Introduction to the QUANTUM ESPRESSO package and its application to computational catalysis Input/Output description

Transcription

1 School on computational materials modeling in catalysis Bangalore, 1-5 September 2014 Introduction to the QUANTUM ESPRESSO package and its application to computational catalysis Input/Output description Stefano Fabris CNR-IOM DEMOCRITOS Simulation Center SISSA - Scuola Internazionale Superiore di Studi Avanzati - Trieste - ITALY

2 Time and Length scales in catalysis Ex: Design and operation of H2-based technologies 1m 10-1 m at%: C 39.7, O 31.1, Ce17.9, Pt nm nm 0 Pt-O-Ce m.23n 50nm 10-9 m m 101 m 10-6 m 11 orders of magnitude in length scales 17 orders of magnitude in time scales Natural divide at around m

3 Macro and homogeneous scale Continuum modeling:! averaged input properties! (reaction rates, transport coefficients, thermal conductivities ) S E 1 m C I V E D 10-1 m at%: C 39.7, O 31.1, Ce17.9, Pt 11.3 Pt-O-Ce nm 5nm nm nm 10-9 m m 101 m 10-6 m GOALS Predict overall performance of device Design and optimise components (no predictions of materials properties)

4 Sub-nm vs macro scale modeling Continuum modeling:! averaged input properties! (reaction rates, transport coefficients, thermal conductivities ) Atomistic modeling:! explicit internal structure! (polycrystalline, interfaces, solution, ) DEVICES 10-1 m 1 m 10 1 m m MATERIALS 10-9 m 10-6 m GOALS Predict overall performance of device Design and optimise components (no predictions of materials properties) GOALS Explain&predict averaged properties of the super-micron scales Provide insight for design and optimisation of materials

5 Time and length scales

6 Methods and approximations DFT-based approaches good compromise between predictive power and accuracy

7 What is QUANTUM ESPRESSO? UANTUM ESPRESSO is an integrated suite of computer codes for atomistic simulations based on DFT, pseudo-potentials, and plane waves QUANTUM ESPRESSO open Source Package for Research in Electronic Structure, Simulation, and Optimization

8 What is QUANTUM ESPRESSO? UANTUM ESPRESSO is an integrated suite of computer codes for atomistic simulations based on DFT, pseudo-potentials, and plane waves QUANTUM ESPRESSO open Source Package for Research in Electronic Structure, Simulation, and Optimization Global collaborative project SISSA, CNR, UNIUD, CINECA, EPFL, ICTP & many other partners in Europe and worldwide

9 What is QUANTUM ESPRESSO? UANTUM ESPRESSO is an integrated suite of computer codes for atomistic simulations based on DFT, pseudo-potentials, and plane waves QUANTUM ESPRESSO open Source Package for Research in Electronic Structure, Simulation, and Optimization Global collaborative project SISSA, CNR, UNIUD, CINECA, EPFL, ICTP & many other partners in Europe and worldwide Credit: S. Baroni NOT a computer program for Q simulations Distribution of many packages performing different tasks and designed to be interoperable

10 QUANTUM ESPRESSO people Dario Alfè, Francesco Antoniella, Gerardo Ballabio, Stefano Baroni, Simon Binnie, Mauro Boero, Claudia Bungaro, Giovanni Bussi, Matteo Calandra, Roberto Car, Carlo Cavazzoni, Paolo Cazzato, Davide Ceresoli, Gabriele Cipriani, Matteo Cococcioni, Andrea Dal Corso, Alberto Debernardi, Gernot Deinzer, Oswaldo Dieguez, Stefano Fabris, Guido Fratesi, Xiaochuan Ge, Ralph Gebauer, Paolo Giannozzi, Stefano de Gironcoli, Martin Hilgeman, Yosuke Kanai, Anton Kokalj, Axel Kohlmeyer, Konstantin Kudin, Michele Lazzeri, Baris Malcioglu, Francesco Mauri, Kurt Mäder, O. Barıs Malcıog lu, Layla Martin Samos Colomer, Nicola Marzari, Nicolas Mounet, Adriano Mosca Conte, Alfredo Pasquarello, Lorenzo Paulatto, Pasquale Pavone, Mickael Profeta, Dario Rocca, Guido Roma, Riccardo Sabatini, Carlo Sbraccia, Sandro Scandolo, Gabriele Sclauzero, Manu Sharma, Alexander Smogunov, Kurt Stokbro, Pascal Thibaudeau, Antonio Tilocca, Iurii Timrov, Luca Tornatore, Andrea Trave, Paolo Umari, Renata Wentzcovitch, Yudong Wu, Xiaofei Wang!... and many others.

11

12 What can QE do? Ground-state calculations Self-consistent total energies, forces, stresses; Kohn-Sham orbitals; Separable norm-conserving and ultrasoft (Vanderbilt) pseudo-potentials, PAW (Projector Augmented Waves); Several exchange-correlation functionals: from LDA to generalized-gradient corrections (PW91, PBE, B88-P86, BLYP) to meta-gga, exact exchange (HF) and hybrid functionals (PBE0, B3LYP, HSE); VdW corrections (DFT-D) or nonlocal VdW functionals (vdw-df); Hubbard U (DFT+U); Berry s phase polarization; Spin-orbit coupling and noncollinear magnetism. Credit: S. Baroni

13 What can QE do? Ground-state calculations Self-consistent total energies, forces, stresses; Kohn-Sham orbitals; Separable norm-conserving and ultrasoft (Vanderbilt) pseudo-potentials, PAW (Projector Augmented Waves); Several exchange-correlation functionals: from LDA to generalized-gradient corrections (PW91, PBE, B88-P86, BLYP) to meta-gga, exact exchange (HF) and hybrid functionals (PBE0, B3LYP, HSE); VdW corrections (DFT-D) or nonlocal VdW functionals (vdw-df); Hubbard U (DFT+U); Berry s phase polarization; Spin-orbit coupling and noncollinear magnetism. Structural optimisations GDIIS with quasi-newton BFGS preconditioning; Damped dynamics.

