Baroni_Structure_Dynamics - Molecular structure and...

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Unformatted text preview: Molecular structure and dynamics with DFT the plane-wave pseudo-potential way Stefano Baroni Scuola Internazionale Superiore di Studi Avanzati & DEMOCRITOS National Simulation Center Trieste - Italy Summer school on Ab initio molecular dynamics methods in chemistr y, MCC-UIUC, 2006 Ab initio simulations Ab initio simulations ∂ Φ(r, R; t) i¯ h = ∂t ¯ 2 ∂2 h ¯ 2 ∂2 h − 2 − 2m ∂ r 2 + V (r, R) Φ(r, R; t) 2M ∂ R I i Ab initio simulations ∂ Φ(r, R; t) i¯ h = ∂t ¯ 2 ∂2 h ¯ 2 ∂2 h − 2 − 2m ∂ r 2 + V (r, R) Φ(r, R; t) 2M ∂ R I i The Born-Oppenheimer approximation (M m) ¨ I = − ∂ E (R) MR ∂ RI ¯ 2 ∂2 h − 2 + V (r, R) Ψ(r |R) = E (R)Ψ(r |R) 2 m ∂ ri Density functional theory e2 ZI ZJ ZI e2 e2 1 V (r, R) = − + 2 |RI − RJ | |ri − RI | 2 |ri − rj | Density functional theory e2 ZI ZJ ZI e2 e2 1 V (r, R) = − + 2 |RI − RJ | |ri − RI | 2 |ri − rj | Density functional theory e2 ZI ZJ ZI e2 e2 1 V (r, R) = − + 2 |RI − RJ | |ri − RI | 2 |ri − rj | DFT e2 ZI ZJ V (r, R) → + v[ρ(r)] (r) 2 |RI − RJ | Density functional theory e2 ZI ZJ ZI e2 e2 1 V (r, R) = − + 2 |RI − RJ | |ri − RI | 2 |ri − rj | DFT e2 ZI ZJ V (r, R) → + v[ρ(r)] (r) 2 |RI − RJ | ρ(r) = v 2 |ψv (r)|2 ∂2 − + v[ρ(r)] (r) ψv (r) = 2 2m ∂ r v ψv (r ) Density functional theory e2 ZI ZJ ZI e2 e2 1 V (r, R) = − + 2 |RI − RJ | |ri − RI | 2 |ri − rj | DFT e2 ZI ZJ V (r, R) → + v[ρ(r)] (r) 2 |RI − RJ | Kohn-Sham Hamiltonian ρ(r) = v 2 |ψv (r)|2 ∂2 − + v[ρ(r)] (r) ψv (r) = 2 2m ∂ r v ψv (r ) Kohn-Sham equations from functional minimization E [{ψ }, R] = − 2 2m v ∂ 2 ψv (r) ∗ ψv (r) dr + 2 ∂r e2 2 V (r, R)ρ(r)dr+ ρ(r)ρ(r ) drdr + Exc [ρ(r)] |r − r | E (R) = min E [{ψ }, R] ∗ ψu (r)ψv (r)dr = δuv Kohn-Sham equations from functional minimization E [{ψ }, R] = − 2 2m v ∂ 2 ψv (r) ∗ ψv (r) dr + 2 ∂r e2 2 ρ(r)ρ(r ) drdr + Exc [ρ(r)] |r − r | E (R) = min E [{ψ }, R] ∗ ψu (r)ψv (r)dr = δuv Kohn & Sham HK S ψ v = v ψv V (r, R)ρ(r)dr+ Kohn-Sham equations from functional minimization E [{ψ }, R] = − 2 2m v ∂ 2 ψv (r) ∗ ψv (r) dr + 2 ∂r e2 2 V (r, R)ρ(r)dr+ ρ(r)ρ(r ) drdr + Exc [ρ(r)] |r − r | E (R) = min E [{ψ }, R] ∗ ψu (r)ψv (r)dr = δuv Helmann & Feynman Kohn & Sham HK S ψ v = v ψv ∂ E (R) = ∂ RI ∂ v (r, R) n(r)dr ∂ RI Solving the Kohn-Sham equations 2 − 2m 2 + V (r) ψn (r) = n ψn (r) Solving the Kohn-Sham equations 2 − 2m 2 + V (r) ψn (r) = ψn (r) = n ψn (r) c(i, n)φi (r) i Solving the Kohn-Sham equations 2 − 2m 2 + V (r) ψn (r) = ψn (r) = n ψn (r) c(i, n)φi (r) i ψn (r) c(n, i) representation and s → matrix eigenvalue Solving the Kohn-Sham equations 2 − 2m 2 + V (r) ψn (r) = ψn (r) = c(i, n)φi (r) i ψn (r) n ψn (r) representation & storage c(n, i) representation and s → matrix eigenvalue Solving the Kohn-Sham equations 2 − 2m 2 + V (r) ψn (r) = ψn (r) = c(i, n)φi (r) i ψn (r) n ψn (r) representation & storage c(n, i) representation and s → matrix eigenvalue matrix eigenvalue problem h(i, j )c(j, n) = j n c(i, n) Requirements Requirements ‣ (effective) completeness easily checked and systematically improved Requirements ‣ (effective) completeness easily checked and systematically improved ‣ matrix elements easy to calculate and/or Hψ products easily calculated on the fly Requirements ‣ (effective) completeness easily checked and systematically improved ‣ matrix elements easy to calculate and/or Hψ products easily calculated on the fly ‣ Hartree and XC potentials easy to represent and calculate Requirements ‣ (effective) completeness easily checked and systematically improved ‣ matrix elements easy to calculate and/or Hψ products easily calculated on the fly ‣ Hartree and XC potentials easy to represent and calculate ‣ orthogonality is a plus Bloch states & plane waves ψn,k (r) = e ik·r un,k (r) Bloch states & plane waves ψn,k (r) = e periodic over “L” ik·r un,k (r) Bloch states & plane waves ψn,k (r) = e periodic over “L” ik·r un,k (r) periodic over “a” Bloch states & plane waves ψn,k (r) = e ik·r un,k (r) periodic over “L” periodic over “a” un,k (r) = cnk (G)e G iG·r Bloch states & plane waves ψn,k (r) = e ik·r un,k (r) periodic over “L” periodic over “a” un,k (r) = cnk (G)e iG·r G ρ(r) = |ψn,k (r)| 2 nk = |un,k (r)| 2 nk Using plane waves − 2 ψ (r) −→ V (r)ψ (r) −→ |k + G|2 cnk (G) e−iG·r V (r)unk (r)dr Using plane waves − 2 ψ (r) −→ V (r)ψ (r) −→ |k + G|2 cnk (G) e−iG·r V (r)unk (r)dr scatter cnk (G) FFT cnk (n1 G1 + n2 G2 + n3 G3 ) gather unk (m1 r1 + m2 r2 + m3 r3 ) FFT-1 Using plane waves − 2 ψ (r) −→ V (r)ψ (r) −→ |k + G|2 cnk (G) e−iG·r V (r)unk (r)dr scatter cnk (G) FFT cnk (n1 G1 + n2 G2 + n3 G3 ) gather unk (m1 r1 + m2 r2 + m3 r3 ) FFT-1 ρ(r) = nk |un,k (r)|2 Vxc (r) = µxc ρ(r) Using plane waves − 2 ψ (r) −→ V (r)ψ (r) −→ |k + G|2 cnk (G) e−iG·r V (r)unk (r)dr scatter cnk (G) FFT cnk (n1 G1 + n2 G2 + n3 G3 ) gather unk (m1 r1 + m2 r2 + m3 r3 ) FFT-1 ρ(r) = nk VH (r) = e 2 |un,k (r)|2 Vxc (r) = µxc ρ(r) ρ(r ) dr = e2 |r − r | e G=0 iG·r 4π ρ(G) ˜ 2 G Pros & cons