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Tutorial: Basics of electronic structure theory Introduction Ralf Gehrke and Alexandre Tkatchenko Fritz-Haber-Institut der Max-Planck-Gesellschaft Berlin, 23 th June 2009 Hands-on Tutorial on Ab Initio Molecular Simulations: Toward a First-Principles Understanding of Materials Properties and Functions Goal of this tutorial binding energy d [Å] bond distances vibrational spectra 2.85 Å 2.19 Å 2.19 Å Si 3 PBE-GGA N 2 d 0 = ? N 2
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Tutorial: Basics of electronic structure theory Introductionth.fhi-berlin.mpg.de/th/Meetings/.../0623...introduction_basics_v2.pdf · Tutorial: Basics of electronic structure theory

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Page 1: Tutorial: Basics of electronic structure theory Introductionth.fhi-berlin.mpg.de/th/Meetings/.../0623...introduction_basics_v2.pdf · Tutorial: Basics of electronic structure theory

Tutorial: Basics of electronic structure theoryIntroduction

Ralf Gehrke and Alexandre Tkatchenko

Fritz-Haber-Institut der Max-Planck-GesellschaftBerlin, 23th June 2009

Hands-on Tutorial on Ab Initio Molecular Simulations:Toward a First-Principles Understanding of Materials Properties and Functions

Goal of this tutorial� binding energy

d [Å]� bond distances

� vibrational spectra 2.85 Å

2.19 Å2.19 Å

Si3 PBE-GGA

N2

d0 = ?N2

Page 2: Tutorial: Basics of electronic structure theory Introductionth.fhi-berlin.mpg.de/th/Meetings/.../0623...introduction_basics_v2.pdf · Tutorial: Basics of electronic structure theory

Goal of this tutorial� structure prediction X(+)Si3 X=Sc, Ti, V, Cr

mpirun -np 2 aims.workshop.mpi.x | tee calculation.out

� two input files are required in the working directory (units: eV, Å):control.ingeometry.in

� FHI-aims is simply called and main output is written to STDOUT

� further output files are generated if requiredcharge density plotsdensity of states

� for each exercise, a separate directory should be created— mkdir tutorial1� cd tutorial1� mkdir N2

vi, emacs,...

General aspects

Page 3: Tutorial: Basics of electronic structure theory Introductionth.fhi-berlin.mpg.de/th/Meetings/.../0623...introduction_basics_v2.pdf · Tutorial: Basics of electronic structure theory

General aspects� directory with reference files, e.g. /usr/local/aimsfiles/tutorial1/N2

geometry.in.N2.ref control.in.pw-lda.coarse.refN.pbe.out.ref control.in.basic

� the aims-binary as well as several tools are in the binary pathmoldenvmdjmolgdis

� additional auxiliary scripts needed for this tutorial can be found in

/usr/local/aimsfiles/scripts

visualization

xmgrace gnuplot emacs vi kwrite

editor

plotting tools

� FHI-aims manual can be found on your desktop for reference

The geometry.in file

The input files

atom 0.0 0.0 0.0 Natom 1.1 0.0 0.0 N

Geometry specification� Atoms� Periodic boundary conditions� Initialization of charge/spin density

Simplest example (N2): More complex case (Cu fcc):atom 0.0 0.0 0.0 Culattice_vector 1.8 1.8 0.0lattice_vector 0.0 1.8 1.8lattice_vector 1.8 0.0 1.8

Page 4: Tutorial: Basics of electronic structure theory Introductionth.fhi-berlin.mpg.de/th/Meetings/.../0623...introduction_basics_v2.pdf · Tutorial: Basics of electronic structure theory

The control.in fileTwo sections:

� General section (method, spin, etc.)� Species specification (basis set, etc.)

Example:xc pw-ldaspin collinearmultiplicity 1relativistic nonecharge 0empty_states 5#occupation_type gaussian 0.001mixer pulay n_max_pulay 10 charge_mix_param 0.2

species N

The input files

The control.in fileTwo sections:

� General section (method, spin, etc.)� Species specification (basis set, etc.)

Example:

nin���1 ��n in

opt� R n inopt �

ninopt��

�max

�n in�� �

f � ��E F� ��1

2 �1�erf ��EF� ��

xc pw-ldaspin collinearmultiplicity 1relativistic nonecharge 0empty_states 5#occupation_type gaussian 0.001mixer pulay n_max_pulay 10 charge_mix_param 0.2

species N

see manual, chapter 2.3

The input files

Page 5: Tutorial: Basics of electronic structure theory Introductionth.fhi-berlin.mpg.de/th/Meetings/.../0623...introduction_basics_v2.pdf · Tutorial: Basics of electronic structure theory

The species defaults

� “light” : fast prerelaxations should always be followed by a tightly converged post-

processing calculation

� “tight” : tightly converged settings, the basis set might still need to be increased for light elements, though

/usr/local/aimsfiles/species_defaults/light

/usr/local/aimsfiles/species_defaults/tight

to be pasted into the control.in file

The input files

The main output The FHI-aims output

------------------------------------------------------------ Invoking FHI-aims ... Version 020109 Compiled on 2009/02/03 at 16:00:22

When using FHI-aims, please cite the following reference:

Volker Blum, Ralf Gehrke, Felix Hanke, Paula Havu, Ville Havu, Xinguo Ren, Karsten Reuter, and Matthias Scheffler, 'Ab Initio Molecular Simulations with Numeric Atom-Centered Orbitals: FHI-aims', Computer Physics Communications [volume], [page] (2008).

