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Electronic excited states in deep variational Monte Carlo. Nat Commun 2023; 14:274. [PMID: 36650151 PMCID: PMC9845370 DOI: 10.1038/s41467-022-35534-5] [Citation(s) in RCA: 3] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/04/2022] [Accepted: 12/08/2022] [Indexed: 01/19/2023] Open
Abstract
Obtaining accurate ground and low-lying excited states of electronic systems is crucial in a multitude of important applications. One ab initio method for solving the Schrödinger equation that scales favorably for large systems is variational quantum Monte Carlo (QMC). The recently introduced deep QMC approach uses ansatzes represented by deep neural networks and generates nearly exact ground-state solutions for molecules containing up to a few dozen electrons, with the potential to scale to much larger systems where other highly accurate methods are not feasible. In this paper, we extend one such ansatz (PauliNet) to compute electronic excited states. We demonstrate our method on various small atoms and molecules and consistently achieve high accuracy for low-lying states. To highlight the method's potential, we compute the first excited state of the much larger benzene molecule, as well as the conical intersection of ethylene, with PauliNet matching results of more expensive high-level methods.
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2
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Rajpurohit S, Simoni J, Tan LZ. Photo-induced phase-transitions in complex solids. NANOSCALE ADVANCES 2022; 4:4997-5008. [PMID: 36504738 PMCID: PMC9680828 DOI: 10.1039/d2na00481j] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Received: 07/25/2022] [Accepted: 11/01/2022] [Indexed: 06/17/2023]
Abstract
Photo-induced phase-transitions (PIPTs) driven by highly cooperative interactions are of fundamental interest as they offer a way to tune and control material properties on ultrafast timescales. Due to strong correlations and interactions, complex quantum materials host several fascinating PIPTs such as light-induced charge density waves and ferroelectricity and have become a desirable setting for studying these PIPTs. A central issue in this field is the proper understanding of the underlying mechanisms driving the PIPTs. As these PIPTs are highly nonlinear processes and often involve multiple time and length scales, different theoretical approaches are often needed to understand the underlying mechanisms. In this review, we present a brief overview of PIPTs realized in complex materials, followed by a discussion of the available theoretical methods with selected examples of recent progress in understanding of the nonequilibrium pathways of PIPTs.
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Affiliation(s)
| | - Jacopo Simoni
- Molecular Foundry, Lawrence Berkeley National Laboratory USA
| | - Liang Z Tan
- Molecular Foundry, Lawrence Berkeley National Laboratory USA
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3
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Giarrusso S, Neugarten R, Baerends EJ, Giesbertz KJH. Secondary Kinetic Peak in the Kohn-Sham Potential and Its Connection to the Response Step. J Chem Theory Comput 2022; 18:4762-4773. [PMID: 35895974 DOI: 10.1021/acs.jctc.2c00332] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Abstract
We consider a prototypical 1D model Hamiltonian for a stretched heteronuclear molecule and construct individual components of the corresponding KS potential, namely, the kinetic, the N - 1, and the conditional potentials. These components show very special features, such as peaks and steps, in regions where the density is drastically low. Some of these features are quite well-known, whereas others, such as a secondary peak in the kinetic potential or a second bump in the conditional potential, are less or not known at all. We discuss these features building on the analytical model treated in Giarrusso et al. J. Chem. Theory Comput. 2018, 14, 4151. In particular, we provide an explanation for the underlying mechanism which determines the appearance of both peaks in the kinetic potential and elucidate why these peaks delineate the region over which the plateau structure, due to the N - 1 potential, stretches. We assess the validity of the Heitler-London Ansatz at large but finite internuclear distance, showing that, if optimal orbitals are used, this model is an excellent approximation to the exact wave function. Notably, we find that the second natural orbital presents an extra node very far out on the side of the more electronegative atom.
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Affiliation(s)
- Sara Giarrusso
- Department of Chemistry and Biochemistry, University of California Merced, 5200 North Lake Road, Merced, California 95343, United States
| | - Roeland Neugarten
- Department of Theoretical Chemistry and Amsterdam Center for Multiscale Modeling, FEW, Vrije Universiteit, De Boelelaan 1083, 1081HV Amsterdam, The Netherlands
| | - Evert Jan Baerends
- Department of Theoretical Chemistry and Amsterdam Center for Multiscale Modeling, FEW, Vrije Universiteit, De Boelelaan 1083, 1081HV Amsterdam, The Netherlands
| | - Klaas J H Giesbertz
- Department of Theoretical Chemistry and Amsterdam Center for Multiscale Modeling, FEW, Vrije Universiteit, De Boelelaan 1083, 1081HV Amsterdam, The Netherlands
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4
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Baerends EJ. Chemical potential, derivative discontinuity, fractional electrons, jump of the Kohn-Sham potential, atoms as thermodynamic open systems, and other (mis)conceptions of the density functional theory of electrons in molecules. Phys Chem Chem Phys 2022; 24:12745-12766. [PMID: 35593143 DOI: 10.1039/d2cp01585d] [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
Many references exist in the density functional theory (DFT) literature to the chemical potential of the electrons in an atom or a molecule. The origin of this notion has been the identification of the Lagrange multiplier μ = ∂E/∂N in the Euler-Lagrange variational equation for the ground state density as the chemical potential of the electrons. We first discuss why the Lagrange multiplier in this case is an arbitrary constant and therefore cannot be a physical characteristic of an atom or molecule. The switching of the energy derivative ("chemical potential") from -I to -A when the electron number crosses the integer, called integer discontinuity or derivative discontinuity, is not physical but only occurs when the nonphysical noninteger electron systems and the corresponding energy and derivative ∂E/∂N are chosen in a specific discontinuous way. The question is discussed whether in fact the thermodynamical concept of a chemical potential can be defined for the electrons in such few-electron systems as atoms and molecules. The conclusion is that such systems lack important characteristics of thermodynamic systems and do not afford the definition of a chemical potential. They also cannot be considered as analogues of the open systems of thermodynamics that can exchange particles with an environment (a particle bath or other members of a Gibbsian ensemble). Thermodynamical (statistical mechanical) concepts like chemical potential, open systems, grand canonical ensemble etc. are not applicable to a few electron system like an atom or molecule. A number of topics in DFT are critically reviewed in light of these findings: jumps in the Kohn-Sham potential when crossing an integer number of electrons, the band gap problem, the deviation-from-straight-lines error, and the role of ensembles in DFT.
