ASSESSMENT OF DFT METHODS FOR SOLIDS
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1 MSSC Ab Initio Modeling in Solid State Chemistry ASSESSMENT OF DFT METHODS FOR SOLIDS Raffaella Demichelis Università di Torino Dipartimento di Chimica IFM 1 MSSC September, 10 th 2009
2 Table of Contents DFT: a quick overview PBE s type functionals Hybrid GGA functionals DFT & CRYSTAL CRYSTAL input for DFT calculation DFT functionals available in CRYSTAL Integration grid and numerical accuracy control Performance of DFT functionals for describing periodic systems quasi-1d systems: SWCNTs and Chrysotile Aluminosilicates Relative stability of polymorphs 2
3 DFT: a quick overview E=E[ρ(r)]=E nuclear +E kinetic +E nucl-electron +E coulomb +E XC DFT energy Hohenberg, Kohn; Phys. Rev. 1964, 136, 864 Kohn, Sham, Phys. Rev. 1965, 140, 1133 The Jacob s Ladder (Perdew, Schmidt; AIP Conf. Proc. 2001, 577, 1-20) DFT HEAVEN Exact exchange, exact partial correlation Exact exchange, compatible correlation meta-gga GGA LDA HARTREE WORLD 3
4 DFT: a quick overview PBE s type exchange functionals E X = % $! " # X," [! " ] F(s " [! ",&! " ])dr " Reduced spin density Spin density Exchange energy density Different forms of F(s σ ) were proposed: PBE (1996) WC* (2006) revpbe (1998) PBEsol* (2008) RPBE (1999) SOGGA* (2008) [1/2 PBE+ 1/2 RPBE] mpbe (2002) *CRYSTAL09 (B. Civalleri ) 4
5 DFT: a quick overview HF/DFT hybrid functionals E XC =a*[e X (HF)-E X (DFT)] + E XC (DFT) (e.g. PBE0) E X =(1-a)*[E X (LDA)+b*E X (XXX)]+a*E X (HF) E C =(1-c)*E C (VWN)+c*E C (YYY) (XXX, YYY: non-local exchange and correlation) a=fraction of exact exchange (e.g. B3LYP: XXX=B, YYY=LYP B3PW: XXX=B, YYY=PW91) 5
6 DFT: a quick overview HF/DFT hybrid functionals Use of hybrid functionals in solid state simulation *a matter of discussion in the scientific community claimed lacks in accuracy use of empirical parameters bad description of narrow-gap and conducting systems *largely diffuse (e.g. B3LYP, B3PW, PBE0) and often proved to provide the best results for structural, electronic, thermodynamical and dynamical properties of nonconducting systems (in particular H-containing systems) F. Corà, M. Alfredsson, G. Mallia, D.S. Middlemiss, W.C. Mackrodt, R. Dovesi, R. Orlando, Volume 113, Springer-Verlag, Heidelberg (2004). 6
7 DFT: a quick overview HF/DFT hybrid functionals The example of Brucite, Mg(OH) 2 Hybrids Differences between calculated and experimental results: a,c: lattice parameters, Å ΔV%: volumes, relative difference (calc-exp)/exp*100 OH: bond length of OH group, Å v: anharmonic stretching of the OH oscillator, cm -1 7
8 DFT: a quick overview HF/DFT hybrid functionals J/K SVWN PBE B3LYP PBE0 HF Exp KMnF 3 exchange coupling constant (J in Kelvin) Calculated by A. Meyer, CRYSTAL06, 2009 pyrope grossular andradite spessartine uvarovite SVWN PBE B3LYP PBE0 HF Exp Closed-shell Open-shell Calculated vs experimental dielectric constants of garnets. No experimental data for almandine A. Meyer, M. Ferrero, L. Valenzano, C. M. Zicovich-Wilson, R. Orlando, R. Dovesi In preparation 8
9 CRYSTAL input for DFT calculation title 1 - GEOMETRY block 2 - BASIS SET block 3 - HAMILTONIAN and SCF block Structure of CRYSTAL input In block 3: DFT options END DFT input block Options: 1 - Choice of the exchange-correlation functionals 2 - Integration grid and numerical accuracy control 3 - Atomic parameters (and add SPIN for open-shell systems) For points 2-3 default values are supplied Point 1 must be set 9
