Théorie de la fonctionnnelle de la densité avec séparation de portée pour les forces de van der Waals
|
|
|
- Kerry Kennedy
- 6 years ago
- Views:
Transcription
1 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 Théorique, UPMC Univ Paris 6 et CNRS, Paris, France 2 Université de Toulouse, INSA-UPS, LPCNO, Toulouse, France 3 Fachbereich Chemie, Universität Duisburg-Essen, Essen, Germany 4 CRM2, Institut Jean Barriol, Université de Nancy et CNRS, Vandoeuvre-lès-Nancy, France julien.toulouse@upmc.fr Page web : novembre 28
2 1 Kohn-Sham DFT and ACFDT approaches 2 Range-separated multideterminant DFT 3 Short-range density functionals 4 Range-separated ACFDT method 5 Some results
3 1 Kohn-Sham DFT and ACFDT approaches 2 Range-separated multideterminant DFT 3 Short-range density functionals 4 Range-separated ACFDT method 5 Some results
4 Kohn-Sham DFT Kohn-Sham (KS) scheme { } E = min Φ ˆT + ˆV ne Φ + E H [n Φ ] + E xc [n Φ ] Φ Φ : single-determinant wave function
5 Kohn-Sham DFT Kohn-Sham (KS) scheme { } E = min Φ ˆT + ˆV ne Φ + E H [n Φ ] + E xc [n Φ ] Φ Φ : single-determinant wave function One problem (among others): Usual approximations for exchange-correlation functional E xc [n] (LDA, GGA,...) do not describe well (long-range) van der Waals dispersion forces
6 Example: interaction energy curve of Ne 2 LDA and PBE functionals, aug-cc-pv5z basis: Interaction energy (mhartree) Ne 2 Accurate LDA PBE Interatomic distance (Bohr)
7 ACFDT approach to DFT Starting from the adiabatic connection formula for correlation energy: 1 { } E c = dλ Ψ λ Ŵ ee Ψ λ Φ KS Ŵ ee Φ KS
8 ACFDT approach to DFT Starting from the adiabatic connection formula for correlation energy: 1 { } E c = dλ Ψ λ Ŵ ee Ψ λ Φ KS Ŵ ee Φ KS or, with a compact notation, E c = dλ Tr[w ee P c,λ ]
9 ACFDT approach to DFT Starting from the adiabatic connection formula for correlation energy: 1 { } E c = dλ Ψ λ Ŵ ee Ψ λ Φ KS Ŵ ee Φ KS or, with a compact notation, E c = dλ Tr[w ee P c,λ ] and using the fluctuation-dissipation theorem P c,λ = 1 π dω [χ λ (iω) χ KS (iω)]
10 ACFDT approach to DFT Starting from the adiabatic connection formula for correlation energy: 1 { } E c = dλ Ψ λ Ŵ ee Ψ λ Φ KS Ŵ ee Φ KS or, with a compact notation, E c = dλ Tr[w ee P c,λ ] and using the fluctuation-dissipation theorem leads to E c = 1 2π P c,λ = 1 π 1 dλ dω [χ λ (iω) χ KS (iω)] dω Tr[w ee (χ λ (iω) χ KS (iω))]
11 ACFDT approach to DFT Starting from the adiabatic connection formula for correlation energy: 1 { } E c = dλ Ψ λ Ŵ ee Ψ λ Φ KS Ŵ ee Φ KS or, with a compact notation, E c = dλ Tr[w ee P c,λ ] and using the fluctuation-dissipation theorem leads to E c = 1 2π P c,λ = 1 π 1 dλ dω [χ λ (iω) χ KS (iω)] dω Tr[w ee (χ λ (iω) χ KS (iω))] where the response function χ λ (iω) is given by χ λ (iω) 1 = χ KS (iω) 1 f Hxc,λ (iω)
12 Random Phase Approximation (RPA) RPA approximation: f xc,λ =
13 Random Phase Approximation (RPA) RPA approximation: f xc,λ = So, total energy is E = Φ KS ˆT + ˆV ne Φ KS + E H + E x,exact + E c,rpa
14 Random Phase Approximation (RPA) RPA approximation: f xc,λ = So, total energy is E = Φ KS ˆT + ˆV ne Φ KS + E H + E x,exact + E c,rpa = increasing interest in the DFT community: Perdew, Dobson, Furche, Gonze, Kresse, Scuseria,...
15 Random Phase Approximation (RPA) RPA approximation: f xc,λ = So, total energy is E = Φ KS ˆT + ˆV ne Φ KS + E H + E x,exact + E c,rpa = increasing interest in the DFT community: Perdew, Dobson, Furche, Gonze, Kresse, Scuseria,... Encouraging results: consistent with exact exchange correct dispersion forces at (very) large separation good cohesive energies and lattice constants of solids some improvement in description of bond dissociation
16 Random Phase Approximation (RPA) RPA approximation: f xc,λ = So, total energy is E = Φ KS ˆT + ˆV ne Φ KS + E H + E x,exact + E c,rpa = increasing interest in the DFT community: Perdew, Dobson, Furche, Gonze, Kresse, Scuseria,... Encouraging results: consistent with exact exchange correct dispersion forces at (very) large separation good cohesive energies and lattice constants of solids some improvement in description of bond dissociation But several unsatisfactory aspects: correlation energies far too negative strong dependence on basis size bump at intermediate distances in some dissociation curves dependence on input orbitals embarrassing results for simple van der Waals dimers!
