Exploring non-adiabatic approximations to the exchange–correlation functional of TDDFT

Fuks, Johanna I.; Lacombe, Lionel; Nielsen, Søren E.  B.; Maitra, Neepa T.

doi:10.1039/c8cp03957g

Title: Exploring non-adiabatic approximations to the exchange–correlation functional of TDDFT

Journal Article · Tue Oct 02 00:00:00 EDT 2018 · Physical Chemistry Chemical Physics. PCCP

DOI:https://doi.org/10.1039/c8cp03957g· OSTI ID:1612279

^[1]; Lacombe, Lionel ^[2]; Nielsen, Søren E. B. ^[3];

^[2]

Univ. of Buenos Aires (Argentina)
City Univ. of New York (CUNY), NY (United States)
Max Planck Institute for the Structure and Dynamics of Matter and Center for Free-Electron Laser Science, Hamburg (Germany)

A decomposition of the exact exchange–correlation potential of time-dependent density functional theory into an interaction component and a kinetic component offers a new starting point for non-adiabatic approximations. The components are expressed in terms of the exchange–correlation hole and the difference between the one-body density matrix of the interacting and Kohn–Sham systems, which must be approximated in terms of quantities accessible from the Kohn–Sham evolution. We explore several preliminary approximations, evaluate their fulfillment of known exact conditions, and test their performance on simple model systems for which available exact solutions indicate the significance of going beyond the adiabatic approximation.

View Accepted Manuscript (DOE)

Cite

Export

Save

Research Organization:: City Univ. of New York (CUNY), NY (United States)

Sponsoring Organization:: USDOE Office of Science (SC), Basic Energy Sciences (BES)

Grant/Contract Number:: SC0015344

OSTI ID:: 1612279

Alternate ID(s):: OSTI ID: 1477207

Journal Information:: Physical Chemistry Chemical Physics. PCCP, Vol. 20, Issue 41; ISSN 1463-9076

Publisher:: Royal Society of ChemistryCopyright Statement

Country of Publication:: United States

Language:: English

Citation Metrics:

Cited by: 20 works

Citation information provided by
Web of Science

References (64)

