FONCTIONNELLES DE DENSITÉ AVEC SÉPARATION DE PORTÉE: AU CIEL DFT SANS ÉCHELLE DE JACOB

Size: px

Start display at page:

Download "FONCTIONNELLES DE DENSITÉ AVEC SÉPARATION DE PORTÉE: AU CIEL DFT SANS ÉCHELLE DE JACOB"

Clinton Taylor
5 years ago
Views:

1 FONCTIONNELLES DE DENSITÉ AVEC SÉPARATION DE PORTÉE: AU CIEL DFT SANS ÉCHELLE DE JACOB, Iann Gerber, Paola Gori-Giorgi, Julien Toulouse, Andreas Savin Équipe de Modélisation Quantique et Cristallographique Laboratoire de Cristallographie et de Modélisation des Matériaux Minéraux et Biologiques Université de Nancy & CNRS, Vandoeuvre-lès-Nancy, France Laboratoire de Chimie Théorique Université de Pierre et Marie Curie & CNRS, Paris, France GdR-DFT, Autrans, 28 Mars 2007

2 Outline 1 Methods and implementations 2 General tests 3 Dissociation of homonuclear diatomic cations 4 Barriers of atom transfer reactions 5 RSH+MP2: London dispersion forces 6 Charge transfer in donor/acceptor complexes 7 Conclusions

3 1 Methods and implementations Introduction Implementations 2 General tests 3 Dissociation of homonuclear diatomic cations 4 Barriers of atom transfer reactions 5 RSH+MP2: London dispersion forces 6 Charge transfer in donor/acceptor complexes 7 Conclusions

4 Kohn-Sham density functional theory Constrained search formulation { } E = min min Ψ 0 ˆT Ψ 0 + E Hxc [ρ] + E ne [ρ] ρ N Ψ 0 ρ Independent-particle effective Schrödinger equation ( ˆT + ˆV ne + ˆV Hxc ) Ψ0 = E Ψ 0 Exact if E xc [ρ] were known E xc [ρ] guessed by a transferability hypothesis LDA is correct for r ij 0 Can be improved locally by gradients, etc. Approaching chemical accuracy in best cases

5 Hierarchy of exchange-correlation functionals E xc = drρ(r) ε xc (ρ, ρ, ρ, ρ, τ, τ,...)

6 Hierarchy of exchange-correlation functionals E xc = drρ(r) ε xc (ρ, ρ, ρ, ρ, τ, τ,...) Jacob s ladder (J. Perdew) More and more ingredients OEP:... {φ i(r), φ a(r)} hyper-gga:... {φ i(r)} meta-gga:... τ(r), 2 ρ(r) GGA:... ρ(r) LSDA: ρ(r) Hartree desert "And he dreamed, and behold a ladder set up on the earth, and the top of it reached to heaven..." (Gen 28:12)

7 Hierarchy of exchange-correlation functionals E xc = drρ(r) ε xc (ρ, ρ, ρ, ρ, τ, τ,...) Jacob s ladder (J. Perdew) More and more ingredients OEP:... {φ i(r), φ a(r)} hyper-gga:... {φ i(r)} meta-gga:... τ(r), 2 ρ(r) GGA:... ρ(r) LSDA: ρ(r) Hartree desert "And he dreamed, and behold a ladder set up on the earth, and the top of it reached to heaven..." (Gen 28:12)

8 Hierarchy of exchange-correlation functionals E xc = drρ(r) ε xc (ρ, ρ, ρ, ρ, τ, τ,...) Jacob s ladder (J. Perdew) More and more ingredients OEP:... {φ i(r), φ a(r)} hyper-gga:... {φ i(r)} meta-gga:... τ(r), 2 ρ(r) GGA:... ρ(r) LSDA: ρ(r) Hartree desert "And he dreamed, and behold a ladder set up on the earth, and the top of it reached to heaven..." (Gen 28:12)

9 Hierarchy of exchange-correlation functionals E xc = drρ(r) ε xc (ρ, ρ, ρ, ρ, τ, τ,...) Jacob s ladder (J. Perdew) More and more ingredients OEP:... {φ i(r), φ a(r)} hyper-gga:... {φ i(r)} meta-gga:... τ(r), 2 ρ(r) GGA:... ρ(r) LSDA: ρ(r) Hartree desert "And he dreamed, and behold a ladder set up on the earth, and the top of it reached to heaven..." (Gen 28:12)