14 What can QE do? Ground-state calculations Self-consistent total energies, forces, stresses; Kohn-Sham orbitals; Separable norm-conserving and ultrasoft (Vanderbilt) pseudo-potentials, PAW (Projector Augmented Waves); Several exchange-correlation functionals: from LDA to generalized-gradient corrections (PW91, PBE, B88-P86, BLYP) to meta-gga, exact exchange (HF) and hybrid functionals (PBE0, B3LYP, HSE); VdW corrections (DFT-D) or nonlocal VdW functionals (vdw-df); Hubbard U (DFT+U); Berry s phase polarization; Spin-orbit coupling and noncollinear magnetism. Structural optimisations GDIIS with quasi-newton BFGS preconditioning; Damped dynamics. PES, Transition states and MEP Nudged Elastic Band method; Meta-Dynamics using the PLUMED plug-in; (Basin Hopping algorithm, coming soon).

15 What can QE do? Ab-initio molecular dynamics Car-Parrinello Molecular Dynamics (CP package); Born-Oppenheimer Molecular Dynamics (PWscf package).

16 What can QE do? Ab-initio molecular dynamics Car-Parrinello Molecular Dynamics (CP package); Born-Oppenheimer Molecular Dynamics (PWscf package). Response properties (DFPT) Phonon frequencies and eigenvectors at any wavevector; Full phonon dispersions; inter-atomic force constants in real space; Translational and rotational acoustic sum rules; Effective charges and dielectric tensors; Electron-phonon interactions; Third-order anharmonic phonon lifetimes; Infrared and (non-resonant) Raman cross-sections; EPR and NMR chemical shifts using the QE-GIPAW package.

17 What can QE do? Ab-initio molecular dynamics Car-Parrinello Molecular Dynamics (CP package); Born-Oppenheimer Molecular Dynamics (PWscf package). Response properties (DFPT) Phonon frequencies and eigenvectors at any wavevector; Full phonon dispersions; inter-atomic force constants in real space; Translational and rotational acoustic sum rules; Effective charges and dielectric tensors; Electron-phonon interactions; Third-order anharmonic phonon lifetimes; Infrared and (non-resonant) Raman cross-sections; EPR and NMR chemical shifts using the QE-GIPAW package. Spectroscopic properties K- and L1-edge X-ray Absorption Spectra (XSpectra package); Time-Dependent Density Functional Perturbation Theory (TurboTDDFT); Electronic excitations with Many-Body Perturbation Theory using YAMBO. Electronic excitations with Many-Body Perturbation Theory using GWL.

18 What can QE do? Quantum transport Ballistic Transport ( PWCOND package); Coherent Transport from Maximally Localized Wannier Functions (WanT); Maximally-localized Wannier functions and transport properties ( WANNIER90)

19 What can QE do? Quantum transport Ballistic Transport ( PWCOND package); Coherent Transport from Maximally Localized Wannier Functions (WanT); Maximally-localized Wannier functions and transport properties ( WANNIER90) Multiscale modeling QM/MM simulations - interface with LAMMPS;

20 QE is an Open Source distribution Free download, free use, open to your contribution GNU project & GPL (General Public Licence) distribution the source code is available to everybody you can do whatever you want with the sources, but if you distribute any derived work, you have to distribute under GPL the sources of the derived work

21 QE is an Open Source distribution Free download, free use, open to your contribution GNU project & GPL (General Public Licence) distribution the source code is available to everybody you can do whatever you want with the sources, but if you distribute any derived work, you have to distribute under GPL the sources of the derived work Advantages nobody can steal the code and give nothing back to the community everybody, including commercial companies, can contribute, use, and re- distribute the software everybody has access to algorithms and can check how results are obtained Credit: S. Baroni

22 How to develop and contribute The QE forge web portal QEforge is a web portal offering source code management for developments in field of computer simulation and numerical modeling of matter and materials at the atomic scale.

23 How to download From the QE Forge website

24 How to download From the Q-E Forge website

25 What do you get stefano$ tar xvf espresso-5.1.tar!! stefano$ cd espresso-5.1!! stefano$ ls!! COUPLE!! PW!!!! flib!! CPV!!!! README!! include!! Doc!!!! archive!! install!! License!! clib!!! pseudo!! Makefile!! configure! upftools!! Modules!! dev-tools! PP!! environment_variables

26 Installation and compilation QE runs on: Linux 32- and 64-bit PCs (all Intel and AMD CPUs) and PC clusters SGI Altix IBM SP and BlueGene machines, NEC SX, Cray XT machines, Mac OS X, MS-Windows PCs, several GPU-accelerated hardware (experts only)

27 Installation and compilation QE runs on: Linux 32- and 64-bit PCs (all Intel and AMD CPUs) and PC clusters SGI Altix IBM SP and BlueGene machines, NEC SX, Cray XT machines, Mac OS X, MS-Windows PCs, several GPU-accelerated hardware (experts only) For many standard machines!! cd espresso-5.1.0/!!./configure! make all Requires: C and fortran compilers! (MPI /OpenMP-aware libraries and parallel compiler) BLAS, LAPACK, FFTW If in trouble read the manual and browse the pw_forum

28 This workshop: PWscf & CP codes Successful installations generate the executables:! xxyyzz/espresso-5.1/bin/pw.x!! xxyyzz/espresso-5.1/bin/cp.x Running the PWscf code:! xxyyzz/espresso-5.1/bin/pw.x < pw.in > pw.out!! OR! xxyyzz/espresso-5.1/bin/pw.x -inp pw.in > pw.out

29 This workshop: PWscf & CP codes Successful installations generate the executables:! xxyyzz/espresso-5.1/bin/pw.x!! xxyyzz/espresso-5.1/bin/cp.x Running the PWscf code:! xxyyzz/espresso-5.1/bin/pw.x < pw.in > pw.out!! OR! xxyyzz/espresso-5.1/bin/pw.x -inp pw.in > pw.out INPUT FILE! Define structure of model system AND parameters of DFT calculation

30 Main steps of a xxx simulation Set-up simulation cell & initial conditions # of atoms, species, periodic cell, initial positions, etc. etc Set-up electronic-structure parameters YOU YOU Parameters validation QE + Production run hardware Analysis Post processing YOU + computer code +

31 Main steps of a xxx simulation HEY! TURN ME ON!!! Set-up simulation cell Setting & up the INPUT FILE must be initial conditions done with great YOU care # of atoms, species, periodic cell, initial positions, etc. etc Set-up electronic-structure parameters YOU Parameters validation QE + Production run hardware Analysis Post processing YOU + computer code +

32 Main steps of a xxx simulation HEY! TURN ME ON!!! Set-up simulation cell Setting & up the INPUT FILE must be initial conditions done with great YOU care # of atoms, species, periodic cell, initial positions, etc. etc Set-up electronic-structure parameters YOU RUBBISH IN Parameters validation QE + Production run hardware Analysis Post processing RUBBISH OUT YOU + computer code +

33 PWscf INPUT FILE &control!! calculation = 'scf',!! outdir=./tmp/,!! prefix = 'Si_exc1',! /! &system!! ibrav = 2, celldm(1) = 10.26,!! nat = 2, ntyp = 1,! ecutwfc = 20! /! &electrons!! mixing_beta = 0.7 /! ATOMIC_SPECIES Si Si.pbe-rrkj.UPF! ATOMIC_POSITIONS (alat)! Si Si ! K_POINTS (automatic)!