10 DFT functionals available in CRYSTAL EXCHANGE CORRELATION LDA LDA (=S) PWLSD VWN PZ VBH VBH GGA BECKE LYP PWGGA (=PW91) PWGGA (=PW91) PBE PBE PBESOL* PBESOL* WCGGA* (=WC) P86 SOGGA* WL *CRYSTAL09 (References in the CRYSTAL users manual) 10
11 CRYSTAL input for DFT calculation 1 - Choice of the functional DFT EXCHANGE.. CORRELAT.. If not set, E X (HF) used If not set, no E C HYBRID NONLOCAL Percentage of E X (HF), if not set: pure DFT Non-local weighting parameters for E C 11
12 CRYSTAL input for DFT calculation 1 - Choice of the functional GLOBAL KEYWORDS EXCHANGE CORRELAT HYBRID NONLOCAL SOGGAXC* SOGGA PBE - - PBE1PBE* PBE PBE 25 - (PBE0) B3PW BECKE PWGGA B3LYP BECKE LYP *CRYSTAL09 (References in the CRYSTAL users manual) 12
13 Integration grid and numerical accuracy control E XC and its gradient are evaluated by numerical integration over the cell volume: an integration grid is required - Grid based on atomic partition method (Becke), V cell partitioned into atomic volumes: V A centered on atom A - Radial and angular components (Gauss-Legendre radial quadrature, Lebedev 2-dimensional angular point distribution; points associated to a weight, w) Uniform (or unpruned) grid 13
14 Integration grid and numerical accuracy control For reducing the grid size and maintaining its effectiveness: pruned grid (not radially uniform): the number of angular points is maximum in the valence region and gradually decreases in both directions 14
15 Integration grid and numerical accuracy control O O The example of MgO (R. Orlando ) Mg Grid of Mg Grid of O Radial points: Gauss formula (n r =number of radial points) O 001 plane of a unit cell of MgO O Angular points: Lebedev distribution (L=Lebedev accuracy parameter)
16 Integration grid and numerical accuracy control unpruned grid pruned grid n r =55 L=13 n r =75 L=13 n r =75 L= (31878) (42956) (96038) (11552) (20542) (41530) (R. Orlando )
17 Integration grid and numerical accuracy control: use of symmetry 55, 13 75, 13 75, 16 size of grid t elapsed (s) (R. Orlando )
18 CRYSTAL input for DFT calculation 2 - Integration grid and numerical accuracy control RADIAL ANGULAR Number of intervals, integration interval limits, number of radial points in the i th interval, n r Number of intervals, integration interval limits, accuracy level (L) of each integral 18
19 CRYSTAL input for DFT calculation 2 - Integration grid and numerical accuracy control Default grid: (55,434)p angular points in the valence region RADIAL ANGULAR ( ) Angular points generated n r L 19
20 CRYSTAL input for DFT calculation 2 - Integration grid and numerical accuracy control GLOBAL KEYWORDS: LGRID --> n r =75, L=13; (75,434)p XLGRID --> n r =75, L=16; (75,974)p XXLGRID --> n r =99, L=18; (99,1454)p (see CRYSTAL users manual for details) Numerically integrated density (NID) Diaspore, 4AlOOH in the unit cell, 120 electrons Grid NID Δ DEFAULT E-03 XLGRID E-05 XXLGRID E-05 (n r =99,L=22) E-06 20
21 CRYSTAL input for DFT calculation 2 - Integration grid and numerical accuracy control Calcite: effect of the grid on geometry and vibrational modes default LGRID XLGRID 75,16 unpr 75,18 unpr 0 Reference (IR+Raman+silent) Average of Abs diff. Maximum difference Minimum difference Grid points µ-electron (TOT: 100 e) µ-hartree Å Å M. Prencipe, F. Pascale, C. M. Zicovich-Wilson, V. R. Saunders, R. Orlando, R. Dovesi; Phys. Chem. Miner., 2004, 31,