10 Hierarchy of exchange-correlation functionals E xc = drρ(r) ε xc (ρ, ρ, ρ, ρ, τ, τ,...) Jacob s ladder (J. Perdew) More and more ingredients OEP:... {φ i(r), φ a(r)} hyper-gga:... {φ i(r)} meta-gga:... τ(r), 2 ρ(r) GGA:... ρ(r) LSDA: ρ(r) Hartree desert "And he dreamed, and behold a ladder set up on the earth, and the top of it reached to heaven..." (Gen 28:12)

11 Hierarchy of exchange-correlation functionals E xc = drρ(r) ε xc (ρ, ρ, ρ, ρ, τ, τ,...) Jacob s ladder (J. Perdew) More and more ingredients OEP:... {φ i(r), φ a(r)} hyper-gga:... {φ i(r)} meta-gga:... τ(r), 2 ρ(r) GGA:... ρ(r) LSDA: ρ(r) Hartree desert "And he dreamed, and behold a ladder set up on the earth, and the top of it reached to heaven..." (Gen 28:12)

12 Hierarchy of exchange-correlation functionals E xc = drρ(r) ε xc (ρ, ρ, ρ, ρ, τ, τ,...) Jacob s ladder (J. Perdew) More and more ingredients OEP:... {φ i(r), φ a(r)} hyper-gga:... {φ i(r)} meta-gga:... τ(r), 2 ρ(r) GGA:... ρ(r) LSDA: ρ(r) Hartree desert "And he dreamed, and behold a ladder set up on the earth, and the top of it reached to heaven..." (Gen 28:12)

13 Where standard functionals fail H + 2 dissociation H 2 dissociation H 2+H H + H 2 reaction barrier He 2 van der Waals dimer

14 Where standard functionals fail H + 2 dissociation long-range self-interaction error H 2 dissociation H 2+H H + H 2 reaction barrier He 2 van der Waals dimer LDA, RHF

15 Where standard functionals fail H + 2 dissociation H 2 dissociation long-range non-dynamic correlation missing H 2+H H + H 2 reaction barrier He 2 van der Waals dimer RHF,LDA,FCI

16 Where standard functionals fail H + 2 dissociation H 2 dissociation H 2+H H + H 2 reaction barrier long-range self-interaction error He 2 van der Waals dimer LDA,exp.

17 Where standard functionals fail H + 2 dissociation H 2 dissociation H 2+H H + H 2 reaction barrier He 2 van der Waals dimer long-range dynamic correlation missing LDA,RHF,CCSD(T)

18 Common problems Long-range exchange: long-range self interaction Long-range correlation: dynamic or non-dynamic Both are strongly system specific (non-transferable) Badly accounted for on the lower rungs of Jacob s ladder Could be described correctly by WFT methods

19 Another way to the DFT heaven...

20 Another way to the DFT heaven... Elias chariot "...a fiery chariot, and fiery horses parted them both asunder, and Elias went up by a whirlwind into heaven." (2 Kings 2:11)

21 Another way to the DFT heaven... Elias chariot Separation of the e-e interaction w ee (r) = w lr,µ ee (r) + w sr,µ (r) ee 1 erf(µ r) erfc(µ r) = + r r r "...a fiery chariot, and fiery horses parted them both asunder, and Elias went up by a whirlwind into heaven." (2 Kings 2:11) w lr,µ ee (r) is not singular at r = 0

Another way to the DFT heaven... Elias chariot Separation of the e-e interaction w ee (r) = w lr,µ ee (r) + w sr,µ (r) ee 1 erf(µ r) erfc(µ r) = + r r r 3.0 2.5 2.0 1.5 1.0 0.5 0.0 0.0 0.5 1.0 1.5 2.0 2.5 3.

22 Another way to the DFT heaven... Elias chariot Separation of the e-e interaction w ee (r) = w lr,µ ee (r) + w sr,µ (r) ee 1 erf(µ r) erfc(µ r) = + r r r "...a fiery chariot, and fiery horses parted them both asunder, and Elias went up by a whirlwind into heaven." (2 Kings 2:11) w lr,µ ee (r) is not singular at r = 0

23 Generalization of Kohn-Sham theory (A. Savin) Treat kinetic energy and long-range e-e interaction together { } E = min min Ψ µ ˆT + ˆV ee lr,µ Ψ µ + E sr,µ Hxc [ρ] + drv ne (r)ρ(r) ρ N Ψ µ ρ Long-range "HK-functional" F lr,µ [ρ] = min Ψ µ ρ Ψ µ ˆT + ˆV lr,µ ee Ψ µ Short-range Hartree-exchange-correlation energy functional E sr,µ Hxc [ρ] = F [ρ] F lr,µ [ρ] Ψ µ from the long-range interacting effective Sch. equation ( ˆT + ˆV lr,µ ee + ˆV sr,µ Hxc [ρ Ψ µ ] + ˆV ne ) Ψµ = E µ Ψ µ