Pros & cons approach to completeness easily and systematically checked (|k+G|2<Ecut) Pros & cons approach to completeness easily and systematically checked (|k+G|2<Ecut) basis set independent of nuclear positions (no Pulay forces) Pros & cons approach to completeness easily and systematically checked (|k+G|2<Ecut) basis set independent of nuclear positions (no Pulay forces) matrix elements and Hψ poducts easily calculated Pros & cons approach to completeness easily and systematically checked (|k+G|2<Ecut) basis set independent of nuclear positions (no Pulay forces) matrix elements and Hψ poducts easily calculated density, Hartree, and XC potentials easily calculated Pros & cons approach to completeness easily and systematically checked (|k+G|2<Ecut) basis set independent of nuclear positions (no Pulay forces) matrix elements and Hψ poducts easily calculated density, Hartree, and XC potentials easily calculated orthonormality Pros & cons approach to completeness easily and systematically checked (|k+G|2<Ecut) basis set independent of nuclear positions (no Pulay forces) matrix elements and Hψ poducts easily calculated density, Hartree, and XC potentials easily calculated orthonormality basis set depends on volume shape/size (Pulay stress) Pros & cons approach to completeness easily and systematically checked (|k+G|2<Ecut) basis set independent of nuclear positions (no Pulay forces) matrix elements and Hψ poducts easily calculated density, Hartree, and XC potentials easily calculated orthonormality basis set depends on volume shape/size (Pulay stress) uniform spatial resolution (no core states!) The Hellmann-Feynman theorem E (λ) = min Ψ|H (λ)|Ψ Ψ|Ψ = 1 The Hellmann-Feynman theorem E (λ) = min Ψ|H (λ)|Ψ Ψ|Ψ = 1 g (λ) = min G[x, λ] x The Hellmann-Feynman theorem E (R) = min E [{ψ }, R] E (λ) = min Ψ|H (λ)|Ψ Ψ|Ψ = 1 g (λ) = min G[x, λ] x The Hellmann-Feynman theorem E (R) = min E [{ψ }, R] E (λ) = min Ψ|H (λ)|Ψ Ψ|Ψ = 1 g (λ) = min G[x, λ] x ∂G ∂x =0 x=x(λ) The Hellmann-Feynman theorem E (R) = min E [{ψ }, R] E (λ) = min Ψ|H (λ)|Ψ Ψ|Ψ = 1 g (λ) = min G[x, λ] x g (λ) = G[x(λ), λ] ∂G ∂x =0 x=x(λ) The Hellmann-Feynman theorem E (R) = min E [{ψ }, R] E (λ) = min Ψ|H (λ)|Ψ Ψ|Ψ = 1 g (λ) = min G[x, λ] x g (λ) = G[x(λ), λ] ∂G ∂x =0 x=x(λ) ∂G g (λ) = x (λ) ∂x ∂G + ∂λ x=x(λ) The Hellmann-Feynman theorem E (R) = min E [{ψ }, R] E (λ) = min Ψ|H (λ)|Ψ Ψ|Ψ = 1 g (λ) = min G[x, λ] x g (λ) = G[x(λ), λ] ∂G ∂x =0 x=x(λ) ∂G g (λ) = x (λ) ∂x ∂G + ∂λ x=x(λ) The Hellmann-Feynman theorem E (R) = min E [{ψ }, R] E (λ) = min Ψ|H (λ)|Ψ Ψ|Ψ = 1 g (λ) = min G[x, λ] x g (λ) = G[x(λ), λ] ∂G ∂x =0 x=x(λ) ∂G g (λ) = x (λ) ∂x E (λ) = Ψλ |H (λ)|Ψλ ∂G + ∂λ x=x(λ) Pulay corrections to HF V (r) = V λ (r) −→ φ(r) = φλ (r) Pulay corrections to HF V (r) = V λ (r) −→ φ(r) = φλ (r) E (λ) = E [ψ λ ; λ] ≡ E [cλ , φλ ; λ] Pulay corrections to HF V (r) = V λ (r) −→ φ(r) = φλ (r) E (λ) = E [ψ λ ; λ] ≡ E [cλ , φλ ; λ] Pulay corrections to HF V (r) = V λ (r) −→ φ(r) = φλ (r) E (λ) = E [ψ λ ; λ] ≡ E [cλ , φλ ; λ] dE ∂E ∂c ∂E δE ∂ φ = + + dλ ∂c ∂λ ∂λ δφ ∂ λ Pulay corrections to HF V (r) = V λ (r) −→ φ(r) = φλ (r) E (λ) = E [ψ λ ; λ] ≡ E [cλ , φλ ; λ] dE ∂E ∂c ∂E δE ∂ φ = + + dλ ∂c ∂λ ∂λ δφ ∂ λ Pulay corrections to HF V (r) = V λ (r) −→ φ(r) = φλ (r) E (λ) = E [ψ λ ; λ] ≡ E [cλ , φλ ; λ] dE ∂E ∂c ∂E δE ∂ φ = + + dλ ∂c ∂λ ∂λ δφ ∂ λ HF Pulay corrections to HF V (r) = V λ (r) −→ φ(r) = φλ (r) E (λ) = E [ψ λ ; λ] ≡ E [cλ , φλ ; λ] dE ∂E ∂c ∂E δE ∂ φ = + + dλ ∂c ∂λ ∂λ δφ ∂ λ HF Pulay Atomic forces HF F(R) = − ∂ v (r − R) ρ(r) dr − ∂R Pulay ∂ ρ(r) V (r) ∂R dr P Atomic forces HF F(R) = − ∂ v (r − R) ρ(r) dr − ∂R ρ(r) = Pulay ∂ ρ(r) V (r) ∂R c(i, n)c(j, n)φi (r)φj (r) n ij dr P Atomic forces HF ∂ v (r − R) ρ(r) dr − ∂R F(R) = − ρ(r) = = P n ij ∂ ρ(r) V (r) ∂R dr P c(i, n)c(j, n)φi (r)φj (r) n ∂ ρ(r) ∂R Pulay ij ∂ φi (r) ∂ φj (r) c(i, n)c(j, n) φj (r) + φi (r) ∂R ∂R Atomic forces HF ∂ v (r − R) ρ(r) dr − ∂R F(R) = − ρ(r) = = P n ij ∂ ρ(r) V (r) ∂R c(i, n)c(j, n)φi (r)φj (r) n ∂ ρ(r) ∂R Pulay dr P for PW’s ij ∂ φi (r) ∂ φj (r) c(i, n)c(j, n) φj (r) + φi (r) ∂R ∂R Hydrogen Semiconductors (also known as metalloids) 1 1 H Key: Hydrogen 1.007 94 Group 2 Group 1 3 4 Be Beryllium 9.012 182 2 20 3 Period Magnesium 24.3050 Ca Calcium 40.078 Strontium 87.62 Barium 137.327 4 Radium (226) C Symbol Carbon Name Carbon Ave2.01tomic mass 1rage a 07 12.0107 Nonmetals Halogens Noble gases Other nonmetals Nonmetals B Boron Halogens 10.811 Noble gases Other nonmetals 13 12 15 17 Oxyon n Ne ge 151797 20..9994 16 18 9 F Fluorin 18.998 4 17 Group 12 Group 9 Group 10 Group 11 G oup 10 Grroup 12 Group 11 26 27 28 29 328 0 29 31 87 89 7 114 6 FNutorigen l i ro n 18.14.8 067 2 99 0 403 Ne O Chlorin 35.45 Group 8 Sc V VScaadium an ndium 4509941910 4. . 55 5 38 40 39 41 Y Nb NYotbium it r 88.905 85 92.906 38 56 72 HBanium af r 137..327 178 49 113 5 OCarbon xygen 11290107 5. . 