34 PWscf INPUT FILE &control!! calculation = 'scf',!! outdir=./tmp/,!! prefix = 'Si_exc1',! /! &system!! ibrav = 2, celldm(1) = 10.26,!! nat = 2, ntyp = 1,! ecutwfc = 20! /! &electrons!! mixing_beta = 0.7 /! ATOMIC_SPECIES Si Si.pbe-rrkj.UPF! ATOMIC_POSITIONS (alat)! Si Si ! K_POINTS (automatic)! YOU ARE IN CHARGE! Need to understand the meaning of ALL variables and parameters What if I do not know?

35 Documentation for input The complete list of input variables and their brief description can be found in the Doc directory!! ls xxyyzz/espresso-5.1/doc!! COUPLE!!! PW!!!!! flib!! CPV!!!! README!!! include!! Doc!!!! archive!!! install!! License!!! clib!!!! pseudo!! Makefile!! configure!! upftools!! Modules!!! dev-tools!! PP!

36 Documentation for input The complete list of input variables and their brief description can be found in the Doc directory!! ls xxyyzz/espresso-5.1/doc!! COUPLE!!! PW!!!!! flib!! CPV!!!! README!!! include!! Doc!!!! archive!!! install!! License!!! clib!!!! pseudo!! Makefile!! configure!! upftools!! Modules!!! dev-tools!! PP! ls xxyyzz/espresso-5.1/doc/*html! INPUT_BANDS.html!INPUT_Lanczos.html!INPUT_PWCOND.html! INPUT_CP.html!! INPUT_NEB.html!! INPUT_Spectrum.html! INPUT_CPPP.html! INPUT_PH.html!!! INPUT_bgw2pw.html! INPUT_D3.html!! INPUT_PP.html!!! INPUT_pw2bgw.html! INPUT_DOS.html! INPUT_PROJWFC.html!INPUT_pw_export.html! INPUT_LD1.html! INPUT_PW.html

37 Documentation for input The complete list of input variables and their brief description can be found in the Doc directory!! ls xxyyzz/espresso-5.1/doc!! COUPLE!!! PW!!!!! flib!! CPV!!!! README!!! include!! Doc!!!! archive!!! install!! License!!! clib!!!! pseudo!! Makefile!! configure!! upftools!! Modules!!! dev-tools!! PP! ls xxyyzz/espresso-5.1/doc/*html! INPUT_BANDS.html!INPUT_Lanczos.html!INPUT_PWCOND.html! INPUT_CP.html!! INPUT_NEB.html!! INPUT_Spectrum.html! INPUT_CPPP.html! INPUT_PH.html!!! INPUT_bgw2pw.html! INPUT_D3.html!! INPUT_PP.html!!! INPUT_pw2bgw.html! INPUT_DOS.html! INPUT_PROJWFC.html!INPUT_pw_export.html! INPUT_LD1.html! INPUT_PW.html

38 Setting up the input file Input file is structured in NAMELISTS and INPUT_CARDS &NAMELIST1... /!! &NAMELIST2... /!! &NAMELIST3... /!! INPUT_CARD1!...!...! INPUT_CARD2!......! Credit: P. Giannozzi NAMELISTS! Standard fortran 90input construct! Allow to specify the value of an input variable only when it is needed! Variables can be inserted in any order! NAMELISTS are read in specific order! A default value is assigned to variables that are not explicitly specified in the input file! NAMELISTS that are not required are ignored

39 Setting up the input file Input file is structured in NAMELISTS and INPUT_CARDS &NAMELIST1... /!! &NAMELIST2... /!! &NAMELIST3... /!! INPUT_CARD1!...!...! INPUT_CARD2!......! INPUT_CARDS! Specific of QE input! Provide input data that are ALWAYS needed! More practical way of specifying important variables! INPUT_DATA require data in specific order

40 Mandatory NAMELISTS &control!! calculation = 'scf',!! outdir=./tmp/,!! prefix = 'Si_exc1',! /! &system!! ibrav = 2, celldm(1) = 10.26,!! nat = 2, ntyp = 1,! ecutwfc = 20! /! &electrons!! mixing_beta = 0.7 /! ATOMIC_SPECIES Si Si.pbe-rrkj.UPF! ATOMIC_POSITIONS (alat)! Si Si ! K_POINTS (automatic)! &CONTROL input variables that control the flux of the calculation and the amount of I/O on disk and on the screen

41 Mandatory NAMELISTS &control!! calculation = 'scf',!! outdir=./tmp/,!! prefix = 'Si_exc1',! /! &system!! ibrav = 2, celldm(1) = 10.26,!! nat = 2, ntyp = 1,! ecutwfc = 20! /! &electrons!! mixing_beta = 0.7 /! ATOMIC_SPECIES Si Si.pbe-rrkj.UPF! ATOMIC_POSITIONS (alat)! Si Si ! K_POINTS (automatic)! &CONTROL input variables that control the flux of the calculation and the amount of I/O on disk and on the screen &SYSTEM input variables that specify the system under study

42 Mandatory NAMELISTS &control!! calculation = 'scf',!! outdir=./tmp/,!! prefix = 'Si_exc1',! /! &system!! ibrav = 2, celldm(1) = 10.26,!! nat = 2, ntyp = 1,! ecutwfc = 20! /! &electrons!! mixing_beta = 0.7 /! ATOMIC_SPECIES Si Si.pbe-rrkj.UPF! ATOMIC_POSITIONS (alat)! Si Si ! K_POINTS (automatic)! &CONTROL input variables that control the flux of the calculation and the amount of I/O on disk and on the screen &SYSTEM input variables that specify the system under study &ELECTRONS input variables that control the algorithms used to reach the self-consistent solution of KS equations for the electrons