17 Example: interaction energy curve of Ne 2 RPA (with PBE orbitals), aug-cc-pv5z basis: Interaction energy (mhartree) Ne 2 Accurate RPA Interatomic distance (Bohr)
18 Example: interaction energy curve of Be 2 RPA (with PBE orbitals), cc-pv5z basis: Interaction energy (mhartree) Be 2 Accurate RPA Interatomic distance (Bohr)
19 1 Kohn-Sham DFT and ACFDT approaches 2 Range-separated multideterminant DFT 3 Short-range density functionals 4 Range-separated ACFDT method 5 Some results
20 Range-separated multideterminant DFT Multideterminant extension of KS scheme with range separation Ground-state energy: E = min Ψ { Ψ ˆT + ˆV ne + Ŵ lr ee Ψ + E sr Hxc[n Ψ ] }
21 Range-separated multideterminant DFT Multideterminant extension of KS scheme with range separation Ground-state energy: E = min Ψ Ŵ lr ee = i<j { Ψ ˆT + ˆV ne + Ŵ lr ee Ψ + E sr Hxc[n Ψ ] erf(µr ij ) r ij : long-range electron-electron interaction }
22 Range-separated multideterminant DFT Multideterminant extension of KS scheme with range separation Ground-state energy: E = min Ψ Ŵ lr ee = i<j { Ψ ˆT + ˆV ne + Ŵ lr ee Ψ + E sr Hxc[n Ψ ] erf(µr ij ) r ij : long-range electron-electron interaction EHxc sr [n] : short-range Hxc density functional }
23 Range-separated multideterminant DFT Multideterminant extension of KS scheme with range separation Ground-state energy: E = min Ψ Ŵ lr ee = i<j { Ψ ˆT + ˆV ne + Ŵ lr ee Ψ + E sr Hxc[n Ψ ] erf(µr ij ) r ij : long-range electron-electron interaction EHxc sr [n] : short-range Hxc density functional minimizing wave function Ψ lr = i c iφ i is multi-determinant }
24 Range-separated multideterminant DFT Multideterminant extension of KS scheme with range separation Ground-state energy: E = min Ψ Ŵ lr ee = i<j { Ψ ˆT + ˆV ne + Ŵ lr ee Ψ + E sr Hxc[n Ψ ] erf(µr ij ) r ij : long-range electron-electron interaction EHxc sr [n] : short-range Hxc density functional minimizing wave function Ψ lr = i c iφ i is multi-determinant parameter µ controls the range of separation. Limiting cases: µ = = KS DFT µ = Standard wave function methods }
25 Range-separated multideterminant DFT Multideterminant extension of KS scheme with range separation Ground-state energy: E = min Ψ Ŵ lr ee = i<j { Ψ ˆT + ˆV ne + Ŵ lr ee Ψ + E sr Hxc[n Ψ ] erf(µr ij ) r ij : long-range electron-electron interaction EHxc sr [n] : short-range Hxc density functional minimizing wave function Ψ lr = i c iφ i is multi-determinant parameter µ controls the range of separation. Limiting cases: µ = = KS DFT µ = Standard wave function methods In principle: exact }
26 Range-separated multideterminant DFT Multideterminant extension of KS scheme with range separation Ground-state energy: E = min Ψ Ŵ lr ee = i<j { Ψ ˆT + ˆV ne + Ŵ lr ee Ψ + E sr Hxc[n Ψ ] erf(µr ij ) r ij : long-range electron-electron interaction EHxc sr [n] : short-range Hxc density functional minimizing wave function Ψ lr = i c iφ i is multi-determinant parameter µ controls the range of separation. Limiting cases: µ = = KS DFT µ = Standard wave function methods In principle: exact In practice: approximations are necessary for Ψ lr and E sr xc[n] }
27 Range-separated multideterminant DFT: approximations Approximations for E sr xc[n] short-range LDA short-range GEA short-range GGA...
28 Range-separated multideterminant DFT: approximations Approximations for E sr xc[n] short-range LDA short-range GEA short-range GGA... Approximations for Ψ lr single-determinant = HF+DFT method (or RSH method) MCSCF = MCSCF+DFT method (for near-degeneracy) CI = CI+DFT method CC = CC+DFT method MP2 = RSH+MP2 method (for van der Waals) RPA or TDHF = RSH+TDHF method (for van der Waals)...
29 1 Kohn-Sham DFT and ACFDT approaches 2 Range-separated multideterminant DFT 3 Short-range density functionals 4 Range-separated ACFDT method 5 Some results
30 Short-range exchange energy: LDA E sr,µ x,lda [n] = n(r)ε sr,µ x,unif (n(r))dr
31 Short-range exchange energy: LDA E sr,µ x,lda [n] = n(r)ε sr,µ x,unif (n(r))dr For Be atom: E x sr,μ a.u LDA accurate for a short-range interaction exact LDA Μ a.u.
32 Short-range exchange energy: LDA E sr,µ x,lda [n] = n(r)ε sr,µ x,unif (n(r))dr For Be atom: E x sr,μ a.u LDA accurate for a short-range interaction exact LDA Μ a.u. Asymptotic expansion for µ : Ex sr,µ = A 1 µ 2 n(r) 2 dr + A ( 2 n(r) 2 µ 4 n(r) 2n(r) ) + 4τ(r) dr +
33 Short-range correlation energy: LDA E sr,µ c,lda [n] = n(r)ε sr,µ c,unif (n(r))dr
34 Short-range correlation energy: LDA E sr,µ c,lda [n] = n(r)ε sr,µ c,unif (n(r))dr For Be atom: E c sr,μ a.u LDA accurate for a short-range interaction exact LDA Μ a.u.
35 Short-range correlation energy: LDA E sr,µ c,lda [n] = n(r)ε sr,µ c,unif (n(r))dr For Be atom: E c sr,μ a.u LDA accurate for a short-range interaction exact LDA Μ a.u. Asymptotic expansion for µ : Ec sr,µ = B 1 µ 2 n 2,c (r,r)dr + B 2 µ 3 n 2 (r,r)dr +
36 Short-range exchange energy: GGA Short-range GGA functional of Heyd, Scuseria and Ernzerhof (23) based on the PBE exchange hole: ε sr,µ x,gga (n) = 1 n x,pbe (n, n, r 12 )wee sr,µ (r 12 )dr 12 2 For Be atom:.5 E x sr,μ a.u exact LDA GGA Μ a.u. = GGA describes well a longer range of interaction
37 Short-range correlation energy: GGA Interpolation between PBE at µ = and expansion of LDA for µ : ε sr,µ ε c,gga (n, n ) = c,pbe (n, n ) 1 + d 1 (n)µ + d 2 (n)µ 2 For Be atom:.5 E c sr,μ a.u exact LDA GGA Μ a.u. = GGA describes well a longer range of interaction