Violation of the zero-force theorem in the time-dependent Krieger-Li-Iafrate approximation Mundt, Michael; Kümmel, Stephan; van Leeuwen, Robert Physical Review A, Vol. 75, Issue 5 https://doi.org/10.1103/PhysRevA.75.050501	journal	May 2007
Electrons as probes of dynamics in molecules and clusters: A contribution from Time Dependent Density Functional Theory Wopperer, P.; Dinh, P. M.; Reinhard, P. -G. Physics Reports, Vol. 562 https://doi.org/10.1016/j.physrep.2014.07.003	journal	February 2015
Attosecond Electron Dynamics in Molecules Nisoli, Mauro; Decleva, Piero; Calegari, Francesca Chemical Reviews, Vol. 117, Issue 16 https://doi.org/10.1021/acs.chemrev.6b00453	journal	May 2017
Critical Examination of Explicitly Time-Dependent Density Functional Theory for Coherent Control of Dipole Switching Raghunathan, Shampa; Nest, Mathias Journal of Chemical Theory and Computation, Vol. 7, Issue 8 https://doi.org/10.1021/ct200270t	journal	July 2011
Memory in Time-Dependent Density Functional Theory Maitra, Neepa T.; Burke, Kieron; Woodward, Chris Physical Review Letters, Vol. 89, Issue 2 https://doi.org/10.1103/PhysRevLett.89.023002	journal	June 2002
Studies of spuriously shifting resonances in time-dependent density functional theory Luo, Kai; Fuks, Johanna I.; Maitra, Neepa T. The Journal of Chemical Physics, Vol. 145, Issue 4 https://doi.org/10.1063/1.4955447	journal	July 2016
Time-dependent exchange-correlation functional for a Hubbard dimer: Quantifying nonadiabatic effects Fuks, Johanna I.; Farzanehpour, Mehdi; Tokatly, Ilya V. Physical Review A, Vol. 88, Issue 6 https://doi.org/10.1103/PhysRevA.88.062512	journal	December 2013
Time-Dependent Density-Functional Theory Ullrich, Carsten A. https://doi.org/10.1093/acprof:oso/9780199563029.001.0001	book	December 2011
Universal Dynamical Steps in the Exact Time-Dependent Exchange-Correlation Potential Elliott, P.; Fuks, J. I.; Rubio, A. Physical Review Letters, Vol. 109, Issue 26 https://doi.org/10.1103/PhysRevLett.109.266404	journal	December 2012
Local density-functional theory of frequency-dependent linear response Gross, E. K. U.; Kohn, Walter Physical Review Letters, Vol. 55, Issue 26 https://doi.org/10.1103/PhysRevLett.55.2850	journal	December 1985
Time-Dependent Optimized Effective Potential Ullrich, C. A.; Gossmann, U. J.; Gross, E. K. U. Physical Review Letters, Vol. 74, Issue 6 https://doi.org/10.1103/PhysRevLett.74.872	journal	February 1995
The Lack of Resonance Problem in Coherent Control with Real-Time Time-Dependent Density Functional Theory Raghunathan, Shampa; Nest, Mathias Journal of Chemical Theory and Computation, Vol. 8, Issue 3 https://doi.org/10.1021/ct200905z	journal	February 2012
Analysis of electron interaction and atomic shell structure in terms of local potentials Gritsenko, Oleg; van Leeuwen, Robert; Baerends, Evert Jan The Journal of Chemical Physics, Vol. 101, Issue 10 https://doi.org/10.1063/1.468024	journal	November 1994
Causality and Symmetry in Time-Dependent Density-Functional Theory van Leeuwen, Robert Physical Review Letters, Vol. 80, Issue 6 https://doi.org/10.1103/PhysRevLett.80.1280	journal	February 1998
Local Hartree-exchange and correlation potential defined by local force equations Ruggenthaler, M.; Bauer, D. Physical Review A, Vol. 80, Issue 5 https://doi.org/10.1103/PhysRevA.80.052502	journal	November 2009
Quantum memory effects in the dynamics of electrons in gold clusters Kurzweil, Yair; Baer, Roi Physical Review B, Vol. 73, Issue 7 https://doi.org/10.1103/PhysRevB.73.075413	journal	February 2006
Center of Mass and Relative Motion in Time Dependent Density Functional Theory Vignale, G. Physical Review Letters, Vol. 74, Issue 16 https://doi.org/10.1103/PhysRevLett.74.3233	journal	April 1995
Simulating Pump-Probe Photoelectron and Absorption Spectroscopy on the Attosecond Timescale with Time-Dependent Density Functional Theory De Giovannini, Umberto; Brunetto, Gustavo; Castro, Alberto ChemPhysChem, Vol. 14, Issue 7 https://doi.org/10.1002/cphc.201201007	journal	March 2013
Several Theorems in Time-Dependent Density Functional Theory Hessler, Paul; Park, Jang; Burke, Kieron Physical Review Letters, Vol. 82, Issue 2 https://doi.org/10.1103/PhysRevLett.82.378	journal	January 1999
Time-Dependent Density Functional Theory Beyond the Adiabatic Local Density Approximation Vignale, G.; Ullrich, C. A.; Conti, S. Physical Review Letters, Vol. 79, Issue 24 https://doi.org/10.1103/PhysRevLett.79.4878	journal	December 1997
Perspective: Fundamental aspects of time-dependent density functional theory Maitra, Neepa T. The Journal of Chemical Physics, Vol. 144, Issue 22 https://doi.org/10.1063/1.4953039	journal	June 2016