------------------------------------------------------------

Date : 20090608, Time : 145624.551 Time zero on CPU 1 : 0.199900000000000E-02 s. Internal wall clock time zero : 13704984.551 s.

Obtaining array dimensions for all initial allocations: Parsing control.in ... Parsing geometry.in ... Basic array size parameters: | Number of species : 1 | Number of atoms : 2 | Max. basis fn. angular momentum : 2 | Max. atomic/ionic basis occupied n: 2 | Max. number of basis fn. types : 2 | Max. radial fns per species/type : 3 | Max. logarithmic grid size : 1290 | Max. radial integration grid size : 71 | Max. angular integration grid size: 302 | Max. angular grid division number : 8 | Radial grid for Hartree potential : 1290 | Number of spin channels : 2

------------------------------------------------------------ Reading file control.in.------------------------------------------------------------

Page 6: Tutorial: Basics of electronic structure theory Introductionth.fhi-berlin.mpg.de/th/Meetings/.../0623...introduction_basics_v2.pdf · Tutorial: Basics of electronic structure theory

The main output The FHI-aims output

------------------------------------------------------------ Invoking FHI-aims ... Version 020109 Compiled on 2009/02/03 at 16:00:22

When using FHI-aims, please cite the following reference:

Volker Blum, Ralf Gehrke, Felix Hanke, Paula Havu, Ville Havu, Xinguo Ren, Karsten Reuter, and Matthias Scheffler, 'Ab Initio Molecular Simulations with Numeric Atom-Centered Orbitals: FHI-aims', Computer Physics Communications [volume], [page] (2008).

------------------------------------------------------------

Date : 20090608, Time : 145624.551 Time zero on CPU 1 : 0.199900000000000E-02 s. Internal wall clock time zero : 13704984.551 s.

Obtaining array dimensions for all initial allocations: Parsing control.in ... Parsing geometry.in ... Basic array size parameters: | Number of species : 1 | Number of atoms : 2 | Max. basis fn. angular momentum : 2 | Max. atomic/ionic basis occupied n: 2 | Max. number of basis fn. types : 2 | Max. radial fns per species/type : 3 | Max. logarithmic grid size : 1290 | Max. radial integration grid size : 71 | Max. angular integration grid size: 302 | Max. angular grid division number : 8 | Radial grid for Hartree potential : 1290 | Number of spin channels : 2

------------------------------------------------------------ Reading file control.in.------------------------------------------------------------

introduction

internal parameters

Invoking FHI-aims ...

------------------------------------------------------------ Reading file control.in.------------------------------------------------------------ XC: Using PBE gradient-corrected functionals. Spin treatment: Spin density functional theory - collinear spins. Non-relativistic treatment of kinetic energy. Occupation type: Gaussian broadening, width = 0.100000E-01 eV. Using pulay charge density mixing. Pulay mixing - number of memorized iterations: 10 Charge density mixing - mixing parameter: 0.5000 Convergence accuracy of self-consistent charge density: 0.1000E-04 Convergence accuracy of sum of eigenvalues: 0.1000E-02 Convergence accuracy of total energy: 0.1000E-05 Convergence accuracy of forces: 0.1000E-03 Maximum number of s.-c. iterations : 100 Kohn-Sham eigenvalues and eigenfunctions calculated by lapack diagonalisation. Number of empty states per atom: 5 Geometry relaxation: BFGS (simple quadratic extrapolation). Convergence accuracy for geometry relaxation: Maximum force < 0.100000E-01 eV/A. Reading configuration options for species N . | Found nuclear charge : 7

The main output The FHI-aims output

------------------------------------------------------------ Reading geometry description geometry.in.------------------------------------------------------------ Input structure read successfully. The structure contains 2 atoms, and a total of 14.000 electrons. Input geometry: | No unit cell requested. | Atomic structure: | Atom x [A] y [A] z [A] | 1: Species N 0.000000 0.000000 0.000000 | 2: Species N 0.000000 0.000000 1.100000 Initial moments and charges: | Atom Moment Charge Species | 1 (Hund's rule) 0.000000E+00 N | 2 (Hund's rule) 0.000000E+00 N Structure-dependent array size parameters: | Number of distinct atom types in initial rho : 1 | Maximum number of distinct radial functions : 6 | Maximum number of basis functions : 28 | Number of Kohn-Sham states (occupied + empty): 12------------------------------------------------------------