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Coccia E, Luppi E. Time-dependent ab initioapproaches for high-harmonic generation spectroscopy. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2021; 34:073001. [PMID: 34731835 DOI: 10.1088/1361-648x/ac3608] [Citation(s) in RCA: 6] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/05/2021] [Accepted: 11/03/2021] [Indexed: 06/13/2023]
Abstract
High-harmonic generation (HHG) is a nonlinear physical process used for the production of ultrashort pulses in XUV region, which are then used for investigating ultrafast phenomena in time-resolved spectroscopies. Moreover, HHG signal itself encodes information on electronic structure and dynamics of the target, possibly coupled to the nuclear degrees of freedom. Investigating HHG signal leads to HHG spectroscopy, which is applied to atoms, molecules, solids and recently also to liquids. Analysing the number of generated harmonics, their intensity and shape gives a detailed insight of, e.g., ionisation and recombination channels occurring in the strong-field dynamics. A number of valuable theoretical models has been developed over the years to explain and interpret HHG features, with the three-step model being the most known one. Originally, these models neglect the complexity of the propagating electronic wavefunction, by only using an approximated formulation of ground and continuum states. Many effects unravelled by HHG spectroscopy are instead due to electron correlation effects, quantum interference, and Rydberg-state contributions, which are all properly captured by anab initioelectronic-structure approach. In this review we have collected recent advances in modelling HHG by means ofab initiotime-dependent approaches relying on the propagation of the time-dependent Schrödinger equation (or derived equations) in presence of a very intense electromagnetic field. We limit ourselves to gas-phase atomic and molecular targets, and to solids. We focus on the various levels of theory employed for describing the electronic structure of the target, coupled with strong-field dynamics and ionisation approaches, and on the basis used to represent electronic states. Selected applications and perspectives for future developments are also given.
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Affiliation(s)
- Emanuele Coccia
- Dipartimento di Scienze Chimiche e Farmaceutiche, University of Trieste, via Giorgieri 1, 34127 Trieste, Italy
| | - Eleonora Luppi
- Sorbonne Universités, UPMC Univ Paris 06, UMR 7616, Laboratoire de Chimie Théorique, F-75005 Paris, France
- CNRS, UMR 7616, Laboratoire de Chimie Théorique, F-75005 Paris, France
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6
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Mattiat J, Luber S. Recent Progress in the Simulation of Chiral Systems with Real Time Propagation Methods. Helv Chim Acta 2021. [DOI: 10.1002/hlca.202100154] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/28/2022]
Affiliation(s)
- Johann Mattiat
- Department of Chemistry University of Zurich Winterthurerstrasse 190 CH-8057 Zurich Switzerland
| | - Sandra Luber
- Department of Chemistry University of Zurich Winterthurerstrasse 190 CH-8057 Zurich Switzerland
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7
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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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8
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Kocák J, Kraisler E, Schild A. Charge-Transfer Steps in Density Functional Theory from the Perspective of the Exact Electron Factorization. J Phys Chem Lett 2021; 12:3204-3209. [PMID: 33761257 DOI: 10.1021/acs.jpclett.1c00467] [Citation(s) in RCA: 3] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 06/12/2023]
Abstract
When a molecule dissociates, the exact Kohn-Sham (KS) and Pauli potentials may form step structures. Reproducing these steps correctly is central for the description of dissociation and charge-transfer processes in density functional theory (DFT): The steps align the KS eigenvalues of the dissociating subsystems relative to each other and determine where electrons localize. While the step height can be calculated from the asymptotic behavior of the KS orbitals, this provides limited insight into what causes the steps. We give an explanation of the steps with an exact mapping of the many-electron problem to a one-electron problem, the exact electron factorization (EEF). The potentials appearing in the EEF have a clear physical meaning that translates to the DFT potentials by replacing the interacting many-electron system with the KS system. With a simple model of a diatomic, we illustrate that the steps are a consequence of spatial electron entanglement and are the result of a charge transfer. From this mechanism, the step height can immediately be deduced. Moreover, two methods to approximately reproduce the potentials during dissociation are proposed. One is based on the states of the dissociated system, while the other one is based on an analogy to the Born-Oppenheimer treatment of a molecule. The latter method also shows that the steps connect adiabatic potential energy surfaces. The view of DFT from the EEF thus provides a better understanding of how many-electron effects are encoded in a one-electron theory and how they can be modeled.
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Affiliation(s)
- Jakub Kocák
- Laboratorium für Physikalische Chemie, ETH Zürich, Vladimir-Prelog-Weg 2, 8093 Zürich, Switzerland
| | - Eli Kraisler
- Fritz Haber Center for Molecular Dynamics, Institute of Chemistry, The Hebrew University of Jerusalem, 91904 Jerusalem, Israel
| | - Axel Schild
- Laboratorium für Physikalische Chemie, ETH Zürich, Vladimir-Prelog-Weg 2, 8093 Zürich, Switzerland
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Krumland J, Valencia AM, Pittalis S, Rozzi CA, Cocchi C. Understanding real-time time-dependent density-functional theory simulations of ultrafast laser-induced dynamics in organic molecules. J Chem Phys 2020; 153:054106. [PMID: 32770886 DOI: 10.1063/5.0008194] [Citation(s) in RCA: 13] [Impact Index Per Article: 3.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022] Open
Abstract
Real-time time-dependent density functional theory, in conjunction with the Ehrenfest molecular dynamics scheme, is becoming a popular methodology to investigate ultrafast phenomena on the nanoscale. Thanks to recent developments, it is also possible to explicitly include in the simulations a time-dependent laser pulse, thereby accessing the transient excitation regime. However, the complexity entailed in these calculations calls for in-depth analysis of the accessible and yet approximate (either "dressed" or "bare") quantities in order to evaluate their ability to provide us with a realistic picture of the simulated processes. In this work, we analyze the ultrafast dynamics of three small molecules (ethylene, benzene, and thiophene) excited by a resonant laser pulse in the framework of the adiabatic local-density approximation. The electronic response to the laser perturbation in terms of induced dipole moment and excited-state population is compared to the results given by an exactly solvable two-level model. In this way, we can interpret the charge-carrier dynamics in terms of simple estimators, such as the number of excited electrons. From the computed transient absorption spectra, we unravel the appearance of nonlinear effects such as excited-state absorption and vibronic coupling. In this way, we observe that the laser excitation affects the vibrational spectrum by enhancing the anharmonicities therein, while the coherent vibrational motion contributes to stabilizing the electronic excitation already within a few tens of femtoseconds.
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Affiliation(s)
- Jannis Krumland
- Humboldt-Universität zu Berlin, Physics Department and IRIS Adlershof, 12489 Berlin, Germany
| | - Ana M Valencia
- Humboldt-Universität zu Berlin, Physics Department and IRIS Adlershof, 12489 Berlin, Germany
| | | | | | - Caterina Cocchi
- Humboldt-Universität zu Berlin, Physics Department and IRIS Adlershof, 12489 Berlin, Germany
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10
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Giarrusso S, Gori-Giorgi P. Exchange-Correlation Energy Densities and Response Potentials: Connection between Two Definitions and Analytical Model for the Strong-Coupling Limit of a Stretched Bond. J Phys Chem A 2020; 124:2473-2482. [PMID: 32118422 PMCID: PMC7104238 DOI: 10.1021/acs.jpca.9b10538] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Abstract
![]()
We
analyze in depth two widely used definitions (from the theory
of conditional probability amplitudes and from the adiabatic connection
formalism) of the exchange-correlation energy density and of the response
potential of Kohn–Sham density functional theory. We introduce
a local form of the coupling-constant-dependent Hohenberg–Kohn functional, showing that
the difference between the two definitions is due to a corresponding
local first-order term in the coupling constant, which disappears
globally (when integrated over all space), but not locally. We also
design an analytic representation for the response potential in the
strong-coupling limit of density functional theory for a model single
stretched bond.
