Exchange-Correla.on Func.onals for Chemical
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1 Exchange-Correla.on Func.onals for Chemical Applica.ons from the Strong Coupling Limit of DFT Stefan Vuckovic Theore.cal Chemistry, VU University Amsterdam
2 Density fixed Adiaba.c Connec.on of DFT electron density [ ], which minimizes ht + Vee i
3 Density fixed Adiaba.c Connec.on of DFT electron density [ ], which minimizes ht + Vee i
4 Density fixed Adiaba.c Connec.on of DFT [ ], which minimizes ht + Vee i Z 1 Z electron density Exc [ ] = d dr (r)w (r) in the gauge of the XC hole 0
5 Density fixed Adiaba.c Connec.on of DFT [ ], which minimizes ht + Vee i Z 1 Z electron density Exc [ ] = d dr (r)w (r) in the gauge of the XC hole 0
6 Density fixed Adiaba.c Connec.on of DFT [ ], which minimizes ht + Vee i Z 1 Z electron density Exc [ ] = d dr (r)w (r) in the gauge of the XC hole In the presence of strong correla.on, tradi.onal DFT approxima.ons can give even qualita.ve failures: () / - - () / Hydrogen molecule dissocia.on curves
7 Density fixed Adiaba.c Connec.on of DFT [ ], which minimizes ht + Vee i Z 1 Z electron density Exc [ ] = d dr (r)w (r) in the gauge of the XC hole 0
8 Density fixed Adiaba.c Connec.on of DFT [ ], which minimizes ht + Vee i Z 1 Z electron density Exc [ ] = d dr (r)w (r) in the gauge of the XC hole 0!1 Seidl, PRA 60, 4387 (1999) Seidl, Gori-Giorgi and Savin, PRA 75, (2007)
9 Strong coupling limit: a way to address the strong correla.on problem - - () / - - () - (λ ) / Hydrogen molecule dissocia.on curves from restricted Kohn Sham approaches Vuckovic, Wagner, Mirtschink, Gori-Giorgi, JCTC 11, 3153 (2015)
10 The strong-coupling limit : two parallel approaches for its use in DFT Fully nonlocal func.onals inspired by SCL Vuckovic, Gori-Giorgi, J. Phys. Chem. LeZ. 8, 2799 (2017) Vuckovic, Irons, Wagner, Teale, Gori-Giorgi, PCCP 19, 6169, (2017) Vuckovic, Irons, Savin, Teale, Gori-Giorgi, JCTC 12, 2598 (2016) Vuckovic, Levy, Giorgi, arxiv: , (2017) Vuckovic, Wagner, Mirtschink, Gori-Giorgi, JCTC 11, 3153 (2015) Zhou, Bahmann & Ernzerhof, JCP 143, (2015) Extensive tests of lower level approxima.ons to SCL Fabiano, Gori-Giorgi, Seidl, Della Sala, JCTC 12, 4485 (2016) Vuckovic, Gori-Giorgi, Della Sala, Fabiano, in prepara(on
11 The strong-coupling limit : two parallel approaches for its use in DFT Fully nonlocal func.onals inspired by SCL Vuckovic, Gori-Giorgi, J. Phys. Chem. LeZ. 8, 2799 (2017) Vuckovic, Irons, Wagner, Teale, Gori-Giorgi, PCCP 19, 6169, (2017) Vuckovic, Irons, Savin, Teale, Gori-Giorgi, JCTC 12, 2598 (2016) Vuckovic, Levy, Giorgi, arxiv: , (2017) Vuckovic, Wagner, Mirtschink, Gori-Giorgi, JCTC 11, 3153 (2015) Zhou, Bahmann & Ernzerhof, JCP 143, (2015) Extensive tests of lower level approxima.ons to SCL Fabiano, Gori-Giorgi, Seidl, Della Sala, JCTC 12, 4485 (2016) Vuckovic, Gori-Giorgi, Della Sala, Fabiano, in prepara(on
12 Mathema.cal structure of SCL! 1 limit we can understand better Looking at the electronic correlation: ρ() / N=4 / Mirtschink, Seidl,Gori-Giorgi, JCTC 8, 3097 (2012) Vuckovic, Wagner, Mirtschink, Gori-Giorgi, JCTC 11, 3153 (2015) see also: Vuckovic, Levy, Giorgi, arxiv: , (2017)
13 Mathema.cal structure of SCL ρ() /! 1 limit we can understand better Looking at the electronic correlation: N=4 Reference electron x / Mirtschink, Seidl,Gori-Giorgi, JCTC 8, 3097 (2012) Vuckovic, Wagner, Mirtschink, Gori-Giorgi, JCTC 11, 3153 (2015) see also: Vuckovic, Levy, Giorgi, arxiv: , (2017)