38 1 Kohn-Sham DFT and ACFDT approaches 2 Range-separated multideterminant DFT 3 Short-range density functionals 4 Range-separated ACFDT method 5 Some results
39 Range-separated hybrid (RSH) scheme Restriction to single-determinant wave functions Φ: { } E RSH = min Φ ˆT + ˆV ne + Ŵee Φ lr + EHxc[n sr Φ ] Φ
40 Range-separated hybrid (RSH) scheme Restriction to single-determinant wave functions Φ: { } E RSH = min Φ ˆT + ˆV ne + Ŵee Φ lr + EHxc[n sr Φ ] Φ The minimizing RSH determinant Φ RSH is given by ) (ˆT + ˆV ne + ˆV Hx,HF lr + ˆV Hxc sr Φ RSH = E Φ RSH,
41 Range-separated hybrid (RSH) scheme Restriction to single-determinant wave functions Φ: { } E RSH = min Φ ˆT + ˆV ne + Ŵee Φ lr + EHxc[n sr Φ ] Φ The minimizing RSH determinant Φ RSH is given by ) (ˆT + ˆV ne + ˆV Hx,HF lr + ˆV Hxc sr Φ RSH = E Φ RSH, So the RSH energy is E RSH = Φ RSH ˆT+ˆV ne Φ RSH +E H [n ΦRSH ]+E lr x,hf[φ RSH ]+E sr xc[n ΦRSH ]
42 Adiabatic connection starting from RSH Exact energy = RSH energy + long-range correlation energy E = E RSH + E lr c
43 Adiabatic connection starting from RSH Exact energy = RSH energy + long-range correlation energy E = E RSH + E lr c Let s define the following adiabatic connection { E λ = min Ψ ˆT + ˆV ne + ˆV Hx,HF lr + λŵ lr Ψ + E sr Ψ with the long-range perturbation operator Ŵ lr = Ŵ lr ee ˆV lr Hx,HF Hxc[n Ψ ] }
44 Adiabatic connection starting from RSH Exact energy = RSH energy + long-range correlation energy E = E RSH + E lr c Let s define the following adiabatic connection { E λ = min Ψ ˆT + ˆV ne + ˆV Hx,HF lr + λŵ lr Ψ + E sr Ψ with the long-range perturbation operator Ŵ lr = Ŵ lr ee ˆV lr Hx,HF Hxc[n Ψ ] minimizing wave function Ψλ lr is multideterminant }
45 Adiabatic connection starting from RSH Exact energy = RSH energy + long-range correlation energy E = E RSH + E lr c Let s define the following adiabatic connection { E λ = min Ψ ˆT + ˆV ne + ˆV Hx,HF lr + λŵ lr Ψ + E sr Ψ with the long-range perturbation operator Ŵ lr = Ŵ lr ee ˆV lr Hx,HF Hxc[n Ψ ] minimizing wave function Ψλ lr is multideterminant Limits: For λ = : Ψ lr λ= = Φ RSH For λ = 1: Ψ lr λ=1 = Ψlr and E λ=1 = E }
46 Adiabatic connection starting from RSH Exact energy = RSH energy + long-range correlation energy E = E RSH + E lr c Let s define the following adiabatic connection { E λ = min Ψ ˆT + ˆV ne + ˆV Hx,HF lr + λŵ lr Ψ + E sr Ψ with the long-range perturbation operator Ŵ lr = Ŵ lr ee ˆV lr Hx,HF Hxc[n Ψ ] minimizing wave function Ψλ lr is multideterminant Limits: For λ = : Ψ lr λ= = Φ RSH For λ = 1: Ψ lr λ=1 = Ψlr and E λ=1 = E the density is NOT constant on the adiabatic connection }
47 Long-range correlation energy E lr c We have the following adiabatic connection formula: 1 { } Ec lr = dλ Ψ lr λ Ŵ lr Ψλ lr Φ RSH Ŵ lr Φ RSH
48 Long-range correlation energy E lr c We have the following adiabatic connection formula: 1 { } Ec lr = dλ Ψ lr λ Ŵ lr Ψλ lr Φ RSH Ŵ lr Φ RSH = dλ Tr [ w lr Pc,λ lr ]
49 Long-range correlation energy E lr c We have the following adiabatic connection formula: 1 { } Ec lr = dλ Ψ lr λ Ŵ lr Ψλ lr Φ RSH Ŵ lr Φ RSH = 1 2 and using the fluctuation-dissipation theorem P lr c,λ = 1 π 1 dω [ χ lr λ (iω) χ RSH(iω) ] + lr λ where lr λ comes from the variation of the density. So dλ Tr [ w lr Pc,λ lr ]
50 Long-range correlation energy E lr c We have the following adiabatic connection formula: 1 { } Ec lr = dλ Ψ lr λ Ŵ lr Ψλ lr Φ RSH Ŵ lr Φ RSH = 1 2 and using the fluctuation-dissipation theorem P lr c,λ = 1 π 1 dω [ χ lr λ (iω) χ RSH(iω) ] + lr λ where lr λ comes from the variation of the density. So Ec lr = 1 2π dλ dλ Tr [ w lr lr ] λ dω Tr [ w lr ( χ lr λ (iω) χ RSH(iω) )] dλ Tr [ w lr Pc,λ lr ]
51 Long-range correlation energy E lr c We have the following adiabatic connection formula: 1 { } Ec lr = dλ Ψ lr λ Ŵ lr Ψλ lr Φ RSH Ŵ lr Φ RSH = 1 2 and using the fluctuation-dissipation theorem P lr c,λ = 1 π 1 dω [ χ lr λ (iω) χ RSH(iω) ] + lr λ where lr λ comes from the variation of the density. So Ec lr = 1 2π dλ dλ Tr [ w lr lr ] λ dω Tr [ w lr ( χ lr λ (iω) χ RSH(iω) )] The long-range response function χ lr λ (iω) is given by χ lr λ (iω) 1 = χ lr IP,λ (iω) 1 f lr Hxc,λ (iω) dλ Tr [ w lr Pc,λ lr ]
52 Approximations for E lr c Several approximations possible for Ec lr : TDHF approximation: fc,λ lr = = RSH+TDHF method
53 Approximations for E lr c Several approximations possible for Ec lr : TDHF approximation: fc,λ lr = = RSH+TDHF method MP2 approximation (2 nd order in wee) lr = RSH+MP2 method
54 Approximations for E lr c Several approximations possible for Ec lr : TDHF approximation: fc,λ lr = = RSH+TDHF method MP2 approximation (2 nd order in wee) lr = RSH+MP2 method Comparison: RSH+TDHF is an extension of RSH+MP2 RSH+TDHF is expected to supersede RSH+MP2 for systems with small HOMO-LUMO gap
55 Implementation of long-range TDHF Orbital rotation Hessians: (A λ B λ ) iajb = (ǫ a ǫ i )δ ij δ ab + λ ( ij ŵ lr ee ba ia ŵ lr ee jb ) and (A λ + B λ ) iajb = (ǫ a ǫ i )δ ij δ ab + 2λ ij ŵ lr ee ab λ ( ij ŵ lr ee ba + ia ŵ lr ee jb )