43 Mandatory INPUT_CARDS &control!! calculation = 'scf',!! outdir=./tmp/,!! prefix = 'Si_exc1',! /! &system!! ibrav = 2, celldm(1) = 10.26,!! nat = 2, ntyp = 1,! ecutwfc = 20! /! &electrons!! mixing_beta = 0.7 /! ATOMIC_SPECIES Si Si.pbe-rrkj.UPF! ATOMIC_POSITIONS (alat)! Si Si ! K_POINTS (automatic)! ATOMIC_SPECIES name, mass and pseudopotential used for each atomic species present in the system

44 Mandatory INPUT_CARDS &control!! calculation = 'scf',!! outdir=./tmp/,!! prefix = 'Si_exc1',! /! &system!! ibrav = 2, celldm(1) = 10.26,!! nat = 2, ntyp = 1,! ecutwfc = 20! /! &electrons!! mixing_beta = 0.7 /! ATOMIC_SPECIES Si Si.pbe-rrkj.UPF! ATOMIC_POSITIONS (alat)! Si Si ! K_POINTS (automatic)! ATOMIC_SPECIES name, mass and pseudopotential used for each atomic species present in the system ATOMIC_POSITIONS type and coordinates of each atom in the unit cell

45 Mandatory INPUT_CARDS &control!! calculation = 'scf',!! outdir=./tmp/,!! prefix = 'Si_exc1',! /! &system!! ibrav = 2, celldm(1) = 10.26,!! nat = 2, ntyp = 1,! ecutwfc = 20! /! &electrons!! mixing_beta = 0.7 /! ATOMIC_SPECIES Si Si.pbe-rrkj.UPF! ATOMIC_POSITIONS (alat)! Si Si ! K_POINTS (automatic)! ATOMIC_SPECIES name, mass and pseudopotential used for each atomic species present in the system ATOMIC_POSITIONS type and coordinates of each atom in the unit cell K_POINTS coordinates and weights of the k-points used for BZ integration

46 Other INPUT_CARDS &control!! calculation = 'scf',!! outdir=./tmp/,!! prefix = 'Si_exc1',! /! &system!! ibrav = 2, celldm(1) = 10.26,!! nat = 2, ntyp = 1,! ecutwfc = 20! /! &electrons!! mixing_beta = 0.7! /! &ions! /! &cell! /! ATOMIC_SPECIES Si Si.pbe-rrkj.UPF! IONS needed when ATOMS MOVE! IGNORED otherwise! input variables that control ionic motion in molecular dynamics run or structural relaxation CELL needed when CELL MOVES! IGNORED otherwise! input variables that control the cellshape evolution in a variable-cell-shape MD or structural relaxation

47 Setting up an input file for bulk Si &control! /! &system! /! &electrons! /! ATOMIC_SPECIES ATOMIC_POSITIONS! K_POINTS

48 &control!! calculation = 'scf',!! outdir=./tmp/,!! prefix = 'Si_exc1',! /! &system! /! &electrons! /! ATOMIC_SPECIES ATOMIC_POSITIONS! K_POINTS &CONTROL

49 DFT Inner loop KS equations for electrons at fixed nuclei (T e + V ext + V H + V XC )! i(r; R) = i (R) i(r; R) Initial coordinates {R I } Set Vext Initial guess in(r) Calculate initial potential V eff = V ext + V H + V XC New density in(r) 1 2 Solve the KS equation 2 + V eff i = i i Calculate electron density out = i f i i 2 Credit: S. Narasimhan No Self-consistent? Yes Ground state density E tot ; V eff ; i; i

50 &SYSTEM &control!! calculation = 'scf',!! outdir=./tmp/,!! prefix = 'Si_exc1',! /! &system!! ibrav = 2, celldm(1) = 10.26,!! nat = 2, ntyp = 1,! ecutwfc = 20/! &electrons! /! ATOMIC_SPECIES ATOMIC_POSITIONS! K_POINTS Size and shape of computational cell!! Type and number of independent atoms!! Size of plane-wave basis set

51 &SYSTEM &control!! calculation = 'scf',!! outdir=./tmp/,!! prefix = 'Si_exc1',! /! &system!! ibrav = 2, celldm(1) = 10.26,!! nat = 2, ntyp = 1,! ecutwfc = 20/! &electrons! /! ATOMIC_SPECIES ATOMIC_POSITIONS! K_POINTS LATTICE Size and shape of computational cell!! Type and number of independent atoms! Size of plane-wave basis set BASIS +( =(

52 Set the Bravais lattice of unit cell

53 ! /! &system!! ibrav =??,! / Set the Bravais lattice of unit cell Bravais-lattice index NO default, MUST be specified! 0 read unit cell information from CELL_PARAMETRES card! 1!! cubic P (sc)! 2 cubic F (fcc)! 3 cubic I (bcc)! 4!! Hexagonal and Trigonal P! 5!! Trigonal R! 6 Tetragonal P (st)! 7 Tetragonal I (bct)! 8 Orthorhombic! P! 9 Orthorhombic base-centered(bco)! 10 Orthorhombic face-centered! 11 Orthorhombic body-centered! 12!! Monoclinic P! 13!! Monoclinic base-centered! 14!! Triclinic P

54 ! /! &system!! ibrav = 2,! / Set the Bravais lattice of unit cell Bravais-lattice index NO default, MUST be specified! 0 read unit cell information from CELL_PARAMETRES card! 1!! cubic P (sc)! Bulk Si: fcc 2 cubic F (fcc)! 3 cubic I (bcc)! 4!! Hexagonal and Trigonal P! 5!! Trigonal R! 6 Tetragonal P (st)! 7 Tetragonal I (bct)! 8 Orthorhombic! P! 9 Orthorhombic base-centered(bco)! 10 Orthorhombic face-centered! 11 Orthorhombic body-centered! 12!! Monoclinic P! 13!! Monoclinic base-centered! 14!! Triclinic P fcc:( v1(=((a/2)(&1,0,1),((v2(=((a/2)(0,1,1),((v3(=((a/2)(&1,1,0)(