994 F N Sgfn Arulour 32948 39..065 25 27 LanChainum t es um 132.905 5 3 4 8 14 NitBogon r re 1 0 811 14.0.067 O C PChlsphnerus ho ori o 30.5.73 3 61 3 9 45 7 G oup 7 Grroup 9 Ba Hf Carbon 12.0107 N B SSilfiuon u cr 28 085 32..065 5 24 26 Cs La C Group Al s m num Phouphiorus 32699817538 0. . 73 61 G oup 6 Grroup 8 55 57 6 18 0 Silicon 28.0855 223 5 t con um ZSirrontiium 987.62 1.224 Group 16 9 7 Cl G oup 5 Grroup7 Rutbiium m Yt r diu 85.46 85 88.905 78 Grroup 17 G oup 15 86 S Ar 22 24 S Zr Grroup16 Goup 14 75 P Cl G oup 4 Grroup 6 Rb Y Grroup15 G oup 13 6 Si 21 23 TCtalnium ic 40 078 47..867 Group 14 Al P G oup 3 Grroup 5 SPonadisium ca t s um 4439.0983 .955 910 Helium 4.002 602 Aluminum 26.981 538 Magnesium 24.3050 Ci Ta 2 He Si 20 22 K Sc Group 18 Al Mg Group 4 337 9 5 88 Ra Sodium 22.989 770 Average atomic mass 6 Metals Alkali metals Alkaline-earth metals Gr t us Transition meoalp 13 Other metals 5 219 1 56 Ba Na Name Be Beryllium 9.012 182 C Symbol Metals Alkali metals Alkaline-earth metals Transition metals Other metals (also known as metalloids) Group 3 38 Sr Lithium 6.941 11 12 Mg Li A6 mic number to Atomic number Group 2 4 Key: Hydrogen Semiconductors 57 73 L Ta Lanthaumm T al nu 138.9055 180.9479 188 04 189 05 Ti Cr Ti o n Chrtamium 47.8 7 51.9961 40 42 Zr Mo Z rbdeiu m Moliyconnum 1 22 95.94 4 72 74 Hf W THngnitum u af s en 178.49 183.84 104 106 V Mn MVanadiesm ang n u e 5450.94049 .938 15 441 3 Nc Tb N ob um Techinetiium 92(.98) 38 06 73 75 Re Ta RTaenialum h nt um 0 94 186.207 9 105 107 Fr Ac a Rf Ac Db Rf Sg Db Bh F i um Acrtanicium ((223) 227) Ra f i r m Rutherdoudium 226 ((261)) DAcbiniium u t n um ((227) 262) Rut b rrgiu u Seaheofordimm ((261) 266) D hr u um Boubinim ((262) 264) * names and symbolsThe systematic names and symbols eater than 110 will for elements greater than 110 will e approval of trivialbe used until the approval of trivial names by IUPAC. C. Cr Fe ChIrromium on 51.9961 5 845 42 44 Mo Ru Mutlhbdeumm R o yeni nu 195.94 01 07 74 76 W Os T s n is e Oumgutmn 183.84 190.23 106 108 Ss Hg SHabsirgm m e as o u iu 266 ((277)) Mn Co MCobanese ang lt 54.938 049 58.933 200 43 45 Tc Rh Tehodietm m R chn u iu 102.(98) 50 905 75 77 Re Ir Rhdinimm Iri e u u 186.207 192.217 107 109 Bt Mh B t hri ium Meionerum ((264) 268) Fe Iron 55.845 44 Ru Ruthenium 101.07 76 Os Osmium 190.23 108 Hs Hassium (277) Co Cobalt 58.933 200 45 Rh Rhodium 102.905 50 77 Ir Iridium 192.217 109 Mt Meitnerium (268) Ni Nickel 58.6934 46 Pd Palladium 106.42 78 Pt Platinum 195.078 110 Ds Darmstadtium (281) Cu Copper 63.546 47 Ag Silver 107.8682 79 Au Gold 196.966 55 111 Uuu* Unununium (272) N Zni Z ck Niinc el 58 693 65.409 4 446 8 Pd Cd CPallmduum ad a i i m 0 4 42 112.6.11 878 0 Pt Hg Pla i ur m Mertcnuy 195 07 200.59 8 1110 12 UDb* us Darnustbidtmm U m n a u iu ((281) 285) Cu Ga C l i pe Gaolpumr 63.546 69.723 47 49 Ag In InSiiluer d vm 107.8682 14 1 79 81 Al Tu Gli l m Thaloud 196..966 3 5 204 383 5 1111 13 u Uut** Unun r u u Ununtuinimm ((272) 284) 30 32 Ze Gn Zi i Germancum 65 40 72.64 9 48 50 Cd Sn CaTimium dn 112.411 118.710 80 82 Hg Pb Mercd ry L au 05 207.2 9 1112 14 Uub* Uuq* UnUnquadiium u unb u ((285) 289) 331 3 Ga As AGselnuc r al i i m 7469.723 .921 60 549 1 In Sb AnItnmiony i d um 11147818 21. . 60 881 3 T Bil BTsmluith i ha l um 204.38 8 208.980 33 1113 15 Uut Uup* UnUnuntntiium u pe r um ((284) 288) 332 4 G See Gelrenanium S m ium 772964 8. . 6 550 2 Sn Te TelluTin m ru 118 71 127..60 0 882 4 Pb Po Le um Poloniad 7. (209)2 114 Uuq* Ununquadium (289) 33 35 As Br Arse c Brominie 779990460 4. . 21 51 53 Sb I AIntime ny odin o 12121.7647 6.904 0 83 85 Bi At B ati ut Asitsmneh 20(2980 38 8. 10) 34 36 Se Kr 35 Br Seyenon Kr l pt ium 878.96 3.7 8 Bromin 79.90 52 54 53 Te Xe TXelnoin m el ur u 1127.60 31.293 84 86 Po Rn PRaonin m ol do u ((209) 222) I Iodine 126.904 85 At Astatin (210 115 Uup* Ununpentium (288) A eam at La a ence B p keed N e o s al Lab r f o em e s 116 the disc i v y of elem. A team at Lawrence Berkeley Natitonal Laborwtrories reerortley thatidincoveryooatelrieserntportedand 118oneJrune 1999ents 116 and 118 in June 1999. The s r mn Jul m retra T ed the di ery e e n J e y s 113 114di n o 115 h s been te 11 t , 1 bu not c 15 r as d. The same team retracted the discoveay ie teay 2001. cthe discovscovofry liemulnt2001., The , ascd very ofaelemenrs por3ed 14,tand 1onfihmebeen reported 58 Ce Cerium 140.116 90 Th Thorium 232.0381 59 Pr Praseodymium 140.907 65 91 Pa Protactinium 231.035 88 658 0 Ce Nd NeoCermimm dy iu u 0 11 144.24 6 990 2 Th U UThniruum ra o i m 23 0 03 9 238.2.28 81 59 61 Pr Pm Prasmodhmim o e ety iu um 14(1907 65 0. 45) 91 93 Pa Np P ot t ct ium Nrepauninium 23(2035 88 1. 37) 60 62 Nd Sm Namdymimm S eo ariu u 144.24 150.36 92 94 U Pu PlUtonium u ra 23(2028 91 8. 44) 61 Pm Promethium (145) 93 Np Neptunium (237) 62 Sm Samarium 150.36 94 Pu Plutonium (244) 63 Eu Europium 151.964 95 64 Gd Gadolinium 157.25 96 663 5 Eu Tb Eu o u u Terrbipimm 15151.9634 8.925 4 995 7 64 66 Gd Dy G spr l n um Dyadooisiium 1157.25 62.500 96 98 65 67 To Hb HTemiium ol rb um 158.925 34 164.930 32 97 99 Am Cm Ak Bm Cm Cf Bk Es Americium (243) Curium (247) A rke u um Bemerlicim ((243) 247) CalCfurinimm i o uu ((247) 251) EiBetreielium ns k n ((247) 252) 666 8 Dr Ey DErbirosium ysp um 11622500 67. . 