56 Implementation of long-range TDHF Orbital rotation Hessians: (A λ B λ ) iajb = (ǫ a ǫ i )δ ij δ ab + λ ( ij ŵ lr ee ba ia ŵ lr ee jb ) and (A λ + B λ ) iajb = (ǫ a ǫ i )δ ij δ ab + 2λ ij ŵ lr ee ab λ ( ij ŵ lr ee ba + ia ŵ lr ee jb ) Long-range TDHF second-order density matrix P lr c,tdhf,λ = (A λ B λ ) 1/2 M λ 1/2 (A λ B λ ) 1/2 1 where M λ = (A λ B λ ) 1/2 (A λ + B λ )(A λ B λ ) 1/2
57 Implementation of long-range TDHF Orbital rotation Hessians: (A λ B λ ) iajb = (ǫ a ǫ i )δ ij δ ab + λ ( ij ŵ lr ee ba ia ŵ lr ee jb ) and (A λ + B λ ) iajb = (ǫ a ǫ i )δ ij δ ab + 2λ ij ŵ lr ee ab λ ( ij ŵ lr ee ba + ia ŵ lr ee jb ) Long-range TDHF second-order density matrix P lr c,tdhf,λ = (A λ B λ ) 1/2 M λ 1/2 (A λ B λ ) 1/2 1 where M λ = (A λ B λ ) 1/2 (A λ + B λ )(A λ B λ ) 1/2 The TDHF long-range correlation energy is finally E lr c,tdhf = dλ iajb ij ŵ lr ee ab ( P lr c,tdhf,λ ) iajb
58 1 Kohn-Sham DFT and ACFDT approaches 2 Range-separated multideterminant DFT 3 Short-range density functionals 4 Range-separated ACFDT method 5 Some results
59 Dependence on basis size: Ne 2 Total energy (aug-cc-pvnz basis, µ =.5, sr-pbe functional): Total energy (Hartree) Ne 2 Exact TDHF RPA RSH+TDHF Size of one-particle basis (n in aug-cc-pvnz) = RSH+TDHF has a small basis dependence
60 Interaction energy curve of Ne 2 Interaction energy (aug-cc-pv5z basis, µ =.5, sr-pbe functional): Interaction energy (mhartree) Ne 2 Accurate TDHF RPA RSH+TDHF Interatomic distance (Bohr)
61 Interaction energy curve of Be 2 Interaction energy (cc-pv5z basis, µ =.5, sr-pbe functional): Interaction energy (mhartree) Be 2 Accurate TDHF RPA RSH+TDHF Interatomic distance (Bohr)
62 Conclusions and perspectives Conclusions RSH+TDHF method overcomes some problems of standard RPA RSH+TDHF method seems well suited for van der Waals systems RSH+TDHF method has also problems (e.g., dissociation) RSH+MP2 can be a cheaper alternative to RSH+TDHF Perspectives efficient implementation in quantum chemistry software application to larger molecular systems (benzene dimer,...) application to solids exploration of other variants of the method Web page:
DFT basée sur le théorème de fluctuation-dissipation avec séparation de portée pour les interactions de van der Waals
DFT basée sur le théorème de fluctuation-dissipation avec séparation de portée pour les interactions de van der Waals Julien Toulouse 1 Iann Gerber 2, Georg Jansen 3, Andreas Savin 1, János Ángyán 4 1
Adiabatic-connection fluctuation-dissipation density-functional theory based on range separation
Adiabatic-connection fluctuation-dissipation density-functional theory based on range separation Julien Toulouse 1 I. Gerber 2, G. Jansen 3, A. Savin 1, W. Zhu 1, J. Ángyán 4 1 Laboratoire de Chimie Théorique,
Range-separated density-functional theory with long-range random phase approximation
Range-separated density-functional theory with long-range random phase approximation Julien Toulouse 1 Wuming Zhu 1, Andreas Savin 1, János Ángyán2 1 Laboratoire de Chimie Théorique, UPMC Univ Paris 6
Dispersion energies from the random-phase approximation with range separation
1/34 Dispersion energies from the random-phase approximation with range separation Julien Toulouse Université Pierre & Marie Curie and CNRS, Paris, France Web page: www.lct.jussieu.fr/pagesperso/toulouse/
Extending Kohn-Sham density-functional theory
Extending Kohn-Sham density-functional theory Julien Toulouse Université Pierre & Marie Curie and CNRS, Paris, France Email: julien.toulouse@upmc.fr Web page: www.lct.jussieu.fr/pagesperso/toulouse/ January
Long-range/short-range energy decomposition in density functional theory
p. 1/2 Long-range/short-range energy decomposition in density functional theory Julien Toulouse François Colonna, Andreas Savin Laboratoire de Chimie Théorique, Université Pierre et Marie Curie, Paris
Multideterminant density-functional theory for static correlation. Julien Toulouse Université Pierre & Marie Curie and CNRS, Paris, France
Multideterminant density-functional theory for static correlation Julien Toulouse Université Pierre & Marie Curie and CNRS, Paris, France Basel, Switzerland September 2015 Kohn-Sham DFT and static correlation
Combining density-functional theory and many-body methods
Combining density-functional theory and many-body methods Julien Toulouse Université Pierre & Marie Curie and CNRS, Paris, France Vrije Universiteit Amsterdam, Netherlands November 2017 Outline 2/23 1
Combining density-functional theory and many-body methods
Combining density-functional theory and many-body methods Julien Toulouse Université Pierre & Marie Curie and CNRS, Paris, France Albuquerque New Mexico, USA June 2016 Outline 2/23 1 A brief overview of
Assessment of range-separated time-dependent density-functional theory for calculating C 6 dispersion coefficients
1/10 Assessment of range-separated time-dependent density-functional theory for calculating C 6 dispersion coefficients Julien Toulouse 1,2, Elisa Rebolini 1, Tim Gould 3, John F. Dobson 3, Prasenjit Seal
Adiabatic connections in DFT
Adiabatic connections in DFT Andreas Savin Torino, LCC2004, September 9, 2004 Multi reference DFT Kohn Sham: single reference Variable reference space capability to approach the exact result Overview The
Fractional-charge and Fractional-spin errors in Range-Separated Density-Functional Theory with Random Phase Approximation.