24 Practical computational schemes ( ˆT + ˆV lr,µ ee + ˆV sr,µ Hxc [ρ Ψ µ ] + ˆV ne ) Ψµ = E µ Ψ µ

25 Practical computational schemes ( ˆT + ˆV lr,µ ee + ˆV sr,µ Hxc [ρ Ψ µ ] + ˆV ne ) Ψµ = E µ Ψ µ sr exchange sr correlation lr exchange lr correlation RSH DFA DFA HF

26 Practical computational schemes ( ˆT + ˆV lr,µ ee + ˆV sr,µ Hxc [ρ Ψ µ ] + ˆV ne ) Ψµ = E µ Ψ µ sr exchange sr correlation lr exchange lr correlation RSH DFA DFA HF RSHX+MP2 DFA DFA HF MP2

27 Practical computational schemes ( ˆT + ˆV lr,µ ee + ˆV sr,µ Hxc [ρ Ψ µ ] + ˆV ne ) Ψµ = E µ Ψ µ sr exchange sr correlation lr exchange lr correlation RSH DFA DFA HF RSHX+MP2 DFA DFA HF MP2 RSHX DFA DFA HF DFA

28 Practical computational schemes ( ˆT + ˆV lr,µ ee + ˆV sr,µ Hxc [ρ Ψ µ ] + ˆV ne ) Ψµ = E µ Ψ µ sr exchange sr correlation lr exchange lr correlation RSH DFA DFA HF RSHX+MP2 DFA DFA HF MP2 RSHX DFA DFA HF DFA begin with an (approximate) independent-particle calculation (RSH) long-range MP2 (or other correlation method, e.g. CCSD(T), MCSCF) RSHX similar to standard hybrids: exchange mixing is by range

29 Practical computational schemes ( ˆT + ˆV lr,µ ee + ˆV sr,µ Hxc [ρ Ψ µ ] + ˆV ne ) Ψµ = E µ Ψ µ sr exchange sr correlation lr exchange lr correlation RSH DFA DFA HF RSHX+MP2 DFA DFA HF MP2 RSHX DFA DFA HF DFA begin with an (approximate) independent-particle calculation (RSH) long-range MP2 (or other correlation method, e.g. CCSD(T), MCSCF) RSHX similar to standard hybrids: exchange mixing is by range

30 Short-range functionals Short-range exchange functional ε sr,µ x (r) = dr erfc(µ r r ) r r h mod x ( r r ) LDA: h LDA x ( r r ) PBE: h PBE x ( r r ) Short-range correlation functional from model holes Ēc sr,µ [ρ] = E c [ρ] Ec lr,µ Quantum Monte-Carlo evaluation of Ec lr,µ [ρ] on lr-interacting HEG

31 Molecular implementations MOLPRO and DALTON (Gaussian by group of Scuseria) Additional long-range two-electron integrals Solve range-separated hybrid (RSH) equations Correlation available: MP2, CCSD(T); MCSCF (Dalton)

32 Solid state implementation VASP development version Based on the PAW implementation of Hartree-Fock-exchange Modified plane-wave integrals are straightforward (but lengthy) Modified one-center Slater integrals with the spherical harmonic expansion of the short-range interaction kernel erfc (µ R r ) R r = X lm F l (R, r, µ) Y lm(θ, Φ)Y lm (θ, φ)

33 1 Methods and implementations 2 General tests Range separation parameter Test sets for molecules and solids 3 Dissociation of homonuclear diatomic cations 4 Barriers of atom transfer reactions 5 RSH+MP2: London dispersion forces 6 Charge transfer in donor/acceptor complexes 7 Conclusions

34 How to choose range-separation parameter? For a given functional, µ is the unique free parameter R=1/µ Intuitive choice by the reach of sr interactions: Confirmed by thermochemical (and other) data obtained by RSHX MAE [kcal/mol] RSHXLDA LDA PBE µ [a 0-1 ]

35 Heats of formation (G2 set) 30 PBE 30 B3LYP Number PBE0 30 RSHXLDA Number Deviation (Calc-Exp) [kcal/mol] Deviation (Calc-Exp) [kcal/mol] Méthode MAE RMS Max.(-) Max.(+) LDA PBE PBE B3LYP RSHXLDA