59 98 100 FCf m Cerimirum m F al fo niu ( 57) (2251) 667 9 Ho Tm THolmimm hu iu u 11649930232 68. . 34 1 99 101 68 70 Er Yb YttErrbiium e b um 67 25 173.04 9 100 102 69 71 Tu Lm LThetliium ut u um 1174.96721 68.934 101 103 Es Md Fo Nm Mrd L MEindeeiviium e nstlen um ( 58) (2252) NFereliium ob m um ((257) 259) Mw ene i m Laenrdelcivuum ((258) 262) he at r m c t h s p l s ed i of c s ren e refle u t m pr s. si alues lu ted i m The atomic masses listed in thisTtable oefliecmtase esreicitsionn thiurtablt measctreheenteci(Von of cisrrentn easurements. (Values listed in pa s nt teose rr d he tive e emebe of t t s se le or most el mm nt i o op st ) parentheses are the mass numberreof hhses aae itoacmass lnumntsr’smoshotabradioactive coemeons’smtostes.able or most common isotopes.) 70 Yb Ytterbiu 173.0 102 No Nobeliu (259 Hydrogen Semiconductors (also known as metalloids) 1 1 H Key: Hydrogen 1.007 94 Group 2 Group 1 3 4 Beryllium 9.012 182 2 20 3 Period Magnesium 24.3050 Ca Calcium 40.078 Strontium 87.62 Barium 137.327 4 Radium (226) C Symbol Name Carbon Name Carbon Average atomic mass Averag010mic mass 12. e ato 7 12.0107 Nonmetals Halogens Noble gases Other nonmetals Nonmetals B Boron Halogens 10.811 Noble gases Other nonmetals 13 12 Oxargeon Cyb n 15.9994 12.0107 15 13 16 14 F N Flutooigen Ni r r ne 18.14.8 067 2 99 0 403 17 15 Ne O N yge Oxeonn 20.1797 15 99 4 18 6 9 F Fluorin 18.998 4 17 Argfur Sul on 39.948 2 065 Chlorin 35.45 Group 12 Group 8 Group 9 Group 10 Group 11 Grroup 12 G oup 10 Group 11 27 25 26 27 28 29 30 28 31 29 89 87 7 14 NiBrorgen t oon 110.811 4.0067 O C PCosorhneus h hl p i or 35.45 7 30.973 3 61 Group 9 Group 7 Lantesaium C h num 138 905 4 132..905 5 3 Carbon 12.0107 N B Sulifcon Si ur 32 6 28.0855 26 4 La Cs C Group Phoumhnuus Al sp i or m 30.973 761 26.981 538 Group 8 6 57 55 6 18 0 Silicon 28.0855 25 23 V Sc Vanadium Scan 450.9415 0 4.955 91 40 38 Zitrrconium S ont 91.224 87.62 Group 16 9 7 Cl Grroup 7 G oup 5 Yt r u u Rutbidimm 88.5.05 78 9 46 85 Group 17 Group 15 8 6 Ar S 24 22 Zr S Grroup 16 G oup 14 7 5 Cl P Group 6 Group 4 Y Rb Grroup 15 G oup 13 6 Si 23 21 Titalnium C ac 47.867 0 078 Group 14 P Al Group 5 Group 3 Scotndsuum P a as i i m 4439509910 . 9. 5 83 Helium 4.002 602 Aluminum 26.981 538 Magnesium 24.3050 Ti Ca 2 He Si 22 0 Sc K Group 18 Al Mg Group 4 39 37 5 88 Ra Sodium 22.989 770 Beryllium 9.012 182 20 6 Metals Alkali metals Alkaline-earth metals Grtal p Transition meous 13 Other metals 5 21 19 56 Ba Na Be C Symbol Metals Alkali metals Alkaline-earth metals Transition metals Other metals (also known as metalloids) Group 3 38 Sr Lithium 6.941 11 12 Mg Li IP (eV) Be A6mic number to Atomic number Group 2 4 Key: Hydrogen Semiconductors 41 39 Nb Y 10 NYotbium it r 92..906 38 88 905 85 72 56 73 57 Ha Bf Ta L Hafriium Ba n um 178.49 137.327 LTantaaumm anth l nu 180..9479 138 9055 104 88 189 05 Cr Ti CTirtomiium h an um 5479867 1. . 961 42 40 Mo Zr MZilrcbdninum o y o e um 95 94 91..224 74 72 W Hf THafgsitem un n u n 183..84 178 49 106 104 Mn V Maanadiese V ngan um 5459394049 . 0. 8 15 43 41 Tb Nc TeNhobituum c i ne i m 92(906 38 . 8) 75 73 Re Ta Rhenauum Tant i l m 6 20 180.9479 107 105 Ac Fr f Ra Db Ac Sg Rf Bh Db Acaincuum Fr t i i m ((223) 227) RutRerdoudium ha f i rm (261) 26 Dubinium Act (262) (227) Se her g um Rutabofroridium (266) (261) Bohrnuum Dub i i m ((262) 264) names and symbols he systematic names and symbols *T reater than 110 will for elements greater than 110 will he approval of trivialbe used until the approval of trivial C. names by IUPAC. Fe Cr rm ChrIoonium 55 845 51..9961 44 2 Ro Mu R o heni n m Multybdeuum 195..94 01 07 76 4 Os W Osm u en Tungistm 190.23 83 84 108 06 Ss Hg Seaasorumm H b si giu 66 (277)) Cn Mo Cobal Mangantese 58..933 200 54 938 049 45 43 Rh Tc TRhhneuimm ec odi t u 102.(905 50 98) 77 75 Rre I I i e u um Rrhdinim 192..217 186 207 109 107 Mt Bh MBioneiruum e t hr i m (268)) (264 Fe Co Iron 55.845 Cobalt 58.933 200 44 45 Ru Ruthenium 101.07 76 Rh Rhodium 102.905 50 77 Os Ir Osmium 190.23 Iridium 192.217 108 109 Mt Hs Meitnerium (268) Hassium (277) Ni Nickel 58.6934 46 Pd Palladium 106.42 78 Pt Platinum 195.078 110 Ds Darmstadtium (281) Cu Copper 63.546 47 Ag Silver 107.8682 79 Au Gold 196.966 55 111 Uuu* Unununium (272) Zn Ni Z cc Ninkel 65 409 58.6934 48 46 Cd P Cadlmduum Pal a i i m 1106.42 2.411 80 78 Hg Pt Mlercnuy P ati ur m 200 59 195.078 112 110 Uub* Ds U m t bi t u Darnusnaduimm ((281) 285) Gu Ca Galpum Co li per 69..723 63 546 49 47 In Ag Indliver Si um 114 818 107..8682 81 79 Tu Al ThGloilum al d 204.3833 196.966 55 113 111 t* Uuu* Ununtrnuum ui im ((284)) 272 32 30 Gn Ze Germianium Z nc 72 64 65..409 50 48 Sn Cd Tin Cadmium 118..710 112 411 82 80 Pb Hg Le cu Merad ry 207 2 200..59 114 112 Uuq* Uub Unununaduum U nqubi i m ((285) 289) 33 31 As Ga Araelinim G sl u c 746927260 . 9. 