1
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Sahni V. Perspectives on determinism in quantum mechanics: Born, Bohm, and the "Quantal Newtonian" laws. J Chem Phys 2022; 157:244106. [PMID: 36586987 DOI: 10.1063/5.0130945] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/15/2022] Open
Abstract
Quantum mechanics has a deterministic Schrödinger equation for the wave function. The Göttingen-Copenhagen statistical interpretation is based on the Born Rule that interprets the wave function as a "probability amplitude." A precept of this interpretation is the lack of determinism in quantum mechanics. The Bohm interpretation is that the wave function is a source of a field experienced by the electrons, thereby attributing determinism to quantum theory. In this paper, we present a new perspective on such determinism. The ideas are based on the equations of motion or "Quantal Newtonian" Laws obeyed by each electron. These Laws, derived from the temporal and stationary-state Schrödinger equation, are interpreted in terms of "classical" fields whose sources are quantal expectations of Hermitian operators taken with respect to the wave function. According to the Second Law, each electron experiences an external field-the quantal Coulomb-Lorentz law. It also experiences an internal field representative of properties of the system: correlations due to Coulomb repulsion and Pauli principle; the density; kinetic effects; and an internal magnetic field component. There is a response field. The First Law states that the sum of the external and internal fields experienced by each electron vanishes. These fields are akin to those of classical physics: They pervade all space; their structure is descriptive of the quantum system; the energy of the system is stored in these fields. It is in the classical behavior of these fields, which arise from quantal sources that one may then speak of determinism in quantum mechanics.
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Affiliation(s)
- Viraht Sahni
- Brooklyn College and The Graduate Center of the City University of New York, Brooklyn, New York 11210, USA
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2
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Della Sala F. Orbital-Free Methods for Plasmonics: Linear Response. J Chem Phys 2022; 157:104101. [DOI: 10.1063/5.0100797] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
Plasmonic systems, such as metal nanoparticles, are widely used in different application areas, going from biology to photovoltaics.The modeling of the optical response of such systems is of fundamental importance to analyze their behavior and to design new systems with required properties.When the characteristic sizes/distances reach a few nanometers, non-local and spill-out effects become relevant and conventional classical electrodynamics models are no more appropriate. Methods based on the Time-Dependent Density-Functional Theory (TD-DFT) represent the current reference for the description of quantum effects. However, TD-DFT is based on knowledge of all occupied orbitals whose calculation is computationally prohibitive to model large plasmonic systems of interest for applications.On the other hand, methods based on the Orbital-Free (OF) formulation of TD-DFT, can scale linearly with the system size.In this Review, OF methods ranging from semiclassical models to the quantum hydrodynamic theory, will be derived from the linear response TD-DFT, so that the key approximations and properties of each method can be clearly highlighted. The accuracy of the various approximations will be then validated for the linear optical properties of jellium nanoparticles, the most relevant model system in plasmonics. OF methods can describe the collective excitations in plasmonic systems with great accuracy andwithout system-tuned parameters. The accuracy on these methods depends only on the accuracy on the (universal) kinetic energy functional of the ground-state electronic density. Current approximations and future development directions will be indicated.
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Affiliation(s)
- Fabio Della Sala
- CNR-IMM, IMM CNR Lecce, Italy
- Istituto Italiano di Tecnologia Center for Biomolecular Nanotechnologies
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3
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Nonadiabatic Exchange-Correlation Potential for Strongly Correlated Materials in the Weak and Strong Interaction Limits. COMPUTATION 2022. [DOI: 10.3390/computation10050077] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 11/16/2022]
Abstract
In this work, nonadiabatic exchange-correlation (XC) potentials for time-dependent density-functional theory (TDDFT) for strongly correlated materials are derived in the limits of strong and weak correlations. After summarizing some essentials of the available dynamical mean-field theory (DMFT) XC potentials valid for these systems, we present details of the Sham–Schluter equation approach that we use to obtain, in principle, an exact XC potential from a many-body theory solution for the nonequilibrium electron self-energy. We derive the XC potentials for the one-band Hubbard model in the limits of weak and strong on-site Coulomb repulsion. To test the accuracy of the obtained potentials, we compare the TDDFT results obtained with these potentials with the corresponding nonequilibrium DMFT solution for the one-band Hubbard model and find that the agreement between the solutions is rather good. We also discuss possible directions to obtain a universal XC potential that would be appropriate for the case of intermediate interaction strengths, i.e., a nonadiabatic potential that can be used to perform TDDFT analysis of nonequilibrium phenomena, such as transport and other ultrafast properties of materials with any strength of electron correlation at any value in the applied perturbing field.