36 Lattice constants 2 Relative error [%] LDA RSHXLDA PBE Li Na Al Cu Pd Ag BN BP Si SiC GaN GaP GaAs C MgO LiF LiCl NaF NaCl At least as good as LDA form metals Improvement for ionic systems

37 Bulk modulus Relative error [%] LDA RSHXLDA PBE -20 Li Na Al Cu Pd Ag BN BP Si SiC GaN GaP GaAs C MgO LiF LiCl NaF NaCl Better than LDA and PBE Optimal µ is smaller than for molecules (0.25 a.u.)

38 1 Methods and implementations 2 General tests 3 Dissociation of homonuclear diatomic cations H2+ prototype system 4 Barriers of atom transfer reactions 5 RSH+MP2: London dispersion forces 6 Charge transfer in donor/acceptor complexes 7 Conclusions

39 Case of H + 2 Wrong dissociation curve for H + 2 LDA self-interaction error strongly distance-dependent

40 Case of H + 2 Wrong dissociation curve for H + 2 LDA self-interaction error strongly distance-dependent Using lr Hartree-Fock exchange (RSH or RSHX) corrects the long-range self-interaction error RSH/RSHX self-interaction error small and constant Improvement for A + 2 cations Correct handling charge transfer systems

41 A2+ dications

42 1 Methods and implementations 2 General tests 3 Dissociation of homonuclear diatomic cations 4 Barriers of atom transfer reactions 5 RSH+MP2: London dispersion forces 6 Charge transfer in donor/acceptor complexes 7 Conclusions

43 H 2 + H H + H 2 reaction lr-sie problem at LDA (GGA, etc.) level RSHX functionals give good results H H H +9.6 kcal/mol +7.0 kcal/mol Perdew-Zunger correction happens to work for this reaction......but less favorable for other H-transfer reactions H 2 +H H+H kcal/mol

44 H transfer reactions H+HCl=Cl+H 2 OH+H 2=H+H 2O CH 3+H 2=H+CH 4 OH+CH 4=CH 3+H 2O H+CH 3OH=CH 2OH+H 2 H+H 2=H 2+H OH+NH 3=H 2O+NH 2 CH 3+HCl =Cl+CH 4 OH+C 2H 6=C2H5+H 2O F+H 2=HF+H CH 3+OH=CH 4+O H+PH 3=PH 2+H 2 H+OH=H 2+O H+N 2H 2=H 2+N 2H H+H 2S=H 2+SH O+HCl=OH+Cl NH 2+CH 3=CH 4+NH NH 2+C 2H5=C 2H 6+NH NH 2+C 2H 6=C2H 5+NH 3 NH 2+CH 4=CH 3+NH 3 cis-c5h 8=cis-C5H 8 (Truhlar s reaction barrier database)

45 H atom transfer reaction barriers LDA vs. exp.

46 H atom transfer reaction barriers PBE vs. exp.

47 H atom transfer reaction barriers PBE0 vs. exp.

48 H atom transfer reaction barriers RSHX/LDA (µ = 0.5) vs. exp.

49 H atom transfer reaction barriers RSHX/PBE (µ = 0.4) vs. exp.

50 Atom transfer reaction barriers H-transf Atom-transf S N 2 MSE MAE MSE MAE MSE MAE PBE B3LYP M05-2X RSHXLDA RSHXPBE RSHPBE slightly better than RSHLDA RSHPBE as good as M05-2X (empirical hybrid meta-gga) For some classes of reactions less advantage Reaction energies remain good with RSHX functionals!

51 1 Methods and implementations 2 General tests 3 Dissociation of homonuclear diatomic cations 4 Barriers of atom transfer reactions 5 RSH+MP2: London dispersion forces Origin of dispersion forces RSH+MP2 results 6 Charge transfer in donor/acceptor complexes 7 Conclusions

52 London dispersion forces Correlation of spontaneous dipolar (and multipolar) fluctuations E disp = 1 2π dω universal (also for vibrational and thermal fluctuations) always attractive and decays as R 6 (or R 7 ) long-range dynamical correlation

53 London dispersion forces Correlation of spontaneous dipolar (and multipolar) fluctuations E disp = 1 2π dω χ 1 (r 1, r 1 iω) universal (also for vibrational and thermal fluctuations) always attractive and decays as R 6 (or R 7 ) long-range dynamical correlation

