First-principles calculations (ab initio) Dominik Legut

Nanotechnology and IT4Innovations Centres, VSB-Technical University of Ostrava, Ostrava, Czech Republic email: [email protected], PI-324

Dominik Legut VSB-TU Ostrava

ES 2013

Outline Theory + practical session: 1 2

Brief introduction to the first-principles calculations - theory PROJECT: Calculation of equilibrium lattice constant, bulk moduli and ideal volume tensile strenght of cubic transition metals Introduction - Hooks law - stress vs. strain Goal n. 1: to determine equilibrium lattice constant Goal n. 2: to calculate Bulk modulus (B) Goal n. 3: to calculate Ideal volume tensile strenght (σth ) Simple electronic structure analysis, draw DOS at equilibrium and at (σth ) Loggin into the cluster, editing inputs (midnight commander), getting outputs How to run the calculations ? What will contain protocol ? Dominik Legut VSB-TU Ostrava

ES 2013

Calculations on the supercomputer Many chemical and physical properties could be calculated from first-principles (ab initio) electronic structure calculations based on solving of:

Fundamental quantum theory, Schr¨ odinger/Dirac equations & Density functional theory∗ (DFT) The only input: atomic number of constituents some structural information ∗

in 1998 awarded by Nobel prize in Chemistry, W. Kohn & J. Pople

Dominik Legut VSB-TU Ostrava

ES 2013

Quantities from Ab initio calculations Selected list of quantities Structural stability of phases Magnetic order, non-magnetic, ferro-, antiferro-, spin-spirals, transition temperatures Elasticity, is it brittle or ductile? Young moduli, strenght Defects, lattice vibrations, thermal expansion Optical and magneto-optical properties Kerr, Faraday, Voigt x-ray absorption Relativistic effects Superconductivity

Dominik Legut VSB-TU Ostrava

ES 2013

Drawbacks of DFT Approximations: Oppenheimer approximation, i.e. separation of motion of electrons and nuclei electron - electron interactions, so-called exchange-correlation energy is UNKNOWN ! Here approximations (LSDA, GGA, GGA-PBE, LSDA+U, hybrids, B3LYP, Wu06, local ω-GGA) DFT in general does not give good band gaps (some semiconductors, large gap insulators) phonons, superconductivity need atomic(nucleus) motions, at least 2 orders of magnitude more demanding calculations all calculations are at T = 0K inclusion of temperatures via phonons (atomic vibrations)

Dominik Legut VSB-TU Ostrava

ES 2013

Hamiltonian, Schroedinger eq. etc Hψ(r) = E ψ(r) H = He + HN + He−N , H = Te + Ve + TN + VN + He−N

He = −

HN = −

n

n

j=1

i,j

1 1X e2 ~2 X 2 5rj + 2m 4πε0 2 | rj − rk |

N N ~2 X 1 1 1 X ZJ ZK e 2 52Rj + 2 MJ 4πε0 2 | RJ − RK | J=1

He−N = −

J,K

n N 1 X X Zj e 2 4πε0 | rj − Rj | j

Dominik Legut VSB-TU Ostrava

J

ES 2013

Hartreeho Aproximace a Self-Consistent-Field cycle (SCF) 0

Z

ρ(r) 0 0 dr 4πε0 | r − r |

VH (r ) =

Veff (r) = VH (r) + VN (r)

VN (r) =

X i

−

Zi e 4πε0 | r − Ri |

h2 ∇2 ψj (r) + Veff (r)ψj (r) = εj ψj (r). 8π 2 m ρ(r) =

X

ψj (rψj∗ (r

joccupied

Dominik Legut VSB-TU Ostrava

ES 2013

Self-consistent cycle of DFT calculation

Dominik Legut VSB-TU Ostrava

ES 2013

Hooke law, bulk moduli, tensile strenght (σth )

σij = Cijkl εkl

σ=

V 1 dEtot ,v = V0 dv V0 1 d 2 Etot =0 V0 dv 2 B=

1 d 2 Etot V dv 2

We want total energy as a function of volume (lattice parameter) Dominik Legut VSB-TU Ostrava

ES 2013

Getting on cluster only from VSB site Linux/MacOs terminal: ssh [email protected]

basic unix commands ls...listing of directories pwd...actual path

Win: use Putty: host=cluster.cz, port 22 (ssh protocol), login: your last name

cd....return to your home directory e.g. cd Mo...go into the directory Mo

Password: XXXXX editing by “mc” (midnight commander) or “nano“

cd .. go to directory one level above

go to directory of your element, e.g. “cd Mo”

mkdir...create directory

5 files there: POSCAR, POTCAR, KPOINTS, INCAR, gop-vasp46

rm -r name... remove directory

Dominik Legut VSB-TU Ostrava

rm file... remove file

ES 2013

Input files: POSCAR, POTCAR, KPOINTS, and INCAR

POSCAR Structure description example, bcc Mo bcc metal XXXXXX 0.5 0.5 −0.5 −0.5 0.5 0.5 0.5 −0.5 0.5 1 Direct 0 0 0