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4
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Li X, Govind N, Isborn C, DePrince AE, Lopata K. Real-Time Time-Dependent Electronic Structure Theory. Chem Rev 2020; 120:9951-9993. [DOI: 10.1021/acs.chemrev.0c00223] [Citation(s) in RCA: 64] [Impact Index Per Article: 16.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Affiliation(s)
- Xiaosong Li
- Department of Chemistry, University of Washington, Seattle, Washington 98195-1700, United States
| | - Niranjan Govind
- Physical and Computational Sciences Directorate, Pacific Northwest National Laboratory, Richland, Washington 99354, United States
| | - Christine Isborn
- Department of Chemistry and Chemical Biology, University of California, Merced, California 95343, United States
| | - A. Eugene DePrince
- Department of Chemistry and Biochemistry, Florida State University, Tallahassee, Florida 32306-4390, United States
| | - Kenneth Lopata
- Department of Chemistry, Louisiana State University, Baton Rouge, Louisiana 70803, United States
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5
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Nenov A, Segatta F, Bruner A, Mukamel S, Garavelli M. X-ray linear and non-linear spectroscopy of the ESCA molecule. J Chem Phys 2019; 151:114110. [DOI: 10.1063/1.5116699] [Citation(s) in RCA: 12] [Impact Index Per Article: 2.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/11/2022] Open
Affiliation(s)
- Artur Nenov
- Dipartimento di Chimica Industriale “Toso Montanari”, Università degli studi di Bologna, Viale del Risorgimento 4,
40136 Bologna, Italy
| | - Francesco Segatta
- Dipartimento di Chimica Industriale “Toso Montanari”, Università degli studi di Bologna, Viale del Risorgimento 4,
40136 Bologna, Italy
| | - Adam Bruner
- Department of Chemistry and Physics and Astronomy, University of California, Irvine, California 92697,
USA
| | - Shaul Mukamel
- Department of Chemistry and Physics and Astronomy, University of California, Irvine, California 92697,
USA
| | - Marco Garavelli
- Dipartimento di Chimica Industriale “Toso Montanari”, Università degli studi di Bologna, Viale del Risorgimento 4,
40136 Bologna, Italy
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6
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Zanoli S, Roca-Maza X, Colò G, Shen S. Harmonic Potential Theorem: Extension to Spin-, Velocity-, and Density-Dependent Interactions. PHYSICAL REVIEW LETTERS 2019; 123:112501. [PMID: 31573255 DOI: 10.1103/physrevlett.123.112501] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/03/2019] [Revised: 07/18/2019] [Indexed: 06/10/2023]
Abstract
One of the few exact results for the description of the time evolution of an inhomogeneous, interacting many-particle system is given by the harmonic potential theorem (HPT). The relevance of this theorem is that it sets a tight constraint on time-dependent many-body approximations. In this contribution, we show that the original formulation of the HPT is valid also for the case of spin-, velocity-, and density-dependent interactions. This result is completely general and relevant, among the rest, for nuclear structure theory both in the case of ab initio and of more phenomenological approaches. As an example, we report on a numerical implementation by testing the small-amplitude limit of the time-dependent Hartree-Fock-also known as the random phase approximation-for the translational frequencies of a neutron system trapped in a harmonic potential.
