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Iyengar SS, Kumar A, Saha D, Sabry A. Synthesis of Hidden Subgroup Quantum Algorithms and Quantum Chemical Dynamics. J Chem Theory Comput 2023; 19:6082-6092. [PMID: 37703187 DOI: 10.1021/acs.jctc.3c00404] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 09/15/2023]
Abstract
We describe a general formalism for quantum dynamics and show how this formalism subsumes several quantum algorithms, including the Deutsch, Deutsch-Jozsa, Bernstein-Vazirani, Simon, and Shor algorithms as well as the conventional approach to quantum dynamics based on tensor networks. The common framework exposes similarities among quantum algorithms and natural quantum phenomena: we illustrate this connection by showing how the correlated behavior of protons in water wire systems that are common in many biological and materials systems parallels the structure of Shor's algorithm.
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Affiliation(s)
- Srinivasan S Iyengar
- Department of Chemistry, Indiana University, Bloomington, Indiana 47405-7102, United States
- Quantum Science and Engineering Center (QSEc), Indiana University, Bloomington, Indiana 47405-7102, United States
| | - Anup Kumar
- Department of Chemistry, Indiana University, Bloomington, Indiana 47405-7102, United States
| | - Debadrita Saha
- Department of Chemistry, Indiana University, Bloomington, Indiana 47405-7102, United States
| | - Amr Sabry
- Quantum Science and Engineering Center (QSEc), Indiana University, Bloomington, Indiana 47405-7102, United States
- Department of Computer Science, Luddy School of Informatics, Computing, and Engineering, Indiana University, Bloomington, Indiana 47405-7102, United States
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2
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Schäfer C, Johansson G. Shortcut to Self-Consistent Light-Matter Interaction and Realistic Spectra from First Principles. PHYSICAL REVIEW LETTERS 2022; 128:156402. [PMID: 35499896 DOI: 10.1103/physrevlett.128.156402] [Citation(s) in RCA: 11] [Impact Index Per Article: 5.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/24/2021] [Revised: 10/27/2021] [Accepted: 03/23/2022] [Indexed: 06/14/2023]
Abstract
We introduce a simple approach to how an electromagnetic environment can be efficiently embedded into state-of-the-art electronic structure methods, taking the form of radiation-reaction forces. We demonstrate that this self-consistently provides access to radiative emission, natural linewidth, Lamb shifts, strong coupling, electromagnetically induced transparency, Purcell-enhanced and superradiant emission. As an example, we illustrate its seamless integration into time-dependent density-functional theory with virtually no additional cost, presenting a convenient shortcut to light-matter interactions.
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Affiliation(s)
- Christian Schäfer
- Department of Microtechnology and Nanoscience, MC2, Chalmers University of Technology, 412 96 Göteborg, Sweden
- Department of Physics, Chalmers University of Technology, 412 96 Göteborg, Sweden
| | - Göran Johansson
- Department of Microtechnology and Nanoscience, MC2, Chalmers University of Technology, 412 96 Göteborg, Sweden
- Department of Physics, Chalmers University of Technology, 412 96 Göteborg, Sweden
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3
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An Application of the Madelung Formalism for Dissipating and Decaying Systems. Symmetry (Basel) 2021. [DOI: 10.3390/sym13050812] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/17/2022] Open
Abstract
This paper is concerned with the modeling and analysis of quantum dissipation and diffusion phenomena in the Schrödinger picture. We derive and investigate in detail the Schrödinger-type equations accounting for dissipation and diffusion effects. From a mathematical viewpoint, this equation allows one to achieve and analyze all aspects of the quantum dissipative systems, regarding the wave equation, Hamilton–Jacobi and continuity equations. This simplification requires the performance of “the Madelung decomposition” of “the wave function”, which is rigorously attained under the general Lagrangian justification for this modification of quantum mechanics. It is proved that most of the important equations of dissipative quantum physics, such as convection-diffusion, Fokker–Planck and quantum Boltzmann, have a common origin and can be unified in one equation.
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4
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Guandalini A, Cocchi C, Pittalis S, Ruini A, Rozzi CA. Nonlinear light absorption in many-electron systems excited by an instantaneous electric field: a non-perturbative approach. Phys Chem Chem Phys 2021; 23:10059-10069. [PMID: 33870971 DOI: 10.1039/d0cp04958a] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/21/2022]
Abstract
Applications of low-cost non-perturbative approaches in real time, such as time-dependent density functional theory, for the study of nonlinear optical properties of large and complex systems are gaining increasing popularity. However, their assessment still requires the analysis and understanding of elementary dynamical processes in simple model systems. Motivated by the aim of simulating optical nonlinearities in molecules, here exemplified by the case of the quaterthiophene oligomer, we investigate light absorption in many-electron interacting systems beyond the linear regime by using a single broadband impulse of an electric field; i.e. an electrical impulse in the instantaneous limit. We determine non-pertubatively the absorption cross section from the Fourier transform of the time-dependent induced dipole moment, which can be obtained from the time evolution of the wavefunction. We discuss the dependence of the resulting cross section on the magnitude of the impulse and we highlight the advantages of this method in comparison with perturbation theory by working on a one-dimensional model system for which numerically exact solutions are accessible. Thus, we demonstrate that the considered non-pertubative approach provides us with an effective tool for investigating fluence-dependent nonlinear optical excitations.