55 ! Set the dimensions of unit cell /! &system!! ibrav = 2,!! celldm(1) = 10.26,! / fcc:( v1(=((a/2)(&1,0,1),((v2(=((a/2)(0,1,1),((v3(=((a/2)(&1,1,0)( Dimensions of unit cells can be set with the celldm() variables:! celldm(1) = a / bohr_radius_angs = alat! celldm(2) = b / a celldm(3) = c / a celldm(4) = cosab! celldm(5) = cosac! celldm(6) = cosbc internal unit of lenght (in Bohr)

56 ! Set the dimensions of unit cell /! &system!! ibrav = 2,!! celldm(1) = 10.26,! / fcc:( v1(=((a/2)(&1,0,1),((v2(=((a/2)(0,1,1),((v3(=((a/2)(&1,1,0)( Dimensions of unit cells can be set with the celldm() variables:! celldm(1) = a / bohr_radius_angs = alat! celldm(2) = b / a celldm(3) = c / a celldm(4) = cosab! celldm(5) = cosac! celldm(6) = cosbc internal unit of lenght (in Bohr)

57 Fill in the unit cell! /! &system!! ibrav = 2,!! celldm(1) = 10.26,!! nat = 2, ntyp = 1, / Number of atoms in the basis Number of species in the basis fcc:( +( =(

58 Fill in the unit cell! /! &system!! ibrav = 2,!! celldm(1) = 10.26,!! nat = 2, ntyp = 1, /!!! ATOMIC_SPECIES Si Si.pbe-rrkj.UPF!!! fcc:( Label, Mass, Pseudopotential if PP are not in./ then specify location in &system pseudo_dir= /where/my/pseudos/are

59 Database of pseudo potentials pseudopotentials/

60 Fill in the unit cell! /! &system!! ibrav = 2,!! celldm(1) = 10.26,!! nat = 2, ntyp = 1, /!!! ATOMIC_SPECIES Si Si.pbe-rrkj.UPF! ATOMIC_POSITIONS (alat)! Si Si fcc:( Position of each atom label_type, X, Y, Z alat (default), bohr, angstrom or crystal

61 DFT Inner loop KS equations for electrons at fixed nuclei (T e + V ext + V H + V XC )! i(r; R) = i (R) i(r; R) Initial coordinates {R I } Set Vext Initial guess in(r) Calculate initial potential V eff = V ext + V H + V XC New density in(r) 1 2 Solve the KS equation 2 + V eff i = i i Calculate electron density out = i f i i 2 Credit: S. Narasimhan No Self-consistent? Yes Ground state density E tot ; V eff ; i; i

62 DFT Inner loop KS equations for electrons at fixed nuclei (T e + V ext + V H + V XC )! i(r; R) = i (R) i(r; R) Initial coordinates {R I } Initial guess in(r) electron density Calculate initial potential V eff = V ext + V H + V XC New density in(r) 1 2 Solve the KS equation 2 + V eff i = i i Calculate electron density out = i f i i 2 Credit: S. Narasimhan No Self-consistent? Yes Ground state density E tot ; V eff ; i; i

63 Size of the plane-waves basis set! /! &system!! ibrav = 2,!! celldm(1) = 10.26,!! nat = 2, ntyp = 1,! ecutwfc = 20! /!!! ATOMIC_SPECIES Kinetic energy cut off for wave functions (in Ry) Si Si.pbe-rrkj.UPF! ATOMIC_POSITIONS (alat)! Si Si

64 Size of the plane-waves basis set Crystal wavefunctions are periodic in the direct space and can be expanded in a complete set of Fourier components i(r) = X k c i,k 1 p e ik r expansion coefficients orthonormal PW basis

65 Size of the plane-waves basis set Crystal wavefunctions are periodic in the direct space and can be expanded in a complete set of Fourier components i(r) = X k c i,k 1 p e ik r expansion coefficients orthonormal PW basis Bloch: Wavefunctions are PW modulated by a periodic function i(k, r) = e i(k) r u ik (r)

66 Size of the plane-waves basis set Crystal wavefunctions are periodic in the direct space and can be expanded in a complete set of Fourier components i(r) = X k c i,k 1 p e ik r expansion coefficients orthonormal PW basis Bloch: Wavefunctions are PW modulated by a periodic function i(k, r) = e i(k) r u ik (r) We have chosen to expand the periodic part in PWs i(k, r) = 1 V gm c ik (g m ) e i(k+g m ) r

67 Size of the plane-waves basis set Crystal wavefunctions are periodic in the direct space and can be expanded in a complete set of Fourier components i(r) = X k c i,k 1 p e ik r expansion coefficients orthonormal PW basis Bloch: Wavefunctions are PW modulated by a periodic function i(k, r) = e i(k) r Other choices are possible: localized basis set,... u ik (r) We have chosen to expand the periodic part in PWs i(k, r) = 1 V gm c ik (g m ) e i(k+g m ) r

68 Size of the plane-waves basis set Crystal wavefunctions are periodic in the direct space and can be expanded in a complete set of Fourier components i(r) = X k c i,k 1 p e ik r expansion coefficients orthonormal PW basis Bloch: Wavefunctions are PW modulated by a periodic function i(k, r) = e i(k) r k is discrete due to PBC u ik (r) We have chosen to expand the periodic part in PWs i(k, r) = 1 V gm c ik (g m ) e i(k+g m ) r

69 Size of the plane-waves basis set Any numerical representation of wf will require a finite basis set PW expansion has to be truncated i(k, r) = 1 V gm c ik (g m ) e i(k+g m ) r Small contribution from high Fourier components

70 Size of the plane-waves basis set Any numerical representation of wf will require a finite basis set PW expansion has to be truncated i(k, r) = 1 V gm c ik (g m ) e i(k+g m ) r Basis set is truncated at some value of k+g Criterium for cut off on kinetic energy of PWs 2 2m k + g m 2 E cut

71 Size of the plane-waves basis set Basis set is truncated at some value of k+g 2 2m k + g m 2 E cut What determines the value of Ecut? 1) Core electrons are localized 2) Valence electrons have nodes close to the nucleus An all-electron calculation would require high Ecut Value of Ecut depends on the pseudo potential

