Skip to main content
U.S. Department of Energy
Office of Scientific and Technical Information

Double and Charge-Transfer Excitations in Time-Dependent Density Functional Theory

Journal Article · · Annual Review of Physical Chemistry
 [1]
  1. Department of Physics, Rutgers University at Newark, Newark, New Jersey, USA,

Time-dependent density functional theory has emerged as a method of choice for calculations of spectra and response properties in physics, chemistry, and biology, with its system-size scaling enabling computations on systems much larger than otherwise possible. While increasingly complex and interesting systems have been successfully tackled with relatively simple functional approximations, there has also been increasing awareness that these functionals tend to fail for certain classes of approximations. Here I review the fundamental challenges the approximate functionals have in describing double excitations and charge-transfer excitations, which are two of the most common impediments for the theory to be applied in a black-box way. At the same time, I describe the progress made in recent decades in developing functional approximations that give useful predictions for these excitations.

Research Organization:
Rutgers Univ., Piscataway, NJ (United States)
Sponsoring Organization:
USDOE Office of Science (SC)
DOE Contract Number:
SC0020044
OSTI ID:
1980850
Journal Information:
Annual Review of Physical Chemistry, Vol. 73, Issue 1; ISSN 0066-426X
Publisher:
Annual Reviews
Country of Publication:
United States
Language:
English

References (133)