54 London dispersion forces Correlation of spontaneous dipolar (and multipolar) fluctuations R -3 E disp = 1 2π dω χ 1 (r 1, r 1 iω) v(r 1, r 2 ) universal (also for vibrational and thermal fluctuations) always attractive and decays as R 6 (or R 7 ) long-range dynamical correlation

55 London dispersion forces Correlation of spontaneous dipolar (and multipolar) fluctuations R -3 E disp = 1 2π dω χ 1 (r 1, r 1 iω) v(r 1, r 2 ) χ 2 (r 2, r 2 iω) universal (also for vibrational and thermal fluctuations) always attractive and decays as R 6 (or R 7 ) long-range dynamical correlation

56 London dispersion forces Correlation of spontaneous dipolar (and multipolar) fluctuations R -3 R -3 E disp = 1 2π dω χ 1 (r 1, r 1 iω) v(r 1, r 2 ) χ 2 (r 2, r 2 iω) v(r 2, r 1) universal (also for vibrational and thermal fluctuations) always attractive and decays as R 6 (or R 7 ) long-range dynamical correlation

57 Prototype systems: rare gas dimers Bonding by long-range dynamic correlation Experimental data Syst. R ref [a 0] U ref [µh] He-He Ne-Ne Ar-Ar Kr-Kr Tang-Toennies potential 5X U(R) = Ae br f 2n(bR) C2n R 2n n=3 ε(ξ)=u(r)/u(r ref ) σ He 2 Ne 2 Ar 2 Kr 2 Use reduced potential curves Allows direct comparison of -1.0 different systems ξ=r/r ref -0.8

58 Rare gas dimers U m MAE Std. Dev. LDA PBE TPSS CCSD(T) D/Dexp r m MAE Std. Dev. LDA PBE TPSS CCSD(T) R/Rexp LDA PBE TPSS Random behaviour of various functionals

59 Rare gas dimers U m MAE Std. Dev. LDA PBE TPSS CCSD(T) r m MAE Std. Dev. LDA PBE TPSS CCSD(T) PBE Wave function methods are more reliable TPSS CCSD(T)

Other van der Waals systems Layered minerals Stacking in molecular crystals V 2O 5 PW91 exp a 11.55 11.51 2 % b 3.85 3.

60 Other van der Waals systems Layered minerals Stacking in molecular crystals V 2O 5 PW91 exp a % b % c % MoS 2 PW91 exp a % thick % dist % Pyrazine DFT vs. experimental structure

61 RSH+MP2 approach Long-range dynamic correlation of electron pairs Double counting of correlation is avoided Correct 1/R 6 asymptotic behaviour Simple energy correction at 2nd order occ. virt. K lr E RSH+MP2 = E RSH iajb Kibja lr + 2 ɛ i + ɛ j ɛ a ɛ b i<j a<b Higher-order approaches are possible (e.g. CCSD(T))

62 Rare gas dimers 10 homo- and hetero-dimers XY (X,Y=He, Ne, Ar et Kr) aug-cc-pvqz basis Percentage deviations of bond lengths and binding energies LDA PBE M05-2X CCSD(T) MP2 RSH+MP2 MA%E M%E SDEV = RSH+MP2 better than standard GGA and MP2 = RSH+MP2 is of similar quality as CCSD(T)

63 Rare gas dimers: BSSE effects BSSE effect in % of U ref PBE TPSS MP2 CCSD(T) RSH+MP2 0 He 2 Ne 2 Ar 2 Kr 2 HeNe HeAr HeKr NeAr NeKr ArKr BSSE much smaller than with MP2 or CCSD(T)

Benzene dimer Stacked parallel T-shaped Parallel displaced 3 2 1 LDA RHF MP2 RSH RSH+MP2 CCSD(T)

vdw-df DF-SAPT 0-1 LDA MP2 RSH+MP2 CCSD(T) Extrap.