1 3 34 32 Se Ge S l m i niu Gerenaum m 78.96 72.64 51 49 52 50 Sb In Annidiumy I t mon 121.760 114.818 Te Sn Telluriin m Tu 27 60 118.710 83 81 84 82 Bi Tl Bihmluuh T s al i t m 208.4.80 33 20 9 38 38 115 113 Uup* Uut Unununtnituum U npe r i m ((288)) 284 Po b Poloeaum L ni d (207.) 209 2 114 Uuq* Ununquadium (289) 35 33 Bs Ar BAoseinie r r m nc 779.904 0 4.921 6 53 51 I Sb o i ine AIntdmony 126.904 47 121.760 85 83 At Bi Asisatiute B tmn h 20(2980 38 8. 10) 36 4 Ke Sr 35 Br K en um Serlyption 878796 3. . 98 Bromin 79.90 54 2 53 Xe T X l n in Teleuroum 1127260 31. . 93 86 4 Rn Po R oni n Poladoum (222) 09 I Iodine 126.904 85 At Astatin (210 115 Uup* Ununpentium (288) A team at Lawrence Berkeley NAtionm Laboratonce repoetled NatidisaoLabooftelrees entso1t16 ahe di18oiveJune el999ents 116 and 118 in June 1999. a teaal at Lawreries Berk r ey the on cl very ra o i m rep r ed t nd 1 sc n ry of 1 em . The same team retracted the diThovsamie tJeay 2re0ra.cTed thscdiveryvof y inment2001. ,The4disndv11y ofaelemen ts porte114, tanot 115 fhased. en reported sc e ery n ul m 0 t 1 t he die o sco er ele July s 113 11 , a co er 5 h s be en re 113, d bu nd con irm be 58 Ce 0 59 Pr 60 58 Nd Ce 61 59 Pm Pr Cerium 140.116 Praseodymium 140.907 65 Neodymmm Ceriu iu 4 24 140.116 P o eod hium Prrasmetymium ( . 45) 1401907 65 90 91 92 90 93 1 Th Thorium 232.0381 Pa Protactinium 231.035 88 10 U Th Urhoriium T an um 23 0 03 91 238.2.28 81 Np Pa N ot tu i i i m Prepactnnuum 231237) 88 ( .035 62 60 Sm Nd 61 62 Pm Sm Sam y iu u Neodarmimm 150..36 144 24 Promethium (145) Samarium 150.36 94 92 93 94 20 Pu U PUrtanium lu o 23(2028 91 8. 44) Np 30 Neptunium (237) Pu Plutonium (244) 63 Eu 64 Gd 65 63 Tb Eu 66 64 Dy Gd Europium 151.964 Gadolinium 157.25 Te o u um Eurbipim 1515929634 8. 1. 5 4 Dysdoonium Ga pr li s 1157525 62. . 00 95 96 97 95 98 96 Americium (243) Curium (247) Berkeilcuum Amer i i m ((243) 247) 40 50 Am Cm Bk Am Z Cf Cm CaCfurrinimm li o u u (247) (251) 67 65 Hb To 68 66 Ey Dr 69 67 Tm Ho 70 68 Yb Er Holrbium Te m 164..930 32 158 925 34 Erbi osi Dysprumum 167.259 162.500 Thumim Hol liu um 168.934 21 164.930 32 YtEerbuum t rbi i m 73 04 167.259 99 97 198 00 101 99 102 100 60 Ek Bs EiBertkenium ns ei l (247) (252) 70 Fm Cf Fe i o i niu Calrfmrum m ((251) 257) 80 71 69 Lu Tm LThutium ute l 17 9 96 2 168.4.34 7 1 103 1 Md Es No Fm Ld Mr Meindteenium E sel i v m ((252) 258) Nobmium Fer el 257 ((259)) Laenrenevuum M w del ci i m 58 (262) T t e l t refle mass p lisi e o i i u tablt ref ect em prec (ion o is en m The atomic masses listed in this habaeomic ct theesrectsid nnotfhcs rrene melasurthe ents.isValuefsclurtred tin easurements. (Values listed in pa e of those radihe tive e ement rs o ost st e r e io m i st el mmnts most st .) parentheses are the mass numbers ntheses are toacmass lnumbes’ mf thosablador actove coemeon ’isotopesable or most common isotopes.) 70 Yb Ytterbiu 173.0 102 No Nobeliu (259 1s ∼Z 2 a1s 1 ∼ Z 1s Ecut ∼ Z 2 ∼Z 2 a1s 1 ∼ Z 1s Ecut ∼ Z 2 ∼Z 2 a1s NP W = 1 ∼ Z 4π 3 Ω kcut 3 (2π )3 ∼Z 3 1s Ecut ∼ Z 2 ∼Z 2 a1s NP W = 1 ∼ Z 4π 3 Ω kcut 3 (2π )3 ∼Z IP ∼ 1 3 a∼1 First principle of computational physics First principle of computational physics If two systems have similar physical and chemical properties, their simulation should require a similar amount of computer resources Power to the imagination Power to the imagination Chemically similar atoms have potentials with very different, possibly nasty, mathematical properties? Well ... Power to the imagination Chemically similar atoms have potentials with very different, possibly nasty, mathematical properties? Well ... Imagine pseudo atoms whose chemical properties are very similar to those of real atoms, but whose (pseudo) potentials are as gentle as possible. Properties of pseudopotentials Properties of pseudopotentials Vps does not have core states: valence states of any given angular symmetry are the lowest-lying states of that symmetry: ps φval is nodeless and smooth Properties of pseudopotentials Vps does not have core states: valence states of any given angular symmetry are the lowest-lying states of that symmetry: ps φval is nodeless and smooth The chemical properties of the pseudo-atom are the same as those of the true atom: ps v al = ps φval (r) ae v al = ae φval (r) for r > rc 3s Si 0 1 2 3 4 r (a.u.) 5 6 7 8 3s Si 0 1 2 3 4 r (a.u.) 5 6 7 8 3p Si 0 1 2 3 4 r (a.u.) 5 6 7 8 3p Si 0 1 2 3 4 r (a.u.) 5 6 7 8 3d Si 0 1 2 3 4 r (a.u.) 5 6 7 8 3d Si 0 1 2 3 4 r (a.u.) 5 6 7 8 US pseudopotentials US pseudopotentials HU S φn = n S φn φn |S |φm = δnm Structural optimisation E (R) Equilibrium geometries: minimum-energy configurations ∂ E (R) F(R) = − =0 ∂R Structural optimisation steepest descent E (R) ˙ R = F(R) discretization Rn = Rn−1 + F(Rn−1 ) Structural optimisation steepest descent E (R) ˙ R = F(R) discretization Rn = Rn−1 + F(Rn−1 ) The minimum is reached !!! Molecular Dynamics R(t) Molecular Dynamics dynamics, spectroscopy R(t) Molecular Dynamics dynamics, spectroscopy R(t) 1T A≈ A R(t) dt T0 Equilibrium statistical mechanics