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Affiliation(s)
- Sara Giarrusso
- Department of Theoretical Chemistry and Amsterdam Center for Multiscale Modeling, FEW, Vrije Universiteit, De Boelelaan 1083, Amsterdam, 1081HV, The Netherlands
| | - Paola Gori-Giorgi
- Department of Theoretical Chemistry and Amsterdam Center for Multiscale Modeling, FEW, Vrije Universiteit, De Boelelaan 1083, Amsterdam, 1081HV, The Netherlands
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11
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Lacombe L, Maitra NT. Developing new and understanding old approximations in TDDFT. Faraday Discuss 2020; 224:382-401. [PMID: 32926040 DOI: 10.1039/d0fd00049c] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/21/2022]
Abstract
When a system has evolved far from a ground-state, the adiabatic approximations commonly used in time-dependent density functional theory calculations completely fail in some applications, while giving qualitatively good predictions in others, and sometimes even quantitative predictions. It is not clearly understood why this is so, and developing practical approximations going beyond the adiabatic approximation remains a challenge. This paper explores three different lines of investigation. First, an expression for the exact time-dependent exchange-correlation potential suggests that the accuracy of an adiabatic approximation is intimately related to the deviation between the natural orbital occupation numbers of the physical system and those of the Kohn-Sham system, and we explore this on some exactly-solvable model systems. The exact expression further suggests a path to go beyond the adiabatic approximations, and in the second part we discuss a newly proposed class of memory-dependent approximations developed in this way. Finally, we derive a new expression for the exact exchange-correlation potential from a coupling-constant path integration.
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Affiliation(s)
- Lionel Lacombe
- Department of Physics, Rutgers University, Newark, New Jersey 07102, USA.
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12
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Lee Y, Yao X, Fischetti MV, Cho K. Real-time ab initio simulation of inelastic electron scattering using the exact, density functional, and alternative approaches. Phys Chem Chem Phys 2020; 22:8616-8624. [DOI: 10.1039/c9cp06376e] [Citation(s) in RCA: 4] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/20/2022]
Abstract
Inelastic electron scattering phenomena in chemical/physical/materials interests: electron radiation damage in materials; DNA damaged by electron scattering; electron therapy; electron microscope; electron-beam-induced deposition for nanofabrication.
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Affiliation(s)
- Yeonghun Lee
- Department of Materials Science and Engineering
- University of Texas at Dallas
- Richardson
- USA
| | - Xiaolong Yao
- Department of Materials Science and Engineering
- University of Texas at Dallas
- Richardson
- USA
| | - Massimo V. Fischetti
- Department of Materials Science and Engineering
- University of Texas at Dallas
- Richardson
- USA
| | - Kyeongjae Cho
- Department of Materials Science and Engineering
- University of Texas at Dallas
- Richardson
- USA
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13
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Brütting M, Trepl T, de Las Heras D, Schmidt M. Superadiabatic Forces via the Acceleration Gradient in Quantum Many-Body Dynamics. Molecules 2019; 24:molecules24203660. [PMID: 31614514 PMCID: PMC6832129 DOI: 10.3390/molecules24203660] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/12/2019] [Revised: 09/15/2019] [Accepted: 09/30/2019] [Indexed: 11/30/2022] Open
Abstract
We apply the formally exact quantum power functional framework (J. Chem. Phys.2015, 143, 174108) to a one-dimensional Hooke’s helium model atom. The physical dynamics are described on the one-body level beyond the density-based adiabatic approximation. We show that gradients of both the microscopic velocity and acceleration field are required to correctly describe the effects due to interparticle interactions. We validate the proposed analytical forms of the superadiabatic force and transport contributions by comparison to one-body data from exact numerical solution of the Schrödinger equation. Superadiabatic contributions beyond the adiabatic approximation are important in the dynamics and they include effective dissipation.
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Affiliation(s)
- Moritz Brütting
- Theoretische Physik II, Physikalisches Institut, Universitat Bayreuth, D-95440 Bayreuth, Germany
| | - Thomas Trepl
- Theoretische Physik II, Physikalisches Institut, Universitat Bayreuth, D-95440 Bayreuth, Germany
| | - Daniel de Las Heras
- Theoretische Physik II, Physikalisches Institut, Universitat Bayreuth, D-95440 Bayreuth, Germany
| | - Matthias Schmidt
- Theoretische Physik II, Physikalisches Institut, Universitat Bayreuth, D-95440 Bayreuth, Germany.
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14
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Mordovina U, Reinhard TE, Theophilou I, Appel H, Rubio A. Self-Consistent Density-Functional Embedding: A Novel Approach for Density-Functional Approximations. J Chem Theory Comput 2019; 15:5209-5220. [PMID: 31490684 PMCID: PMC6785802 DOI: 10.1021/acs.jctc.9b00063] [Citation(s) in RCA: 10] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/23/2019] [Indexed: 11/29/2022]
Abstract
In the present work, we introduce a self-consistent density-functional embedding technique, which leaves the realm of standard energy-functional approaches in density functional theory and targets directly the density-to-potential mapping that lies at its heart. Inspired by the density matrix embedding theory, we project the full system onto a set of small interacting fragments that can be solved accurately. Based on the rigorous relation of density and potential in density functional theory, we then invert the fragment densities to local potentials. Combining these results in a continuous manner provides an update for the Kohn-Sham potential of the full system, which is then used to update the projection. We benchmark our approach for molecular bond stretching in one and two dimensions and show that, in these cases, the scheme converges to accurate approximations for densities and Kohn-Sham potentials. We demonstrate that the known steps and peaks of the exact exchange-correlation potential are reproduced by our method with remarkable accuracy.
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Affiliation(s)
- Uliana Mordovina
- Max
Planck Institute for the Structure and Dynamics of Matter, 22761 Hamburg, Germany
| | - Teresa E. Reinhard
- Max
Planck Institute for the Structure and Dynamics of Matter, 22761 Hamburg, Germany
| | - Iris Theophilou
- Max
Planck Institute for the Structure and Dynamics of Matter, 22761 Hamburg, Germany
| | - Heiko Appel
- Max
Planck Institute for the Structure and Dynamics of Matter, 22761 Hamburg, Germany
| | - Angel Rubio
- Max
Planck Institute for the Structure and Dynamics of Matter, 22761 Hamburg, Germany
- Center
for Computational Quantum Physics (CCQ), Flatiron Institute, 162 Fifth Avenue, New York, New York 10010, United
States
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15
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Baerends EJ. On derivatives of the energy with respect to total electron number and orbital occupation numbers. A critique of Janak's theorem. Mol Phys 2019. [DOI: 10.1080/00268976.2019.1612955] [Citation(s) in RCA: 7] [Impact Index Per Article: 1.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/26/2022]
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16
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Lacombe L, Maitra NT. Density-Matrix Coupled Time-Dependent Exchange-Correlation Functional Approximations. J Chem Theory Comput 2019; 15:1672-1678. [DOI: 10.1021/acs.jctc.8b01159] [Citation(s) in RCA: 8] [Impact Index Per Article: 1.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Affiliation(s)
- Lionel Lacombe
- Department of Physics and Astronomy, Hunter College and the Graduate Center of the City University of New York, 695 Park Avenue, New York, New York 10065, United States
| | - Neepa T. Maitra
- Department of Physics and Astronomy, Hunter College and the Graduate Center of the City University of New York, 695 Park Avenue, New York, New York 10065, United States
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17
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Lian C, Hu SQ, Guan MX, Meng S. Momentum-resolved TDDFT algorithm in atomic basis for real time tracking of electronic excitation. J Chem Phys 2018; 149:154104. [PMID: 30342439 DOI: 10.1063/1.5036543] [Citation(s) in RCA: 13] [Impact Index Per Article: 2.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
Ultrafast electronic dynamics in solids lies at the core of modern condensed matter and materials physics. To build up a practical ab initio method for studying solids under photoexcitation, we develop a momentum-resolved real-time time dependent density functional theory (rt-TDDFT) algorithm using numerical atomic basis, together with the implementation of both the length and vector gauge of the electromagnetic field. When applied to simulate elementary excitations in two-dimensional materials such as graphene, different excitation modes, only distinguishable in momentum space, are observed. The momentum-resolved rt-TDDFT is important and computationally efficient for the study of ultrafast dynamics in extended systems.