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Affiliation(s)
- S Zanoli
- Dipartimento di Fisica "Aldo Pontremoli", Università degli Studi di Milano, 20133 Milano, Italy and INFN, Sezione di Milano, 20133 Milano, Italy
| | - X Roca-Maza
- Dipartimento di Fisica "Aldo Pontremoli", Università degli Studi di Milano, 20133 Milano, Italy and INFN, Sezione di Milano, 20133 Milano, Italy
| | - G Colò
- Dipartimento di Fisica "Aldo Pontremoli", Università degli Studi di Milano, 20133 Milano, Italy and INFN, Sezione di Milano, 20133 Milano, Italy
| | - Shihang Shen
- Dipartimento di Fisica "Aldo Pontremoli", Università degli Studi di Milano, 20133 Milano, Italy and INFN, Sezione di Milano, 20133 Milano, Italy
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7
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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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8
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Slamet M, Sahni V. Kinetic effects in 2D and 3D quantum dots: Comparison between high and low electron correlation regimes. COMPUT THEOR CHEM 2018. [DOI: 10.1016/j.comptc.2018.06.001] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/14/2022]
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9
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Batalov SV, Shagalov AG, Friedland L. Autoresonant excitation of Bose-Einstein condensates. Phys Rev E 2018; 97:032210. [PMID: 29776039 DOI: 10.1103/physreve.97.032210] [Citation(s) in RCA: 8] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/13/2017] [Indexed: 11/06/2022]
Abstract
Controlling the state of a Bose-Einstein condensate driven by a chirped frequency perturbation in a one-dimensional anharmonic trapping potential is discussed. By identifying four characteristic time scales in this chirped-driven problem, three dimensionless parameters P_{1,2,3} are defined describing the driving strength, the anharmonicity of the trapping potential, and the strength of the particles interaction, respectively. As the driving frequency passes the linear resonance in the problem, and depending on the location in the P_{1,2,3} parameter space, the system may exhibit two very different evolutions, i.e., the quantum energy ladder climbing (LC) and the classical autoresonance (AR). These regimes are analyzed both in theory and simulations with the emphasis on the effect of the interaction parameter P_{3}. In particular, the transition thresholds on the driving parameter P_{1} and their width in P_{1} in both the AR and LC regimes are discussed. Different driving protocols are also illustrated, showing efficient control of excitation and deexcitation of the condensate.
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Affiliation(s)
- S V Batalov
- Institute of Metal Physics, Ekaterinburg 620990, Russian Federation and Ural Federal University, Mira 19, Ekaterinburg 620002, Russian Federation
| | - A G Shagalov
- Institute of Metal Physics, Ekaterinburg 620990, Russian Federation and Ural Federal University, Mira 19, Ekaterinburg 620002, Russian Federation
| | - L Friedland
- Racah Institute of Physics, Hebrew University of Jerusalem, Jerusalem 91904, Israel
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10
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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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11
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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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12
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Baillie D, Wilson RM, Blakie PB. Collective Excitations of Self-Bound Droplets of a Dipolar Quantum Fluid. PHYSICAL REVIEW LETTERS 2017; 119:255302. [PMID: 29303342 DOI: 10.1103/physrevlett.119.255302] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/21/2017] [Indexed: 06/07/2023]
Abstract
We calculate the collective excitations of a dipolar Bose-Einstein condensate in the regime where it self-binds into droplets stabilized by quantum fluctuations. We show that the filament-shaped droplets act as a quasi-one-dimensional waveguide along which low-angular-momentum phonons propagate. The evaporation (unbinding) threshold occurring as the atom number N is reduced to the critical value N_{c} is associated with a monopolelike excitation going soft as ε_{0}∼(N-N_{c})^{1/4}. Considering the system in the presence of a trapping potential, we quantify the crossover from a trap-bound condensate to a self-bound droplet.