14 Mathema.cal structure of SCL ρ() /! 1 limit we can understand better Looking at the electronic correlation: N=4 Reference electron x () () () / Mirtschink, Seidl,Gori-Giorgi, JCTC 8, 3097 (2012) Vuckovic, Wagner, Mirtschink, Gori-Giorgi, JCTC 11, 3153 (2015) see also: Vuckovic, Levy, Giorgi, arxiv: , (2017)
15 Mathema.cal structure of SCL ρ() /! 1 limit we can understand better Looking at the electronic correlation: N=4 Reference electron x () () () Hartree potential / Mirtschink, Seidl,Gori-Giorgi, JCTC 8, 3097 (2012) Vuckovic, Wagner, Mirtschink, Gori-Giorgi, JCTC 11, 3153 (2015) see also: Vuckovic, Levy, Giorgi, arxiv: , (2017)
16 MRF Func.onal for the full coupling strength Mul.ple Radii Func.onals : Based on the SCL mathema.cs Vuckovic, Gori-Giorgi, J. Phys. Chem. LeZ. 8, 2799 (2017)
17 MRF Func.onal for the full coupling strength Mul.ple Radii Func.onals : Based on the SCL mathema.cs Limit rescaled to λ=1 Vuckovic, Gori-Giorgi, J. Phys. Chem. LeZ. 8, 2799 (2017)
18 MRF Func.onal for the full coupling strength Mul.ple Radii Func.onals : Based on the SCL mathema.cs Limit rescaled to λ=1 Fully nonlocal Vuckovic, Gori-Giorgi, J. Phys. Chem. LeZ. 8, 2799 (2017)
19 MRF Func.onal for the full coupling strength Mul.ple Radii Func.onals : Based on the SCL mathema.cs Limit rescaled to λ=1 Fully nonlocal spherically averaged density around r Ne (r, x) = Z x (r, u)du 0 Vuckovic, Gori-Giorgi, J. Phys. Chem. LeZ. 8, 2799 (2017)
20 MRF Func.onal for the full coupling strength Mul.ple Radii Func.onals : Based on the SCL mathema.cs Limit rescaled to λ=1 Fully nonlocal spherically averaged density around r Ne (r, x) = Z x (r, u)du 0 Provides accurate XC energy densi.es ( at λ=1 and in the gauge of the XC hole) with the correct asympto.c behavior: Vuckovic, Gori-Giorgi, J. Phys. Chem. LeZ. 8, 2799 (2017)
21 MRF Func.onal for the full coupling strength Mul.ple Radii Func.onals : spherically averaged density around r Based on the SCL mathema.cs Limit rescaled to λ=1 Fully nonlocal Ne (r, x) = Z x (r, u)du 0 Provides accurate XC energy densi.es ( at λ=1 and in the gauge of the XC hole) with the correct asympto.c behavior: δ () / =1: () / - - / - - / XC Energy density in the gauge of the XC hole for Ne at the full coupling strength obtained with different approaches Vuckovic, Gori-Giorgi, J. Phys. Chem. LeZ. 8, 2799 (2017)
22 MRF Func.onal for the full coupling strength Mul.ple Radii Func.onals : Based on the SCL mathema.cs Limit rescaled to λ=1 Fully nonlocal spherically averaged density around r Ne (r, x) = Z x (r, u)du 0 Provides accurate XC energy densi.es ( at λ=1 and in the gauge of the XC hole) with the correct asympto.c behavior: =1: Vuckovic, Gori-Giorgi, J. Phys. Chem. LeZ. 8, 2799 (2017)
23 MRF Func.onal for the full coupling strength Mul.ple Radii Func.onals : spherically averaged density around r Based on the SCL mathema.cs Limit rescaled to λ=1 Fully nonlocal Ne (r, x) = Z x (r, u)du 0 Provides accurate XC energy densi.es ( at λ=1 and in the gauge of the XC hole) with the correct asympto.c behavior: - δ () / =1: () / / H / XC Energy density in the gauge of the XC hole for H- at the full coupling strength obtained with different approaches Vuckovic, Gori-Giorgi, J. Phys. Chem. LeZ. 8, 2799 (2017)
24 MRF Func.onal for the full coupling strength Mul.ple Radii Func.onal: Hartree potential Vuckovic, Gori-Giorgi, J. Phys. Chem. LeZ. 8, 2799 (2017)
25 MRF Func.onal for the full coupling strength Mul.ple Radii Func.onal: Hartree potential MRF1: Ri =1 ([ ]; r) key quan.ty of MRF1: Ne (r, x) = Z x (r, u)du 0 spherically averaged density around r Vuckovic, Gori-Giorgi, J. Phys. Chem. LeZ. 8, 2799 (2017)
