assessment of dft methods for solids · 3 mssc2009 - september, 10th 2009 - raffaella demichelis -...

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ASSESSMENT OF DFT METHODSASSESSMENT OF DFT METHODSFOR SOLIDSFOR SOLIDS

Università di TorinoDipartimento di Chimica IFM

MSSC2009 - Ab Initio Modeling in Solid State Chemistry

Raffaella Demichelis

MSSC2009 - September, 10th 2009

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Table of Contents

MSSC2009 - September, 10th 2009 - Raffaella Demichelis - Assessment of DFT methods for solids

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

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DFT energy

The Jacob’s Ladder(Perdew, Schmidt; AIP Conf. Proc. 2001, 577, 1-20)

LDAGGA

meta-GGA Exact exchange, compatible correlation


Hohenberg, Kohn; Phys. Rev. 1964, 136, 864Kohn, Sham, Phys. Rev. 1965, 140, 1133

DFT HEAVEN

E=E[ρ(r)]=Enuclear+Ekinetic+Enucl-electron+Ecoulomb+EXC

Exact exchange, exact partial correlation

HARTREE WORLD

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PBE’s type exchange functionals

EX= !"#X ," [!" ]$

"% F(s" [!" ,&!" ])dr

Spin density

Reduced spin density

Exchange energy density

Different forms of F(sσ) 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 - 2008)

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HF/DFT hybrid functionals

EXC=a*[EX(HF)-EX(DFT)] + EXC(DFT) (e.g. PBE0)

a=fraction of exact exchange

EX=(1-a)*[EX(LDA)+b*EX(XXX)]+a*EX(HF) EC=(1-c)*EC(VWN)+c*EC(YYY)

(XXX, YYY: non-local exchange and correlation)

(e.g. B3LYP: XXX=B, YYY=LYP B3PW: XXX=B, YYY=PW91)

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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 provedto provide the best results for structural, electronic, thermodynamical and dynamical properties of non-conducting systems (in particular H-containing systems)

F. Corà, M. Alfredsson, G. Mallia, D.S. Middlemiss, W.C. Mackrodt, R. Dovesi, R. Orlando, Volume 113, 171-232.Springer-Verlag, Heidelberg (2004).

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HF/DFT hybrid functionalsThe example of Brucite, Mg(OH)2

Differences between calculated and experimental results:a,c: lattice parameters, Å ΔV%: volumes, relative difference (calc-exp)/exp*100OH: bond length of OH group, Å v: anharmonic stretching of the OH oscillator, cm-1

Hybrids

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SVWNPBEB3LYPPBE0HFExp. -3.65

J/K

KMnF3 exchange coupling constant

(J in Kelvin)Calculated by A. Meyer,

CRYSTAL06, 2009

pyrope grossular andradite spessartine uvaroviteSVWN PBEB3LYPPBE0HFExp. 3.06 2.96 3.53 3.24 3.42

Calculated vs experimental dielectric constants ofgarnets. No experimental data for almandine

Open-shellClosed-shell

A. Meyer, M. Ferrero, L. Valenzano, C. M. Zicovich-Wilson, R. Orlando, R. DovesiIn preparation

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DFT & CRYSTAL


title1 - GEOMETRY block2 - BASIS SET block3 - HAMILTONIAN and SCF block

Structure ofCRYSTAL input

DFToptionsEND

Options:1 - Choice of the exchange-correlation functionals2 - Integration grid and numerical accuracy control3 - Atomic parameters(and add SPIN for open-shell systems)

DFT input block

In block 3:

For points 2-3 default values are suppliedPoint 1 must be set

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DFT & CRYSTAL

DFT functionals available in CRYSTAL

EXCHANGE CORRELATION

LDA LDA (=S) PWLSDVWNPZ

VBH VBH

GGA BECKE LYPPWGGA (=PW91) PWGGA (=PW91)PBE PBEPBESOL* PBESOL*WCGGA* (=WC) P86SOGGA* WL

(References in the CRYSTAL users’ manual)*CRYSTAL09

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DFT & CRYSTAL

DFTEXCHANGE……..CORRELAT……..

If not set, EX(HF) used

If not set, no EC

Percentage of EX(HF), if notset: pure DFT

Non-local weightingparameters for EC

HYBRID…NONLOCAL… …

1 - Choice of the functional

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DFT & CRYSTAL

GLOBAL KEYWORDS EXCHANGE CORRELAT HYBRID NONLOCAL

SOGGAXC* SOGGA PBE - -

PBE1PBE* PBE PBE 25 -(PBE0)

B3PW BECKE PWGGA 20 0.9 0.81

B3LYP BECKE LYP 20 0.9 0.81

(References in the CRYSTAL users’ manual)


1 - Choice of the functional

*CRYSTAL09

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DFT & CRYSTAL


EXC and its gradient are evaluated by numerical integration over the cell volume: an integration grid is required

- Grid based on atomic partition method (Becke), Vcell partitioned into atomic volumes: VA 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

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DFT & CRYSTAL


For reducing the grid size and maintaining its effectiveness:

pruned grid (not radially uniform):

the number of angular points is maximum in the valence regionand gradually decreases in both directions

Mg

O

O

O

O

Radial points: Gauss’ formula(nr=number of radial points)

Angular points: Lebedev distribution(L=Lebedev accuracy parameter)

001 plane of a unit cell of MgO

Grid of Mg

Grid of O

The example of MgO(R. Orlando - 2006)


DFT & CRYSTAL



unpruned grid pruned grid

nr=55 L=13

nr=75 L=13

nr=75 L=16

-275.43121602 (31878)

-275.43123518 (42956)