Fractional-charge and Fractional-spin errors in Range-Separated Density-Functional Theory with Random Phase Approximation. Bastien Mussard, Julien Toulouse Laboratoire de Chimie Théorique Institut du Calcul
Density-functional theory at noninteger electron numbers
Density-functional theory at noninteger electron numbers Tim Gould 1, Julien Toulouse 2 1 Griffith University, Brisbane, Australia 2 Université Pierre & Marie Curie and CRS, Paris, France July 215 Introduction
RPA step by step. Bastien Mussard, János G. Ángyán, Sébastien Lebègue CRM 2, FacultÃl des Sciences UniversitÃl Henry PoincarÃl, Nancy
RPA step by step Bastien Mussard, János G. Ángyán, Sébastien Lebègue CRM, FacultÃl des Sciences UniversitÃl Henry PoincarÃl, Nancy Eötvös University Faculty of Science Budapest, Hungaria 0 mars 01 bastien.mussard@uhp-nancy.fr
Density functional theory in the solid state
Density functional theory in the solid state Ari P Seitsonen IMPMC, CNRS & Universités 6 et 7 Paris, IPGP Department of Applied Physics, Helsinki University of Technology Physikalisch-Chemisches Institut
CLIMBING THE LADDER OF DENSITY FUNCTIONAL APPROXIMATIONS JOHN P. PERDEW DEPARTMENT OF PHYSICS TEMPLE UNIVERSITY PHILADELPHIA, PA 19122
CLIMBING THE LADDER OF DENSITY FUNCTIONAL APPROXIMATIONS JOHN P. PERDEW DEPARTMENT OF PHYSICS TEMPLE UNIVERSITY PHILADELPHIA, PA 191 THANKS TO MANY COLLABORATORS, INCLUDING SY VOSKO DAVID LANGRETH ALEX
FONCTIONNELLES DE DENSITÉ AVEC SÉPARATION DE PORTÉE: AU CIEL DFT SANS ÉCHELLE DE JACOB
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
van der Waals forces in density functional theory: Perturbational long-range electron-interaction corrections
van der Waals forces in density functional theory: Perturbational long-range electron-interaction corrections János G. Ángyán and Iann C. Gerber Laboratoire de Cristallographie et de Modélisation des Matériaux
A new generation of density-functional methods based on the adiabatic-connection fluctuation-dissipation theorem
A new generation of density-functional methods based on the adiabatic-connection fluctuation-dissipation theorem Andreas Görling, Patrick Bleiziffer, Daniel Schmidtel, and Andreas Heßelmann Lehrstuhl für
Introduction to density-functional theory. Emmanuel Fromager
Institut de Chimie, Strasbourg, France Page 1 Emmanuel Fromager Institut de Chimie de Strasbourg - Laboratoire de Chimie Quantique - Université de Strasbourg /CNRS M2 lecture, Strasbourg, France. Institut
Recent advances in quantum Monte Carlo for quantum chemistry: optimization of wave functions and calculation of observables
Recent advances in quantum Monte Carlo for quantum chemistry: optimization of wave functions and calculation of observables Julien Toulouse 1, Cyrus J. Umrigar 2, Roland Assaraf 1 1 Laboratoire de Chimie
JULIEN TOULOUSE, PAOLA GORI-GIORGI, ANDREAS SAVIN
Scaling Relations, Virial Theorem, and Energy Densities for Long-Range and Short-Range Density Functionals JULIEN TOULOUSE, PAOLA GORI-GIORGI, ANDREAS SAVIN Laboratoire de Chimie Théorique, CNRS et Université
Model Hamiltonians in Density Functional Theory
Centre de Recherches Mathématiques CRM Proceedings and Lecture Notes Volume 41, 2006 Model Hamiltonians in Density Functional Theory Paola Gori-Giorgi, Julien Toulouse, and Andreas Savin Abstract. The
Importing ab-initio theory into DFT: Some applications of the Lieb variation principle
Importing ab-initio theory into DFT: Some applications of the Lieb variation principle Trygve Helgaker, Andy Teale, and Sonia Coriani Centre for Theoretical and Computational Chemistry (CTCC), Department
Developments in Electronic Structure Theory.
Developments in Electronic Structure Theory. Bastien Mussard Laboratoire de Chimie Théorique Institut du Calcul et de la Simulation Sorbonne Universités, Université Pierre et Marie Curie bastien.mussard@upmc.fr
Analytical Gradients for the Range-Separated Random Phase Approximation Correlation Energies Using a Lagrangian Framework
Analytical Gradients for the Range-Separated Random Phase Approximation Correlation Energies Using a Lagrangian Framework Bastien Mussard a, János G. Ángyán a, Péter G. Szalay b a CRM 2, Université de
The calculation of the universal density functional by Lieb maximization
The calculation of the universal density functional by Lieb maximization Trygve Helgaker, Andy Teale, and Sonia Coriani Centre for Theoretical and Computational Chemistry (CTCC), Department of Chemistry,
Developments in Electronic Structure Theory.
Developments in Electronic Structure Theory. Bastien Mussard Laboratoire de Chimie Théorique Institut du Calcul et de la Simulation Sorbonne Universités, Université Pierre et Marie Curie bastien.mussard@upmc.fr
Intermediate DFT. Kieron Burke and Lucas Wagner. Departments of Physics and of Chemistry, University of California, Irvine, CA 92697, USA
Intermediate DFT Kieron Burke and Lucas Wagner Departments of Physics and of Chemistry, University of California, Irvine, CA 92697, USA October 10-19th, 2012 Kieron (UC Irvine) Intermediate DFT Lausanne12
Linear response time-dependent density functional theory
Linear response time-dependent density functional theory Emmanuel Fromager Laboratoire de Chimie Quantique, Université de Strasbourg, France fromagere@unistra.fr Emmanuel Fromager (UdS) Cours RFCT, Strasbourg,
Short Course on Density Functional Theory and Applications VII. Hybrid, Range-Separated, and One-shot Functionals