26 MRF Func.onal for the full coupling strength Mul.ple Radii Func.onal: Hartree potential MRF1: Ri =1 ([ ]; r) key quan.ty of MRF1: Ne (r, x) = δ () / =1: () / - - / - x (r, u)du 0 spherically averaged density around r - Z / XC Energy density in the gauge of the XC hole for Ne at the full coupling strength obtained with different approaches Vuckovic, Gori-Giorgi, J. Phys. Chem. LeZ. 8, 2799 (2017)
27 MRF Func.onal for the full coupling strength Mul.ple Radii Func.onal: Hartree potential MRF1: Ri =1 ([ ]; r) key quan.ty of MRF1: Ne (r, x) = Z x (r, u)du 0 spherically averaged density around r =1: Vuckovic, Gori-Giorgi, J. Phys. Chem. LeZ. 8, 2799 (2017)
28 MRF Func.onal for the full coupling strength Mul.ple Radii Func.onal: Hartree potential MRF1: Ri =1 ([ ]; r) key quan.ty of MRF1: Ne (r, x) = Z x (r, u)du 0 spherically averaged density around r =1: Vuckovic, Gori-Giorgi, J. Phys. Chem. LeZ. 8, 2799 (2017)
29 MRF Func.onal for the full coupling strength Mul.ple Radii Func.onal: Hartree potential MRF1: Ri =1 ([ ]; r) key quan.ty of MRF1: Ne (r, x) = - δ () / () / =1: x (r, u)du 0 spherically averaged density around r - Z / H / XC Energy density in the gauge of the XC hole for H- at the full coupling strength obtained with different approaches Vuckovic, Gori-Giorgi, J. Phys. Chem. LeZ. 8, 2799 (2017)
30 Hydrogen molecule dissocia.on +
31 Hydrogen molecule dissocia.on correla.on component of the kine.c energy (posi.ve) +
32 Hydrogen molecule dissocia.on as in Vuckovic et al, JCTC 2016, 12, 2598 correla.on component of the kine.c energy (posi.ve) +
33 Hydrogen molecule dissocia.on as in Vuckovic et al, JCTC 2016, 12, 2598 correla.on component of the kine.c energy (posi.ve) MRF IS ALSO SELF-INTERACTION FREE AND EXACT FOR H2.+
34 Appling MRF to the uniform electron gas (UEG) at =1 Perdew, Wang, PRB 45, 13244, (1992) Vuckovic, Gori-Giorgi, JPCL , (2017)
35 Appling MRF to the uniform electron gas (UEG) at =1 Perdew, Wang, PRB 45, 13244, (1992) Vuckovic, Gori-Giorgi, JPCL , (2017) Work in progress: making MRF exact for UEG
36 The strong-coupling limit : two parallel approaches for its use in DFT Fully nonlocal func.onals inspired by SCL MRF TURBOMOLE (cost Ex [ ]) required ingredients already implemented: Zhou, Bahmann & Ernzerhof, JCP 143, (2015) Fully nonlocal MRF energy density is compa.ble with the exact exchange energy density Local hybrids H. Bahmann
37 The strong-coupling limit : two parallel approaches for its use in DFT Fully nonlocal func.onals inspired by SCL MRF TURBOMOLE (cost Ex [ ]) required ingredients already implemented: Zhou, Bahmann & Ernzerhof, JCP 143, (2015) Fully nonlocal MRF energy density is compa.ble with the exact exchange energy density Local hybrids H. Bahmann Extensive tests of lower level approxima.ons to SCL
38 Noncovalent interac.ons from ISI With the Interac.on strength interpola.on (ISI) approach XC func.onal is obtained via the interpola.on between the weak and strong coupling limit. Seidl, Perdew, Levy, PRA 59, 51 (1999) Seidl, Perdew, Kurth, PRL 84, 5070 (2000). These nonempirical func.onals use the exchange, MP2 correla.on and simple semilocal approxima.ons to the SCL MAEs (kcal/mol) for the func.onal from the strong coupling limit and MP2 for the S22 and S66 datasets: Vuckovic, Gori-Giorgi, Della Sala, Fabiano, in prepara(on
39 Acknowledgments Supervisor: Collaborators: Andreas Savin UMPC Paris Paola Gori-Giorgi, VU Amsterdam A. Teale & T. Irons Nojngham University Lucas Wagner Mel Levy Tulane University
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