-275.43127155 (96038)

-275.43123079 (11552)

-275.43123451 (20542)

-275.43127167 (41530)(R. Orlando - 2006)

DFT & CRYSTAL


size of grid

telapsed (s)

20542

7.27

41530

14.13

11552

4.41

55, 13 75, 13 75, 16

41530

1437

14.13

1.56

20542

882

7.27

0.86

11552

513

4.41

0.42MSSC2009 - September, 10th 2009 - Raffaella Demichelis - Assessment of DFT methods for solids

DFT & CRYSTAL

Integration grid and numerical accuracy control: use of symmetry

(R. Orlando- 2006)

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DFT & CRYSTAL

RADIAL… … …ANGULAR… … …

2 - Integration grid and numerical accuracy control

Number of intervals, integration interval limits,number of radial points in the ith interval, nr

Number of intervals, integration interval limits,accuracy level (L) of each integral

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DFT & CRYSTAL

RADIAL14.055ANGULAR100.4 0.6 0.8 0.9 1.1 2.3 2.4 2.6 2.8 9999.01 2 5 8 11 13 11 8 5 1

Angular points generated(38 50 110 194 302 434 302 194 110 38)

Default grid: (55,434)p -- 434 angular points in the valence region


L

nr

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DFT & CRYSTAL

GLOBAL KEYWORDS:LGRID --> nr=75, L=13; (75,434)pXLGRID --> nr=75, L=16; (75,974)p

XXLGRID --> nr=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 ΔDEFAULT 119.998710 1.3E-03 XLGRID 120.000054 -5.4E-05XXLGRID 119.999986 1.4E-05(nr=99,L=22) 119.999999 1.0E-06


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DFT & CRYSTAL


default LGRID XLGRID 75,16 unpr 75,18 unpr

18 (IR+Raman+silent)Average of Abs diff.Maximum differenceMinimum differenceGrid pointsµ-electron (TOT: 100 e)µ-hartreeÅÅ

Calcite: effect of the grid on geometry and vibrational modes

M. Prencipe, F. Pascale, C. M. Zicovich-Wilson, V. R. Saunders, R. Orlando, R. Dovesi; Phys. Chem. Miner.,2004, 31, 559-564

0 Reference00

0

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DFT & CRYSTAL


55,434 77’870 0.9621 382275,434 106’210 0.9623 3843 (LGRID) 49’894 0.0002 -0.899,434 140’038 0.9622 384255,974 174’066 0.9619 382475,974 237’164 0.9619 3846 (XLGRID) 100’554 0.0001 -1.499,974 311’570 0.9619 384499,1454 463’462 0.9619 3844

nr,L N. points O-H ν(OH)h Pruned Np O-H ν(OH)h

(uniform)

OH vibrational data of brucite:Effect of pruned and unpruned grid size

S. Tosoni, F. Pascale, P. Ugliengo, R. Orlando, V. R. Saunders, R. Dovesi; Mol. Phys., 2005, 103, 2549-2558

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DFT & CRYSTAL


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, 559-564

F. Pascale, C. M. Zicovich-Wilson, R. Orlando, C. Roetti, P. Ugliengo, R.Dovesi; J. Phys. Chem. B, 2005, 109, 6146-6152

S. Tosoni, F. Pascale, P. Ugliengo, R. Orlando, V. R. Saunders, R. Dovesi;Mol. Phys., 2005, 103, 2549-2558

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DFT & CRYSTAL


2 - Integration grid and numerical accuracy control- unpruned grid can be set- thresholds on grid weigths and electronic density can be increased ordecreased with respect to default- different methods for the point weights- keywords for memory menagement

3 - Atomic parameters - set atomic radius and formal charge different fromthe computed one

(see CRYSTAL users’ manual for details)

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Performance of DFT functionals for describing periodic systems

TEST SYSTEMS:

+ SW-carbon nanotubes+ SW-chrysotile

+ 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

quasi-1D

3D

POSTER N. 4R. Demichelis, B. Civalleri,Y. Noel and R. Dovesi

TEST FUNCTIONALS: SWVN, SPWLSD (LDA)PBE, PW91, PBEsol,WC-PBE,SOGGA-PBE (GGA)B1WC, WC1LYP, B3PW, B3LYP, PBE0 (hybrids)

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SWCNTs: all the tested DFT functionals (LDA, GGA, hybrids)provide reasonable results for structure, energetics andvibrational frequencies. The choice of Hamiltonian iscrucial for the description of the band gap.

Chrysotile: comparison PBE0 vs B3LYP. Both provide good structures and relative stability. PBE0 structural data arehowever more accurate.

Quasi-1D systems

P. D'Arco, Y. Noel, R. Demichelis, R. Dovesi (2009) J. Chem. Phys., accepted

R. Demichelis, Y. Noel, P. D'Arco, R. Dovesi (2009) in preparation.

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Aluminosilicates

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Aluminosilicates

ΔV%

1- R. Demichelis, B. Civalleri, MFerrabone and R. Dovesi;Int. J. Quantum Chem. (2009)DOI: 10.1002/qua.22301

2- R. Demichelis, B. Civalleri, P.DʼArco, R. Dovesi; (2009) inpreparation

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The relative stability of the polymorphs

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In general:

+

++

1- R. Demichelis, B. Civalleri, P. DʼArco, R. Dovesi; (2009) in preparation

+

2- L. Valenzano, M. Ferrabone, B. Civalleri, R. Dovesi; (2009) in preparation

The relative stability of the polymorphs

assessment of dft methods for solids · 3 mssc2009 - september, 10th 2009 - raffaella demichelis -...

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