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Affiliation(s)
- Alberto Guandalini
- CNR - Istituto Nanoscienze, Via Campi 213A, I-41125 Modena, Italy. .,Dipartimento di Scienze Fisiche, Informatiche e Matematiche, Università di Modena e Reggio Emilia, Via Campi 213A, I-41125 Modena, Italy
| | - Caterina Cocchi
- Physics Department and IRIS Adlershof, Humboldt-Universität zu Berlin, Zum Großen Windkanal 2, D-12489 Berlin, Germany.,Physics Department, Carl von Ossietzky Universität Oldenburg, Carl-von-Ossietzky-Straße 9, 26129 Oldenburg, Germany
| | - Stefano Pittalis
- CNR - Istituto Nanoscienze, Via Campi 213A, I-41125 Modena, Italy.
| | - Alice Ruini
- Dipartimento di Scienze Fisiche, Informatiche e Matematiche, Università di Modena e Reggio Emilia, Via Campi 213A, I-41125 Modena, Italy
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5
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Baiardi A, Reiher M. The density matrix renormalization group in chemistry and molecular physics: Recent developments and new challenges. J Chem Phys 2020; 152:040903. [DOI: 10.1063/1.5129672] [Citation(s) in RCA: 85] [Impact Index Per Article: 21.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 02/03/2023] Open
Affiliation(s)
- Alberto Baiardi
- ETH Zürich, Laboratorium für Physikalische Chemie, Vladimir-Prelog-Weg 2, 8093 Zürich, Switzerland
| | - Markus Reiher
- ETH Zürich, Laboratorium für Physikalische Chemie, Vladimir-Prelog-Weg 2, 8093 Zürich, Switzerland
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6
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Biele R, D’Agosta R. Beyond the State of the Art: Novel Approaches for Thermal and Electrical Transport in Nanoscale Devices. ENTROPY 2019; 21:e21080752. [PMID: 33267466 PMCID: PMC7515281 DOI: 10.3390/e21080752] [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: 07/05/2019] [Revised: 07/28/2019] [Accepted: 07/29/2019] [Indexed: 11/16/2022]
Abstract
Almost any interaction between two physical entities can be described through the transfer of either charge, spin, momentum, or energy. Therefore, any theory able to describe these transport phenomena can shed light on a variety of physical, chemical, and biological effects, enriching our understanding of complex, yet fundamental, natural processes, e.g., catalysis or photosynthesis. In this review, we will discuss the standard workhorses for transport in nanoscale devices, namely Boltzmann's equation and Landauer's approach. We will emphasize their strengths, but also analyze their limits, proposing theories and models useful to go beyond the state of the art in the investigation of transport in nanoscale devices.
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Affiliation(s)
- Robert Biele
- Institute for Materials Science and Max Bergmann Center of Biomaterials, TU Dresden, 01062 Dresden, Germany
- Correspondence: (R.B.); (R.D.); Tel.: +34-943-015-803 (R.D.)
| | - Roberto D’Agosta
- Nano-Bio Spectroscopy Group and European Theoretical Spectroscopy Facility (ETSF), Universidad del Pais Vasco CFM CSIC-UPV/EHU-MPC and DIPC, Av. Tolosa 72, 20018 San Sebastian, Spain
- IKERBASQUE, Basque Foundation for Science Maria Diaz de Haro 3, 6 Solairua, 48013 Bilbao, Spain
- Correspondence: (R.B.); (R.D.); Tel.: +34-943-015-803 (R.D.)
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7
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Affiliation(s)
- Zhu Ruan
- Fritz Haber Center for Molecular Dynamics, Institute of Chemistry, The Hebrew University of Jerusalem , Jerusalem, Israel
| | - Roi Baer
- Fritz Haber Center for Molecular Dynamics, Institute of Chemistry, The Hebrew University of Jerusalem , Jerusalem, Israel
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8
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Chen S, Kwok Y, Chen G. Time-Dependent Density Functional Theory for Open Systems and Its Applications. Acc Chem Res 2018; 51:385-393. [PMID: 29350516 DOI: 10.1021/acs.accounts.7b00382] [Citation(s) in RCA: 11] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/25/2023]
Abstract
Photovoltaic devices, electrochemical cells, catalysis processes, light emitting diodes, scanning tunneling microscopes, molecular electronics, and related devices have one thing in common: open quantum systems where energy and matter are not conserved. Traditionally quantum chemistry is confined to isolated and closed systems, while quantum dissipation theory studies open quantum systems. The key quantity in quantum dissipation theory is the reduced system density matrix. As the reduced system density matrix is an O(M! × M!) matrix, where M is the number of the particles of the system of interest, quantum dissipation theory can only be employed to simulate systems of a few particles or degrees of freedom. It is thus important to combine quantum chemistry and quantum dissipation theory so that realistic open quantum systems can be simulated from first-principles. We have developed a first-principles method to simulate the dynamics of open electronic systems, the time-dependent density functional theory for open systems (TDDFT-OS). Instead of the reduced system density matrix, the key quantity is the reduced single-electron density matrix, which is an N × N matrix where N is the number of the atomic bases of the system of interest. As the dimension of the key quantity is drastically reduced, the TDDFT-OS can thus be used to simulate the dynamics of realistic open electronic systems and efficient numerical algorithms have been developed. As an application, we apply the method to study how quantum interference develops in a molecular transistor in time domain. We include electron-phonon interaction in our simulation and show that quantum interference in the given system is robust against nuclear vibration not only in the steady state but also in the transient dynamics. As another application, by combining TDDFT-OS with Ehrenfest dynamics, we study current-induced dissociation of water molecules under scanning tunneling microscopy and follow its time dependent dynamics. Given the rapid development in ultrafast experiments with atomic resolution in recent years, time dependent simulation of open electronic systems will be useful to gain insight and understanding of such experiments. This Account will mainly focus on the practical aspects of the TDDFT-OS method, describing the numerical implementation and demonstrating the method with applications.