72 Size of the plane-waves basis set! /! &system!! ibrav = 2,!! celldm(1) = 10.26,!! nat = 2, ntyp = 1,! ecutwfc = 20! /!!! ATOMIC_SPECIES Kinetic energy cut off for wave functions (in Ry) Si Si.pbe-rrkj.UPF! ATOMIC_POSITIONS (alat)! Si Si

73 Size of the plane-waves basis set! /! &system!! ibrav = 2,!! celldm(1) = 10.26,!! nat = 2, ntyp = 1,! ecutwfc = 20!! ecutrho = 200! /!!! ATOMIC_SPECIES Si Si.pbe-rrkj.UPF! ATOMIC_POSITIONS (alat)! Si Si Required for ultrasoft pseudopotentials

74 DFT Inner loop KS equations for electrons at fixed nuclei (T e + V ext + V H + V XC )! i(r; R) = i (R) i(r; R) Initial coordinates {R I } Initial guess in(r) Calculate initial potential V eff = V ext + V H + V XC Set initial electron density New density in(r) 1 2 Solve the KS equation 2 + V eff i = i i Calculate electron density out = i f i i 2 Credit: S. Narasimhan No Self-consistent? Yes Ground state density E tot ; V eff ; i; i

75 Set the initial electron density! /! &system!! ibrav = 2,!! celldm(1) = 10.26,!! nat = 2, ntyp = 1,! ecutwfc = 20! /! &electrons!! starting_wfc= atomic! /! ATOMIC_SPECIES Si Si.pbe-rrkj.UPF! ATOMIC_POSITIONS (alat)! Si Si Set initial electron density

76 Set the initial electron density! /! &system!! ibrav = 2,!! celldm(1) = 10.26,!! nat = 2, ntyp = 1,! ecutwfc = 20! /! &electrons!! starting_wfc= atomic! /! ATOMIC_SPECIES Si Si.pbe-rrkj.UPF! ATOMIC_POSITIONS (alat)! Si Si Set initial electron density

77 DFT Inner loop KS equations for electrons at fixed nuclei (T e + V ext + V H + V XC )! i(r; R) = i (R) i(r; R) Initial coordinates {R I } Initial guess in(r) Calculate initial potential V eff = V ext + V H + V XC Expand Veff on PW basis New density in(r) 1 2 Solve the KS equation 2 + V eff i = i i Calculate electron density out = i f i i 2 Credit: S. Narasimhan No Self-consistent? Yes Ground state density E tot ; V eff ; i; i

78 Matrix equation Ĥ e i =[ 2 2m 2 + V e (r)] i = i i k + g m Hˆ e k + g m = 2 2m k + g m 2 mm + V e (g m g m ) S. eq for a periodic effective potential reduces to the matrix equation m H mm (k) c im (k) = i (k) c im (k)

79 DFT Inner loop KS equations for electrons at fixed nuclei (T e + V ext + V H + V XC )! i(r; R) = i (R) i(r; R) Initial coordinates {R I } Initial guess in(r) Calculate initial potential V eff = V ext + V H + V XC New density in(r) 1 2 Solve the KS equation 2 + V eff i = i i Which XC functional? Calculate electron density out = i f i i 2 Credit: S. Narasimhan No Self-consistent? Yes Ground state density E tot ; V eff ; i; i

80 Set the XC functional! /! &system!! ibrav = 2,!! celldm(1) = 10.26,!! nat = 2, ntyp = 1,! ecutwfc = 20! /! &electrons!! starting_wfc= atomic! /! ATOMIC_SPECIES Si Si.pbe-rrkj.UPF! ATOMIC_POSITIONS (alat)! Si Si DEFAULT: XC functional read in PP file

81 XC functional set in PP file <PP_INFO>( Generated(using(Andrea(Dal(Corso(code((rrkj3)( Author:(Andrea(Dal(Corso(((Genera6on(date:(unknown( Info:(((Si(PBE(3s2(3p2(RRKJ3( ((((0((((((((The(Pseudo(was(generated(with(a(Non&Rela6vis6c(Calcula6on( (( E+00((((Local(Poten6al(cutoff(radius( nl(pn((l(((occ(((((((((((((((rcut((((((((((((rcut(us(((((((((((((e(pseu( 3S((1((0((2.00(((((( (((((( (((((( ( 3S((1((0((0.00(((((( (((((( (((((( ( 3P((2((1((2.00(((((( (((((( (((((( ( 3D((3((2((0.00(((((( (((((( (((((( ( </PP_INFO>( <PP_HEADER>( (((0(((((((((((((((((((Version(Number( ((Si(((((((((((((((((((Element( (((NC((((((((((((((((((Norm(&(Conserving(pseudopoten6al( ((((F((((((((((((((((((Nonlinear(Core(Correc6on( (SLA((PW(((PBE((PBE((((PBE((Exchange&Correla6on(func6onal( (((( ((((((Z(valence( (((& ((((((Total(energy( (( (( (Suggested(cutoff(for(wfc(and(rho( ((((2((((((((((((((((((Max(angular(momentum(component( ((883((((((((((((((((((Number(of(points(in(mesh( ((((2((((3(((((((((((((Number(of(Wavefunc6ons,(Number(of(Projectors( (Wavefunc6ons(((((((((nl((l(((occ( (((((((((((((((((((((((3S((0((2.00( (((((((((((((((((((((((3P((1((2.00( </PP_HEADER>( <PP_MESH>( ((<PP_R>( (( E&04(( E&04(( E&04(( E&04( (( E&04(( E&04(( E&04(( E&04( (( E&04(( E&04(( E&04(( E&04( (( E&04(( E&04(( E&04(( E&04( (( E&04(( E&04(( E&04(( E&04( (( E&04(( E&04(( E&04(( E&04( (

82 Set the initial electron density! /! &system!! ibrav = 2,!! celldm(1) = 10.26,!! nat = 2, ntyp = 1,! ecutwfc = 20!! input_dft = pbe! /! &electrons!! starting_wfc= atomic! /! ATOMIC_SPECIES Si Si.pbe-rrkj.UPF! ATOMIC_POSITIONS (alat)! Si Si DEFAULT: XC functional read in PP file