The Verlet algorithm ˙ R(t ± ) = R(t) ± R(t) + 2 2 ¨ R(t) ± 3 8 ⋯ (t) + O( 4 ) R The Verlet algorithm ˙ R(t ± ) = R(t) ± R(t) + 2 2 ¨ R(t) ± R(t + ) = 2R(t) − R(t − ) + 2 M 3 8 ⋯ (t) + O( 4 ) R F R(t) + O( 4 ) The Verlet algorithm ˙ R(t ± ) = R(t) ± R(t) + 2 2 ¨ R(t) ± R(t + ) = 2R(t) − R(t − ) + 1 A≈ N 2 M 8 ⋯ (t) + O( 4 ) R F R(t) + O( 4 ) N A Rn n=1 3 The tricks of the trade The tricks of the trade • Plane waves require supercells for treating finite (or semiinfinite) systems The tricks of the trade • Plane waves require supercells for treating finite (or semiinfinite) systems • Plane-wave basis sets are usually large: iterative diagonalization vs. global minimization The tricks of the trade • Plane waves require supercells for treating finite (or semiinfinite) systems • Plane-wave basis sets are usually large: iterative diagonalization vs. global minimization • Summing over occupied states: special-point and Gaussiansmearing techniques The tricks of the trade • Plane waves require supercells for treating finite (or semiinfinite) systems • Plane-wave basis sets are usually large: iterative diagonalization vs. global minimization • Summing over occupied states: special-point and Gaussiansmearing techniques • Non-linear extrapolation for SCF acceleration and density prediction in MD The tricks of the trade • Plane waves require supercells for treating finite (or semiinfinite) systems • Plane-wave basis sets are usually large: iterative diagonalization vs. global minimization • Summing over occupied states: special-point and Gaussiansmearing techniques • Non-linear extrapolation for SCF acceleration and density prediction in MD • Choice of fictitious masses in CP dynamics The tricks of the trade • Plane waves require supercells for treating finite (or semiinfinite) systems • Plane-wave basis sets are usually large: iterative diagonalization vs. global minimization • Summing over occupied states: special-point and Gaussiansmearing techniques • Non-linear extrapolation for SCF acceleration and density prediction in MD • • Choice of fictitious masses in CP dynamics . . . and many others (and you got to know them all!) Accuracy vs. approximations Accuracy vs. approximations Theoretical approximations / limitations Accuracy vs. approximations Theoretical approximations / limitations The Born-Oppenheimer approximation • Accuracy vs. approximations Theoretical approximations / limitations The Born-Oppenheimer approximation DFT functionals (LDA, GGA, ...) • • Accuracy vs. approximations Theoretical approximations / limitations The Born-Oppenheimer approximation DFT functionals (LDA, GGA, ...) Pseudopotentials • • • Accuracy vs. approximations Theoretical approximations / limitations The Born-Oppenheimer approximation DFT functionals (LDA, GGA, ...) Pseudopotentials No easy access to electronic excited states and/or quantum dynamics • • • • Accuracy vs. approximations Theoretical approximations / limitations The Born-Oppenheimer approximation DFT functionals (LDA, GGA, ...) Pseudopotentials No easy access to electronic excited states and/or quantum dynamics ... • • • • • Accuracy vs. approximations Theoretical approximations / limitations The Born-Oppenheimer approximation DFT functionals (LDA, GGA, ...) Pseudopotentials No easy access to electronic excited states and/or quantum dynamics ... • • • • • Numerical approximations / limitations Accuracy vs. approximations Theoretical approximations / limitations The Born-Oppenheimer approximation DFT functionals (LDA, GGA, ...) Pseudopotentials No easy access to electronic excited states and/or quantum dynamics ... • • • • • Numerical approximations / limitations Finite/limited size/time • Accuracy vs. approximations Theoretical approximations / limitations The Born-Oppenheimer approximation DFT functionals (LDA, GGA, ...) Pseudopotentials No easy access to electronic excited states and/or quantum dynamics ... • • • • • Numerical approximations / limitations Finite/limited size/time Finite basis set • • Accuracy vs. approximations Theoretical approximations / limitations The Born-Oppenheimer approximation DFT functionals (LDA, GGA, ...) Pseudopotentials No easy access to electronic excited states and/or quantum dynamics ... • • • • • Numerical approximations / limitations Finite/limited size/time Finite basis set Differentiation / integration / interpolation • • • Accuracy vs. approximations Theoretical approximations / limitations The Born-Oppenheimer approximation DFT functionals (LDA, GGA, ...) Pseudopotentials No easy access to electronic excited states and/or quantum dynamics ... • • • • • Numerical approximations / limitations Finite/limited size/time Finite basis set Differentiation / integration / interpolation ... • • • • What do I (can’t I) calculate today? What do I (can’t I) calculate today? Strong covalent and metallic bonds What do I (can’t I) calculate today? Strong covalent and metallic bonds Weak e-e correlations What do I (can’t I) calculate today? Strong covalent and