Emilio Artacho Julian Gale Alberto García Javier Junquera Pablo Ordejón Daniel Sánchez-Portal José M. Soler

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1 DFT calculations with num e r ical atom ic or b itals: the S I E S TA m e thod Emilio Artacho Julian Gale Alberto García Javier Junquera Pablo Ordejón Daniel Sánchez-Portal José M. Soler University of Cambridge Curtin Univ. Perth Basque Country Univ. Bilbao Univ. of Cantabria, Santander Spanish Res. Council, Barcelona Donostia Int. Physics Center Autonomous Univ. Madrid

2 O utline Specifications: - Standard DFT - Order-N - From quick & dirty to highly accurate Methods: - Norm-conserving pseudopotentials - Numerical LCAO basis - Uniform real-space grid - Order-N functional

3 DFT: succe ssf ul b ut he av y Much m o r e e x p e n s i v e ( t i m e s ) t ha n e m p i r i ca l a t o m i c s i m ul a t i o n s U p t o ~ a t o m s i n s up e r co m p ut e r s Computational load ~ N 3

4 L ine ar s c aling = O r d e r ( N) CPU l o a d ~ N 3 E ar l y 9 0 s ~ N ~ N (# atoms)

5 Pauli exclusion principle ( ) ψ ( ) d 3 δ i j ij ψ r r r = ψ i ψ i ψ j ψ j B l h f u n c W n i e r f u n c C P U C P U oc ti on s an ti on s N 3 N

6 Order-N f u n c t i o n a l Mauri, Galli & Car, PRB 47, 9973 (1993) Ordejon et al, PRB 48, (1993) Kim, Mauri & Galli, PRB 52, 1640 (1995) S ij = ψ i ψ j ψ k = Σ j ψ j S -1/2 jk E KS = Σ k ψ k H ψ k = Σ ijk S -1/2 ki ψ i H ψ j S -1/2 jk = Tr[ S -1 H ] Kohn-Sham E O(N) = Tr[ (2I-S) H ] Order-N

7 Order-N v s K S f u n c t i o n a l s O(N) Non-or t h og ona l i t y KS p e na l t y S ij = δ ij E O(N) = E KS

8 Orb i t a l l o c a l i z a t i o n φ µ ψ i r c R c ψ i (r) = Σ µ c iµ φ µ (r)

9 i n i t e-ra n g e b a s i s o rb i t a l s O. F. Sankey and D. J. Niklewski, Phys. Rv. B 40, ( ) E. A r t ac h o et al, Phys. S t a t. S o l ( b ) 2 1 5, ( ) F i r s t ζ: ε PAO R c S e c o n d ζ: S p l i t -v a l e n c e S p l i t -n o r m

10 P o l a ri z a t i o n o rb i t a l s Si d o r b it a l s p P A O p e r t u r b e d b y e l e c t r i c f i e l d d PAO

11 S o f t c o n f i n i n g p o t en t i a l s r ( a.u.) r ( a.u.) B e t t e r b a s i s ( v a r i a t i o n a l l y & o t h e r r e s u l t s ) R e m o v e s t h e di s c o n t i n u i t y i n t h e de r i v a t i v e J. Ju nq u er a et al. Phys. Re v. B 6 4, ( ) E. A ng lada et al. Phys. Re v. B 6 6, ( )

12 B a s i s s et c o n v erg en c e J. J u n q u e r a e t a l. P h y s. R e v. B, 6 4, ( ) E q u i v a l e n t P W c u t o f f s ( Ry ) f o r b a s i s o p t i m A t o m i z e d i n So lid SZ DZ T Z SZ P DZ P T Z P T Z DP

13 M a t ri x el em en t s H = T + V ion ( r ) + V nl + V H ( r ) + V x c ( r ) Long range V na (r) = V ion (r) + V H [ρ atoms (r)] δv H (r) = V H [ρ SCF (r)] - V H [ρ atoms (r)] H = T + V nl + V na (r) + δv H (r) + V xc (r) Two-c e n t e r i n t e g r a l s G r i d i n t e g r a l s

14 G ri d w o rk ψ ρ i µν (r) = = ρ(r) = i i µ c iµ ψ c c 2 i iµ iν φ µ (r) = (r) µν ρ µν φ µ (r)φ ν (r) ϕ µ (r) δρ(r) = ρ ρ(r) V SCF xc FFT δρ(r) δv (r) ρ (r) H (r) atoms (r) (r) ϕ ν