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Affiliation(s)
- Chao Lian
- Beijing National Laboratory for Condensed Matter Physics and Institute of Physics, Chinese Academy of Sciences, Beijing 100190, People's Republic of China
| | - Shi-Qi Hu
- Beijing National Laboratory for Condensed Matter Physics and Institute of Physics, Chinese Academy of Sciences, Beijing 100190, People's Republic of China
| | - Meng-Xue Guan
- Beijing National Laboratory for Condensed Matter Physics and Institute of Physics, Chinese Academy of Sciences, Beijing 100190, People's Republic of China
| | - Sheng Meng
- Beijing National Laboratory for Condensed Matter Physics and Institute of Physics, Chinese Academy of Sciences, Beijing 100190, People's Republic of China
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18
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Peng WT, Fales BS, Levine BG. Simulating Electron Dynamics of Complex Molecules with Time-Dependent Complete Active Space Configuration Interaction. J Chem Theory Comput 2018; 14:4129-4138. [PMID: 29986143 DOI: 10.1021/acs.jctc.8b00381] [Citation(s) in RCA: 25] [Impact Index Per Article: 4.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Abstract
Time-dependent electronic structure methods are growing in popularity as tools for modeling ultrafast and/or nonlinear processes, for computing spectra, and as the electronic structure component of mean-field molecular dynamics simulations. Time-dependent configuration interaction (TD-CI) offers several advantages over the widely used real-time time-dependent density functional theory: namely, that it correctly models Rabi oscillations; it offers a spin-pure description of open-shell systems; and a hierarchy of TD-CI methods can be defined that systematically approach the exact solution of the time-dependent Schrodinger equation (TDSE). In this work, we present a novel TD-CI approach that extends TD-CI to large complete active-space configuration expansions. Such extension is enabled by use of a direct configuration interaction approach that eliminates the need to explicitly build, store, or diagonalize the Hamiltonian matrix. Graphics processing unit (GPU) acceleration enables fast solution of the TDSE even for large active spaces-up to 12 electrons in 12 orbitals (853776 determinants) in this work. A symplectic split operator propagator yields long-time norm conservation. We demonstrate the applicability of our approach by computing the response of a large molecule with a strongly correlated ground state, decacene (C42H24), to various pulses (δ-function, transform limited, chirped). Our simulations predict that chirped pulses can be used to induce dipole-forbidden transitions. Simulations of decacene using the 6-31G(d) basis set and a 12 electrons/12 orbitals active space took 20.1 h to propagate for 100 fs with a 1 attosecond time step on a single NVIDIA K40 GPU. Convergence with respect to time step is found to depend on the property being computed and the chosen active space.
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Affiliation(s)
- Wei-Tao Peng
- Department of Chemistry , Michigan State University , East Lansing , Michigan 48824 , United States
| | - B Scott Fales
- Department of Chemistry and the PULSE Institute , Stanford University , Stanford , California 94305 , United States.,SLAC National Accelerator Laboratory , Menlo Park , California 94025 , United States
| | - Benjamin G Levine
- Department of Chemistry , Michigan State University , East Lansing , Michigan 48824 , United States
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19
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Dittmann N, Splettstoesser J, Helbig N. Nonadiabatic Dynamics in Single-Electron Tunneling Devices with Time-Dependent Density-Functional Theory. PHYSICAL REVIEW LETTERS 2018; 120:157701. [PMID: 29756889 DOI: 10.1103/physrevlett.120.157701] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/26/2017] [Revised: 11/28/2017] [Indexed: 06/08/2023]
Abstract
We simulate the dynamics of a single-electron source, modeled as a quantum dot with on-site Coulomb interaction and tunnel coupling to an adjacent lead in time-dependent density-functional theory. Based on this system, we develop a time-nonlocal exchange-correlation potential by exploiting analogies with quantum-transport theory. The time nonlocality manifests itself in a dynamical potential step. We explicitly link the time evolution of the dynamical step to physical relaxation timescales of the electron dynamics. Finally, we discuss prospects for simulations of larger mesoscopic systems.
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Affiliation(s)
- Niklas Dittmann
- Department of Microtechnology and Nanoscience (MC2), Chalmers University of Technology, SE-41298 Göteborg, Sweden
- Institute for Theory of Statistical Physics, RWTH Aachen, 52056 Aachen, Germany
- Peter-Grünberg Institut and Institute for Advanced Simulation, Forschungszentrum Jülich, 52425 Jülich, Germany
| | - Janine Splettstoesser
- Department of Microtechnology and Nanoscience (MC2), Chalmers University of Technology, SE-41298 Göteborg, Sweden
| | - Nicole Helbig
- Peter-Grünberg Institut and Institute for Advanced Simulation, Forschungszentrum Jülich, 52425 Jülich, Germany
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20
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Fuks JI, Lacombe L, Nielsen SEB, Maitra NT. Exploring non-adiabatic approximations to the exchange–correlation functional of TDDFT. Phys Chem Chem Phys 2018; 20:26145-26160. [DOI: 10.1039/c8cp03957g] [Citation(s) in RCA: 15] [Impact Index Per Article: 2.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/13/2022]
Abstract
Decomposition of the exact time-dependent exchange–correlation potential offers a new starting point to build approximations with memory.
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Affiliation(s)
- Johanna I. Fuks
- Departamento de Física and IFIBA
- FCEN
- Universidad de Buenos Aires
- Ciudad Universitaria
- C1428EHA Ciudad de Buenos Aires
| | - Lionel Lacombe
- Department of Physics and Astronomy
- Hunter College and the Graduate Center of the City University of New York
- New York
- USA
| | - Søren E. B. Nielsen
- Max Planck Institute for the Structure and Dynamics of Matter and Center for Free-Electron Laser Science
- 22761 Hamburg
- Germany
| | - Neepa T. Maitra
- Department of Physics and Astronomy
- Hunter College and the Graduate Center of the City University of New York
- New York
- USA
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21
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Suzuki Y, Lacombe L, Watanabe K, Maitra NT. Exact Time-Dependent Exchange-Correlation Potential in Electron Scattering Processes. PHYSICAL REVIEW LETTERS 2017; 119:263401. [PMID: 29328727 DOI: 10.1103/physrevlett.119.263401] [Citation(s) in RCA: 12] [Impact Index Per Article: 1.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/29/2017] [Indexed: 06/07/2023]
Abstract
We identify peak and valley structures in the exact exchange-correlation potential of time-dependent density functional theory that are crucial for time-resolved electron scattering in a model one-dimensional system. These structures are completely missed by adiabatic approximations that, consequently, significantly underestimate the scattering probability. A recently proposed nonadiabatic approximation is shown to correctly capture the approach of the electron to the target when the initial Kohn-Sham state is chosen judiciously, and it is more accurate than standard adiabatic functionals but ultimately fails to accurately capture reflection. These results may explain the underestimation of scattering probabilities in some recent studies on molecules and surfaces.