Electron scattering in time-dependent density functional theory Lacombe, Lionel; Suzuki, Yasumitsu; Watanabe, Kazuyuki The European Physical Journal B, Vol. 91, Issue 6 https://doi.org/10.1140/epjb/e2018-90101-2	journal	June 2018
Sum rule for the linear density response of a driven electronic system Vignale, Giovanni Physics Letters A, Vol. 209, Issue 3-4 https://doi.org/10.1016/0375-9601(95)00855-3	journal	December 1995
Coherent control and time-dependent density functional theory: Towards creation of wave packets by ultrashort laser pulses Raghunathan, Shampa; Nest, Mathias The Journal of Chemical Physics, Vol. 136, Issue 6 https://doi.org/10.1063/1.3682980	journal	February 2012
Time-dependent density functional theory for charge-transfer dynamics: review of the causes of failure and success* Fuks, Johanna I. The European Physical Journal B, Vol. 89, Issue 11 https://doi.org/10.1140/epjb/e2016-70110-y	journal	November 2016
Time-dependent density functional theory beyond Kohn–Sham Slater determinants Fuks, Johanna I.; Nielsen, Søren E. B.; Ruggenthaler, Michael Physical Chemistry Chemical Physics, Vol. 18, Issue 31 https://doi.org/10.1039/C6CP00722H	journal	January 2016
Two-electron Rabi oscillations in real-time time-dependent density-functional theory Habenicht, Bradley F.; Tani, Noriyuki P.; Provorse, Makenzie R. The Journal of Chemical Physics, Vol. 141, Issue 18 https://doi.org/10.1063/1.4900514	journal	November 2014
Current-Dependent Exchange-Correlation Potential for Dynamical Linear Response Theory Vignale, G.; Kohn, Walter Physical Review Letters, Vol. 77, Issue 10 https://doi.org/10.1103/PhysRevLett.77.2037	journal	September 1996
Adiabatic and local approximations for the Kohn-Sham potential in time-dependent Hubbard chains Mancini, L.; Ramsden, J. D.; Hodgson, M. J. P. Physical Review B, Vol. 89, Issue 19 https://doi.org/10.1103/PhysRevB.89.195114	journal	May 2014
Mapping from Densities to Potentials in Time-Dependent Density-Functional Theory van Leeuwen, Robert Physical Review Letters, Vol. 82, Issue 19 https://doi.org/10.1103/PhysRevLett.82.3863	journal	May 1999
Single-active-electron approximation for describing molecules in ultrashort laser pulses and its application to molecular hydrogen Awasthi, Manohar; Vanne, Yulian V.; Saenz, Alejandro Physical Review A, Vol. 77, Issue 6 https://doi.org/10.1103/PhysRevA.77.063403	journal	June 2008
Time-Local Equation for the Exact Optimized Effective Potential in Time-Dependent Density Functional Theory Liao, Sheng-Lun; Ho, Tak-San; Rabitz, Herschel Physical Review Letters, Vol. 118, Issue 24 https://doi.org/10.1103/PhysRevLett.118.243001	journal	June 2017
Harmonic-Potential Theorem: Implications for Approximate Many-Body Theories Dobson, John F. Physical Review Letters, Vol. 73, Issue 16 https://doi.org/10.1103/PhysRevLett.73.2244	journal	October 1994
Theorem for exact local exchange potential Ou-Yang, Hui; Levy, Mel Physical Review Letters, Vol. 65, Issue 8 https://doi.org/10.1103/PhysRevLett.65.1036	journal	August 1990
Perspective: Fifty years of density-functional theory in chemical physics Becke, Axel D. The Journal of Chemical Physics, Vol. 140, Issue 18 https://doi.org/10.1063/1.4869598	journal	May 2014
Electron dynamics with real-time time-dependent density functional theory Provorse, Makenzie R.; Isborn, Christine M. International Journal of Quantum Chemistry, Vol. 116, Issue 10 https://doi.org/10.1002/qua.25096	journal	February 2016
Perspective: Kohn-Sham density functional theory descending a staircase Yu, Haoyu S.; Li, Shaohong L.; Truhlar, Donald G. The Journal of Chemical Physics, Vol. 145, Issue 13 https://doi.org/10.1063/1.4963168	journal	October 2016
Control and analysis of single-determinant electron dynamics Ramakrishnan, Raghunathan; Nest, Mathias Physical Review A, Vol. 85, Issue 5 https://doi.org/10.1103/PhysRevA.85.054501	journal	May 2012
Algorithm to derive exact exchange-correlation potentials from correlated densities in atoms Peirs, K.; Van Neck, D.; Waroquier, M. Physical Review A, Vol. 67, Issue 1 https://doi.org/10.1103/PhysRevA.67.012505	journal	January 2003
Analysis of correlation in terms of exact local potentials: Applications to two-electron systems Buijse, Marten A.; Baerends, Evert Jan; Snijders, Jaap G. Physical Review A, Vol. 40, Issue 8 https://doi.org/10.1103/PhysRevA.40.4190	journal	October 1989
Exact Density-Functional Potentials for Time-Dependent Quasiparticles Ramsden, J. D.; Godby, R. W. Physical Review Letters, Vol. 109, Issue 3 https://doi.org/10.1103/PhysRevLett.109.036402	journal	July 2012
Adiabatic Approximation in Nonperturbative Time-Dependent Density-Functional Theory Thiele, M.; Gross, E. K. U.; Kümmel, S. Physical Review Letters, Vol. 100, Issue 15 https://doi.org/10.1103/PhysRevLett.100.153004	journal	April 2008