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Affiliation(s)
- D Baillie
- Department of Physics, Centre for Quantum Science, and Dodd-Walls Centre for Photonic and Quantum Technologies, University of Otago, Dunedin 9016, New Zealand
| | - R M Wilson
- Department of Physics, United States Naval Academy, Annapolis, Maryland 21402, USA
| | - P B Blakie
- Department of Physics, Centre for Quantum Science, and Dodd-Walls Centre for Photonic and Quantum Technologies, University of Otago, Dunedin 9016, New Zealand
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13
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Slamet M, Sahni V. Electron correlations in an excited state of a quantum dot in a uniform magnetic field. COMPUT THEOR CHEM 2017. [DOI: 10.1016/j.comptc.2017.05.012] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/19/2022]
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14
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Ohno K, Ono S, Isobe T. A simple derivation of the exact quasiparticle theory and its extension to arbitrary initial excited eigenstates. J Chem Phys 2017; 146:084108. [PMID: 28249434 DOI: 10.1063/1.4976553] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
The quasiparticle (QP) energies, which are minus of the energies required by removing or produced by adding one electron from/to the system, corresponding to the photoemission or inverse photoemission (PE/IPE) spectra, are determined together with the QP wave functions, which are not orthonormal and even not linearly independent but somewhat similar to the normal spin orbitals in the theory of the configuration interaction, by self-consistently solving the QP equation coupled with the equation for the self-energy. The electron density, kinetic, and all interaction energies can be calculated using the QP wave functions. We prove in a simple way that the PE/IPE spectroscopy and therefore this QP theory can be applied to an arbitrary initial excited eigenstate. In this proof, we show that the energy-dependence of the self-energy is not an essential difficulty, and the QP picture holds exactly if there is no relaxation mechanism in the system. The validity of the present theory for some initial excited eigenstates is tested using the one-shot GW approximation for several atoms and molecules.
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Affiliation(s)
- Kaoru Ohno
- Department of Physics, Yokohama National University, 79-5 Tokiwadai, Hodogaya-ku, Yokohama 240-8501, Japan
| | - Shota Ono
- Department of Physics, Yokohama National University, 79-5 Tokiwadai, Hodogaya-ku, Yokohama 240-8501, Japan
| | - Tomoharu Isobe
- Department of Physics, Yokohama National University, 79-5 Tokiwadai, Hodogaya-ku, Yokohama 240-8501, Japan
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15
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Lai MY, Pan XY. The generalized harmonic potential theorem in the presence of a time-varying magnetic field. Sci Rep 2016; 6:35412. [PMID: 27748461 PMCID: PMC5066324 DOI: 10.1038/srep35412] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/11/2016] [Accepted: 09/27/2016] [Indexed: 11/08/2022] Open
Abstract
We investigate the evolution of the many-body wave function of a quantum system with time-varying effective mass, confined by a harmonic potential with time-varying frequency in the presence of a uniform time-varying magnetic field, and perturbed by a time-dependent uniform electric field. It is found that the wave function is comprised of a phase factor times the solution to the unperturbed time-dependent Schrödinger equation with the latter being translated by a time-dependent value that satisfies the classical driven equation of motion. In other words, we generalize the harmonic potential theorem to the case when the effective mass, harmonic potential, and the external uniform magnetic field with arbitrary orientation are all time-varying. The results reduce to various special cases obtained in the literature, particulary to that of the harmonic potential theorem wave function when the effective mass and frequency are both static and the external magnetic field is absent.
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Affiliation(s)
- Meng-Yun Lai
- Department of Physics, Ningbo University, Ningbo, 315211, China
| | - Xiao-Yin Pan
- Department of Physics, Ningbo University, Ningbo, 315211, China
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16
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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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17
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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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18
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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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19
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Abstract
Probabilities of single ionization channels or double and multiple simultaneous ionization can be determined from exact master equations for time-dependent Dyson orbitals.
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Affiliation(s)
- O. V. Gritsenko
- Section Theoretical Chemistry
- Vrije Universiteit
- Amsterdam
- The Netherlands
| | - E. J. Baerends
- Section Theoretical Chemistry
- Vrije Universiteit
- Amsterdam
- The Netherlands
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20
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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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21
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Huang C, Libisch F, Peng Q, Carter EA. Time-dependent potential-functional embedding theory. J Chem Phys 2014; 140:124113. [DOI: 10.1063/1.4869538] [Citation(s) in RCA: 17] [Impact Index Per Article: 1.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/02/2023] Open
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22
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Zhu HM, Chen JW, Pan XY, Sahni V. Wave function for harmonically confined electrons in time-dependent electric and magnetostatic fields. J Chem Phys 2014; 140:024318. [PMID: 24437888 DOI: 10.1063/1.4858463] [Citation(s) in RCA: 9] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
We derive via the interaction "representation" the many-body wave function for harmonically confined electrons in the presence of a magnetostatic field and perturbed by a spatially homogeneous time-dependent electric field-the Generalized Kohn Theorem (GKT) wave function. In the absence of the harmonic confinement - the uniform electron gas - the GKT wave function reduces to the Kohn Theorem wave function. Without the magnetostatic field, the GKT wave function is the Harmonic Potential Theorem wave function. We further prove the validity of the connection between the GKT wave function derived and the system in an accelerated frame of reference. Finally, we provide examples of the application of the GKT wave function.