metallic bonds Weak e-e correlations Structural optimization, lattice vibrations, adiabatic dynamics, static response functions What do I (can’t I) calculate today? Strong covalent and metallic bonds Weak e-e correlations Structural optimization, lattice vibrations, adiabatic dynamics, static response functions ? Strong correlations / Mott-Hubbard insulators What do I (can’t I) calculate today? Strong covalent and metallic bonds Weak e-e correlations Structural optimization, lattice vibrations, adiabatic dynamics, static response functions ? Strong correlations / Mott-Hubbard insulators ? Optical properties / excitation energies What do I (can’t I) calculate today? Strong covalent and metallic bonds Weak e-e correlations Structural optimization, lattice vibrations, adiabatic dynamics, static response functions ? Strong correlations / Mott-Hubbard insulators ? Optical properties / excitation energies ? Dispersion forces / weak chemical bonds Which algorithm shall I use? Which algorithm shall I use? Electronic structure: SCF diagonalization vs. energy minimization Which algorithm shall I use? Electronic structure: SCF diagonalization vs. energy minimization Geometry optimization: standard DFT Which algorithm shall I use? Electronic structure: SCF diagonalization vs. energy minimization Geometry optimization: standard DFT Lattice vibrations, static response functions: DFPT Which algorithm shall I use? Electronic structure: SCF diagonalization vs. energy minimization Geometry optimization: standard DFT Lattice vibrations, static response functions: DFPT Dynamics: Car-Parrinello vs. Born-Oppenheimer Which algorithm shall I use? Electronic structure: SCF diagonalization vs. energy minimization Geometry optimization: standard DFT Lattice vibrations, static response functions: DFPT Dynamics: Car-Parrinello vs. Born-Oppenheimer Slow kinetics and rare events: path sampling vs. Parrinello-Laio metadynamics Which algorithm shall I use? Electronic structure: SCF diagonalization vs. energy minimization Geometry optimization: standard DFT Lattice vibrations, static response functions: DFPT Dynamics: Car-Parrinello vs. Born-Oppenheimer Slow kinetics and rare events: path sampling vs. Parrinello-Laio metadynamics Optical properties, excited states: TDDFT vs. MBPT What should I care today? What should I care today? Finite-size effects: What should I care today? Finite-size effects: Finite systems → supercells What should I care today? Finite-size effects: Finite systems → supercells Infinite systems → k-point sampling (+ Gaussian smearing) What should I care today? Finite-size effects: Finite systems → supercells Infinite systems → k-point sampling (+ Gaussian smearing) Finite-basis effects: What should I care today? Finite-size effects: Finite systems → supercells Infinite systems → k-point sampling (+ Gaussian smearing) Finite-basis effects: Choice of the basis set (PW’s, LCAO, PAW’s, LMTO, ...) What should I care today? Finite-size effects: Finite systems → supercells Infinite systems → k-point sampling (+ Gaussian smearing) Finite-basis effects: Choice of the basis set (PW’s, LCAO, PAW’s, LMTO, ...) Size of the basis set What should I care today? Finite-size effects: Finite systems → supercells Infinite systems → k-point sampling (+ Gaussian smearing) Finite-basis effects: Choice of the basis set (PW’s, LCAO, PAW’s, LMTO, ...) Size of the basis set Pseudo-potentials: What should I care today? Finite-size effects: Finite systems → supercells Infinite systems → k-point sampling (+ Gaussian smearing) Finite-basis effects: Choice of the basis set (PW’s, LCAO, PAW’s, LMTO, ...) Size of the basis set Pseudo-potentials: “Hard” node-less orbitals (2p, 3d ...) What should I care today? Finite-size effects: Finite systems → supercells Infinite systems → k-point sampling (+ Gaussian smearing) Finite-basis effects: Choice of the basis set (PW’s, LCAO, PAW’s, LMTO, ...) Size of the basis set Pseudo-potentials: “Hard” node-less orbitals (2p, 3d ...) Semi-core states + NL XC core correction What else should I care? What else should I care? Choice of the diagonalization / minimization algorithms What else should I care? Choice of the diagonalization / minimization algorithms MD time steps & CP fictitious masses What else should I care? Choice of the diagonalization / minimization algorithms MD time steps & CP fictitious masses Numerical and algorithmic details of the implementation What else should I care? Choice of the diagonalization / minimization algorithms MD time steps & CP fictitious masses Numerical and algorithmic details of the implementation Integration & FFT meshes (1D/3D) What else should I care? Choice of the diagonalization / minimization algorithms MD time steps & CP fictitious masses Numerical and algorithmic details of the implementation Integration & FFT meshes (1D/3D) Differentiation and interpolation schemes What else should I care? Choice of the diagonalization / minimization algorithms MD time steps & CP fictitious masses Numerical and