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Affiliation(s)
- Yasumitsu Suzuki
- Department of Physics, Tokyo University of Science, 1-3 Kagurazaka, Shinjuku-ku, Tokyo 162-8601, Japan
| | - Lionel Lacombe
- Department of Physics and Astronomy, Hunter College and the Graduate Center of the City University of New York, 695 Park Avenue, New York, New York 10065, USA
| | - Kazuyuki Watanabe
- Department of Physics, Tokyo University of Science, 1-3 Kagurazaka, Shinjuku-ku, Tokyo 162-8601, Japan
| | - Neepa T Maitra
- Department of Physics and Astronomy, Hunter College and the Graduate Center of the City University of New York, 695 Park Avenue, New York, New York 10065, USA
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22
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Ryabinkin IG, Ospadov E, Staroverov VN. Exact exchange-correlation potentials of singlet two-electron systems. J Chem Phys 2017; 147:164117. [DOI: 10.1063/1.5003825] [Citation(s) in RCA: 20] [Impact Index Per Article: 2.9] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- Ilya G. Ryabinkin
- Department of Physical and Environmental Sciences, University of Toronto Scarborough, Toronto, Ontario M1C 1A4,
Canada
| | - Egor Ospadov
- Department of Chemistry, The University of Western Ontario, London, Ontario N6A 5B7, Canada
| | - Viktor N. Staroverov
- Department of Chemistry, The University of Western Ontario, London, Ontario N6A 5B7, Canada
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23
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Maitra NT. Charge transfer in time-dependent density functional theory. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2017; 29:423001. [PMID: 28766507 DOI: 10.1088/1361-648x/aa836e] [Citation(s) in RCA: 58] [Impact Index Per Article: 8.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/07/2023]
Abstract
Charge transfer plays a crucial role in many processes of interest in physics, chemistry, and bio-chemistry. In many applications the size of the systems involved calls for time-dependent density functional theory (TDDFT) to be used in their computational modeling, due to its unprecedented balance between accuracy and efficiency. However, although exact in principle, in practise approximations must be made for the exchange-correlation functional in this theory, and the standard functional approximations perform poorly for excitations which have a long-range charge-transfer component. Intense progress has been made in developing more sophisticated functionals for this problem, which we review. We point out an essential difference between the properties of the exchange-correlation kernel needed for an accurate description of charge-transfer between open-shell fragments and between closed-shell fragments. We then turn to charge-transfer dynamics, which, in contrast to the excitation problem, is a highly non-equilibrium, non-perturbative, process involving a transfer of one full electron in space. This turns out to be a much more challenging problem for TDDFT functionals. We describe dynamical step and peak features in the exact functional evolving over time, that are missing in the functionals currently used. The latter underestimate the amount of charge transferred and manifest a spurious shift in the charge transfer resonance position. We discuss some explicit examples.
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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, NY 10065, United States of America
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24
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Oberhofer H, Reuter K, Blumberger J. Charge Transport in Molecular Materials: An Assessment of Computational Methods. Chem Rev 2017. [PMID: 28644623 DOI: 10.1021/acs.chemrev.7b00086] [Citation(s) in RCA: 188] [Impact Index Per Article: 26.9] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/18/2022]
Abstract
The booming field of molecular electronics has fostered a surge of computational research on electronic properties of organic molecular solids. In particular, with respect to a microscopic understanding of transport and loss mechanisms, theoretical studies assume an ever-increasing role. Owing to the tremendous diversity of organic molecular materials, a great number of computational methods have been put forward to suit every possible charge transport regime, material, and need for accuracy. With this review article we aim at providing a compendium of the available methods, their theoretical foundations, and their ranges of validity. We illustrate these through applications found in the literature. The focus is on methods available for organic molecular crystals, but mention is made wherever techniques are suitable for use in other related materials such as disordered or polymeric systems.
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Affiliation(s)
- Harald Oberhofer
- Chair for Theoretical Chemistry and Catalysis Research Center, Technische Universität München , Lichtenbergstrasse 4, D-85747 Garching, Germany
| | - Karsten Reuter
- Chair for Theoretical Chemistry and Catalysis Research Center, Technische Universität München , Lichtenbergstrasse 4, D-85747 Garching, Germany
| | - Jochen Blumberger
- Department of Physics and Astronomy, University College London , Gower Street, London WC1E 6BT, United Kingdom.,Institute for Advanced Study, Technische Universität München , Lichtenbergstrasse 2 a, D-85748 Garching, Germany
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25
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Schild A, Gross EKU. Exact Single-Electron Approach to the Dynamics of Molecules in Strong Laser Fields. PHYSICAL REVIEW LETTERS 2017; 118:163202. [PMID: 28474937 DOI: 10.1103/physrevlett.118.163202] [Citation(s) in RCA: 13] [Impact Index Per Article: 1.9] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/10/2017] [Indexed: 06/07/2023]
Abstract
We present an exact single-electron picture that describes the correlated electron dynamics in strong laser fields. Our approach is based on the factorization of the electronic wave function as a product of a marginal and a conditional amplitude. The marginal amplitude, which depends only on one electronic coordinate and yields the exact one-electron density and current density, obeys a time-dependent Schrödinger equation with an effective time-dependent potential. The exact equations are used to derive an approximation that is a step towards general and feasible ab initio single-electron calculations for molecules. The derivation also sheds new light on the usual interpretation of the single-active electron approximation. From the study of model systems, we find that the exact and approximate single-electron potentials for processes with negligible two-electron ionization lead to qualitatively similar dynamics, but that the ionization barrier in the exact single-electron potential may be explicitly time dependent.
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Affiliation(s)
- Axel Schild
- Max-Planck-Institut für Mikrostrukturphysik, Weinberg 2, D-06120 Halle, Germany
| | - E K U Gross
- Max-Planck-Institut für Mikrostrukturphysik, Weinberg 2, D-06120 Halle, Germany
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26
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Pipolo S, Corni S, Cammi R. Equation of motion for the solvent polarization apparent charges in the polarizable continuum model: Application to time-dependent CI. J Chem Phys 2017; 146:064116. [PMID: 28201884 DOI: 10.1063/1.4975620] [Citation(s) in RCA: 11] [Impact Index Per Article: 1.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- Silvio Pipolo
- Institut de Minéralogie, de Physique des Matériaux et de Cosmochimie, Université Pierre et Marie Curie - Sorbonne Universités, Paris, France
| | | | - Roberto Cammi
- Department of Chemistry, Università degli Studi di Parma, Parma, Italy
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27
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Baerends EJ. From the Kohn–Sham band gap to the fundamental gap in solids. An integer electron approach. Phys Chem Chem Phys 2017; 19:15639-15656. [DOI: 10.1039/c7cp02123b] [Citation(s) in RCA: 40] [Impact Index Per Article: 5.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/26/2022]
Abstract
The upshift Δ of the level at the bottom of the conduction band (the LUMO) from the neutral N-electron crystal to the negative N + 1 system, and therefore the fundamental gap εLUMO(N + 1) − εHOMO(N) = I − A, can be calculated simply and cheaply from the response part of vxc.