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Affiliation(s)
- Shuguang Chen
- Department of Chemistry, the University of Hong Kong, Pofkulam Road, Hong Kong
SAR, China
| | - YanHo Kwok
- Department of Chemistry, the University of Hong Kong, Pofkulam Road, Hong Kong
SAR, China
| | - GuanHua Chen
- Department of Chemistry, the University of Hong Kong, Pofkulam Road, Hong Kong
SAR, China
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9
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Ilawe NV, Oviedo MB, Wong BM. Real-Time Quantum Dynamics of Long-Range Electronic Excitation Transfer in Plasmonic Nanoantennas. J Chem Theory Comput 2017; 13:3442-3454. [DOI: 10.1021/acs.jctc.7b00423] [Citation(s) in RCA: 31] [Impact Index Per Article: 4.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/30/2022]
Affiliation(s)
- Niranjan V. Ilawe
- Department of Chemical & Environmental Engineering and Materials Science & Engineering Program, University of California, Riverside, Riverside, California 92521, United States
| | - M. Belén Oviedo
- Department of Chemical & Environmental Engineering and Materials Science & Engineering Program, University of California, Riverside, Riverside, California 92521, United States
| | - Bryan M. Wong
- Department of Chemical & Environmental Engineering and Materials Science & Engineering Program, University of California, Riverside, Riverside, California 92521, United States
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10
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Maitra NT. Perspective: Fundamental aspects of time-dependent density functional theory. J Chem Phys 2016; 144:220901. [DOI: 10.1063/1.4953039] [Citation(s) in RCA: 228] [Impact Index Per Article: 28.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- Neepa T. Maitra
- Department of Physics and Astronomy, Hunter College and the Physics Program at the Graduate Center of the City University of New York, 695 Park Avenue, New York, New York 10065, USA
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11
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Krishtal A, Pavanello M. Revealing electronic open quantum systems with subsystem TDDFT. J Chem Phys 2016; 144:124118. [PMID: 27036438 DOI: 10.1063/1.4944526] [Citation(s) in RCA: 8] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
Open quantum systems (OQSs) are perhaps the most realistic systems one can approach through simulations. In recent years, describing OQSs with Density Functional Theory (DFT) has been a prominent avenue of research with most approaches based on a density matrix partitioning in conjunction with an ad-hoc description of system-bath interactions. We propose a different theoretical approach to OQSs based on partitioning of the electron density. Employing the machinery of subsystem DFT (and its time-dependent extension), we provide a novel way of isolating and analyzing the various terms contributing to the coupling between the system and the surrounding bath. To illustrate the theory, we provide numerical simulations on a toy system (a molecular dimer) and on a condensed phase system (solvated excimer). The simulations show that non-Markovian dynamics in the electronic system-bath interactions are important in chemical applications. For instance, we show that the superexchange mechanism of transport in donor-bridge-acceptor systems is a non-Markovian interaction between the donor-acceptor (OQS) with the bridge (bath) which is fully characterized by real-time subsystem time-dependent DFT.
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Affiliation(s)
- Alisa Krishtal
- Department of Chemistry, Rutgers University, Newark, New Jersey 07102, USA
| | - Michele Pavanello
- Department of Chemistry, Rutgers University, Newark, New Jersey 07102, USA
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12
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Laguna HG, Sagar RP, Tempel DG, Aspuru-Guzik A. The role of interparticle interaction and environmental coupling in a two-particle open quantum system. Phys Chem Chem Phys 2016; 18:436-47. [PMID: 26616490 DOI: 10.1039/c5cp05927e] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/21/2022]
Abstract
The effects of bath coupling on an interacting two-particle quantum system are studied using tools from information theory. Shannon entropies of the one (reduced) and two-particle distribution functions in position, momentum and separable phase-space are examined. Results show that the presence of the bath leads to a delocalization of the distribution functions in position space, and a localization in momentum space. This can be interpreted as a loss of information in position space and a gain of information in momentum space. The entropy sum of the system, in the presence of a bath, is shown to be dependent on the strength of the interparticle potential and also on the strength of the coupling to the bath. The statistical correlation between the particles, and its dependence on the bath and interparticle potential, is examined using mutual information. A stronger repulsive potential between particles, in the presence of the bath, yields a smaller correlation between the particles positions, and a larger one between their momenta.
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Affiliation(s)
- Humberto G Laguna
- Departamento de Matemáticas, Facultad de Ciencias, Universidad Nacional Autónoma de México, Circuito Exterior, Ciudad Universitaria, D.F. 04510, Mexico.