83 DFT Inner loop KS equations for electrons at fixed nuclei (T e + V ext + V H + V XC )! i(r; R) = i (R) i(r; R) Initial coordinates {R I } Initial guess in(r) Calculate initial potential V eff = V ext + V H + V XC New density in(r) 1 2 Solve the KS equation 2 + V eff i = i i Calculate electron density out = i f i i 2 m Diagonalize eigenvalue problem H mm (k) c im (k) = i (k) c im (k) Credit: S. Narasimhan No Self-consistent? Yes Ground state density E tot ; V eff ; i; i

84 Diagonalize eigenvalue problem! /! &system!! ibrav = 2,!! celldm(1) = 10.26,!! nat = 2, ntyp = 1,! ecutwfc = 20! /! &electrons!! starting_wfc= atomic!! diagonalization = davidson! /! ATOMIC_SPECIES Si Si.pbe-rrkj.UPF! ATOMIC_POSITIONS (alat)! Si Si DEFAULT: Davidson diagonalization algorithm

85 Diagonalize eigenvalue problem! /! &system!! ibrav = 2,!! celldm(1) = 10.26,!! nat = 2, ntyp = 1,! ecutwfc = 20! /! &electrons!! starting_wfc= atomic!! diagonalization = davidson! /! ATOMIC_SPECIES Si Si.pbe-rrkj.UPF! ATOMIC_POSITIONS (alat)! Si Si DEFAULT: Davidson diagonalization algorithm

86 DFT Inner loop KS equations for electrons at fixed nuclei (T e + V ext + V H + V XC )! i(r; R) = i (R) i(r; R) Initial coordinates {R I } Initial guess in(r) Calculate initial potential V eff = V ext + V H + V XC New density in(r) 1 2 Solve the KS equation 2 + V eff i = i i Calculate electron density out = i f i i 2 Calculate averages in BZ Credit: S. Narasimhan No Self-consistent? Yes Ground state density E tot ; V eff ; i; i

87 Integrals in BZ Intrinsic properties of crystals are averages over k in the first BZ Ex: charge density (r) = 1 N k ik i (k, r) 2 f( i, k) Averages are calculated numerically as integrals in BZ W = 1 N k k W (k) (2 ) 3 IBZ W (k) dk Requires sampling W on a grid of k points

88 Setting the integrating k-point mesh! /! &system!! ibrav = 2,!! celldm(1) = 10.26,!! nat = 2, ntyp = 1,! ecutwfc = 20! /! &electrons!! starting_wfc= atomic! /! ATOMIC_SPECIES Si Si.pbe-rrkj.UPF! ATOMIC_POSITIONS (alat)! Si Si ! K_POINTS (automatic)! b 2( k ½( 1( k 2( k 3( 0( Set the type of grid IBZ( BZ( automatically generated, read in k-point coordinates, ½( Set the density of the grid b 1(

89 DFT Inner loop KS equations for electrons at fixed nuclei (T e + V ext + V H + V XC )! i(r; R) = i (R) i(r; R) Initial coordinates {R I } Initial guess in(r) Calculate initial potential V eff = V ext + V H + V XC New density in(r) 1 2 Solve the KS equation 2 + V eff i = i i Calculate electron density out = i f i i 2 Credit: S. Narasimhan No Self-consistent? Yes Iterative Ground state solution: density new density E tot ; V eff ; i; i

90 ! /! &system!! ibrav = 2,!! celldm(1) = 10.26,!! nat = 2, ntyp = 1,! ecutwfc = 20! /! &electrons!! mixing_beta = 0.7! /! ATOMIC_SPECIES Si Si.pbe-rrkj.UPF! ATOMIC_POSITIONS (alat)! Si Si ! K_POINTS (automatic)! Mixing densities Mix new and old densities 0.7 = 70% of new density and 30% of old density

91 DFT Inner loop KS equations for electrons at fixed nuclei (T e + V ext + V H + V XC )! i(r; R) = i (R) i(r; R) Initial coordinates {R I } Initial guess in(r) Calculate initial potential V eff = V ext + V H + V XC New density in(r) 1 2 Solve the KS equation 2 + V eff i = i i Calculate electron density out = i f i i 2 Convergency! Credit: S. Narasimhan No Self-consistent? Yes Ground state density E tot ; V eff ; i; i

92 Threshold for self-consistency! /! &system!! ibrav = 2,!! celldm(1) = 10.26,!! nat = 2, ntyp = 1,! ecutwfc = 20! /! &electrons!! mixing_beta = 0.7!! convergence_thr=1.d-6! /! ATOMIC_SPECIES Si Si.pbe-rrkj.UPF! ATOMIC_POSITIONS (alat)! Si Si ! K_POINTS (automatic)! DEFAULT: estimated error < 1.0D-6

93 Running the calculation Running the PWscf code:! xxyyzz/espresso-5.1.0/bin/pw.x < si.scf.in > si.scf.out!

94 The Output file stefano> more si.scf.out!! Program PWSCF v.4.1a starts...! Today is 10Jul2009 at 21:27:20!! Parallel version (MPI)!! Number of processors in use: 1!! For Norm-Conserving or Ultrasoft (Vanderbilt) Pseudopotentials or PAW!! Current dimensions of program pwscf are:! Max number of different atomic species (ntypx) = 10! Max number of k-points (npk) = 40000! Max angular momentum in pseudopotentials (lmaxx) = 3! Waiting for input!! Planes per process (thick) : nr3 = 20 npp = 20 ncplane = 400!! Proc/ planes cols G planes cols G columns G! Pool (dense grid) (smooth grid) (wavefct grid)!

95 The Output file! bravais-lattice index = 2! lattice parameter (a_0) = a.u.! unit-cell volume = (a.u.)^3! number of atoms/cell = 2! number of atomic types = 1! number of electrons = 8.00! number of Kohn-Sham states= 4! kinetic-energy cutoff = Ry! charge density cutoff = Ry! convergence threshold = 1.0E-08! mixing beta = ! number of iterations used = 8 plain mixing! Exchange-correlation = SLA PZ NOGX NOGC (1100)!

96 !!!! celldm(1)= celldm(2)= celldm(3)= ! celldm(4)= celldm(5)= celldm(6)= ! crystal axes: (cart. coord. in units of a_0)! a(1) = ( )! a(2) = ( )! a(3) = ( )! reciprocal axes: (cart. coord. in units 2 pi/a_0)! b(1) = ( )! b(2) = ( )! b(3) = ( )! PseudoPot. # 1 for Si read from file Si.pz-vbc.UPF! Pseudo is Norm-conserving, Zval = 4.0! Generated by new atomic code, or converted to UPF format! Using radial grid of 431 points, 2 beta functions with:! l(1) = 0! l(2) = 1! atomic species valence mass pseudopotential! Si Si( 1.00)!