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Affiliation(s)
- Hong-Ming Zhu
- Department of Physics, Ningbo University, Ningbo 315211, China
| | - Jin-Wang Chen
- Department of Physics, Ningbo University, Ningbo 315211, China
| | - Xiao-Yin Pan
- Department of Physics, Ningbo University, Ningbo 315211, China
| | - Viraht Sahni
- Department of Physics, Brooklyn College and The Graduate School of the City University of New York, New York, New York 10016, USA
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23
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Li YQ, Pan XY, Sahni V. Wave function for time-dependent harmonically confined electrons in a time-dependent electric field. J Chem Phys 2013; 139:114301. [PMID: 24070284 DOI: 10.1063/1.4820245] [Citation(s) in RCA: 7] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022] Open
Abstract
The many-body wave function of a system of interacting particles confined by a time-dependent harmonic potential and perturbed by a time-dependent spatially homogeneous electric field is derived via the Feynman path-integral method. The wave function is comprised of a phase factor times the solution to the unperturbed time-dependent Schrödinger equation with the latter being translated by a time-dependent value that satisfies the classical driven equation of motion. The wave function reduces to that of the Harmonic Potential Theorem wave function for the case of the time-independent harmonic confining potential.
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Affiliation(s)
- Yu-Qi Li
- Department of Physics, Ningbo University, Ningbo 315211, China
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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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Gould T, Jansen G, Tokatly IV, Dobson JF. Quantum continuum mechanics made simple. J Chem Phys 2012; 136:204115. [DOI: 10.1063/1.4721269] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- Tim Gould
- Qld Micro- and Nanotechnology Centre, Griffith University, Nathan, Queensland 4111, Australia
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Dobson JF, Gould T. Calculation of dispersion energies. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2012; 24:073201. [PMID: 22213768 DOI: 10.1088/0953-8984/24/7/073201] [Citation(s) in RCA: 108] [Impact Index Per Article: 9.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/31/2023]
Abstract
We summarize the theory of van der Waals (dispersion) forces, with emphasis on recent microscopic approaches that permit the prediction of forces between solids and nanostructures right down to intimate contact and binding. Some connections are pointed out between microscopic theory and macroscopic Lifshitz theory.
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Affiliation(s)
- John F Dobson
- Queensland Micro- and Nano- Technology Centre, Griffith University, Nathan, Queensland, Australia.
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Abstract
The classic density-functional theory (DFT) formalism introduced by Hohenberg, Kohn, and Sham in the mid-1960s is based on the idea that the complicated N-electron wave function can be replaced with the mathematically simpler 1-electron charge density in electronic structure calculations of the ground stationary state. As such, ordinary DFT cannot treat time-dependent (TD) problems nor describe excited electronic states. In 1984, Runge and Gross proved a theorem making TD-DFT formally exact. Information about electronic excited states may be obtained from this theory through the linear response (LR) theory formalism. Beginning in the mid-1990s, LR-TD-DFT became increasingly popular for calculating absorption and other spectra of medium- and large-sized molecules. Its ease of use and relatively good accuracy has now brought LR-TD-DFT to the forefront for this type of application. As the number and the diversity of applications of TD-DFT have grown, so too has our understanding of the strengths and weaknesses of the approximate functionals commonly used for TD-DFT. The objective of this article is to continue where a previous review of TD-DFT in Volume 55 of the Annual Review of Physical Chemistry left off and highlight some of the problems and solutions from the point of view of applied physical chemistry. Because doubly-excited states have a particularly important role to play in bond dissociation and formation in both thermal and photochemistry, particular emphasis is placed on the problem of going beyond or around the TD-DFT adiabatic approximation, which limits TD-DFT calculations to nominally singly-excited states.