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Affiliation(s)
- E. J. Baerends
- Section Theoretical Chemistry
- Vrije Universiteit
- Amsterdam
- The Netherlands
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28
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Pipolo S, Corni S. Real-Time Description of the Electronic Dynamics for a Molecule Close to a Plasmonic Nanoparticle. THE JOURNAL OF PHYSICAL CHEMISTRY. C, NANOMATERIALS AND INTERFACES 2016; 120:28774-28781. [PMID: 28035246 PMCID: PMC5184370 DOI: 10.1021/acs.jpcc.6b11084] [Citation(s) in RCA: 26] [Impact Index Per Article: 3.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Figures] [Subscribe] [Scholar Register] [Received: 11/03/2016] [Revised: 11/19/2016] [Indexed: 06/06/2023]
Abstract
The optical properties of molecules close to plasmonic nanostructures greatly differ from their isolated molecule counterparts. To theoretically investigate such systems from a quantum-chemistry perspective, one has to take into account that the plasmonic nanostructure (e.g., a metal nanoparticle-NP) is often too large to be treated atomistically. Therefore, a multiscale description, where the molecule is treated by an ab initio approach and the metal NP by a lower level description, is needed. Here we present an extension of one such multiscale model [Corni, S.; Tomasi, J. J. Chem. Phys.2001, 114, 3739], originally inspired by the polarizable continuum model, to a real-time description of the electronic dynamics of the molecule and of the NP. In particular, we adopt a time-dependent configuration interaction (TD CI) approach for the molecule, the metal NP is described as a continuous dielectric of complex shape characterized by a Drude-Lorentz dielectric function, and the molecule-NP electromagnetic coupling is treated by an equation-of-motion (EOM) extension of the quasi-static boundary element method (BEM). The model includes the effects of both the mutual molecule-NP time-dependent polarization and the modification of the probing electromagnetic field due to the plasmonic resonances of the NP. Finally, such an approach is applied to the investigation of the light absorption of a model chromophore, LiCN, in the presence of a metal-NP of complex shape.
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Affiliation(s)
- Silvio Pipolo
- Institut
de Minéralogie, de Physique des Matériaux et de Cosmochimie, Université Pierre et Marie Curie - Sorbonne
Universités, 75005 Paris, France
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29
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Lani G, Di Marino S, Gerolin A, van Leeuwen R, Gori-Giorgi P. The adiabatic strictly-correlated-electrons functional: kernel and exact properties. Phys Chem Chem Phys 2016; 18:21092-101. [PMID: 26986493 DOI: 10.1039/c6cp00339g] [Citation(s) in RCA: 12] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/11/2022]
Abstract
We investigate a number of formal properties of the adiabatic strictly-correlated electrons (SCE) functional, relevant for time-dependent potentials and for kernels in linear response time-dependent density functional theory. Among the former, we focus on the compliance to constraints of exact many-body theories, such as the generalised translational invariance and the zero-force theorem. Within the latter, we derive an analytical expression for the adiabatic SCE Hartree exchange-correlation kernel in one dimensional systems, and we compute it numerically for a variety of model densities. We analyse the non-local features of this kernel, particularly the ones that are relevant in tackling problems where kernels derived from local or semi-local functionals are known to fail.
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Affiliation(s)
- Giovanna Lani
- Department of Theoretical Chemistry and Amsterdam Center for Multiscale Modeling, FEW, Vrije Universiteit, De Boelelaan 1083, 1081HV Amsterdam, The Netherlands.
| | - Simone Di Marino
- Laboratoire de Mathématiques d'Orsay, Univ. Paris-Sud, CNRS, Université Paris-Saclay, 91405 Orsay, France
| | - Augusto Gerolin
- Dipartimento di Matematica, Universitá di Pisa, Largo B. Pontecorvo, 56126 Pisa, Italy
| | - Robert van Leeuwen
- Department of Physics, Nanoscience Center, University of Jyväskylä, 40014 Jyväskylä, Finland and European Theoretical Spectroscopy Facility (ETSF)
| | - Paola Gori-Giorgi
- Department of Theoretical Chemistry and Amsterdam Center for Multiscale Modeling, FEW, Vrije Universiteit, De Boelelaan 1083, 1081HV Amsterdam, The Netherlands.
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30
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Luo K, Fuks JI, Maitra NT. Studies of spuriously shifting resonances in time-dependent density functional theory. J Chem Phys 2016; 145:044101. [DOI: 10.1063/1.4955447] [Citation(s) in RCA: 11] [Impact Index Per Article: 1.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- Kai Luo
- Department of Physics and Astronomy, Hunter College and the Graduate Center of the City University of New York, 695 Park Avenue, New York, New York 10065, USA
- Department of Chemistry and Chemical Biology, Cornell University, 259 East Ave., Ithaca, New York 14850, USA
| | - Johanna I. Fuks
- Department of Physics and Astronomy, Hunter College and the Graduate Center of the City University of New York, 695 Park Avenue, New York, New York 10065, USA
| | - Neepa T. Maitra
- Department of Physics and Astronomy, Hunter College and the Graduate Center of the City University of New York, 695 Park Avenue, New York, New York 10065, USA
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31
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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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32
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Nafziger J, Wasserman A. Fragment-based treatment of delocalization and static correlation errors in density-functional theory. J Chem Phys 2016; 143:234105. [PMID: 26696044 DOI: 10.1063/1.4937771] [Citation(s) in RCA: 18] [Impact Index Per Article: 2.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/23/2022] Open
Abstract
One of the most important open challenges in modern Kohn-Sham (KS) density-functional theory (DFT) is the correct treatment of systems involving fractional electron charges and spins. Approximate exchange-correlation functionals struggle with such systems, leading to pervasive delocalization and static correlation errors. We demonstrate how these errors, which plague density-functional calculations of bond-stretching processes, can be avoided by employing the alternative framework of partition density-functional theory (PDFT) even using the local density approximation for the fragments. Our method is illustrated with explicit calculations on simple systems exhibiting delocalization and static-correlation errors, stretched H2 (+), H2, He2 (+), Li2 (+), and Li2. In all these cases, our method leads to greatly improved dissociation-energy curves. The effective KS potential corresponding to our self-consistent solutions displays key features around the bond midpoint; these are known to be present in the exact KS potential, but are absent from most approximate KS potentials and are essential for the correct description of electron dynamics.
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Affiliation(s)
- Jonathan Nafziger
- Department of Chemistry, Purdue University, 560 Oval Dr., West Lafayette, Indiana 47907, USA
| | - Adam Wasserman
- Department of Chemistry, Purdue University, 560 Oval Dr., West Lafayette, Indiana 47907, USA
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33
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Jensen DS, Wasserman A. Numerical density-to-potential inversions in time-dependent density functional theory. Phys Chem Chem Phys 2016; 18:21079-91. [PMID: 26984427 DOI: 10.1039/c6cp00312e] [Citation(s) in RCA: 9] [Impact Index Per Article: 1.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/21/2022]
Abstract
We present an unconditionally stable TDDFT inversion algorithm based on a constrained partial differential equation optimization framework and capable of recovering highly singular potentials.