Time-Dependent Density Functional Response Theory for Molecules book November 1995
Reference Energies for Double Excitations journal January 2019
QUESTDB : A database of highly accurate excitation energies for the electronic structure community journal February 2021
Time-Dependent Density-Functional Theory book December 2011
Fundamentals of Time-Dependent Density Functional Theory book January 2012
Perspective: Fundamental aspects of time-dependent density functional theory journal June 2016
Progress in Time-Dependent Density-Functional Theory journal May 2012
Inhomogeneous Electron Gas journal November 1964
Time-Dependent Density Functional Response Theory of Molecular Systems: Theory, Computational Methods, and Functionals book January 1996
Introduction to TDDFT book January 2012
Molecular excitation energies from time-dependent density functional theory journal April 2000
Excitations in Time-Dependent Density-Functional Theory journal January 2003
Perspective on density functional theory journal April 2012
Perspective: Fifty years of density-functional theory in chemical physics journal May 2014
Perspective: Kohn-Sham density functional theory descending a staircase journal October 2016
A Trip to the Density Functional Theory Zoo: Warnings and Recommendations for the User journal January 2019
Electronic Polarizabilities of Ions from the Hartree-Fock Wave Functions journal November 1954
Time-dependent density functional theory scheme for efficient calculations of dynamic (hyper)polarizabilities journal May 2007
Real-time, real-space implementation of the linear response time-dependent density-functional theory journal April 2006
Perspectives on double-excitations in TDDFT journal November 2011
Adiabatic connection for near degenerate excited states journal May 2004
New approaches to study excited states in density functional theory: general discussion journal January 2020
Doubly Excited Character or Static Correlation of the Reference State in the Controversial 2 1 A g State of trans -Butadiene? journal September 2017
Excitation Number: Characterizing Multiply Excited States journal December 2017
Dynamic polarizabilities and excitation spectra from a molecular implementation of time‐dependent density‐functional response theory: N 2 as a case study journal April 1996
On the determination of excitation energies using density functional theory journal January 2000
Double excitations within time-dependent density functional theory linear response journal April 2004
Dynamical kernels for optical excitations journal November 2020
Photoabsorption spectra from adiabatically exact time-dependent density-functional theory in real time journal January 2009
Frequency Dependence of the Exact Exchange-Correlation Kernel of Time-Dependent Density-Functional Theory journal February 2014
Exact exchange-correlation kernels for optical spectra of model systems journal April 2019
Insights from exact exchange-correlation kernels journal March 2021
Linear density response function within the time-dependent exact-exchange approximation journal September 2008
Discontinuities of the exchange-correlation kernel and charge-transfer excitations in time-dependent density-functional theory journal February 2012
Analytic density functionals with initial-state dependence and memory journal August 2013
Challenging adiabatic time-dependent density functional theory with a Hubbard dimer: the case of time-resolved long-range charge transfer journal January 2014
Exchange-correlation kernel in time-dependent density functional theory journal October 2002
Nonadiabatic time-dependent spin-density functional theory for strongly correlated systems journal November 2013
Linear response time-dependent density functional theory of the Hubbard dimer journal July 2018
A dressed TDDFT treatment of the 21Ag states of butadiene and hexatriene journal May 2004
Application of the dressed time-dependent density functional theory for the excited states of linear polyenes journal April 2009
Dressed TDDFT study of low-lying electronic excited states in selected linear polyenes and diphenylopolyenes journal September 2010
Double excitation effect in non-adiabatic time-dependent density functional theory with an analytic construction of the exchange–correlation kernel in the common energy denominator approximation journal January 2009
Propagator corrections to adiabatic time-dependent density-functional theory linear response theory journal February 2005
Double excitations in finite systems journal January 2009
Many-Body Perturbation Theory Using the Density-Functional Concept: Beyond the G W Approximation journal May 2005
Transforming Nonlocality into a Frequency Dependence: A Shortcut to Spectroscopy journal August 2007
Double excitations in correlated systems: A many–body approach journal January 2011
Assessment of dressed time-dependent density-functional theory for the low-lying valence states of 28 organic chromophores journal November 2011
Long-range excitations in time-dependent density functional theory journal November 2006
Undoing static correlation: Long-range charge transfer in time-dependent density-functional theory journal June 2005
Mixed time-dependent density-functional theory/classical trajectory surface hopping study of oxirane photochemistry journal September 2008
Excitation energies of dissociating H2: A problematic case for the adiabatic approximation of time-dependent density functional theory journal November 2000
Benchmarking TD-DFT and Wave Function Methods for Oscillator Strengths and Excited-State Dipole Moments journal January 2021
Resonant nonlinear polarizabilities in the time-dependent density functional theory journal November 2003
The spin–flip approach within time-dependent density functional theory: Theory and applications to diradicals journal March 2003
Spin-flip time dependent density functional theory applied to excited states with single, double, or mixed electron excitation character journal September 2010
The performance of time-dependent density functional theory based on a noncollinear exchange-correlation potential in the calculations of excitation energies journal February 2005
Double, Rydberg and charge transfer excitations from pairing matrix fluctuation and particle-particle random phase approximation journal December 2013
Excitation energies from particle-particle random phase approximation: Davidson algorithm and benchmark studies journal September 2014
Orbital Optimized Density Functional Theory for Electronic Excited States journal May 2021
The formulation of a constricted variational density functional theory for double excitations journal October 2013
Low-lying excited states by constrained DFT journal April 2018
Density-functional theory for ensembles of fractionally occupied states. I. Basic formalism journal April 1988
Rayleigh-Ritz variational principle for ensembles of fractionally occupied states journal April 1988
Spurious Interactions, and Their Correction, in the Ensemble-Kohn-Sham Scheme for Excited States journal January 2002
An approximation to the ensemble Kohn–Sham exchange potential for excited states of atoms journal August 2003
Accurate double excitations from ensemble density functional calculations journal October 2018
A weight-dependent local correlation density-functional approximation for ensembles journal June 2020
Weight dependence of local exchange–correlation functionals in ensemble density-functional theory: double excitations in two-electron systems journal January 2020
Excitations and benchmark ensemble density functional theory for two electrons journal May 2014
