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15
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Marcolongo JP, Zeida A, Semelak JA, Foglia NO, Morzan UN, Estrin DA, González Lebrero MC, Scherlis DA. Chemical Reactivity and Spectroscopy Explored From QM/MM Molecular Dynamics Simulations Using the LIO Code. Front Chem 2018; 6:70. [PMID: 29619365 PMCID: PMC5871697 DOI: 10.3389/fchem.2018.00070] [Citation(s) in RCA: 25] [Impact Index Per Article: 4.2] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/02/2018] [Accepted: 03/05/2018] [Indexed: 12/13/2022] Open
Abstract
In this work we present the current advances in the development and the applications of LIO, a lab-made code designed for density functional theory calculations in graphical processing units (GPU), that can be coupled with different classical molecular dynamics engines. This code has been thoroughly optimized to perform efficient molecular dynamics simulations at the QM/MM DFT level, allowing for an exhaustive sampling of the configurational space. Selected examples are presented for the description of chemical reactivity in terms of free energy profiles, and also for the computation of optical properties, such as vibrational and electronic spectra in solvent and protein environments.
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Affiliation(s)
- Juan P Marcolongo
- DQIAyQF, INQUIMAE-CONICET, Facultad de Ciencias Exactas y Naturales, Universidad de Buenos Aires, Buenos Aires, Argentina
| | - Ari Zeida
- DQIAyQF, INQUIMAE-CONICET, Facultad de Ciencias Exactas y Naturales, Universidad de Buenos Aires, Buenos Aires, Argentina.,Departamento de Bioquímica and Center for Free Radical and Biomedical Research, Facultad de Medicina, Universidad de la República, Montevideo, Uruguay
| | - Jonathan A Semelak
- DQIAyQF, INQUIMAE-CONICET, Facultad de Ciencias Exactas y Naturales, Universidad de Buenos Aires, Buenos Aires, Argentina
| | - Nicolás O Foglia
- DQIAyQF, INQUIMAE-CONICET, Facultad de Ciencias Exactas y Naturales, Universidad de Buenos Aires, Buenos Aires, Argentina
| | - Uriel N Morzan
- DQIAyQF, INQUIMAE-CONICET, Facultad de Ciencias Exactas y Naturales, Universidad de Buenos Aires, Buenos Aires, Argentina
| | - Dario A Estrin
- DQIAyQF, INQUIMAE-CONICET, Facultad de Ciencias Exactas y Naturales, Universidad de Buenos Aires, Buenos Aires, Argentina
| | - Mariano C González Lebrero
- DQIAyQF, INQUIMAE-CONICET, Facultad de Ciencias Exactas y Naturales, Universidad de Buenos Aires, Buenos Aires, Argentina
| | - Damián A Scherlis
- DQIAyQF, INQUIMAE-CONICET, Facultad de Ciencias Exactas y Naturales, Universidad de Buenos Aires, Buenos Aires, Argentina
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16
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Gruss D, Smolyanitsky A, Zwolak M. Communication: Relaxation-limited electronic currents in extended reservoir simulations. J Chem Phys 2017; 147:141102. [PMID: 29031250 PMCID: PMC5718372 DOI: 10.1063/1.4997022] [Citation(s) in RCA: 17] [Impact Index Per Article: 2.4] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/31/2023] Open
Abstract
Open-system approaches are gaining traction in the simulation of charge transport in nanoscale and molecular electronic devices. In particular, "extended reservoir" simulations, where explicit reservoir degrees of freedom are present, allow for the computation of both real-time and steady-state properties but require relaxation of the extended reservoirs. The strength of this relaxation, γ, influences the conductance, giving rise to a "turnover" behavior analogous to Kramers turnover in chemical reaction rates. We derive explicit, general expressions for the weak and strong relaxation limits. For weak relaxation, the conductance increases linearly with γ and every electronic state of the total explicit system contributes to the electronic current according to its "reduced" weight in the two extended reservoir regions. Essentially, this represents two conductors in series-one at each interface with the implicit reservoirs that provide the relaxation. For strong relaxation, a "dual" expression-one with the same functional form-results, except now proportional to 1/γ and dependent on the system of interest's electronic states, reflecting that the strong relaxation is localizing electrons in the extended reservoirs. Higher order behavior (e.g., γ2 or 1/γ2) can occur when there is a gap in the frequency spectrum. Moreover, inhomogeneity in the frequency spacing can give rise to a pseudo-plateau regime. These findings yield a physically motivated approach to diagnosing numerical simulations and understanding the influence of relaxation, and we examine their occurrence in both simple models and a realistic, fluctuating graphene nanoribbon.
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Affiliation(s)
- Daniel Gruss
- Center for Nanoscale Science and Technology, National Institute of Standards and Technology, Gaithersburg, MD 20899, USA
- Maryland Nanocenter, University of Maryland, College Park, MD 20742, USA
| | - Alex Smolyanitsky
- Applied Chemicals and Materials Division, National Institute of Standards and Technology, Boulder, CO 80305, USA
| | - Michael Zwolak
- Center for Nanoscale Science and Technology, National Institute of Standards and Technology, Gaithersburg, MD 20899, USA
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17
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Zelovich T, Hansen T, Liu ZF, Neaton JB, Kronik L, Hod O. Parameter-free driven Liouville-von Neumann approach for time-dependent electronic transport simulations in open quantum systems. J Chem Phys 2017. [DOI: 10.1063/1.4976731] [Citation(s) in RCA: 33] [Impact Index Per Article: 4.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/04/2023] Open
Affiliation(s)
- Tamar Zelovich
- Department of Physical Chemistry, School of Chemistry, The Raymond and Beverly Sackler Faculty of Exact Sciences and The Sackler Center for Computational Molecular and Materials Science, Tel Aviv University, Tel Aviv 6997801, Israel
| | - Thorsten Hansen
- Department of Chemistry, Copenhagen University, Universitetsparken 5, DK-2100 Copenhagen Ø, Denmark
| | - Zhen-Fei Liu
- Department of Physics, University of California, Berkeley, Berkeley, California 94720-7300, USA
- Materials Sciences Division, Lawrence Berkeley National Laboratory, Berkeley, California 94720, USA
- Molecular Foundry, Lawrence Berkeley National Laboratory, Berkeley, California 94720, USA
| | - Jeffrey B. Neaton
- Department of Physics, University of California, Berkeley, Berkeley, California 94720-7300, USA
- Materials Sciences Division, Lawrence Berkeley National Laboratory, Berkeley, California 94720, USA
- Molecular Foundry, Lawrence Berkeley National Laboratory, Berkeley, California 94720, USA
- Kavli Energy NanoSciences Institute, Berkeley, California 94720, USA
| | - Leeor Kronik
- Department of Materials and Interfaces, Weizmann Institute of Science, Rehovoth 76100, Israel
| | - Oded Hod
- Department of Physical Chemistry, School of Chemistry, The Raymond and Beverly Sackler Faculty of Exact Sciences and The Sackler Center for Computational Molecular and Materials Science, Tel Aviv University, Tel Aviv 6997801, Israel
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