Dynamics of Charge-Transfer Processes with Time-Dependent Density Functional Theory Fuks, J. I.; Elliott, P.; Rubio, A. The Journal of Physical Chemistry Letters, Vol. 4, Issue 5 https://doi.org/10.1021/jz302099f	journal	February 2013
Many-body quantum dynamics from the density Nielsen, S. E. B.; Ruggenthaler, M.; van Leeuwen, R. EPL (Europhysics Letters), Vol. 101, Issue 3 https://doi.org/10.1209/0295-5075/101/33001	journal	February 2013
Exact Time-Dependent Exchange-Correlation Potential in Electron Scattering Processes Suzuki, Yasumitsu; Lacombe, Lionel; Watanabe, Kazuyuki Physical Review Letters, Vol. 119, Issue 26 https://doi.org/10.1103/PhysRevLett.119.263401	journal	December 2017
Time-Resolved Spectroscopy in Time-Dependent Density Functional Theory: An Exact Condition Fuks, Johanna I.; Luo, Kai; Sandoval, Ernesto D. Physical Review Letters, Vol. 114, Issue 18 https://doi.org/10.1103/PhysRevLett.114.183002	journal	May 2015
Computational Benchmarking for Ultrafast Electron Dynamics: Wave Function Methods vs Density Functional Theory Oliveira, Micael J. T.; Mignolet, Benoit; Kus, Tomasz Journal of Chemical Theory and Computation, Vol. 11, Issue 5 https://doi.org/10.1021/acs.jctc.5b00167	journal	April 2015
Molecular exchange‐correlation Kohn–Sham potential and energy density from ab initio first‐ and second‐order density matrices: Examples for XH (X=Li, B, F) Gritsenko, Oleg V.; Leeuwen, Robert van; Baerends, Evert Jan The Journal of Chemical Physics, Vol. 104, Issue 21 https://doi.org/10.1063/1.471602	journal	June 1996
Perspective on density functional theory Burke, Kieron The Journal of Chemical Physics, Vol. 136, Issue 15 https://doi.org/10.1063/1.4704546	journal	April 2012
Nonlinear phenomena in time-dependent density-functional theory: What Rabi oscillations can teach us Fuks, J. I.; Helbig, N.; Tokatly, I. V. Physical Review B, Vol. 84, Issue 7 https://doi.org/10.1103/PhysRevB.84.075107	journal	August 2011
Kinetic and interaction components of the exact time-dependent correlation potential Luo, Kai; Fuks, Johanna I.; Sandoval, Ernesto D. The Journal of Chemical Physics, Vol. 140, Issue 18 https://doi.org/10.1063/1.4867002	journal	May 2014
Effect of molecular dissociation on the exchange-correlation Kohn-Sham potential Gritsenko, Oleg V.; Baerends, Evert Jan Physical Review A, Vol. 54, Issue 3 https://doi.org/10.1103/PhysRevA.54.1957	journal	September 1996
Propagation of initially excited states in time-dependent density-functional theory Elliott, Peter; Maitra, Neepa T. Physical Review A, Vol. 85, Issue 5 https://doi.org/10.1103/PhysRevA.85.052510	journal	May 2012
Attosecond Electron Dynamics in Molecules Nisoli, Mauro; Decleva, Piero; Calegari, Francesca Deutsches Elektronen-Synchrotron, DESY, Hamburg https://doi.org/10.3204/pubdb-2017-10784	text	January 2017
Local Density-Functional Theory of Frequency-Dependent Linear Response Gross, E. K. U.; Kohn, Walter Physical Review Letters, Vol. 57, Issue 7 https://doi.org/10.1103/physrevlett.57.923.2	journal	August 1986
Perspective on density functional theory Burke, Kieron arXiv https://doi.org/10.48550/arxiv.1201.3679	text	January 2012
Exact density-functional potentials for time-dependent quasiparticles Ramsden, J. D.; Godby, R. W. arXiv https://doi.org/10.48550/arxiv.1206.6035	text	January 2012
The time-dependent exchange-correlation functional for a Hubbard dimer: quantifying non-adiabatic effect Fuks, Johanna I.; Farzanehpour, Mehdi; Tokatly, Ilya V. arXiv https://doi.org/10.48550/arxiv.1312.1667	text	January 2013
Electrons as probes of dynamics in molecules and clusters : a contribution from Time Dependent Density Functional Theory Wopperer, P.; Dinh, P. M.; Reinhard, P. -G. arXiv https://doi.org/10.48550/arxiv.1407.4965	text	January 2014
Time-resolved spectroscopy in time dependent density functional theory: An exact condition Fuks, Johanna I.; Luo, Kai; Sandoval, Ernesto D. arXiv https://doi.org/10.48550/arxiv.1412.0586	text	January 2014
Strongly Constrained and Appropriately Normed Semilocal Density Functional Sun, Jianwei; Ruzsinszky, Adrienn; Perdew, John P. arXiv https://doi.org/10.48550/arxiv.1504.03028	preprint	January 2015
Studies of Spuriously Shifting Resonances in Time-dependent Density Functional Theory Luo, Kai; Fuks, Johanna I.; Maitra, Neepa T. arXiv https://doi.org/10.48550/arxiv.1605.05800	text	January 2016
Center of mass and relative motion in time dependent density functional theory Vignale, G. arXiv https://doi.org/10.48550/arxiv.cond-mat/9412100	text	January 1994
Current-dependent exchange-correlation potential for dynamical linear response theory Vignale, G.; Kohn, Walter arXiv https://doi.org/10.48550/arxiv.cond-mat/9605052	text	January 1996