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Affiliation(s)
- M E Casida
- Laboratoire de Chimie Théorique, Département de Chimie Moléculaire, Institut de Chimie Moléculaire de Grenoble, Université Joseph Fourier, France.
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Abstract
We investigate the accuracy and efficiency of the semiclassical frozen Gaussian method in describing electron dynamics in real time. Model systems of two soft-Coulomb-interacting electrons are used to study correlated dynamics under non-perturbative electric fields, as well as the excitation spectrum. The results show that a recently proposed method that combines exact-exchange with semiclassical correlation to propagate the one-body density-matrix holds promise for electron dynamics in many situations that either wavefunction or density-functional methods have difficulty describing. The results also however point out challenges in such a method that need to be addressed before it can become widely applicable.
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Affiliation(s)
- Peter Elliott
- 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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29
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Wu Z, Zaremba E. Dissipative dynamics of a harmonically confined Bose-Einstein condensate. PHYSICAL REVIEW LETTERS 2011; 106:165301. [PMID: 21599378 DOI: 10.1103/physrevlett.106.165301] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/06/2011] [Revised: 02/24/2011] [Indexed: 05/30/2023]
Abstract
We study the dissipation of the center of mass oscillation of a harmonically confined condensate in the presence of a disorder potential. An extension of the harmonic potential theorem allows one to formulate the dynamics from the point of view of an oscillating disorder potential. This formulation leads to a rigorous result for the damping rate in the limit of weak disorder.
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Affiliation(s)
- Z Wu
- Department of Physics, Astronomy and Engineeering Physics, Queen's University, Kingston, Ontario, Canada
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30
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Neuhauser D, Pistinner S, Coomar A, Zhang X, Lu G. Dynamic kinetic energy potential for orbital-free density functional theory. J Chem Phys 2011; 134:144101. [DOI: 10.1063/1.3574347] [Citation(s) in RCA: 23] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/29/2022] Open
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31
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Ullrich CA, Gossmann UJ, Gross EKU. Density-Functional Approach to Atoms in Strong Laser Pulses. ACTA ACUST UNITED AC 2010. [DOI: 10.1002/bbpc.19950990338] [Citation(s) in RCA: 74] [Impact Index Per Article: 5.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/07/2022]
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Affiliation(s)
- Roi Baer
- Fritz Haber Center for Molecular Dynamics, Institute of Chemistry, The Hebrew University of Jerusalem, Jerusalem 91904 Israel;
| | - Ester Livshits
- Fritz Haber Center for Molecular Dynamics, Institute of Chemistry, The Hebrew University of Jerusalem, Jerusalem 91904 Israel;
| | - Ulrike Salzner
- Department of Chemistry, Bilkent University, 06800 Bilkent, Ankara, Turkey
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Manfredi G, Hervieux PA, Yin Y, Crouseilles N. Collective Electron Dynamics in Metallic and Semiconductor Nanostructures. ADVANCES IN THE ATOMIC-SCALE MODELING OF NANOSYSTEMS AND NANOSTRUCTURED MATERIALS 2010. [DOI: 10.1007/978-3-642-04650-6_1] [Citation(s) in RCA: 14] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 02/10/2023]
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Baer R. Prevalence of the adiabatic exchange-correlation potential approximation in time-dependent density functional theory. ACTA ACUST UNITED AC 2009. [DOI: 10.1016/j.theochem.2009.04.018] [Citation(s) in RCA: 19] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
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Niehaus TA, March NH. Brief review related to the foundations of time-dependent density functional theory. Theor Chem Acc 2009. [DOI: 10.1007/s00214-009-0578-0] [Citation(s) in RCA: 11] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/24/2022]
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Romaniello P, Sangalli D, Berger JA, Sottile F, Molinari LG, Reining L, Onida G. Double excitations in finite systems. J Chem Phys 2009; 130:044108. [DOI: 10.1063/1.3065669] [Citation(s) in RCA: 85] [Impact Index Per Article: 5.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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Thiele M, Kümmel S. Photoabsorption spectra from adiabatically exact time-dependent density-functional theory in real time. Phys Chem Chem Phys 2009; 11:4631-9. [DOI: 10.1039/b902567g] [Citation(s) in RCA: 28] [Impact Index Per Article: 1.9] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/21/2022]