22 CRYSTAL input for DFT calculation 2 - Integration grid and numerical accuracy control OH vibrational data of brucite: Effect of pruned and unpruned grid size n r,l N. points O-H ν(oh)h Pruned Np O-H ν(oh)h 55, , (LGRID) , , , (XLGRID) , , (uniform) S. Tosoni, F. Pascale, P. Ugliengo, R. Orlando, V. R. Saunders, R. Dovesi; Mol. Phys., 2005, 103,
23 CRYSTAL input for DFT calculation 2 - Integration grid and numerical accuracy control Details on the grid size and its performance: M. Prencipe, F. Pascale, C. M. Zicovich-Wilson, V. R. Saunders, R. Orlando, R. Dovesi; Phys. Chem. Miner., 2004, 31, F. Pascale, C. M. Zicovich-Wilson, R. Orlando, C. Roetti, P. Ugliengo, R. Dovesi; J. Phys. Chem. B, 2005, 109, S. Tosoni, F. Pascale, P. Ugliengo, R. Orlando, V. R. Saunders, R. Dovesi; Mol. Phys., 2005, 103,
24 CRYSTAL input for DFT calculation 2 - Integration grid and numerical accuracy control - unpruned grid can be set - thresholds on grid weigths and electronic density can be increased or decreased with respect to default - different methods for the point weights - keywords for memory menagement 3 - Atomic parameters - set atomic radius and formal charge different from the computed one (see CRYSTAL users manual for details) 24
25 Performance of DFT functionals for describing periodic systems quasi-1d TEST SYSTEMS: + SW-carbon nanotubes + SW-chrysotile POSTER N. 4 R. Demichelis, B. Civalleri,Y. Noel and R. Dovesi 3D + aluminium hydroxides semi-ionic, H-containing, HBs, layered and non-layered + brucite semi-ionic, H-containing, no HBs, layered + orthosilicates semi-ionic, H-free + garnets + olivine + Si and Al oxides (+ diamond, silicon pure-covalent, ) work in progress (+ MgO pure-ionic, ) work in progress TEST FUNCTIONALS: SWVN, SPWLSD (LDA) PBE, PW91, PBEsol,WC-PBE,SOGGA-PBE (GGA) B1WC, WC1LYP, B3PW, B3LYP, PBE0 (hybrids) 25
26 Performance of DFT functionals for describing periodic systems Quasi-1D systems SWCNTs: all the tested DFT functionals (LDA, GGA, hybrids) provide reasonable results for structure, energetics and vibrational frequencies. The choice of Hamiltonian is crucial for the description of the band gap. R. Demichelis, Y. Noel, P. D'Arco, R. Dovesi (2009) in preparation. Chrysotile: comparison PBE0 vs B3LYP. Both provide good structures and relative stability. PBE0 structural data are however more accurate. P. D'Arco, Y. Noel, R. Demichelis, R. Dovesi (2009) J. Chem. Phys., accepted 26
27 Performance of DFT functionals for describing periodic systems Aluminosilicates 27
28 Performance of DFT functionals for describing periodic systems ΔV% Aluminosilicates 1- R. Demichelis, B. Civalleri, M Ferrabone and R. Dovesi; Int. J. Quantum Chem. (2009) DOI: /qua R. Demichelis, B. Civalleri, P. DʼArco, R. Dovesi; (2009) in preparation 28
29 29
30 Performance of DFT functionals for describing periodic systems The relative stability of the polymorphs 30
31 Performance of DFT functionals for describing periodic systems In general: The relative stability of the polymorphs 1- R. Demichelis, B. Civalleri, P. DʼArco, R. Dovesi; (2009) in preparation + 2- L. Valenzano, M. Ferrabone, B. Civalleri, R. Dovesi; (2009) in preparation 31
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