Constrained Density Functional Theory journal November 2011
Charge transfer in time-dependent density functional theory journal September 2017
Relationship between long-range charge-transfer excitation energy error and integer discontinuity in Kohn–Sham theory journal December 2003
Failure of Time-Dependent Density Functional Theory for Long-Range Charge-Transfer Excited States:  The Zincbacteriochlorin−Bacteriochlorin and Bacteriochlorophyll−Spheroidene Complexes journal March 2004
Photoinduced Intramolecular Charge Transfer in 4-(Dimethyl)aminobenzonitrile − A Theoretical Perspective journal February 2004
Charge-Transfer Excitations: A Challenge for Time-Dependent Density Functional Theory That Has Been Met journal May 2017
Excitation energies in density functional theory: An evaluation and a diagnostic test journal January 2008
On the Metric of Charge Transfer Molecular Excitations: A Simple Chemical Descriptor journal June 2013
The particle-hole map: Formal derivation and numerical implementation journal October 2016
Generalized Kohn-Sham schemes and the band-gap problem journal February 1996
Hybrid schemes combining the Hartree–Fock method and density-functional theory: Underlying formalism and properties of correlation functionals journal February 1997
Physical Content of the Exact Kohn-Sham Orbital Energies: Band Gaps and Derivative Discontinuities journal November 1983
Density-Functional Theory of the Energy Gap journal November 1983
What do the Kohn-Sham Orbital Energies Mean? How do Atoms Dissociate? book
Density-Functional Theory for Fractional Particle Number: Derivative Discontinuities of the Energy journal December 1982
Long-range charge-transfer excited states in time-dependent density functional theory require non-local exchange journal August 2003
Asymptotic correction of the exchange–correlation kernel of time-dependent density functional theory for long-range charge-transfer excitations journal July 2004
Correlation-energy functional and its high-density limit obtained from a coupling-constant perturbation expansion journal May 1993
Exchange and Correlation Kernels at the Resonance Frequency: Implications for Excitation Energies in Density-Functional Theory journal May 1999
Charge-transfer excitation energies with a time-dependent density-functional method suitable for orbital-dependent exchange-correlation kernels journal July 2009
Qualitatively Correct Charge-Transfer Excitation Energies in HeH + by Time-Dependent Density-Functional Theory Due to Exact Exchange Kohn−Sham Eigenvalue Differences journal March 2009
Discontinuous functional for linear-response time-dependent density-functional theory: The exact-exchange kernel and approximate forms journal November 2013
Derivative Discontinuities in Time-Dependent Density-Functional Theory journal November 2005
Combining long-range configuration interaction with short-range density functionals journal August 1997
A long-range correction scheme for generalized-gradient-approximation exchange functionals journal August 2001
A new hybrid exchange–correlation functional using the Coulomb-attenuating method (CAM-B3LYP) journal July 2004
Range Separation and Local Hybridization in Density Functional Theory journal December 2008
A long-range-corrected time-dependent density functional theory journal May 2004
Tuned Range-Separated Hybrids in Density Functional Theory journal March 2010
A long-range-corrected density functional that performs well for both ground-state properties and time-dependent density functional theory excitation energies, including charge-transfer excited states journal February 2009
Generalized gradient approximation model exchange holes for range-separated hybrids journal May 2008
Excitation Gaps of Finite-Sized Systems from Optimally Tuned Range-Separated Hybrid Functionals journal April 2012
Reliable Prediction of Charge Transfer Excitations in Molecular Complexes Using Time-Dependent Density Functional Theory journal March 2009
Organic Electronic Materials: Recent Advances in the DFT Description of the Ground and Excited States Using Tuned Range-Separated Hybrid Functionals journal April 2014
Outer-valence Electron Spectra of Prototypical Aromatic Heterocycles from an Optimally Tuned Range-Separated Hybrid Functional journal April 2014
Using optimally tuned range separated hybrid functionals in ground-state calculations: Consequences and caveats journal May 2013
A self-interaction-free local hybrid functional: Accurate binding energies vis-à-vis accurate ionization potentials from Kohn-Sham eigenvalues journal May 2014
Self-interaction correction in a real-time Kohn-Sham scheme: Access to difficult excitations in time-dependent density functional theory journal August 2012
Self-interaction correction and the optimized effective potential journal July 2008
Ultranonlocality and accurate band gaps from a meta-generalized gradient approximation journal November 2019
Molecular excitations from meta-generalized gradient approximations in the Kohn–Sham scheme journal September 2020
Double-hybrid density functional theory for excited electronic states of molecules journal October 2007
Density Functional for Spectroscopy:  No Long-Range Self-Interaction Error, Good Performance for Rydberg and Charge-Transfer States, and Better Performance on Average than B3LYP for Ground States journal December 2006
Revisiting Molecular Dissociation in Density Functional Theory: A Simple Model journal March 2009
Effect of molecular dissociation on the exchange-correlation Kohn-Sham potential journal September 1996
Exact Kohn–Sham potential of strongly correlated finite systems journal December 2009
An approximate exchange-correlation hole density as a functional of the natural orbitals journal February 2002
Correct dissociation limit for the exchange-correlation energy and potential journal January 2006
Response Potential in the Strong-Interaction Limit of Density Functional Theory: Analysis and Comparison with the Coupling-Constant Average journal June 2018
Functional derivative of the zero-point-energy functional from the strong-interaction limit of density-functional theory journal May 2019
Exchange-Correlation Energy Densities and Response Potentials: Connection between Two Definitions and Analytical Model for the Strong-Coupling Limit of a Stretched Bond journal March 2020
Conical intersections and double excitations in time-dependent density functional theory journal March 2006
Developing new and understanding old approximations in TDDFT journal January 2020
Charge transfer excitations from exact and approximate ensemble Kohn-Sham theory journal May 2018
Generalised adiabatic connection in ensemble density-functional theory for excited states: example of the H 2 molecule journal November 2013
Is the Bethe–Salpeter Formalism Accurate for Excitation Energies? Comparisons with TD-DFT, CASPT2, and EOM-CCSD journal March 2017
All-electron ab initio Bethe-Salpeter equation approach to neutral excitations in molecules with numeric atom-centered orbitals journal January 2020
Many-body perturbation theory for understanding optical excitations in organic molecules and solids journal March 2018
Dynamical correction to the Bethe–Salpeter equation beyond the plasmon-pole approximation journal September 2020
Charge Transfer, Double and Bond-Breaking Excitations with Time-Dependent Density Matrix Functional Theory journal July 2008
Excitation energies with time-dependent density matrix functional theory: Singlet two-electron systems journal March 2009
Response Calculations with an Independent Particle System with an Exact One-Particle Density Matrix journal July 2010