Dominik Legut VSB-TU Ostrava

Line description 1 2

3

4

5

6

1st line: comment 2nd line: lattice constant replace XXXXXX 3nd -6th line: primitive vectors of bcc(fcc)structure 4th line: number of atoms of one type 5th line: relative or absolute co-ordinates 6th line: atom basis

ES 2013

POSCAR - BCC lattice body-centered cubic (bcc) bcc metal XXXXXX 1 0 0 1 0 0 2 Direct 0 0 0.5 0.5 or

bcc metal XXXXXX 0.5 0.5 −0.5 0.5 0.5 −0.5 1 Direct 0 0

1 0 1

body-centered cubic (bcc)

0 0.5

−0.5 0.5 0.5

0

Dominik Legut VSB-TU Ostrava

ES 2013

POSCAR - FCC lattice fcc metal XXXXXX 1 0 1 0 1 0 0 0 1 4 Direct 0 0 0 0 0.5 0.5 0.5 0 0.5 0 0.5 0.5 or

fcc metal XXXXXX 0 0.5 0.5 0.5 0 0.5 0.5 0.5 0 1 Direct 0Dominik Legut 0 VSB-TU 0 Ostrava

face-centered cubic (fcc)

ES 2013

POTCAR and KPOINTS POTCAR describe radial and spherical part of core and valence electron configuration top lines of the POTCAR, valence electron configuration (“head” -4 POTCAR) PAW PBE Ir 06Sep2000 9.00000000000000000 parameters from PSCTR are: VRHFIN =Ir: s1d8

KPOINTS sampling of the Brillouin zone k-points 0 Auto 80

grep ’irreducible k-points’ OUTCAR Dominik Legut VSB-TU Ostrava

ES 2013

INCAR calculation parameters SYSTEM = fcc metal ISTART = 0 ! start from scratch - new calculation ICHARG = 2 ! start from superposition of atomic charge densities ENCUT = 480 ! energy cut-off EDIFF = 1E-07 ! convergence criteria for total energy PREC = Accurate ! the most accurate setup of many parameters LWAVE = .FALSE. ! Orbitals are not written on disk, saving time and space! LCHARG = .FALSE. ! Charge density is not written on disk, saving time and space! LREAL = .FALSE. ! Keep calculations in reciprocal space, more precise method! ISMEAR = -5 ! Tetrahedron method for integration of Brillouin zone! ##### dos ##### NEDOS = 3001 ! number of points in energy grid for density of states! Dominik Legut VSB-TU Ostrava

ES 2013

running calculations queueing system SGE (Sun grid engine) in each directory is gop-vasp46 file submit job: “qsub gop-vasp46” “qstat -f“ to see status of the job ”qdel YYYY”, where YYYY is job ID (number)

example [legut@v 2test − Ca]$ qsub gop-vasp46 Your job 1044 (”ES”) has been submitted [legut@v 2test − Ca]$ qstat -f queuename qtype resv/used/tot. load avg arch states ——————————————————————————— [email protected] BIP 0/8/24 0.00 lx26-amd64 1044 0.55500 ES legut r 04/04/2013 07:42:47 8 ——————————————————————————— [email protected] BIP 0/0/24 0.00 lx26-amd64 ——————————————————————————— [email protected] BIP 0/0/8 0.00 lx26-amd64 ——————————————————————————— [email protected] BIP 0/0/24 0.00 lx26-amd64 ——————————————————————————— Dominik Legut VSB-TU Ostrava [email protected] BIP 0/0/24 0.00 lx26-amd64

ES 2013

Outputs OUTCAR Many informations in the OUTCAR (total energy, magnetic moment, external pressure, forces on atoms, number of k-points, Fermi energy) “grep TOTEN OUTCAR” at the end is how long the calculation lasts DOSCAR 1100 0.4390400E+02 0.3959798E-09 0.3959798E-09 0.3959798E-09 0.5000000E-15 1.00000000000000005E-004 CAR fcc metal 8.15508248 -23.09503086 3001 2.03302827 1.00000000 -23.095 0.0000E+00 0.0000E+00 -23.085 0.0000E+00 0.0000E+00 -23.074 0.0000E+00 0.0000E+00 Dominik Legut VSB-TU Ostrava

ES 2013

PROTOCOL will contain Equilibrium lattice constant and compare with experiment Bulk modulus (B in GPa), your calculation vs. experimental data. Including formula and the factor to get GPa from the dependence of total energy in eV vs. volume in ˚ A Ideal volume tensile strenght (σth ), if experimental data available also this one. Total density of the states for equlibrium structure and for structure where σth occurs Always use References from where the experimental data are from. Send to [email protected] in pdf format, e.g. use Lyx, openoffice etc. Dominik Legut VSB-TU Ostrava

ES 2013