Short Course on Density Functional Theory and Applications VII. Hybrid, Range-Separated, and One-shot Functionals Samuel B. Trickey Sept. 2008 Quantum Theory Project Dept. of Physics and Dept. of Chemistry
XYZ of ground-state DFT
XYZ of ground-state DFT Kieron Burke and Lucas Wagner Departments of Physics and of Chemistry, University of California, Irvine, CA 92697, USA January 5-9th, 2014 Kieron (UC Irvine) XYZ of ground-state
Optimization of quantum Monte Carlo wave functions by energy minimization
Optimization of quantum Monte Carlo wave functions by energy minimization Julien Toulouse, Roland Assaraf, Cyrus J. Umrigar Laboratoire de Chimie Théorique, Université Pierre et Marie Curie and CNRS, Paris,
1 Density functional theory (DFT)
1 Density functional theory (DFT) 1.1 Introduction Density functional theory is an alternative to ab initio methods for solving the nonrelativistic, time-independent Schrödinger equation H Φ = E Φ. The
Introduction to density-functional theory
Introduction to density-functional theory Julien Toulouse Laboratoire de Chimie Théorique Université Pierre et Marie Curie et CNRS, 75005 Paris, France julien.toulouse@upmc.fr June 21, 2017 http://www.lct.jussieu.fr/pagesperso/toulouse/enseignement/introduction_dft.pdf
Time-dependent linear response theory: exact and approximate formulations. Emmanuel Fromager
June 215 ISTPC 215 summer school, Aussois, France Page 1 Time-dependent linear response theory: exact and approximate formulations Emmanuel Fromager Institut de Chimie de Strasbourg - Laboratoire de Chimie
Random-phase approximation and beyond for materials: concepts, practice, and future perspectives. Xinguo Ren
Random-phase approximation and beyond for materials: concepts, practice, and future perspectives Xinguo Ren University of Science and Technology of China, Hefei USTC-FHI workshop on frontiers of Advanced
The adiabatic connection
The adiabatic connection Trygve Helgaker, Andy Teale, and Sonia Coriani Centre for Theoretical and Computational Chemistry (CTCC), Department of Chemistry, University of Oslo, Norway Dipartimento di Scienze
Role of van der Waals Interactions in Physics, Chemistry, and Biology
Role of van der Waals Interactions in Physics, Chemistry, and Biology How can we describe vdw forces in materials accurately? Failure of DFT Approximations for (Long-Range) Van der Waals Interactions 1
Exchange-Correlation Functional
Exchange-Correlation Functional Aiichiro Nakano Collaboratory for Advanced Computing & Simulations Depts. of Computer Science, Physics & Astronomy, Chemical Engineering & Materials Science, and Biological
Electronic structure theory: Fundamentals to frontiers. 2. Density functional theory
Electronic structure theory: Fundamentals to frontiers. 2. Density functional theory MARTIN HEAD-GORDON, Department of Chemistry, University of California, and Chemical Sciences Division, Lawrence Berkeley
Convergence behavior of RPA renormalized many-body perturbation theory
Convergence behavior of RPA renormalized many-body perturbation theory Understanding why low-order, non-perturbative expansions work Jefferson E. Bates, Jonathon Sensenig, Niladri Sengupta, & Adrienn Ruzsinszky
Comparison of exchange-correlation functionals: from LDA to GGA and beyond
Comparison of ehange-correlation functionals: from LDA to GGA and beyond Martin Fuchs Fritz-Haber-Institut der MPG, Berlin, Germany Density-Functional Theory Calculations for Modeling Materials and Bio-Molecular
Density Functional Theory - II part
Density Functional Theory - II part antonino.polimeno@unipd.it Overview From theory to practice Implementation Functionals Local functionals Gradient Others From theory to practice From now on, if not
Evaluating van der Waals energies from dielectric response functions
Evaluating van der Waals energies from dielectric response functions Deyu Lu Department of chemistry, UC Davis Electronic structure workshop, Davis, CA 06/23/2009 Motivation vdw forces play important roles
arxiv: v2 [physics.chem-ph] 14 Jan 2013
![arxiv: v2 [physics.chem-ph] 14 Jan 2013](/thumbs/92/109238681.jpg "arxiv: v2 [physics.chem-ph] 14 Jan 2013")
Multi-configuration time-dependent density-functional theory based on range separation Emmanuel Fromager a, Stefan Knecht b and Hans Jørgen Aa. Jensen b a Laboratoire de Chimie Quantique, arxiv:1211.4829v2
Advanced Quantum Chemistry III: Part 3. Haruyuki Nakano. Kyushu University
Advanced Quantum Chemistry III: Part 3 Haruyuki Nakano Kyushu University 2013 Winter Term 1. Hartree-Fock theory Density Functional Theory 2. Hohenberg-Kohn theorem 3. Kohn-Sham method 4. Exchange-correlation
Combining many-body methods and density-functional theory. Julien Toulouse Université Pierre & Marie Curie and CNRS, Paris, France
Combining many-body methods and density-funtional theory Julien Toulouse Université Pierre & Marie Curie and CNRS, Paris, Frane September 2014 2/1 Hybrids ombining many-body methods and DFT Goal: improve
RPA, TDDFT AND RELATED RESPONSE FUNCTIONS : APPLICATION TO CORRELATION ENERGIES
RPA, TDDFT AND RELATED RESPONSE FUNCTIONS : APPLICATION TO CORRELATION ENERGIES John Dobson, Qld Micro & Nano Tech. Centre, Griffith University, Qld, Australia FAST collaboration: Janos Angyan, Sebastien
Resolution of identity approach for the Kohn-Sham correlation energy within the exact-exchange random-phase approximation
Resolution of identity approach for the Kohn-Sham correlation energy within the exact-exchange random-phase approximation Patrick Bleiziffer, Andreas Heßelmann, and Andreas Görling Citation: J. Chem. Phys.
