Representing the thermal state in time-dependent density functional theory
Abstract
Classical molecular dynamics (MD) provides a powerful and widely used approach to determining thermodynamic properties by integrating the classical equations of motion of a system of atoms. Time-Dependent Density Functional Theory (TDDFT) provides a powerful and increasingly useful approach to integrating the quantum equations of motion for a system of electrons. TDDFT efficiently captures the unitary evolution of a many-electron state by mapping the system into a fictitious non-interacting system. In analogy to MD, one could imagine obtaining the thermodynamic properties of an electronic system from a TDDFT simulation in which the electrons are excited from their ground state by a time-dependent potential and then allowed to evolve freely in time while statistical data are captured from periodic snapshots of the system. For a variety of systems (e.g., many metals), the electrons reach an effective state of internal equilibrium due to electron-electron interactions on a time scale that is short compared to electron-phonon equilibration. During the initial time-evolution of such systems following electronic excitation, electron-phonon interactions should be negligible, and therefore, TDDFT should successfully capture the internal thermalization of the electrons. However, it is unclear how TDDFT represents the resulting thermal state. In particular, the thermal state is usually representedmore »
- Authors:
-
- Sandia National Lab. (SNL-NM), Albuquerque, NM (United States)
- Samsung Semiconductor, Inc., Austin, TX (United States). Advanced Logic Lab,
- Publication Date:
- Research Org.:
- Sandia National Lab. (SNL-NM), Albuquerque, NM (United States)
- Sponsoring Org.:
- USDOE National Nuclear Security Administration (NNSA)
- OSTI Identifier:
- 1110660
- Report Number(s):
- SAND-2013-7774J
Journal ID: ISSN 0021-9606; JCPSA6; 474165
- Grant/Contract Number:
- AC04-94AL85000
- Resource Type:
- Journal Article: Accepted Manuscript
- Journal Name:
- Journal of Chemical Physics
- Additional Journal Information:
- Journal Volume: 142; Journal Issue: 20; Journal ID: ISSN 0021-9606
- Publisher:
- American Institute of Physics (AIP)
- Country of Publication:
- United States
- Language:
- English
- Subject:
- 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS
Citation Formats
Modine, N. A., and Hatcher, R. M. Representing the thermal state in time-dependent density functional theory. United States: N. p., 2015.
Web. doi:10.1063/1.4921690.
Modine, N. A., & Hatcher, R. M. Representing the thermal state in time-dependent density functional theory. United States. https://doi.org/10.1063/1.4921690
Modine, N. A., and Hatcher, R. M. 2015.
"Representing the thermal state in time-dependent density functional theory". United States. https://doi.org/10.1063/1.4921690. https://www.osti.gov/servlets/purl/1110660.
@article{osti_1110660,
title = {Representing the thermal state in time-dependent density functional theory},
author = {Modine, N. A. and Hatcher, R. M.},
abstractNote = {Classical molecular dynamics (MD) provides a powerful and widely used approach to determining thermodynamic properties by integrating the classical equations of motion of a system of atoms. Time-Dependent Density Functional Theory (TDDFT) provides a powerful and increasingly useful approach to integrating the quantum equations of motion for a system of electrons. TDDFT efficiently captures the unitary evolution of a many-electron state by mapping the system into a fictitious non-interacting system. In analogy to MD, one could imagine obtaining the thermodynamic properties of an electronic system from a TDDFT simulation in which the electrons are excited from their ground state by a time-dependent potential and then allowed to evolve freely in time while statistical data are captured from periodic snapshots of the system. For a variety of systems (e.g., many metals), the electrons reach an effective state of internal equilibrium due to electron-electron interactions on a time scale that is short compared to electron-phonon equilibration. During the initial time-evolution of such systems following electronic