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Tokatly IV. Time-dependent current density functional theory via time-dependent deformation functional theory: a constrained search formulation in the time domain. Phys Chem Chem Phys 2009; 11:4621-30. [DOI: 10.1039/b903666k] [Citation(s) in RCA: 13] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/21/2022]
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Tao J, Vignale G. Time-dependent density-functional theory beyond the local-density approximation. PHYSICAL REVIEW LETTERS 2006; 97:036403. [PMID: 16907522 DOI: 10.1103/physrevlett.97.036403] [Citation(s) in RCA: 11] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/17/2006] [Indexed: 05/11/2023]
Abstract
Approximations for the ground-state exchange-correlation potential of density-functional theory have reached a high level of sophistication. By contrast, time- or frequency-dependent exchange-correlation potentials are still being treated in a local approximation. Here we propose a novel approximation scheme, which effectively brings the power of the generalized gradient approximation (GGA) and meta-GGA to time-dependent density-functional theory. The theory should allow a more accurate treatment of strongly inhomogeneous electronic systems (e.g. molecular junctions) while remaining essentially exact for slowly varying densities and slowly varying external potentials.
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Affiliation(s)
- Jianmin Tao
- Department of Physics, University of Missouri-Columbia, Columbia, Missouri 65211, USA
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42
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Generalized functional theory of interacting coupled Liouvillean Quantum Fields of condensed matter. Top Curr Chem (Cham) 2005. [DOI: 10.1007/bfb0016644] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/25/2022]
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Baer R, Kurzweil Y, Cederbaum LS. Time-dependent density functional theory for nonadiabatic processes. Isr J Chem 2005. [DOI: 10.1560/n7n9-j2au-5tb9-5frl] [Citation(s) in RCA: 26] [Impact Index Per Article: 1.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/18/2022]
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45
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Bulgac A, Bertsch GF. Collective oscillations of a trapped fermi gas near the unitary limit. PHYSICAL REVIEW LETTERS 2005; 94:070401. [PMID: 15783790 DOI: 10.1103/physrevlett.94.070401] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/28/2004] [Indexed: 05/24/2023]
Abstract
We calculate the oscillation frequencies of trapped Fermi condensate with particular emphasis on the equation of state of the interacting Fermi system. We confirm Stringari's finding that the frequencies are independent of the interaction in the unitary limit, and we extend the theory away from that limit, where the interaction does affect the frequencies of the compressional modes only.
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Affiliation(s)
- Aurel Bulgac
- Department of Physics, University of Washington, Seattle, Washington 98195-1560, USA
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Casida ME. Propagator corrections to adiabatic time-dependent density-functional theory linear response theory. J Chem Phys 2005; 122:54111. [PMID: 15740314 DOI: 10.1063/1.1836757] [Citation(s) in RCA: 88] [Impact Index Per Article: 4.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
It has long been known that only one-electron excitations are available from adiabatic time-dependent density functional theory (TDDFT). This is particularly clear in Casida's formulation of TDDFT linear response theory. Nevertheless the explicit inclusion of two- and higher-electron excitations is necessary for an adequate description of some excited states, notably the first excited singlet states of butadiene and quartet excited states of molecules with a doublet ground state. The equation-of-motion superoperator approach is used here to derive a Casida-like propagator equation which can be clearly separated into an adiabatic part and a nonadiabatic part. The adiabatic part is identified as corresponding to Casida's equation for adiabatic TDDFT linear response theory. This equivalence is confirmed by deriving a general formula which includes the result that Gonze and Scheffler derived to show the equivalence of TDDFT and Gorling-Levy adiabatic connection perturbation theory for the exchange-only optimized effective potential. The nonadiabatic part explicitly corrects adiabatic TDDFT for two- and higher-electron excitations. The "dressed TDDFT" of Maitra, Zhang, Cave, and Burke is obtained as a special case where the ground state is closed shell. The extension of dressed TDDFT to the case where the ground state is an open-shell doublet is presented, highlighting the importance of correctly accounting for symmetry in this theory. The extension to other ground state spin symmetries is a straightforward consequence of the present work.