Cited By (3)

Propagation of maximally localized Wannier functions in real-time TDDFT Yost, Dillon C.; Yao, Yi; Kanai, Yosuke The Journal of Chemical Physics, Vol. 150, Issue 19 https://doi.org/10.1063/1.5095631	journal	May 2019
X-ray linear and non-linear spectroscopy of the ESCA molecule Nenov, Artur; Segatta, Francesco; Bruner, Adam The Journal of Chemical Physics, Vol. 151, Issue 11 https://doi.org/10.1063/1.5116699	journal	September 2019
Propagation of maximally localized Wannier functions in real-time TDDFT Yost, Dillon C.; Yao, Yi; Kanai, Yosuke arXiv https://doi.org/10.48550/arxiv.1903.05081	text	January 2019

Similar Records

Developing new and understanding old approximations in TDDFT

Journal Article · Tue Jun 02 00:00:00 EDT 2020 · Faraday Discussions · OSTI ID:1612279

Lacombe, Lionel; Maitra, Neepa T.

Exact thermal density functional theory for a model system: Correlation components and accuracy of the zero-temperature exchange-correlation approximation

Journal Article · Tue Jun 14 00:00:00 EDT 2016 · Physical Review B · OSTI ID:1612279

Smith, J. C.; Pribram-Jones, A.; Burke, K.

Reconstructing the adiabatic exchange-correlation kernel of time-dependent density-functional theory

Journal Article · Wed Jul 15 00:00:00 EDT 2009 · Physical Review. A · OSTI ID:1612279

Thiele, M; Kuemmel, S

Related Subjects

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CHEMISTRY
Chemistry
Physics

Title: Exploring non-adiabatic approximations to the exchange–correlation functional of TDDFT

Citation Formats

References (64)

Cited By (3)

Similar Records

Related Subjects