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13
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Larsen AH, De Giovannini U, Rubio A. Dynamical Processes in Open Quantum Systems from a TDDFT Perspective: Resonances and Electron Photoemission. Top Curr Chem (Cham) 2016; 368:219-271. [PMID: 25860253 DOI: 10.1007/128_2014_616] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 06/04/2023]
Abstract
We present a review of different computational methods to describe time-dependent phenomena in open quantum systems and their extension to a density-functional framework. We focus the discussion on electron emission processes in atoms and molecules addressing excited-state lifetimes and dissipative processes. Initially we analyze the concept of an electronic resonance, a central concept in spectroscopy associated with a metastable state from which an electron eventually escapes (electronic lifetime). Resonances play a fundamental role in many time-dependent molecular phenomena but can be rationalized from a time-independent context in terms of scattering states. We introduce the method of complex scaling, which is used to capture resonant states as localized states in the spirit of usual bound-state methods, and work on its extension to static and time-dependent density-functional theory. In a time-dependent setting, complex scaling can be used to describe excitations in the continuum as well as wave packet dynamics leading to electron emission. This process can also be treated by using open boundary conditions which allow time-dependent simulations of emission processes without artificial reflections at the boundaries (i.e., borders of the simulation box). We compare in detail different schemes to implement open boundaries, namely transparent boundaries using Green functions, and absorbing boundaries in the form of complex absorbing potentials and mask functions. The last two are regularly used together with time-dependent density-functional theory to describe the electron emission dynamics of atoms and molecules. Finally, we discuss approaches to the calculation of energy and angle-resolved time-dependent pump-probe photoelectron spectroscopy of molecular systems.
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Affiliation(s)
- Ask Hjorth Larsen
- Nano-bio Spectroscopy Group and European Theoretical Spectroscopy Facility (ETSF), Centro de Física de Materiales CSIC-UPV and DIPC, Universidad del País Vasco UPV/EHU, E-20018, Donostia-San Sebastián, Spain,
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14
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Modine NA, Hatcher RM. Representing the thermal state in time-dependent density functional theory. J Chem Phys 2015; 142:204111. [PMID: 26026438 DOI: 10.1063/1.4921690] [Citation(s) in RCA: 8] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
Classical molecular dynamics (MD) provides a powerful and widely used approach to determining thermodynamic properties by integrating the classical equations of motion of a system of atoms. Time-Dependent Density Functional Theory (TDDFT) provides a powerful and increasingly useful approach to integrating the quantum equations of motion for a system of electrons. TDDFT efficiently captures the unitary evolution of a many-electron state by mapping the system into a fictitious non-interacting system. In analogy to MD, one could imagine obtaining the thermodynamic properties of an electronic system from a TDDFT simulation in which the electrons are excited from their ground state by a time-dependent potential and then allowed to evolve freely in time while statistical data are captured from periodic snapshots of the system. For a variety of systems (e.g., many metals), the electrons reach an effective state of internal equilibrium due to electron-electron interactions on a time scale that is short compared to electron-phonon equilibration. During the initial time-evolution of such systems following electronic excitation, electron-phonon interactions should be negligible, and therefore, TDDFT should successfully capture the internal thermalization of the electrons. However, it is unclear how TDDFT represents the resulting thermal state. In particular, the thermal state is usually represented in quantum statistical mechanics as a mixed state, while the occupations of the TDDFT wavefunctions are fixed by the initial state in TDDFT. We work to address this puzzle by (A) reformulating quantum statistical mechanics so that thermodynamic expectations can be obtained as an unweighted average over a set of many-body pure states and (B) constructing a family of non-interacting (single determinant) TDDFT states that approximate the required many-body states for the canonical ensemble.
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Affiliation(s)
- N A Modine
- Sandia National Laboratories, Albuquerque, New Mexico 87185-1315, USA
| | - R M Hatcher
- Advanced Logic Lab, Samsung Semiconductor, Inc., Austin, Texas 78754, USA
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15
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Ruggenthaler M, Penz M, van Leeuwen R. Existence, uniqueness, and construction of the density-potential mapping in time-dependent density-functional theory. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2015; 27:203202. [PMID: 25921322 DOI: 10.1088/0953-8984/27/20/203202] [Citation(s) in RCA: 19] [Impact Index Per Article: 2.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/04/2023]
Abstract
In this work we review the mapping from densities to potentials in quantum mechanics, which is the basic building block of time-dependent density-functional theory and the Kohn-Sham construction. We first present detailed conditions such that a mapping from potentials to densities is defined by solving the time-dependent Schrödinger equation. We specifically discuss intricacies connected with the unboundedness of the Hamiltonian and derive the local-force equation. This equation is then used to set up an iterative sequence that determines a potential that generates a specified density via time propagation of an initial state. This fixed-point procedure needs the invertibility of a certain Sturm-Liouville problem, which we discuss for different situations. Based on these considerations we then present a discussion of the famous Runge-Gross theorem which provides a density-potential mapping for time-analytic potentials. Further we give conditions such that the general fixed-point approach is well-defined and converges under certain assumptions. Then the application of such a fixed-point procedure to lattice Hamiltonians is discussed and the numerical realization of the density-potential mapping is shown. We conclude by presenting an extension of the density-potential mapping to include vector-potentials and photons.
