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Multi-configurational DFT
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1) General Theory: Savin and collaborators
2) Toulouse et al. paper on multi-reference DFT
3) Approximations for practical calculations
RANGE SEPARATED FUNCTIONALS
1) CAM-B3LYP
2) Peach et al. Charge-transfer excitations
3) Other: S. Gusarov, K. Hirao, G. Scuseria, Jenesen,
J. Angyan, R. Baer, M. Head-Gordon, W. Yang, P.
Gill, ...
EPFL 2016, T. Wesolowski, University of Geneva
Multi-configurational DFT
1
General Theory
EPFL 2016, T. Wesolowski, University of Geneva
Numerical illustration: exact/accurate
J. Toulouse, F. Colonna, A. Savin, Phys. Rev. A, 70, (2004) 062505
[1] A. Savin, in Recent Advances in Density Functional Theory,
edited by D. P. Chong (World Scientific, Singapore, 1996).
[2] A. Savin, in Recent Developments of Modern Density Functional
Theory, edited by J. M. Seminario (Elsevier, Amsterdam, 1996), pp. 327–
357.
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Adiabatic connection
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General theory (Savin)
Approximations
for Excm[n]
Range-separated Fm[n]
Range-separated Excm[n]
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Variational principle
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General theory (Savin)
Euler-Lagrange Equation
Adiabatic connections and range separation
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Toulouse et al. PRA 2004
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Conventional
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Multi-configurational DFT:numerical illustration Toulouse et al. PRA 2004
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A) Get very accurate no(r) (MRCISD or Full CI)
B) Generate the range-separated vxcm[no](r)
C) Solve Euler-Lagrange equation (with vxcm[no](r) from B)
Use one of available multi-determinantal method of QC to obtain Ym
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Multi-configurational DFT with
various active spaces for YBe
Em is evaluated using MRCISD and EmS some truncated CI form of Ym in
J. Toulouse, F. Colonna, A. Savin, Phys. Rev. A, 70, (2004) 062505
7EPFL 2016, T. Wesolowski, University of Geneva
Multi-configurational DFT:numerical illustration Toulouse et al. PRA 2004
8EPFL 2016, T. Wesolowski, University of Geneva
How good is LDA for Exm [n] and Ec
m[n]? Range-separated Excm[n]
Excm,unif [n] obtained as an analytic fit to data obtained from (high
level) wave-function uniform electron gas with modified vee .
[Toulouse et al, Int.J. Quantum Chem., 100 (2004) 1047]
9EPFL 2016, T. Wesolowski, University of Geneva
How good is LDA for Exm [n] and Ec
m[n]? Range-separated Excm[n]
Excm,unif [n] obtained as an analytic fit to data obtained from (high
level) wave-function uniform electron gas with modified vee .
[Toulouse et al, Int.J. Quantum Chem., 100 (2004) 1047]
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Euler-Lagrange equation
Variational principle
a) No double-counting – by construction
b) Long-range Y
c) Short range n(r)
d) For accurate solution of SE with veem smaller number of determinants than for vee.
e) Local density approximation quite good at small m.
Summary: multi-determinantal DFT
EPFL 2016, T. Wesolowski, University of Geneva
Multi-determinantal DFT
Kohn-Sham DFT
Wave-functions
If m is small:
need of good DFA
no good description of quasi degeneracy, van der Waals, etc.
Mmulti-determinantal DFT vs other methods
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Approximations for solving the Euler-Lagrange equation
- For Y: method for solving (modified) SE equation
- Fm[n]: approximations, m-LDA, m-GGA, etc.
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Remark on the numerics:
For other integrals recursive procedures:
Obara-Saika, McMurchie-Davidson, Gill et al., Lindth et al. :
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All sort of approaches based on range separation for Vee:
- 1 determinant:
Angyan, Yang, Baer, Hirao, Scuseria, Handy, Gill, Head-Hordon,…
- MP2 Angyan
- MCSCF: Jensen
- CC: Stoll (CC)
- ……
Possible confusing terminology:
- adiabatic connection,
- range-separation,
- Coulomb attenuation,
- Multideterminantal DFT,
- …
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Alcalin-Rare gas complexesGoll et al, Chem. Phys, 329 (2006) 276
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Alcalin-Rare gas complexes: Kohn-ShamGoll et al, Chem. Phys, 329 (2006) 276
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Alcalin-Rare gas complexes: range-separated DFTGoll et al, Chem. Phys, 329 (2006) 276
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Rare gas dimers
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Tawada et al. Yanai et al. (CAM)
Y.Tawada,S.Yanagisawa,T.Yanai, K.Hirao, J.Chem.Phys.120,8425(2004). T.Yanai,D.P.Tew, N.C.Handy, Chem.Phys.Lett. 393,51(2004).
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Y.Tawada,S.Yanagisawa,T.Yanai, K.Hirao, J.Chem.Phys.120,8425(2004).
EPFL 2016, T. Wesolowski, University of Geneva21Y.Tawada,S.Yanagisawa,T.Yanai, K.Hirao, J.Chem.Phys.120,8425(2004).
Charge-transfer excitations from
LR-TDDFT
Excitation energies in density
functional theory: An evaluation
and a diagnostic test
Michael J. G. Peach, Peter Benfield,
Trygve Helgaker, and David J. Tozer
Citation: The Journal of Chemical
Physics 128, 044118 (2008);
EPFL 2016, T. Wesolowski, University of Geneva22
Charge-transfer excitations from
LR-TDDFT
Excitation energies in density
functional theory: An evaluation
and a diagnostic test
Michael J. G. Peach, Peter Benfield,
Trygve Helgaker, and David J. Tozer
Citation: The Journal of Chemical
Physics 128, 044118 (2008);
EPFL 2016, T. Wesolowski, University of Geneva23
LR-TDDFT Failures:Charge-transfer excitations
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