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Affiliation(s)
- Mark E Casida
- Equipe de Chimie Théorique, Laboratoire d'Etudes Dynamiques et Structurales de la Sélectivité, Institut de Chimie Moleculaire de Grenoble, Université Joseph Fourier, F38041 Grenoble, France.
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Furche F, Burke K. Chapter 2 Time-Dependent Density Functional Theoryin Quantum Chemistry. ANNUAL REPORTS IN COMPUTATIONAL CHEMISTRY 2005. [DOI: 10.1016/s1574-1400(05)01002-9] [Citation(s) in RCA: 41] [Impact Index Per Article: 2.2] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 12/02/2022]
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Kurzweil Y, Baer R. Time-dependent exchange-correlation current density functionals with memory. J Chem Phys 2004; 121:8731-41. [PMID: 15527336 DOI: 10.1063/1.1802793] [Citation(s) in RCA: 42] [Impact Index Per Article: 2.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
Most present applications of time-dependent density functional theory use adiabatic functionals, i.e., the effective potential at time t is determined solely by the density at the same time. This paper discusses a method that aims to go beyond this approximation, by incorporating "memory" effects: the derived exchange-correlation potential will depend not only on present densities but also on the past. In order to ensure the potentials are causal, we formulate the action on the Keldysh contour for electrons in electromagnetic fields, from which we derive suitable Kohn-Sham equations. The exchange-correlation action is now a functional of the electron density and velocity field. A specific action functional is constructed which is Galilean invariant and yields a causal exchange-correlation vector potential for the Kohn-Sham equations incorporating memory effects. We show explicitly that the net exchange-correlation Lorentz force is zero. The potential is consistent with known dynamical properties of the homogeneous electron gas (in the linear response limit).
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Affiliation(s)
- Yair Kurzweil
- Department of Physical Chemistry and the Lise Meitner Minerva-Center for Computational Quantum Chemistry, The Hebrew University of Jerusalem, Jerusalem 91904, Israel
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van Faassen M, de Boeij PL. Excitation energies for a benchmark set of molecules obtained within time-dependent current-density functional theory using the Vignale–Kohn functional. J Chem Phys 2004; 120:8353-63. [PMID: 15267758 DOI: 10.1063/1.1697372] [Citation(s) in RCA: 41] [Impact Index Per Article: 2.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
In this article we explain how the existing linear response theory of time-dependent density-functional theory can be extended to obtain excitation energies in the framework of time-dependent current-density-functional theory. We use the Vignale-Kohn current-functional [G. Vignale and W. Kohn, Phys. Rev. Lett. 77, 2037 (1996)] which has proven to be successful for describing ultranonlocal exchange-correlation effects in the case of the axial polarizability of molecular chains [M. van Faassen, P. L. de Boeij, R. van Leeuwen, J. A. Berger, and J. G. Snijders, Phys. Rev. Lett. 88, 186401 (2002); J. Chem. Phys. 118, 1044 (2003)]. We study a variety of singlet excitations for a benchmark set of molecules. The pi(*)<--pi transitions obtained with the Vignale-Kohn functional are in good agreement with experiment and other theoretical results and they are in general an improvement upon the adiabatic local density approximation. In case of the pi(*)<--n transitions the Vignale-Kohn functional fails, giving results that strongly overestimate the experimental and other theoretical results. The benchmark set also contains some other types of excitations for which no clear failures or improvements are observed.
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Affiliation(s)
- M van Faassen
- Theoretical Chemistry, Materials Science Centre, Rijksuniversiteit Groningen, Nijenborgh 4, 9747 AG Groningen, The Netherlands
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