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Affiliation(s)
- Michael Ruggenthaler
- Institut für Theoretische Physik, Universität Innsbruck, Technikerstraße 21a, A-6020 Innsbruck, Austria
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16
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Wang R, Zheng X, Kwok Y, Xie H, Chen G, Yam C. Time-dependent density functional theory for open systems with a positivity-preserving decomposition scheme for environment spectral functions. J Chem Phys 2015; 142:144112. [PMID: 25877567 DOI: 10.1063/1.4917172] [Citation(s) in RCA: 8] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
Understanding electronic dynamics on material surfaces is fundamentally important for applications including nanoelectronics, inhomogeneous catalysis, and photovoltaics. Practical approaches based on time-dependent density functional theory for open systems have been developed to characterize the dissipative dynamics of electrons in bulk materials. The accuracy and reliability of such approaches depend critically on how the electronic structure and memory effects of surrounding material environment are accounted for. In this work, we develop a novel squared-Lorentzian decomposition scheme, which preserves the positive semi-definiteness of the environment spectral matrix. The resulting electronic dynamics is guaranteed to be both accurate and convergent even in the long-time limit. The long-time stability of electronic dynamics simulation is thus greatly improved within the current decomposition scheme. The validity and usefulness of our new approach are exemplified via two prototypical model systems: quasi-one-dimensional atomic chains and two-dimensional bilayer graphene.
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Affiliation(s)
- RuLin Wang
- Beijing Computational Science Research Center, No. 3 He-Qing Road, Beijing 100084, China
| | - Xiao Zheng
- Hefei National Laboratory for Physical Sciences at the Microscale, University of Science and Technology of China, Hefei, Anhui 230026, China
| | - YanHo Kwok
- Department of Chemistry, The University of Hong Kong, Pokfulam Road, Hong Kong, China
| | - Hang Xie
- Department of Chemistry, The University of Hong Kong, Pokfulam Road, Hong Kong, China
| | - GuanHua Chen
- Department of Chemistry, The University of Hong Kong, Pokfulam Road, Hong Kong, China
| | - ChiYung Yam
- Beijing Computational Science Research Center, No. 3 He-Qing Road, Beijing 100084, China
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17
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Meng L, Yin Z, Yam C, Koo S, Chen Q, Wong N, Chen G. Frequency-domain multiscale quantum mechanics/electromagnetics simulation method. J Chem Phys 2013; 139:244111. [DOI: 10.1063/1.4853635] [Citation(s) in RCA: 17] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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18
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Hofmann-Mees D, Appel H, Di Ventra M, Kümmel S. Determining excitation-energy transfer times and mechanisms from stochastic time-dependent density functional theory. J Phys Chem B 2013; 117:14408-19. [PMID: 24147662 DOI: 10.1021/jp404982d] [Citation(s) in RCA: 7] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Abstract
We developed an approach for calculating excitation-energy transfer times in supermolecular arrangements based on stochastic time-dependent density functional theory (STDDFT). The combination of real-time propagation and the stochastic Schrödinger equation with a Kohn-Sham Hamiltonian allows for simulating how an excitation spreads through an assembly of molecular systems. The influence that approximations, such as the dipole-dipole coupling approximation of Förster theory, have on energy-transfer times can be checked explicitly. As a first application of our approach we investigate a light-harvesting-inspired model ring system, calculating the time it takes for an excitation to travel from one side of the ring to the opposite side under ideal and perturbed conditions. Among other things we find that completely removing a molecule from the ring may inhibit energy transfer less than having an energetically detuned molecule in the ring. In addition, Förster's dipole coupling approximation may noticeably overestimate excitation-energy transfer efficiency.
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Affiliation(s)
- D Hofmann-Mees
- Theoretical Physics IV, University of Bayreuth , D-95440 Bayreuth, Germany
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19
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20
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Babbush R, Parkhill J, Aspuru-Guzik A. Force-field functor theory: classical force-fields which reproduce equilibrium quantum distributions. Front Chem 2013; 1:26. [PMID: 24790954 PMCID: PMC3982527 DOI: 10.3389/fchem.2013.00026] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/17/2013] [Accepted: 10/08/2013] [Indexed: 11/13/2022] Open
Abstract
Feynman and Hibbs were the first to variationally determine an effective potential whose associated classical canonical ensemble approximates the exact quantum partition function. We examine the existence of a map between the local potential and an effective classical potential which matches the exact quantum equilibrium density and partition function. The usefulness of such a mapping rests in its ability to readily improve Born-Oppenheimer potentials for use with classical sampling. We show that such a map is unique and must exist. To explore the feasibility of using this result to improve classical molecular mechanics, we numerically produce a map from a library of randomly generated one-dimensional potential/effective potential pairs then evaluate its performance on independent test problems. We also apply the map to simulate liquid para-hydrogen, finding that the resulting radial pair distribution functions agree well with path integral Monte Carlo simulations. The surprising accessibility and transferability of the technique suggest a quantitative route to adapting Born-Oppenheimer potentials, with a motivation similar in spirit to the powerful ideas and approximations of density functional theory.