excitation, electron-phonon interactions should be negligible, and therefore, TDDFT should successfully capture the internal thermalization of the electrons. However, it is unclear how TDDFT represents the resulting thermal state. In particular, the thermal state is usually represented in quantum statistical mechanics as a mixed state, while the occupations of the TDDFT wave functions are fixed by the initial state in TDDFT. Two key questions involve (1) reformulating quantum statistical mechanics so that thermodynamic expectations can be obtained as an unweighted average over a set of many-body pure states and (2) constructing a family of non-interacting (single determinant) TDDFT states that approximate the required many-body states for the canonical ensemble. In Section II, we will address these questions by first demonstrating that thermodynamic expectations can be evaluated by averaging over certain many-body pure states, which we will call thermal states, and then constructing TDDFT states that approximate these thermal states. In Section III, we will present some numerical tests of the resulting theory, and in Section IV, we will summarize our main results and discuss some possible future directions for this work.},
doi = {10.1063/1.4921690},
url = {https://www.osti.gov/biblio/1110660},
journal = {Journal of Chemical Physics},
issn = {0021-9606},
number = 20,
volume = 142,
place = {United States},
year = {Thu May 28 00:00:00 EDT 2015},
month = {Thu May 28 00:00:00 EDT 2015}
}
Web of Science
Works referenced in this record:
Signatures of Short-Range Many-Body Effects in the Dielectric Function of Silicon for Finite Momentum Transfer
journal, December 2006
- Weissker, Hans-Christian; Serrano, Jorge; Huotari, Simo
- Physical Review Letters, Vol. 97, Issue 23
Progress in Time-Dependent Density-Functional Theory
journal, May 2012
- Casida, M. E.; Huix-Rotllant, M.
- Annual Review of Physical Chemistry, Vol. 63, Issue 1
Dynamic screening effects in x-ray absorption spectra
journal, March 2003
- Ankudinov, A. L.; Nesvizhskii, A. I.; Rehr, J. J.
- Physical Review B, Vol. 67, Issue 11
Time-dependent density functional theory: Past, present, and future
journal, August 2005
- Burke, Kieron; Werschnik, Jan; Gross, E. K. U.
- The Journal of Chemical Physics, Vol. 123, Issue 6
Excitation Energies from Time-Dependent Density-Functional Theory
journal, February 1996
- Petersilka, M.; Gossmann, U. J.; Gross, E. K. U.
- Physical Review Letters, Vol. 76, Issue 8
On the generators of quantum dynamical semigroups
journal, June 1976
- Lindblad, G.
- Communications in Mathematical Physics, Vol. 48, Issue 2
Electron-hole and plasmon excitations in transition metals: Ab initio calculations and inelastic x-ray scattering measurements
journal, September 2005
- Gurtubay, I. G.; Pitarke, J. M.; Ku, Wei
- Physical Review B, Vol. 72, Issue 12
Stochastic Time-Dependent Current-Density-Functional Theory
journal, June 2007
- Di Ventra, Massimiliano; D’Agosta, Roberto
- Physical Review Letters, Vol. 98, Issue 22
Theory of the Linewidth of Intersubband Plasmons in Quantum Wells
journal, July 2001
- Ullrich, C. A.; Vignale, G.
- Physical Review Letters, Vol. 87, Issue 3
Density-Functional Theory for Time-Dependent Systems
journal, March 1984
- Runge, Erich; Gross, E. K. U.
- Physical Review Letters, Vol. 52, Issue 12
Time-Dependent Density Functional Theory for Open Quantum Systems with Unitary Propagation
journal, January 2010
- Yuen-Zhou, Joel; Tempel, David G.; Rodríguez-Rosario, César A.
- Physical Review Letters, Vol. 104, Issue 4
A Stochastic Estimator of the Trace of the Influence Matrix for Laplacian Smoothing Splines
journal, January 1989
- Hutchinson, M. F.
- Communications in Statistics - Simulation and Computation, Vol. 18, Issue 3
Density functional calculations of nanoscale conductance
journal, February 2008
- Koentopp, Max; Chang, Connie; Burke, Kieron
- Journal of Physics: Condensed Matter, Vol. 20, Issue 8
Completely positive dynamical semigroups of N-level systems
journal, January 1976
- Gorini, Vittorio
- Journal of Mathematical Physics, Vol. 17, Issue 5
Stochastic pure state representation for open quantum systems
journal, March 1986
- Diósi, L.