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Affiliation(s)
- Daniel S. Jensen
- Department of Physics and Astronomy
- Purdue University
- West Lafayette
- USA
| | - Adam Wasserman
- Department of Physics and Astronomy
- Purdue University
- West Lafayette
- USA
- Department of Chemistry
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34
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Fuks JI, Nielsen SEB, Ruggenthaler M, Maitra NT. Time-dependent density functional theory beyond Kohn–Sham Slater determinants. Phys Chem Chem Phys 2016; 18:20976-85. [DOI: 10.1039/c6cp00722h] [Citation(s) in RCA: 22] [Impact Index Per Article: 2.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/22/2022]
Abstract
Different choices of initial Kohn Sham wavefunction shape the time-dependent exchange–correlation potential.
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Affiliation(s)
- Johanna I. Fuks
- Department of Physics and Astronomy
- Hunter College and the Graduate Center of the City University of New York
- New York
- USA
| | - Søren E. B. Nielsen
- Max Planck Institute for the Structure and Dynamics of Matter and Center for Free-Electron Laser Science & Department of Physics
- 22761 Hamburg
- Germany
- Institut für Theoretische Physik
- Universität Innsbruck
| | - Michael Ruggenthaler
- Max Planck Institute for the Structure and Dynamics of Matter and Center for Free-Electron Laser Science & Department of Physics
- 22761 Hamburg
- Germany
- Institut für Theoretische Physik
- Universität Innsbruck
| | - Neepa T. Maitra
- Department of Physics and Astronomy
- Hunter College and the Graduate Center of the City University of New York
- New York
- USA
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35
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Kohn-Sham approach to quantum electrodynamical density-functional theory: Exact time-dependent effective potentials in real space. Proc Natl Acad Sci U S A 2015; 112:15285-90. [PMID: 26627715 DOI: 10.1073/pnas.1518224112] [Citation(s) in RCA: 53] [Impact Index Per Article: 5.9] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/18/2022] Open
Abstract
The density-functional approach to quantum electrodynamics extends traditional density-functional theory and opens the possibility to describe electron-photon interactions in terms of effective Kohn-Sham potentials. In this work, we numerically construct the exact electron-photon Kohn-Sham potentials for a prototype system that consists of a trapped electron coupled to a quantized electromagnetic mode in an optical high-Q cavity. Although the effective current that acts on the photons is known explicitly, the exact effective potential that describes the forces exerted by the photons on the electrons is obtained from a fixed-point inversion scheme. This procedure allows us to uncover important beyond-mean-field features of the effective potential that mark the breakdown of classical light-matter interactions. We observe peak and step structures in the effective potentials, which can be attributed solely to the quantum nature of light; i.e., they are real-space signatures of the photons. Our findings show how the ubiquitous dipole interaction with a classical electromagnetic field has to be modified in real space to take the quantum nature of the electromagnetic field fully into account.
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36
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de Queiroz TB, Kümmel S. Tuned range separated hybrid functionals for solvated low bandgap oligomers. J Chem Phys 2015. [PMID: 26203008 DOI: 10.1063/1.4926468] [Citation(s) in RCA: 39] [Impact Index Per Article: 4.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
The description of charge transfer excitations has long been a challenge to time dependent density functional theory. The recently developed concept of "optimally tuned range separated hybrid (OT-RSH) functionals" has proven to describe charge transfer excitations accurately in many cases. However, describing solvated or embedded systems is yet a challenge. This challenge is not only computational but also conceptual, because the tuning requires identifying a specific orbital, typically the highest occupied one of the molecule under study. For solvated molecules, this orbital may be delocalized over the solvent. We here demonstrate that one way of overcoming this problem is to use a locally projected self-consistent field diagonalization on an absolutely localized molecular orbital expansion. We employ this approach to determine ionization energies and the optical gap of solvated oligothiophenes, i.e., paradigm low gap systems that are of relevance in organic electronics. Dioxane solvent molecules are explicitly represented in our calculations, and the ambiguities of straightforward parameter tuning in solution are elucidated. We show that a consistent estimate of the optimal range separated parameter (ω) at the limit of bulk solvation can be obtained by gradually extending the solvated system. In particular, ω is influenced by the solvent beyond the first coordination sphere. For determining ionization energies, a considerable number of solvent molecules on the first solvation shell must be taken into account. We demonstrate that accurately calculating optical gaps of solvated systems using OT-RSH can be done in three steps: (i) including the chemical environment when determining the range-separation parameter, (ii) taking into account the screening due to the solvent, and (iii) using realistic molecular geometries.
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Affiliation(s)
| | - Stephan Kümmel
- Theoretical Physics IV, University of Bayreuth, D-95440 Bayreuth, Germany
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37
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Provorse MR, Habenicht BF, Isborn CM. Peak-Shifting in Real-Time Time-Dependent Density Functional Theory. J Chem Theory Comput 2015; 11:4791-802. [DOI: 10.1021/acs.jctc.5b00559] [Citation(s) in RCA: 42] [Impact Index Per Article: 4.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Affiliation(s)
- Makenzie R. Provorse
- Chemistry and Chemical Biology, University of California Merced, Merced, California 95343, United States
| | - Bradley F. Habenicht
- Chemistry and Chemical Biology, University of California Merced, Merced, California 95343, United States
| | - Christine M. Isborn
- Chemistry and Chemical Biology, University of California Merced, Merced, California 95343, United States
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38
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Fuks JI, Luo K, Sandoval ED, Maitra NT. Time-resolved spectroscopy in time-dependent density functional theory: an exact condition. PHYSICAL REVIEW LETTERS 2015; 114:183002. [PMID: 26000998 PMCID: PMC6135656 DOI: 10.1103/physrevlett.114.183002] [Citation(s) in RCA: 35] [Impact Index Per Article: 3.9] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/23/2014] [Indexed: 05/17/2023]
Abstract
A fundamental property of a quantum system driven by an external field is that when the field is turned off the positions of its response frequencies are independent of the time at which the field is turned off. We show that this leads to an exact condition for the exchange-correlation potential of time-dependent density functional theory. The Kohn-Sham potential typically continues to evolve after the field is turned off, which leads to time dependence in the response frequencies of the Kohn-Sham response function. The exchange-correlation kernel must cancel out this time dependence. The condition is typically violated by approximations currently in use, as we demonstrate by several examples, which has severe consequences for their predictions of time-resolved spectroscopy.