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Affiliation(s)
- Ryan Babbush
- Department of Chemistry and Chemical Biology, Harvard UniversityCambridge, MA, USA
| | - John Parkhill
- Department of Chemistry, The University of Notre DameSouth Bend, IN, USA
| | - Alán Aspuru-Guzik
- Department of Chemistry and Chemical Biology, Harvard UniversityCambridge, MA, USA
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21
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Nassar AB, Miret-Artés S. Dividing line between quantum and classical trajectories in a measurement problem: Bohmian time constant. PHYSICAL REVIEW LETTERS 2013; 111:150401. [PMID: 24160580 DOI: 10.1103/physrevlett.111.150401] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/09/2013] [Revised: 08/06/2013] [Indexed: 06/02/2023]
Abstract
This Letter proposes an answer to a challenge posed by Bell on the lack of clarity in regards to the dividing line between the quantum and classical regimes in a measurement problem. To this end, a generalized logarithmic nonlinear Schrödinger equation is proposed to describe the time evolution of a quantum dissipative system under continuous measurement. Within the Bohmian mechanics framework, a solution to this equation reveals a novel result: it displays a time constant that should represent the dividing line between the quantum and classical trajectories. It is shown that continuous measurements and damping not only disturb the particle but compel the system to converge in time to a Newtonian regime. While the width of the wave packet may reach a stationary regime, its quantum trajectories converge exponentially in time to classical trajectories. In particular, it is shown that damping tends to suppress further quantum effects on a time scale shorter than the relaxation time of the system. If the initial wave packet width is taken to be equal to 2.8×10(-15) m (the approximate size of an electron), the Bohmian time constant is found to have an upper limit, i.e., τ(Bmax)=10(-26) s.
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Affiliation(s)
- Antonio B Nassar
- Science Department, Harvard-Westlake School, 3700 Coldwater Canyon, Studio City, California 91604, USA and Department of Sciences, University of California, Los Angeles, Extension Program, 10995 Le Conte Avenue, Los Angeles, California 90024, USA
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22
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Franco I, Appel H. Reduced purities as measures of decoherence in many-electron systems. J Chem Phys 2013; 139:094109. [PMID: 24028104 DOI: 10.1063/1.4819819] [Citation(s) in RCA: 7] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
A hierarchy of measures of decoherence for many-electron systems that is based on the purity and the hierarchy of reduced electronic density matrices is presented. These reduced purities can be used to characterize electronic decoherence in the common case when the many-body electronic density matrix is not known and only reduced information about the electronic subsystem is available. Being defined from reduced electronic quantities, the interpretation of the reduced purities is more intricate than the usual (many-body) purity. This is because the nonidempotency of the r-body reduced electronic density matrix that is the basis of the reduced purity measures can arise due to decoherence or due to electronic correlations. To guide the interpretation, explicit expressions are provided for the one-body and two-body reduced purities for a general electronic state. Using them, the information content and structure of the one-body and two-body reduced purities is established, and limits on the changes that decoherence can induce are elucidated. The practical use of the reduced purities to understand decoherence dynamics in many-electron systems is exemplified through an analysis of the electronic decoherence dynamics in a model molecular system.
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Affiliation(s)
- Ignacio Franco
- Theory Department, Fritz Haber Institute of the Max Planck Society, Faradayweg 4-6, 14195 Berlin, Germany
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Mosquera MA, Jensen D, Wasserman A. Fragment-based time-dependent density functional theory. PHYSICAL REVIEW LETTERS 2013; 111:023001. [PMID: 23889390 DOI: 10.1103/physrevlett.111.023001] [Citation(s) in RCA: 15] [Impact Index Per Article: 1.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/25/2013] [Indexed: 06/02/2023]
Abstract
Using the Runge-Gross theorem that establishes the foundation of time-dependent density functional theory, we prove that for a given electronic Hamiltonian, choice of initial state, and choice of fragmentation, there is a unique single-particle potential (dubbed time-dependent partition potential) which, when added to each of the preselected fragment potentials, forces the fragment densities to evolve in such a way that their sum equals the exact molecular density at all times. This uniqueness theorem suggests new ways of computing the time-dependent properties of electronic systems via fragment-time-dependent density functional theory calculations. We derive a formally exact relationship between the partition potential and the total density, and illustrate our approach on a simple model system for binary fragmentation in a laser field.
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Affiliation(s)
- Martín A Mosquera
- Department of Chemistry, Purdue University, West Lafayette, Indiana 47907, USA
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24
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Tokatly IV. Time-dependent density functional theory for many-electron systems interacting with cavity photons. PHYSICAL REVIEW LETTERS 2013; 110:233001. [PMID: 25167487 DOI: 10.1103/physrevlett.110.233001] [Citation(s) in RCA: 68] [Impact Index Per Article: 6.2] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/08/2013] [Indexed: 05/20/2023]
Abstract
Time-dependent (current) density functional theory for many-electron systems strongly coupled to quantized electromagnetic modes of a microcavity is proposed. It is shown that the electron-photon wave function is a unique functional of the electronic (current) density and the expectation values of photonic coordinates. The Kohn-Sham system is constructed, which allows us to calculate the above basic variables by solving self-consistent equations for noninteracting particles. We suggest possible approximations for the exchange-correlation potentials and discuss implications of this approach for the theory of open quantum systems. In particular we show that it naturally leads to time-dependent density functional theory for systems coupled to the Caldeira-Leggett bath.
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Affiliation(s)
- I V Tokatly
- Nano-bio Spectroscopy group and ETSF Scientific Development Centre, Departamento de Física de Materiales, Universidad del País Vasco UPV/EHU, E-20018 San Sebastían, Spain and IKERBASQUE, Basque Foundation for Science, 48011 Bilbao, Spain
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25
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Chen S, Xie H, Zhang Y, Cui X, Chen G. Quantum transport through an array of quantum dots. NANOSCALE 2013; 5:169-173. [PMID: 23175291 DOI: 10.1039/c2nr32343e] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/01/2023]
Abstract
The transient current through an array of as many as 1000 quantum dots is simulated with two newly developed quantum mechanical methods. To our surprise, upon switching on the bias voltage, the current increases linearly with time before reaching its steady state value. And the time required for the current to reach its steady state value is proportional to the length of the array, and more interestingly, is exactly the time for a conducting electron to travel through the array at the Fermi velocity. These quantum phenomena can be understood by a simple analysis on the energetics of an equivalent classical circuit. An experimental design is proposed to confirm the numerical findings.