- Physics Letters A, Vol. 114, Issue 8-9
Hohenberg-Kohn theorem for time-dependent ensembles
journal, March 1985
- Li, Tie-cheng; Tong, Pei-qing
- Physical Review A, Vol. 31, Issue 3
Time-dependent density-functional theory for extended systems
journal, February 2007
- Botti, Silvana; Schindlmayr, Arno; Sole, Rodolfo Del
- Reports on Progress in Physics, Vol. 70, Issue 3
Electronic excitations: density-functional versus many-body Green’s-function approaches
journal, June 2002
- Onida, Giovanni; Reining, Lucia; Rubio, Angel
- Reviews of Modern Physics, Vol. 74, Issue 2
Stochastic quantum molecular dynamics
journal, December 2009
- Appel, Heiko; Di Ventra, Massimiliano
- Physical Review B, Vol. 80, Issue 21
Local-field effects and anisotropic plasmon dispersion in diamond
journal, April 2000
- Waidmann, S.; Knupfer, M.; Arnold, B.
- Physical Review B, Vol. 61, Issue 15
On quantum statistical mechanics of non-Hamiltonian systems
journal, December 1972
- Kossakowski, A.
- Reports on Mathematical Physics, Vol. 3, Issue 4
Quantum trajectories and quantum measurement theory
journal, February 1996
- Wiseman, H. M.
- Quantum and Semiclassical Optics: Journal of the European Optical Society Part B, Vol. 8, Issue 1
Stochastic time-dependent current-density-functional theory: A functional theory of open quantum systems
journal, October 2008
- D’Agosta, Roberto; Di Ventra, Massimiliano
- Physical Review B, Vol. 78, Issue 16
Self-interaction correction to density-functional approximations for many-electron systems
journal, May 1981
- Perdew, J. P.; Zunger, Alex
- Physical Review B, Vol. 23, Issue 10, p. 5048-5079
Quantum Collision Current in Electronic Circuits
journal, September 2005
- Gebauer, R.; Piccinin, S.; Car, R.
- ChemPhysChem, Vol. 6, Issue 9
Thermal Properties of the Inhomogeneous Electron Gas
journal, March 1965
- Mermin, N. David
- Physical Review, Vol. 137, Issue 5A
Time-Dependent Density Functional Theory
journal, June 2004
- Marques, M. A. L.; Gross, E. K. U.
- Annual Review of Physical Chemistry, Vol. 55, Issue 1
Ground State of the Electron Gas by a Stochastic Method
journal, August 1980
- Ceperley, D. M.; Alder, B. J.
- Physical Review Letters, Vol. 45, Issue 7, p. 566-569
Works referencing / citing this record:
Carrier Multiplication-Induced Structural Change during Ultrafast Carrier Relaxation and Non-Thermal Phase Transition in Semiconductors
text, January 2016
- Bang, Junhyeok; Sun, Y. Y.; Liu, X. -Q.
- arXiv
Ultrafast electron dynamics and orbital-dependent thermalization in photoexcited metals
journal, September 2018
- Silaeva, E. P.; Bevillon, E.; Stoian, R.
- Physical Review B, Vol. 98, Issue 9
Thermal effects on laser-assisted field evaporation from a Si surface: A real-time first-principles study
journal, July 2019
- Uchida, Kazuki; Suzuki, Yasumitsu; Watanabe, Kazuyuki
- Journal of Applied Physics, Vol. 126, Issue 3
First-Principles Investigation to Ionization of Argon Under Conditions Close to Typical Sonoluminescence Experiments
journal, February 2016
- Kang, Wei; Zhao, Shijun; Zhang, Shen
- Scientific Reports, Vol. 6, Issue 1
Stopping power beyond the adiabatic approximation
journalarticle, January 2017
- Caro, M.; Correa, Aa; Artacho, E.
- Nature Publishing Group