various types of excitations in molecular systems. A wide range of excited states,
which are otherwise inaccessible with the use of TD-DFT, can be studied, including
the charge transfer excitations [105], excitations in extended π-conjugated systems
[59], excitations in molecules undergoing bond breaking/bond formation [39],
conical intersections between the ground and excited electronic states [40, 41, 54,
55, 58, 60, 61, 95], etc. It is also noteworthy that the SI-SA-REKS results can be
obtained at an essentially mean-field cost, avoiding a steeper scaling of the linear
response formalism of TD-DFT.
5 Conclusions and Outlook
Ensemble DFT [18, 20, 21, 23, 29] holds considerable promise for theoretical
description of the excited states of strongly correlated molecular systems. Although
it was conceived more than three decades ago, ensemble DFT still did not find its
way to the repertoire of the methods used by computational chemists on a daily
basis. Perhaps it is the perceived lack of practical implementations of ensemble
DFT that holds down its adoption by a wider computational chemistry community.
Although there is a renewed interest in developing ensemble DFT further [31–33]
and in implementing it in the form of practically affordable computational schemes,
these approaches are largely unknown to ordinary computational chemists.
The REKS computational method, reviewed in this chapter, makes ensemble
DFT affordable. The method has already been used to study various types of
electronic transitions occurring in usual as well as strongly correlated molecular
systems and its ability to describe excitation energies in these systems with a
remarkable accuracy has been demonstrated. Although the currently available
implementation of the REKS formalism is not free of certain limitations, in
particular the size of the active space and the number of excited states are restricted,
these limitations will be removed in the near future and this should considerably
improve the prospects for practical use of the method. Especially promising for
obtaining multiple excited states and for simulating the entire excitation spectra of
strongly correlated molecules appears to be a merger of the REKS methodology
with the variational constricted DFT formalism proposed by Ziegler et al. [102,
104] (see Footnote 6). The work in these directions is currently in progress and will
continue in the future.
References
1. Hohenberg P, Kohn W (1964) Phys Rev 136:B864
2. Kohn W, Sham LJ (1965) Phys Rev 140:A1133
3. Casida ME, Jamorski C, Bohr F, Guan JG, Salahub DR (1994) In: Karna SP, Yeates AT (eds)
Nonlinear optical materials: theory and modeling, ACS symposium series, vol. 628, (Am
Chem Soc, Div Comp Chem, 1996), ACS Symposium Series, vol. 628, pp 145–163.
Ensemble DFT Approach to Excited States of Strongly Correlated Molecular Systems
121
which are otherwise inaccessible with the use of TD-DFT, can be studied, including
the charge transfer excitations [105], excitations in extended π-conjugated systems
[59], excitations in molecules undergoing bond breaking/bond formation [39],
conical intersections between the ground and excited electronic states [40, 41, 54,
55, 58, 60, 61, 95], etc. It is also noteworthy that the SI-SA-REKS results can be
obtained at an essentially mean-field cost, avoiding a steeper scaling of the linear
response formalism of TD-DFT.
5 Conclusions and Outlook
Ensemble DFT [18, 20, 21, 23, 29] holds considerable promise for theoretical
description of the excited states of strongly correlated molecular systems. Although
it was conceived more than three decades ago, ensemble DFT still did not find its
way to the repertoire of the methods used by computational chemists on a daily
basis. Perhaps it is the perceived lack of practical implementations of ensemble
DFT that holds down its adoption by a wider computational chemistry community.
Although there is a renewed interest in developing ensemble DFT further [31–33]
and in implementing it in the form of practically affordable computational schemes,
these approaches are largely unknown to ordinary computational chemists.
The REKS computational method, reviewed in this chapter, makes ensemble
DFT affordable. The method has already been used to study various types of
electronic transitions occurring in usual as well as strongly correlated molecular
systems and its ability to describe excitation energies in these systems with a
remarkable accuracy has been demonstrated. Although the currently available
implementation of the REKS formalism is not free of certain limitations, in
particular the size of the active space and the number of excited states are restricted,
these limitations will be removed in the near future and this should considerably
improve the prospects for practical use of the method. Especially promising for
obtaining multiple excited states and for simulating the entire excitation spectra of
strongly correlated molecules appears to be a merger of the REKS methodology
with the variational constricted DFT formalism proposed by Ziegler et al. [102,
104] (see Footnote 6). The work in these directions is currently in progress and will
continue in the future.
References
1. Hohenberg P, Kohn W (1964) Phys Rev 136:B864
2. Kohn W, Sham LJ (1965) Phys Rev 140:A1133
3. Casida ME, Jamorski C, Bohr F, Guan JG, Salahub DR (1994) In: Karna SP, Yeates AT (eds)
Nonlinear optical materials: theory and modeling, ACS symposium series, vol. 628, (Am
Chem Soc, Div Comp Chem, 1996), ACS Symposium Series, vol. 628, pp 145–163.
Ensemble DFT Approach to Excited States of Strongly Correlated Molecular Systems
121