Density functional theory based methods in quantum chemistry · PDF fileObara-Saika,...

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

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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

EPFL 2016, T. Wesolowski, University of Geneva

General theory (Savin)

Approximations

for Excm[n]

Range-separated Fm[n]

Range-separated Excm[n]

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Variational principle

EPFL 2016, T. Wesolowski, University of Geneva

General theory (Savin)

Euler-Lagrange Equation

Adiabatic connections and range separation

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Toulouse et al. PRA 2004

EPFL 2016, T. Wesolowski, University of Geneva

Conventional

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Multi-configurational DFT:numerical illustration Toulouse et al. PRA 2004

EPFL 2016, T. Wesolowski, University of Geneva

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

EPFL 2016, T. Wesolowski, University of Geneva6

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]

EPFL 2016, T. Wesolowski, University of Geneva10

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

EPFL 2016, T. Wesolowski, University of Geneva

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