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Affiliation(s)
- Johanna I Fuks
- Department of Physics and Astronomy, Hunter College and the Graduate Center of the City University of New York, 695 Park Avenue, New York, New York 10065, USA
| | - Kai Luo
- Department of Physics and Astronomy, Hunter College and the Graduate Center of the City University of New York, 695 Park Avenue, New York, New York 10065, USA
| | - Ernesto D Sandoval
- Department of Physics and Astronomy, Hunter College and the Graduate Center of the City University of New York, 695 Park Avenue, New York, New York 10065, USA
| | - Neepa T Maitra
- Department of Physics and Astronomy, Hunter College and the Graduate Center of the City University of New York, 695 Park Avenue, New York, New York 10065, USA
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39
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Oliveira MJT, Mignolet B, Kus T, Papadopoulos TA, Remacle F, Verstraete MJ. Computational Benchmarking for Ultrafast Electron Dynamics: Wave Function Methods vs Density Functional Theory. J Chem Theory Comput 2015; 11:2221-33. [DOI: 10.1021/acs.jctc.5b00167] [Citation(s) in RCA: 10] [Impact Index Per Article: 1.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Affiliation(s)
- Micael J. T. Oliveira
- Department
of Physics, University of Liège, European Theoretical Spectroscopy Facility, B-4000, Liège, Belgium
| | - Benoit Mignolet
- Department
of Chemistry, University of Liège, B-4000, Liège, Belgium
| | - Tomasz Kus
- Department
of Chemistry, University of Liège, B-4000, Liège, Belgium
| | - Theodoros A. Papadopoulos
- Department
of Natural Sciences, University of Chester, Thornton Science Park, CH2 4NU, Chester, U. K
| | - F. Remacle
- Department
of Chemistry, University of Liège, B-4000, Liège, Belgium
| | - Matthieu J. Verstraete
- Department
of Physics, University of Liège, European Theoretical Spectroscopy Facility, B-4000, Liège, Belgium
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40
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Luo K, Fuks JI, Sandoval ED, Elliott P, Maitra NT. Kinetic and interaction components of the exact time-dependent correlation potential. J Chem Phys 2015; 140:18A515. [PMID: 24832323 DOI: 10.1063/1.4867002] [Citation(s) in RCA: 14] [Impact Index Per Article: 1.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 02/07/2023] Open
Abstract
The exact exchange-correlation (xc) potential of time-dependent density functional theory has been shown to have striking features. For example, step and peak features are generically found when the system is far from its ground-state, and these depend nonlocally on the density in space and time. We analyze the xc potential by decomposing it into kinetic and interaction components and comparing each with their exact-adiabatic counterparts, for a range of dynamical situations in model one-dimensional two-electron systems. We find that often, but not always, the kinetic contribution is largely responsible for these features that are missed by the adiabatic approximation. The adiabatic approximation often makes a smaller error for the interaction component, which we write in two parts, one being the Coulomb potential due to the time-dependent xc hole. Non-adiabatic features of the kinetic component were also larger than those of the interaction component in cases that we studied when there is negligible step structure. In ground-state situations, step and peak structures arise in cases of static correlation, when more than one determinant is essential to describe the interacting state. We investigate the time-dependent natural orbital occupation numbers and find the corresponding relation between these and the dynamical step is more complex than for the ground-state case.
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Affiliation(s)
- Kai Luo
- Department of Physics and Astronomy, Hunter College and the Graduate Center of the City University of New York, 695 Park Avenue, New York, New York 10065, USA
| | - Johanna I Fuks
- Department of Physics and Astronomy, Hunter College and the Graduate Center of the City University of New York, 695 Park Avenue, New York, New York 10065, USA
| | - Ernesto D Sandoval
- Department of Physics and Astronomy, Hunter College and the Graduate Center of the City University of New York, 695 Park Avenue, New York, New York 10065, USA
| | - Peter Elliott
- Max-Planck-Institut für Mikrostrukturphysik, Weinberg 2, 06120 Halle (Saale), Germany
| | - Neepa T Maitra
- Department of Physics and Astronomy, Hunter College and the Graduate Center of the City University of New York, 695 Park Avenue, New York, New York 10065, USA
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41
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Habenicht BF, Tani NP, Provorse MR, Isborn CM. Two-electron Rabi oscillations in real-time time-dependent density-functional theory. J Chem Phys 2014; 141:184112. [DOI: 10.1063/1.4900514] [Citation(s) in RCA: 33] [Impact Index Per Article: 3.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- Bradley F. Habenicht
- Chemistry and Chemical Biology, University of California Merced, Merced, California 95343, USA
| | - Noriyuki P. Tani
- Chemistry and Chemical Biology, University of California Merced, Merced, California 95343, USA
| | - Makenzie R. Provorse
- Chemistry and Chemical Biology, University of California Merced, Merced, California 95343, USA
| | - Christine M. Isborn
- Chemistry and Chemical Biology, University of California Merced, Merced, California 95343, USA
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42
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de Queiroz TB, Kümmel S. Charge-transfer excitations in low-gap systems under the influence of solvation and conformational disorder: Exploring range-separation tuning. J Chem Phys 2014; 141:084303. [DOI: 10.1063/1.4892937] [Citation(s) in RCA: 50] [Impact Index Per Article: 5.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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43
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Uimonen AM, Stefanucci G, van Leeuwen R. Ultra-nonlocality in density functional theory for photo-emission spectroscopy. J Chem Phys 2014; 140:18A526. [DOI: 10.1063/1.4868114] [Citation(s) in RCA: 7] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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44
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Probing Strongly Correlated Materials in Non-equilibrium: Basic Concepts and Possible Future Trends in First Principle Approaches. Top Curr Chem (Cham) 2014; 347:347-84. [DOI: 10.1007/128_2014_528] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 02/11/2023]
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45
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Fuks JI, Maitra NT. Challenging adiabatic time-dependent density functional theory with a Hubbard dimer: the case of time-resolved long-range charge transfer. Phys Chem Chem Phys 2014; 16:14504-13. [DOI: 10.1039/c4cp00118d] [Citation(s) in RCA: 41] [Impact Index Per Article: 4.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/09/2023]
Abstract
Adiabatic TDDFT fails for time-resolved charge-transfer in a simple model, even when linear response spectra is accurate.
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Affiliation(s)
- Johanna I Fuks
- Department of Physics and Astronomy, Hunter College and the City University of New York, 695 Park Avenue, New York, New York 10065, USA.
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46
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Andrade X, Aspuru-Guzik A. Real-Space Density Functional Theory on Graphical Processing Units: Computational Approach and Comparison to Gaussian Basis Set Methods. J Chem Theory Comput 2013; 9:4360-73. [DOI: 10.1021/ct400520e] [Citation(s) in RCA: 45] [Impact Index Per Article: 4.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/26/2023]
Affiliation(s)
- Xavier Andrade
- 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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47
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Kurth S, Stefanucci G. Dynamical correction to linear Kohn-Sham conductances from static density functional theory. PHYSICAL REVIEW LETTERS 2013; 111:030601. [PMID: 23909303 DOI: 10.1103/physrevlett.111.030601] [Citation(s) in RCA: 12] [Impact Index Per Article: 1.1] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/18/2013] [Revised: 05/30/2013] [Indexed: 06/02/2023]
Abstract
For molecules weakly coupled to leads the exact linear Kohn-Sham (KS) conductance can be orders of magnitude larger than the true linear conductance due to the lack of dynamical exchange-correlation (xc) corrections. In this work we show how to incorporate dynamical effects in KS transport calculations. The only quantity needed is the static xc potential in the molecular junction. Our scheme provides a comprehensive description of Coulomb blockade without breaking the spin symmetry. This is explicitly demonstrated in single-wall nanotubes where the corrected conductance is in good agreement with experimental data whereas the KS conductance fails dramatically.
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Affiliation(s)
- S Kurth
- Nano-Bio Spectroscopy Group, Departamento de Física de Materiales, Universidad del País Vasco UPV/EHU, Centro Física de Materiales CSIC-UPV/EHU, Avenida Tolosa 72, E-20018 San Sebastián, Spain
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