97 !!!! 48 Sym.Ops. (with inversion)! Cartesian axes! site n. atom positions (a_0 units)! 1 Si tau( 1) = ( )! 2 Si tau( 2) = ( )! number of k points= 10! cart. coord. in units 2pi/a_0! k( 1) = ( ), wk = ! k( 2) = ( ), wk = ! k( 3) = ( ), wk = ! k( 4) = ( ), wk = ! k( 5) = ( ), wk = ! k( 6) = ( ), wk = ! k( 7) = ( ), wk = ! k( 8) = ( ), wk = ! k( 9) = ( ), wk = ! k( 10) = ( ), wk = ! G cutoff = ( 2733 G-vectors) FFT grid: ( 20, 20, 20)

98 !! Largest allocated arrays est. size (Mb) dimensions! Kohn-Sham Wavefunctions 0.02 Mb ( 350, 4)! NL pseudopotentials 0.04 Mb ( 350, 8)! Each V/rho on FFT grid 0.12 Mb ( 8000)! Each G-vector array 0.02 Mb ( 2733)! G-vector shells 0.00 Mb ( 65)! Largest temporary arrays est. size (Mb) dimensions! Auxiliary wavefunctions 0.09 Mb ( 350, 16)! Each subspace H/S matrix 0.00 Mb ( 16, 16)! Each <psi_i beta_j> matrix 0.00 Mb ( 8, 4)! Arrays for rho mixing 0.98 Mb ( 8000, 8)! Initial potential from superposition of free atoms! starting charge , renormalised to ! Starting wfc are 8 atomic wfcs!

99 total cpu time spent up to now is 0.12 secs! per-process dynamical memory: Self-consistent Calculation! 8.1 Mb! iteration # 1 ecut= Ry beta=0.70! Davidson diagonalization with overlap! ethr = 1.00E-02, avg # of iterations = 2.0! Threshold (ethr) on eigenvalues was too large:! Diagonalizing with lowered threshold! Davidson diagonalization with overlap! ethr = 7.75E-04, avg # of iterations = 1.0! total cpu time spent up to now is 0.30 secs! total energy = Ry! Harris-Foulkes estimate = Ry! estimated scf accuracy < Ry! iteration # 2 ecut= Ry beta=0.70! Davidson diagonalization with overlap! ethr = 7.68E-04, avg # of iterations = 1.0! total cpu time spent up to now is 0.37 secs! total energy = Ry! Harris-Foulkes estimate = Ry! estimated scf accuracy < Ry

100 iteration # 4 ecut= Ry beta=0.70! Davidson diagonalization with overlap! ethr = 8.86E-07, avg # of iterations = 2.1! total cpu time spent up to now is 0.57 secs! total energy = Ry! Harris-Foulkes estimate = Ry! estimated scf accuracy < Ry! iteration # 5 ecut= Ry beta=0.70! Davidson diagonalization with overlap! ethr = 8.52E-08, avg # of iterations = 2.0! total cpu time spent up to now is 0.67 secs!! total energy = Ry! Harris-Foulkes estimate = Ry! estimated scf accuracy < Ry! iteration # 6 ecut= Ry beta=0.70! Davidson diagonalization with overlap! ethr = 7.18E-10, avg # of iterations = 2.7! total cpu time spent up to now is 0.78 secs! End of self-consistent calculation!

101 k = ( 335 PWs) bands (ev):! !! k = ( 343 PWs) bands (ev):! ! total energy = Ry! Harris-Foulkes estimate = Ry! estimated scf accuracy < 8.8E-10 Ry! The total energy is the sum of the following terms:! one-electron contribution = Ry! hartree contribution = Ry! xc contribution = Ry! ewald contribution = Ry! convergence has been achieved in 6 iterations

102

103 How to cite QE Do acknowledge the QE project in your scientific research IOP PUBLISHING JOURNAL OF PHYSICS: CONDENSED MATTER J. Phys.: Condens. Matter 21 (2009) (19pp) doi: / /21/39/ QUANTUM ESPRESSO: a modular and open-source software project for quantum simulations of materials Paolo Giannozzi 1,2,StefanoBaroni 1,3,NicolaBonini 4, Matteo Calandra 5,RobertoCar 6,CarloCavazzoni 7,8, Davide Ceresoli 4,GuidoLChiarotti 9,MatteoCococcioni 10, Ismaila Dabo 11,AndreaDalCorso 1,3,StefanodeGironcoli 1,3, Stefano Fabris 1,3,GuidoFratesi 12,RalphGebauer 1,13, Uwe Gerstmann 14,ChristosGougoussis 5,AntonKokalj 1,15, Michele Lazzeri 5,LaylaMartin-Samos 1,NicolaMarzari 4, Francesco Mauri 5,RiccardoMazzarello 16,StefanoPaolini 3,9, Alfredo Pasquarello 17,18,LorenzoPaulatto 1,3,CarloSbraccia 1,, Sandro Scandolo 1,13,GabrieleSclauzero 1,3,AriPSeitsonen 5, Alexander Smogunov 13,PaoloUmari 1 and Renata M Wentzcovitch 10,19 P. Giannozzi et al., J. Phys.:Condens. Matter 21, (2009)

104 The QE foundation Coordinate and support research within the QE developer community

105 The QE prize QUANTUM ESPRESSO prize for quantum mechanical materials modeling The prize is to be awarded every year to the best PhD thesis completed in the previous year in the field of quantum mechanical materials modeling, and realized with the help of the QUANTUM ESPRESSO suite of computer codes! The prize consists of a diploma and a check of one thousand euros! Excellence will be rewarded for both original applications and methodological innovation

106 School on computational materials modeling in catalysis Bangalore, 1-5 September 2014 Introduction to the QUANTUM ESPRESSO package and its application to computational catalysis Input/Output description Stefano Fabris CNR-IOM DEMOCRITOS Simulation Center SISSA - Scuola Internazionale Superiore di Studi Avanzati - Trieste - ITALY