64 Benzene dimer Stacked parallel T-shaped Parallel displaced LDA RHF MP2 RSH RSH+MP2 CCSD(T) Extrap. vdw-df DF-SAPT 2 1 LDA RHF MP2 RSH RSH+MP2 CCSD(T) Extrap. vdw-df DF-SAPT 0-1 LDA MP2 RSH+MP2 CCSD(T) Extrap. vdw-df DF-SAPT E int [kcal/mol] 0 E int [kcal/mol] 0 E int [kcal/mol] R [u.a] R [u.a] R 2 [u.a]

65 Benzene dimer conf. exp. QMC DFT-SAPT MP2( ) RSH+MP2 (DZ) T -2.5 to ± PD -2.5 to ± S Good ordering of the configurations Stacked conformation is too strongly bound (MP2 error) Global improvement w.r.t. standard MP2 results

66 Conclusions on RSH+MP2 Good answer for the good reasons Long-range exchange correction removes artificial minima Correct 1/R 6 asymptotic behaviour Reasonable vdw minimum Favorable basis set dependence and small BSSE Overestimation of interaction between strongly delocalized systems

67 1 Methods and implementations 2 General tests 3 Dissociation of homonuclear diatomic cations 4 Barriers of atom transfer reactions 5 RSH+MP2: London dispersion forces 6 Charge transfer in donor/acceptor complexes 7 Conclusions

68 Neutral-ionic phase transition in TTF-CA Ionic Neutral H TTF (Tetrathiafulvalene) S S H CA (Chloranil) Cl Cl O O H S S H Cl Cl Donor Acceptor

69 Charge transfer 15 K 105 K IONIC NEUTRAL

valence density l max κ 3 R l (κ r) l=0 15K l m=0 P lm Y m l

70 Experimental density core + spherical valence density ρ at (r) = ρ c (r) + P v κ 3 ρ v (κr) + 105K Inhomogeneity of the valence density l max κ 3 R l (κ r) l=0 15K l m=0 P lm Y m l (θ, φ) Isodensity: e/å 3 Homogeneous overlap Dimerization

71 Experimental charge transfer Method High Temp. Low Temp. IR spectra Absorption band X-ray e-density QTAIM atomic basins : ρ ( r). n ( r) = 0 TTF CA

72 Computational approach Electron density for experimental structures at 15K and 105 K (VASP, PAW calculations) Topological analysis and integration over TTF and CA domains (InteGriTy code: Katan et al., J. Appl. Cryst. 36 (2003) 65.)

73 Computational approach Electron density for experimental structures at 15K and 105 K (VASP, PAW calculations) Topological analysis and integration over TTF and CA domains (InteGriTy code: Katan et al., J. Appl. Cryst. 36 (2003) 65.) Functional Low temp. High temp. LDA PBE Exp

74 Computational approach Electron density for experimental structures at 15K and 105 K (VASP, PAW calculations) Topological analysis and integration over TTF and CA domains (InteGriTy code: Katan et al., J. Appl. Cryst. 36 (2003) 65.) Functional Low temp. High temp. LDA PBE Exp Both calculations are wrong! Low temperature: almost good charge transfer but wrong state High temperature: exaggerated charge transfer for neutral wf

75 Computational approach Electron density for experimental structures at 15K and 105 K (VASP, PAW calculations) Topological analysis and integration over TTF and CA domains (InteGriTy code: Katan et al., J. Appl. Cryst. 36 (2003) 65.) Functional Low temp. High temp. LDA PBE Exp Both calculations are wrong! Low temperature: almost good charge transfer but wrong state High temperature: exaggerated charge transfer for neutral wf

76 RSHX calculations Two possible electronic structures Non-magnetic "neutral" Anti-ferromagnetic "ionic" Symmetric (HT) structure: neutral (NM) ground state Dimerized (LT) structure: ionic (AF) ground state LT geometry HT geometry ionic (AF) neutral (NM) Exp

77 RSHX calculations Two possible electronic structures Non-magnetic "neutral" Anti-ferromagnetic "ionic" Symmetric (HT) structure: neutral (NM) ground state Dimerized (LT) structure: ionic (AF) ground state LT geometry HT geometry ionic (AF) neutral (NM) Exp Coherent picture in reasonable agreement with experiment

78 Ionic structure: Spin density wave spin up and spin down one-dimensional SDW Cl of CA and C atoms of TTF have small spin densities singly occupied frontier orbitals ground state for dimerized structure

79 Conclusions Range separated approach combines the best of DFT and WFT worlds Solves problems related to long-range self-interaction Offers a framework to handle difficult correlation problems without double counting Can be generalized to the ACFD framework Should be more explored for non-dynamic (strong) correlation cases But: in plane wave basis the handling of exact exchange requires large computational resources

Théorie de la fonctionnnelle de la densité avec séparation de portée pour les forces de van der Waals

Théorie de la fonctionnnelle de la densité avec séparation de portée pour les forces de van der Waals Julien Toulouse 1 Iann Gerber 2, Georg Jansen 3, Andreas Savin 1, János Ángyán 4 1 Laboratoire de Chimie