algorithmic details of the implementation Integration & FFT meshes (1D/3D) Differentiation and interpolation schemes Parallelization issues (by band / by k-point / by Gvector) What else should I care? Choice of the diagonalization / minimization algorithms MD time steps & CP fictitious masses Numerical and algorithmic details of the implementation Integration & FFT meshes (1D/3D) Differentiation and interpolation schemes Parallelization issues (by band / by k-point / by Gvector) ... What else should I care? Choice of the diagonalization / minimization algorithms MD time steps & CP fictitious masses Numerical and algorithmic details of the implementation Integration & FFT meshes (1D/3D) Differentiation and interpolation schemes Parallelization issues (by band / by k-point / by Gvector) ... ... The Quantum ESPRESSO suite of ab-initio codes The Quantum ESPRESSO suite of ab-initio codes * *opEn Source Package for Research in in Electronic Structure, Simulation, and Optimization The Quantum ESPRESSO suite of ab-initio codes * *opEn Source Package for Research in in Electronic Structure, Simulation, and Optimization PWscf (Trieste/Pisa/Bologna) The Quantum ESPRESSO suite of ab-initio codes * *opEn Source Package for Research in in Electronic Structure, Simulation, and Optimization PWscf (Trieste/Pisa/Bologna) Phonon (Trieste/Pisa) The Quantum ESPRESSO suite of ab-initio codes * *opEn Source Package for Research in in Electronic Structure, Simulation, and Optimization PWscf (Trieste/Pisa/Bologna) Phonon (Trieste/Pisa) FPMD (Trieste/Bologna) The Quantum ESPRESSO suite of ab-initio codes * *opEn Source Package for Research in in Electronic Structure, Simulation, and Optimization PWscf (Trieste/Pisa/Bologna) Phonon (Trieste/Pisa) FPMD (Trieste/Bologna) CP (Lausanne/Princeton/Pisa/Bologna) The Quantum ESPRESSO suite of ab-initio codes * *opEn Source Package for Research in in Electronic Structure, Simulation, and Optimization PWscf (Trieste/Pisa/Bologna) Phonon (Trieste/Pisa) FPMD (Trieste/Bologna) CP (Lausanne/Princeton/Pisa/Bologna) Utilities and/or graphical applications Quantum ESPRESSO is a community enterprise Quantum ESPRESSO is a community enterprise Don’t ask what Quantum ESPRESSO can do for you, but rather what you can do for Quantum ESPRESSO Quantum ESPRESSO is a community enterprise Don’t ask what Quantum ESPRESSO can do for you, but rather what you can do for Quantum ESPRESSO Be part of the community Quantum ESPRESSO is a community enterprise Don’t ask what Quantum ESPRESSO can do for you, but rather what you can do for Quantum ESPRESSO Be part of the community Do great science with it Quantum ESPRESSO is a community enterprise Don’t ask what Quantum ESPRESSO can do for you, but rather what you can do for Quantum ESPRESSO Be part of the community Do great science with it Report bugs and suggest improvements Quantum ESPRESSO is a community enterprise Don’t ask what Quantum ESPRESSO can do for you, but rather what you can do for Quantum ESPRESSO Be part of the community Do great science with it Report bugs and suggest improvements Even better, fix the bugs and implement the improvements Quantum ESPRESSO is a community enterprise Don’t ask what Quantum ESPRESSO can do for you, but rather what you can do for Quantum ESPRESSO Be part of the community Do great science with it Report bugs and suggest improvements Even better, fix the bugs and implement the improvements Participate in the discussion forums Quantum ESPRESSO is a community enterprise Don’t ask what Quantum ESPRESSO can do for you, but rather what you can do for Quantum ESPRESSO Be part of the community Do great science with it Report bugs and suggest improvements Even better, fix the bugs and implement the improvements Participate in the discussion forums Write some documentation or articles in the QE wiki Quantum ESPRESSO is a community enterprise Don’t ask what Quantum ESPRESSO can do for you, but rather what you can do for Quantum ESPRESSO Be part of the community Do great science with it Report bugs and suggest improvements Even better, fix the bugs and implement the improvements Participate in the discussion forums Write some documentation or articles in the QE wiki Help integrate QE with other OS software Quantum ESPRESSO is a community enterprise Don’t ask what Quantum ESPRESSO can do for you, but rather what you can do for Quantum ESPRESSO Be part of the community Do great science with it Report bugs and suggest improvements Even better, fix the bugs and implement the improvements Participate in the discussion forums Write some documentation or articles in the QE wiki Help integrate QE with other OS software ... To start with ... To start with ... Enjoy this course! www.quantum-espresso.org ...
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This note was uploaded on 12/07/2011 for the course CHEM 350 taught by Professor Duanejohnson during the Summer '06 term at University of Illinois, Urbana Champaign.

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