Introduction to multiconfigurational quantum chemistry. Emmanuel Fromager
Institut de Chimie, Strasbourg, France Page 1 Emmanuel Fromager Institut de Chimie de Strasbourg - Laboratoire de Chimie Quantique - Université de Strasbourg /CNRS M2 lecture, Strasbourg, France. Notations
Short-range exchange and correlation energy density functionals: Beyond the local-density approximation
THE JOURNAL OF CHEMICAL PHYSICS 122, 014110 2005 Short-range exchange and correlation energy density functionals: Beyond the local-density approximation Julien Toulouse, François Colonna, and Andreas Savin
3/23/2010 More basics of DFT Kieron Burke and friends UC Irvine Physics and Chemistry References for ground-state DFT ABC of DFT, by KB and Rudy Magyar, http://dft.uci.edu A Primer in Density Functional
Key concepts in Density Functional Theory (I) Silvana Botti
From the many body problem to the Kohn-Sham scheme European Theoretical Spectroscopy Facility (ETSF) CNRS - Laboratoire des Solides Irradiés Ecole Polytechnique, Palaiseau - France Temporary Address: Centre
Spring College on Computational Nanoscience
2145-29 Spring College on Computational Nanoscience 17-28 May 2010 At the Fifth Rung of Jacob's Ladder: A Discussion of Exact Exchange plus Local- and Nonlocal-density Approximations to the Correlation
TDDFT in Chemistry and Biochemistry III
TDDFT in Chemistry and Biochemistry III Dmitrij Rappoport Department of Chemistry and Chemical Biology Harvard University TDDFT Winter School Benasque, January 2010 Dmitrij Rappoport (Harvard U.) TDDFT
Introduction to Density Functional Theory
Introduction to Density Functional Theory S. Sharma Institut für Physik Karl-Franzens-Universität Graz, Austria 19th October 2005 Synopsis Motivation 1 Motivation : where can one use DFT 2 : 1 Elementary
Electronic Structure Calculations and Density Functional Theory
Electronic Structure Calculations and Density Functional Theory Rodolphe Vuilleumier Pôle de chimie théorique Département de chimie de l ENS CNRS Ecole normale supérieure UPMC Formation ModPhyChem Lyon,
Ab-initio studies of the adiabatic connection in density-functional theory
Ab-initio studies of the adiabatic connection in density-functional theory Trygve Helgaker, Andy Teale, and Sonia Coriani Centre for Theoretical and Computational Chemistry (CTCC), Department of Chemistry,
Teoría del Funcional de la Densidad (Density Functional Theory)
Teoría del Funcional de la Densidad (Density Functional Theory) Motivation: limitations of the standard approach based on the wave function. The electronic density n(r) as the key variable: Functionals
Range-separated hybrids
Range-separated hybrids A. Savin MSSC2009 (Torino) Hybrids Wave function (Y) + density functional (n) hybrid E pluribus unum ("Out of many one") : Seal of the USA Overview Components (Y, n) Hybrids (Y
arxiv:physics/ v1 [physics.chem-ph] 10 Oct 2004
![arxiv:physics/ v1 [physics.chem-ph] 10 Oct 2004](/thumbs/82/86636633.jpg "arxiv:physics/ v1 [physics.chem-ph] 10 Oct 2004")
Long-range/short-range separation of the electron-electron interaction in density functional theory arxiv:physics/4162v1 [physics.chem-ph] 1 Oct 24 Julien Toulouse, François Colonna, and Andreas Savin
Basics of DFT. Kieron Burke and Lucas Wagner. Departments of Physics and of Chemistry, University of California, Irvine, CA 92697, USA
Basics of DFT Kieron Burke and Lucas Wagner Departments of Physics and of Chemistry, University of California, Irvine, CA 92697, USA August 2nd, 2012 Kieron (UC Irvine) Basics of DFT Exciting!12 1 / 66
DFT: Exchange-Correlation
DFT: Exchange-Correlation Local functionals, exact exchange and other post-dft methods Paul Tulip Centre for Materials Physics Department of Physics University of Durham Outline Introduction What is exchange
Multi-configuration time-dependent density-functional theory based on range separation
Multi-configuration time-dependent density-functional theory based on range separation Emmanuel Fromager, Stefan Knecht, and Hans Jørgen Aa. Jensen Citation: J. Chem. Phys. 138, 8411 213); doi: 1.163/1.4792199
ABC of ground-state DFT
ABC of ground-state DFT Kieron Burke and Lucas Wagner Departments of Physics and of Chemistry, University of California, Irvine, CA 92697, USA January 5-9th, 2014 Kieron (UC Irvine) ABC of ground-state
Basics of DFT. Kieron Burke and Lucas Wagner. Departments of Physics and Chemistry, University of California, Irvine, CA 92697, USA.
Basics of DFT Kieron Burke and Lucas Wagner Departments of Physics and Chemistry, University of California, Irvine, CA 92697, USA Mar 15, 2011 Kieron (UC Irvine) Basics of DFT IPAM 1 / 61 Outline 1 General
The potential of Potential Functional Theory
The potential of Potential Functional Theory IPAM DFT School 2016 Attila Cangi August, 22 2016 Max Planck Institute of Microstructure Physics, Germany P. Elliott, AC, S. Pittalis, E.K.U. Gross, K. Burke,
Optimization of quantum Monte Carlo (QMC) wave functions by energy minimization
Optimization of quantum Monte Carlo (QMC) wave functions by energy minimization Julien Toulouse, Cyrus Umrigar, Roland Assaraf Cornell Theory Center, Cornell University, Ithaca, New York, USA. Laboratoire
1 Back to the ground-state: electron gas
1 Back to the ground-state: electron gas Manfred Lein and Eberhard K. U. Gross 1.1 Introduction In this chapter, we explore how concepts of time-dependent density functional theory can be useful in the
Pseudopotentials for hybrid density functionals and SCAN
Pseudopotentials for hybrid density functionals and SCAN Jing Yang, Liang Z. Tan, Julian Gebhardt, and Andrew M. Rappe Department of Chemistry University of Pennsylvania Why do we need pseudopotentials?
Pseudo-Hermitian eigenvalue equations in linear-response electronic-structure theory
1/11 Pseudo-Hermitian eigenvalue equations in linear-response electronic-structure theory Julien Toulouse Université Pierre & Marie Curie and CNRS, 4 place Jussieu, Paris, France Web page: www.lct.jussieu.fr/pagesperso/toulouse/
Magnetism in transition metal oxides by post-dft methods
Magnetism in transition metal oxides by post-dft methods Cesare Franchini Faculty of Physics & Center for Computational Materials Science University of Vienna, Austria Workshop on Magnetism in Complex
Casimir Polder size consistency a constraint violated by some dispersion theories
Casimir Polder size consistency a constraint violated by some dispersion theories Tim Gould,, Julien Toulouse, János G. Ángyán, and John F. Dobson, arxiv:1711.8727v1 [physics.chem-ph] 23 Nov 217 Qld Micro-
Computational Chemistry I
Computational Chemistry I Text book Cramer: Essentials of Quantum Chemistry, Wiley (2 ed.) Chapter 3. Post Hartree-Fock methods (Cramer: chapter 7) There are many ways to improve the HF method. Most of