15 Actual linear scaling c-s i s u p e r ce l l s, s i n g l e -ζ Single Pentium I I I M H z. 1 G b R A M atoms in 64 nod e s

16 Dual-s t e p m o le c ular d y n am i c s E. Anglada et al. Ph y s. R ev E 68, ( )

17 Ap p licatio ns Over g ro u p s u s e S I E S T A w o rl d w i d e m b i o m a t eri a l s s u rf a c es o l ec u l es n a n o s t ru c t u res l i q u i d s, et c Reviews: P. O r d e j o n Phys. Stat.Solidi (b) 217, ( ) D. S á n c h e z -Po r t a l e t a l. Str u c tu r e an d B on din g, 113, ( ) M o r e up d a ted inf o r ma tio n: h ttp : / / w w w.u am.es / s i es ta

lectro ns in D N A 1 b a p a t h u n c l ( 7 1 5 a t o m a x a t n ( ~ 8 0 0 s s ; ~ 7 F / s ; ~ 5 O ( N ) / F ) F u l l d g o n a l t n a t t h d E [ O ( N ) ] E [ d g ] ~ 5 m / a t o m A.

18 lectro ns in D N A 1 b a p a t h u n c l ( a t o m a x a t n ( ~ s s ; ~ 7 F / s ; ~ 5 O ( N ) / F ) F u l l d g o n a l t n a t t h d E [ O ( N ) ] E [ d g ] ~ 5 m / a t o m A. r u a l f o r c O ( N ) 2 m / A n g d g 6 m / A n g 1 se ir s in e it el s) Rel io tep SC tep iter SC ia isa io e en : ia ev vg esid e : ev ia : ev E lec tr o s ta tic p o tentia l ( c o lo ur s ) o n is o -d ens ity s ur f a c e

19 and co nd uctio n? P. J. d e Pa b l o e t al. Phys. R e v. L e tt. 8 5, ( ) E. A r t a c h o e t a l, M ol. Phys. 10 1, ( ) HOMO states C y to s i ne L U M O G u ani ne H O M O

20 P o laro ns in D N A S. S. Alex andr e et al. Ph y s. R ev. L ett. 9 1, ( ) E b = e V E h o p = e V

21 G o ld nano p articles I.L. G ar z o n et al. Ph y s. R ev. L ett. 8 1, ( )

22 M o nato m ic go ld w ires D. S anc h ez -P o r tal et al. Ph y s. R ev. L ett. 8 3, ( )

23 L iq uid surf ace G. F ab r i c i u s et al. Ph y s. R ev. B 6 0, R ( ) L e n n a r d -J o n e s f l u i d L i q u i d s i l i c o n

24 S eeing m o lecular o rb itals J. I. P as c u al et al. C h em. Ph y s. L ett , 7 8 ( )

25 O S T M / S T S sim ulatio ns. P az et al. Ph y s. R ev. L ett. 9 4, ( ) C o r r u g a t i o n S p e c t r o s c o p y Ex p er i m ent S i m u lati o n

26 F inite nano tub es o n go ld A. R u b i o e t a l, P h y s. Rev. L et t. 8 2, ( )

27 P ressing nano tub es f o r a sw P u sh ed t h em t o g et h er, r el a x ed & c a l c u l a t ed c o n d u c t io n a t t h e c o n t a c t : S W itch I T C H M. F u h r er et a l. Sc ienc e 2 8 8, ( ) Y.-G. Y o o n et a l. Ph y s. R ev. L ett. 8 6, ( )

28 N ew h ard m aterial b ased o n p o ly m erised C 6 0 E. Burgos et al, Phys. Rev. Lett. 85, 2328 (2000)

29 I E S T A in ind ustry M O T O RO L A u sed S I E S T A f o r d evisin g a wa y o f g r o win g st r o n t iu m t it a n a t e o n sil ic o n. Patented based on simulations I t wa s t h en t est ed a n d a t r a n sist o r p r o t o t y p e wa s b u il t b a sed o n t it a n a t e a s d iel ec t r ic f o r t h e g a t e

30 S um m ary F a s t g e n e r a l -p u r p o s e D F T O r d e r -N (f o r i n s u l a t o r s ) F r o m q u i c k & d i r t y t o h i g h l y a c c u r a t e h t t p : / / w w w. u a m. e s / s i e s t a

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