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Affiliation(s)
- Shuguang Chen
- Department of Chemistry, Centre of Theoretical and Computational Physics, The University of Hong Kong, China
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26
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Yuen-Zhou J, Aspuru-Guzik A. Remarks on time-dependent [current]-density functional theory for open quantum systems. Phys Chem Chem Phys 2013; 15:12626-36. [DOI: 10.1039/c3cp51127h] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/21/2022]
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27
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Wen S, Guan W, Su Z, Yan L, Sanvito S. First principle investigation of transport properties of Lindqvist derivatives based molecular junction. J Mol Graph Model 2012; 38:220-5. [DOI: 10.1016/j.jmgm.2012.05.005] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/12/2012] [Revised: 05/19/2012] [Accepted: 05/22/2012] [Indexed: 10/28/2022]
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Xie H, Jiang F, Tian H, Zheng X, Kwok Y, Chen S, Yam C, Yan Y, Chen G. Time-dependent quantum transport: An efficient method based on Liouville-von-Neumann equation for single-electron density matrix. J Chem Phys 2012; 137:044113. [DOI: 10.1063/1.4737864] [Citation(s) in RCA: 45] [Impact Index Per Article: 3.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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Biele R, D'Agosta R. A stochastic approach to open quantum systems. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2012; 24:273201. [PMID: 22713734 DOI: 10.1088/0953-8984/24/27/273201] [Citation(s) in RCA: 22] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/01/2023]
Abstract
Stochastic methods are ubiquitous to a variety of fields, ranging from physics to economics and mathematics. In many cases, in the investigation of natural processes, stochasticity arises every time one considers the dynamics of a system in contact with a somewhat bigger system, an environment with which it is considered in thermal equilibrium. Any small fluctuation of the environment has some random effect on the system. In physics, stochastic methods have been applied to the investigation of phase transitions, thermal and electrical noise, thermal relaxation, quantum information, Brownian motion and so on. In this review, we will focus on the so-called stochastic Schrödinger equation. This is useful as a starting point to investigate the dynamics of open quantum systems capable of exchanging energy and momentum with an external environment. We discuss in some detail the general derivation of a stochastic Schrödinger equation and some of its recent applications to spin thermal transport, thermal relaxation, and Bose-Einstein condensation. We thoroughly discuss the advantages of this formalism with respect to the more common approach in terms of the reduced density matrix. The applications discussed here constitute only a few examples of a much wider range of applicability.
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Affiliation(s)
- R Biele
- Institut für Theoretische Physik, Technische Universität Dresden, D-01062 Dresden, Germany.
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Meng L, Yam C, Koo S, Chen Q, Wong N, Chen G. Dynamic Multiscale Quantum Mechanics/Electromagnetics Simulation Method. J Chem Theory Comput 2012; 8:1190-9. [DOI: 10.1021/ct200859h] [Citation(s) in RCA: 28] [Impact Index Per Article: 2.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/30/2022]
Affiliation(s)
- Lingyi Meng
- Department of Chemistry, The University of Hong Kong, Pokfulam
Road, Hong Kong
| | - ChiYung Yam
- Department of Chemistry, The University of Hong Kong, Pokfulam
Road, Hong Kong
| | - SiuKong Koo
- Department of Chemistry, The University of Hong Kong, Pokfulam
Road, Hong Kong
| | - Quan Chen
- Department of Electrical
and Electronic Engineering, The University of Hong Kong, Pokfulam Road, Hong Kong
| | - Ngai Wong
- Department of Electrical
and Electronic Engineering, The University of Hong Kong, Pokfulam Road, Hong Kong
| | - GuanHua Chen
- Department of Chemistry, The University of Hong Kong, Pokfulam
Road, Hong Kong
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Yang ZH, Maitra NT, Burke K. Effect of cusps in time-dependent quantum mechanics. PHYSICAL REVIEW LETTERS 2012; 108:063003. [PMID: 22401064 DOI: 10.1103/physrevlett.108.063003] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/03/2011] [Indexed: 05/31/2023]
Abstract
Within nonrelativistic quantum mechanics, spatial cusps in initial wave functions can lead to nonanalytic behavior in time. We suggest a method for calculating the short-time behavior in such situations. For these cases, the density does not match its Taylor expansion in time, but the Runge-Gross proof of time-dependent density functional theory still holds, as it requires only the potential to be time analytic.