Computational Methods. Chem 561
Computational Methods Chem 561 Lecture Outline 1. Ab initio methods a) HF SCF b) Post-HF methods 2. Density Functional Theory 3. Semiempirical methods 4. Molecular Mechanics Computational Chemistry " Computational
A multiconfigurational hybrid density-functional theory
THE JOURNAL OF CHEMICAL PHYSICS 137, 044104 (01) A multiconfigurational hybrid density-functional theory Kamal Sharkas, 1,,a) Andreas Savin, 1 Hans Jørgen Aa. Jensen, 3 and Julien Toulouse 1,b) 1 Laboratoire
Advanced Solid State Theory SS Roser Valentí and Harald Jeschke Institut für Theoretische Physik, Goethe-Universität Frankfurt
Advanced Solid State Theory SS 2010 Roser Valentí and Harald Jeschke Institut für Theoretische Physik, Goethe-Universität Frankfurt i 0. Literatur R. M. Martin, Electronic Structure: Basic Theory and
arxiv:cond-mat/ v1 13 Nov 2006
Kohn-Sham calculations combined with an average pair-density functional theory Paola Gori-Giorgi and Andreas Savin Laboratoire de Chimie Théorique, CNRS UMR7616, Université Pierre et Marie Curie, 4 Place
5/27/2012. Role of van der Waals Interactions in Physics, Chemistry, and Biology
Role of van der Waals Interactions in Physics, Chemistry, and Biology 1 Role of van der Waals Interactions in Physics, Chemistry, and Biology Karin Jacobs: Take van der Waals forces into account in theory,
Degeneracy and size consistency in electronic density functional theory
Degeneracy and size consistency in electronic density functional theory Paola Gori-Giorgi and Andreas Savin Laboratoire de Chimie Théorique, CNRS UMR7616 and Université Pierre et Marie Curie, 4 Place Jussieu,
Basics of DFT. Kieron Burke and Lucas Wagner. Departments of Physics and of Chemistry, University of California, Irvine, CA 92697, USA
Basics of DFT Kieron Burke and Lucas Wagner Departments of Physics and of Chemistry, University of California, Irvine, CA 92697, USA October 10-19th, 2012 Kieron (UC Irvine) Basics of DFT Lausanne12 1
Exchange Correlation Functional Investigation of RT-TDDFT on a Sodium Chloride. Dimer. Philip Straughn
Exchange Correlation Functional Investigation of RT-TDDFT on a Sodium Chloride Dimer Philip Straughn Abstract Charge transfer between Na and Cl ions is an important problem in physical chemistry. However,
Quantum Monte Carlo wave functions and their optimization for quantum chemistry
Quantum Monte Carlo wave functions and their optimization for quantum chemistry Julien Toulouse Université Pierre & Marie Curie and CNRS, Paris, France CEA Saclay, SPhN Orme des Merisiers April 2015 Outline
Key concepts in Density Functional Theory (II)
Kohn-Sham scheme and band structures European Theoretical Spectroscopy Facility (ETSF) CNRS - Laboratoire des Solides Irradiés Ecole Polytechnique, Palaiseau - France Present Address: LPMCN Université
Post Hartree-Fock: MP2 and RPA in CP2K
Post Hartree-Fock: MP2 and RPA in CP2K A tutorial Jan Wilhelm jan.wilhelm@chem.uzh.ch 4 September 2015 Further reading MP2 and RPA by Mauro Del Ben, Jürg Hutter, Joost VandeVondele Del Ben, M; Hutter,
Lecture 8: Introduction to Density Functional Theory
Lecture 8: Introduction to Density Functional Theory Marie Curie Tutorial Series: Modeling Biomolecules December 6-11, 2004 Mark Tuckerman Dept. of Chemistry and Courant Institute of Mathematical Science
Electronic band structure, sx-lda, Hybrid DFT, LDA+U and all that. Keith Refson STFC Rutherford Appleton Laboratory
Electronic band structure, sx-lda, Hybrid DFT, LDA+U and all that Keith Refson STFC Rutherford Appleton Laboratory LDA/GGA DFT is good but... Naive LDA/GGA calculation severely underestimates band-gaps.
ABC of ground-state DFT
ABC of ground-state DFT Kieron Burke and Lucas Wagner Departments of Physics and of Chemistry, University of California, Irvine, CA 92697, USA July 31, 2014 Kieron (UC Irvine) ABC of ground-state DFT HoW
arxiv: v1 [physics.chem-ph] 24 Jan 2019
![arxiv: v1 [physics.chem-ph] 24 Jan 2019](/thumbs/88/115448850.jpg "arxiv: v1 [physics.chem-ph] 24 Jan 2019")
Range-separated multideterminant density-functional theory with a short-range correlation functional of the on-top pair density Anthony Ferté, Emmanuel Giner, and Julien Toulouse Laboratoire de Chimie
Density Functional Theory for Electrons in Materials
Density Functional Theory for Electrons in Materials Richard M. Martin Department of Physics and Materials Research Laboratory University of Illinois at Urbana-Champaign 1 Density Functional Theory for
OVERVIEW OF QUANTUM CHEMISTRY METHODS
OVERVIEW OF QUANTUM CHEMISTRY METHODS Outline I Generalities Correlation, basis sets Spin II Wavefunction methods Hartree-Fock Configuration interaction Coupled cluster Perturbative methods III Density
All electron optimized effective potential method for solids
All electron optimized effective potential method for solids Institut für Theoretische Physik Freie Universität Berlin, Germany and Fritz Haber Institute of the Max Planck Society, Berlin, Germany. 22
Orbital Density Dependent Functionals
Orbital Density Dependent Functionals S. Kluepfel1, P. Kluepfel1, Hildur Guðmundsdóttir1 and Hannes Jónsson1,2 1. Univ. of Iceland; 2. Aalto University Outline: Problems with GGA approximation (PBE, RPBE,...)
Answers Quantum Chemistry NWI-MOL406 G. C. Groenenboom and G. A. de Wijs, HG00.307, 8:30-11:30, 21 jan 2014
Answers Quantum Chemistry NWI-MOL406 G. C. Groenenboom and G. A. de Wijs, HG00.307, 8:30-11:30, 21 jan 2014 Question 1: Basis sets Consider the split valence SV3-21G one electron basis set for formaldehyde
van der Waals corrections to approximative DFT functionals
van der Waals corrections to approximative DFT functionals Ari P Seitsonen Physikalisch Chemisches Institut, Universität Zürich February 8, 2011 van der Waals interactions van der Waals interactions important
Finite-Temperature Hartree-Fock Exchange and Exchange- Correlation Free Energy Functionals. Travis Sjostrom. IPAM 2012 Workshop IV
1 of 45 Finite-Temperature Hartree-Fock Exchange and Exchange- Correlation Free Energy Functionals Travis Sjostrom Quantum Theory Project Depts. of Physics and Chemistry IPAM 2012 Workshop IV 2012 2 of
Basic Concepts and First Principles Computations for Surface Science: Applications in Chemical Energy Conversion and Storage.
International Summer School on Basic Concepts and First Principles Computations for Surface Science: Applications in Chemical Energy Conversion and Storage Norderney, Germany, July 21 26, 2013 Let s start
Density Func,onal Theory (Chapter 6, Jensen)
Chem 580: DFT Density Func,onal Theory (Chapter 6, Jensen) Hohenberg- Kohn Theorem (Phys. Rev., 136,B864 (1964)): For molecules with a non degenerate ground state, the ground state molecular energy and