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Affiliation(s)
- Zeng-hui Yang
- Department of Chemistry, University of California-Irvine, Irvine, California 92697, USA
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Tempel DG, Aspuru-Guzik A. Relaxation and dephasing in open quantum systems time-dependent density functional theory: Properties of exact functionals from an exactly-solvable model system. Chem Phys 2011. [DOI: 10.1016/j.chemphys.2011.03.014] [Citation(s) in RCA: 21] [Impact Index Per Article: 1.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/18/2022]
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33
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Rappoport D, Shim S, Aspuru-Guzik A. Simplified Sum-Over-States Approach for Predicting Resonance Raman Spectra. Application to Nucleic Acid Bases. J Phys Chem Lett 2011; 2:1254-1260. [PMID: 26295418 DOI: 10.1021/jz200413g] [Citation(s) in RCA: 18] [Impact Index Per Article: 1.4] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 06/04/2023]
Abstract
Resonance Raman spectra provide a valuable probe into molecular excited-state structures and properties. Moreover, resonance enhancement is of importance for the chemical contribution to surface-enhanced Raman scattering. In this work, we introduce a simplified sum-over-states scheme for computing Raman spectra and Raman excitation profiles. The proposed sum-over-states approach uses derivatives of electronic excitation energies and transition dipole moments, which can be efficiently computed from time-dependent density functional theory. We analyze and interpret the resonance Raman spectra and Raman excitation profiles of nucleic acid bases using the present approach. Contributions of individual excited states under strictly resonant and nonresonant conditions are investigated, and smooth interpolation between both limiting cases is obtained.
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Affiliation(s)
- Dmitrij Rappoport
- Department of Chemistry and Chemical Biology, Harvard University, 12 Oxford Street, Cambridge Massachusetts 02138, United States
| | - Sangwoo Shim
- Department of Chemistry and Chemical Biology, Harvard University, 12 Oxford Street, Cambridge Massachusetts 02138, United States
| | - Alán Aspuru-Guzik
- Department of Chemistry and Chemical Biology, Harvard University, 12 Oxford Street, Cambridge Massachusetts 02138, United States
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Wen S, Koo S, Yam C, Zheng X, Yan Y, Su Z, Fan K, Cao L, Wang W, Chen G. Time-Dependent Current Distributions of a Two-Terminal Carbon Nanotube-Based Electronic Device. J Phys Chem B 2011; 115:5519-25. [DOI: 10.1021/jp1110949] [Citation(s) in RCA: 13] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Affiliation(s)
- Shizheng Wen
- Department of Chemistry, Centre of Theoretical and Computational Physics, The University of Hong Kong, Hong Kong
- Institute of Functional Material Chemistry, Faculty of Chemistry, Northeast Normal University, Changchun 130024, P. R. China
- Department of Chemistry, Hong Kong University of Science and Technology, Hong Kong
| | - SiuKong Koo
- Department of Chemistry, Centre of Theoretical and Computational Physics, The University of Hong Kong, Hong Kong
| | - ChiYung Yam
- Department of Chemistry, Centre of Theoretical and Computational Physics, The University of Hong Kong, Hong Kong
| | - Xiao Zheng
- Department of Chemistry, Hong Kong University of Science and Technology, Hong Kong
| | - YiJing Yan
- Department of Chemistry, Hong Kong University of Science and Technology, Hong Kong
| | - Zhongmin Su
- Institute of Functional Material Chemistry, Faculty of Chemistry, Northeast Normal University, Changchun 130024, P. R. China
| | - Kangnian Fan
- Shanghai Key Laboratory of Molecular Catalysis and Innovative Materials, Center for Theoretical Chemical Physics, Department of Chemistry, Fudan University, Shanghai, 200433, P. R. China
| | - Li Cao
- Department of Computer Science, The University of Hong Kong, Hong Kong
| | - Wenping Wang
- Department of Computer Science, The University of Hong Kong, Hong Kong
| | - GuanHua Chen
- Department of Chemistry, Centre of Theoretical and Computational Physics, The University of Hong Kong, Hong Kong
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Tempel DG, Watson MA, Olivares-Amaya R, Aspuru-Guzik A. Time-dependent density functional theory of open quantum systems in the linear-response regime. J Chem Phys 2011; 134:074116. [DOI: 10.1063/1.3549816] [Citation(s) in RCA: 21] [Impact Index Per Article: 1.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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36
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Pacheco AB, Iyengar SS. Multistageab initioquantum wavepacket dynamics for electronic structure and dynamics in open systems: Momentum representation, coupled electron-nuclear dynamics, and external fields. J Chem Phys 2011; 134:074107. [DOI: 10.1063/1.3534797] [Citation(s) in RCA: 8] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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37
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Chapman CT, Liang W, Li X. Open-system electronic dynamics and thermalized electronic structure. J Chem Phys 2011; 134:024118. [DOI: 10.1063/1.3526027] [Citation(s) in RCA: 11] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/15/2022] Open
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38
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Kocherzhenko AA, Grozema FC, Siebbeles LDA. Single molecule charge transport: from a quantum mechanical to a classical description. Phys Chem Chem Phys 2011; 13:2096-110. [DOI: 10.1039/c0cp01432j] [Citation(s) in RCA: 19] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/12/2022]
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39
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Zheng X, Yam C, Wang F, Chen G. Existence of time-dependent density-functional theory for open electronic systems: Time-dependent holographic electron density theorem. Phys Chem Chem Phys 2011; 13:14358-64. [DOI: 10.1039/c1cp20777f] [Citation(s) in RCA: 19] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/21/2022]
Affiliation(s)
- Xiao Zheng
- Hefei National Laboratory for Physical Sciences at Microscale, University of Science and Technology of China, Hefei, China.
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40
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Masiello DJ, Schatz GC. On the linear response and scattering of an interacting molecule-metal system. J Chem Phys 2010; 132:064102. [DOI: 10.1063/1.3308624] [Citation(s) in RCA: 43] [Impact Index Per Article: 3.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/06/2023] Open
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