Page 7: Tutorial: Basics of electronic structure theory Introductionth.fhi-berlin.mpg.de/th/Meetings/.../0623...introduction_basics_v2.pdf · Tutorial: Basics of electronic structure theory

------------------------------------------------------------ Reading file control.in.------------------------------------------------------------ XC: Using PBE gradient-corrected functionals. Spin treatment: Spin density functional theory - collinear spins. Non-relativistic treatment of kinetic energy. Occupation type: Gaussian broadening, width = 0.100000E-01 eV. Using pulay charge density mixing. Pulay mixing - number of memorized iterations: 10 Charge density mixing - mixing parameter: 0.5000 Convergence accuracy of self-consistent charge density: 0.1000E-04 Convergence accuracy of sum of eigenvalues: 0.1000E-02 Convergence accuracy of total energy: 0.1000E-05 Convergence accuracy of forces: 0.1000E-03 Maximum number of s.-c. iterations : 100 Kohn-Sham eigenvalues and eigenfunctions calculated by lapack diagonalisation. Number of empty states per atom: 5 Geometry relaxation: BFGS (simple quadratic extrapolation). Convergence accuracy for geometry relaxation: Maximum force < 0.100000E-01 eV/A. Reading configuration options for species N . | Found nuclear charge : 7

The main output The FHI-aims output

------------------------------------------------------------ Reading geometry description geometry.in.------------------------------------------------------------ Input structure read successfully. The structure contains 2 atoms, and a total of 14.000 electrons. Input geometry: | No unit cell requested. | Atomic structure: | Atom x [A] y [A] z [A] | 1: Species N 0.000000 0.000000 0.000000 | 2: Species N 0.000000 0.000000 1.100000 Initial moments and charges: | Atom Moment Charge Species | 1 (Hund's rule) 0.000000E+00 N | 2 (Hund's rule) 0.000000E+00 N Structure-dependent array size parameters: | Number of distinct atom types in initial rho : 1 | Maximum number of distinct radial functions : 6 | Maximum number of basis functions : 28 | Number of Kohn-Sham states (occupied + empty): 12------------------------------------------------------------

summary of control.in fileReading file control.in.

------------------------------------------------------------ Reading file control.in.------------------------------------------------------------ XC: Using PBE gradient-corrected functionals. Spin treatment: Spin density functional theory - collinear spins. Non-relativistic treatment of kinetic energy. Occupation type: Gaussian broadening, width = 0.100000E-01 eV. Using pulay charge density mixing. Pulay mixing - number of memorized iterations: 10 Charge density mixing - mixing parameter: 0.5000 Convergence accuracy of self-consistent charge density: 0.1000E-04 Convergence accuracy of sum of eigenvalues: 0.1000E-02 Convergence accuracy of total energy: 0.1000E-05 Convergence accuracy of forces: 0.1000E-03 Maximum number of s.-c. iterations : 100 Kohn-Sham eigenvalues and eigenfunctions calculated by lapack diagonalisation. Number of empty states per atom: 5 Geometry relaxation: BFGS (simple quadratic extrapolation). Convergence accuracy for geometry relaxation: Maximum force < 0.100000E-01 eV/A. Reading configuration options for species N . | Found nuclear charge : 7

The main output The FHI-aims output

------------------------------------------------------------ Reading geometry description geometry.in.------------------------------------------------------------ Input structure read successfully. The structure contains 2 atoms, and a total of 14.000 electrons. Input geometry: | No unit cell requested. | Atomic structure: | Atom x [A] y [A] z [A] | 1: Species N 0.000000 0.000000 0.000000 | 2: Species N 0.000000 0.000000 1.100000 Initial moments and charges: | Atom Moment Charge Species | 1 (Hund's rule) 0.000000E+00 N | 2 (Hund's rule) 0.000000E+00 N Structure-dependent array size parameters: | Number of distinct atom types in initial rho : 1 | Maximum number of distinct radial functions : 6 | Maximum number of basis functions : 28 | Number of Kohn-Sham states (occupied + empty): 12------------------------------------------------------------

summary of control.in file

summary of geometry.in fileReading geometry description geometry.in.

Page 8: Tutorial: Basics of electronic structure theory Introductionth.fhi-berlin.mpg.de/th/Meetings/.../0623...introduction_basics_v2.pdf · Tutorial: Basics of electronic structure theory

The main output The FHI-aims output

------------------------------------------------------------ Begin self-consistency loop: Initialization.

Date : 20090608, Time : 145624.781------------------------------------------------------------

Initializing index lists of integration centers etc. from given atomic structure: | Number of centers in hamiltonian partition_tab : 2 | Number of centers in hartree potential : 2 | Number of centers in hartree multipole : 2 | Number of centers in electron density summation: 2 | Number of centers in basis integrals : 2 | Number of centers in integrals : 2 Partitioning the integration grid into batches with maxmin method. | Maximal weight for a single point: 1.000 | Minimal weight for a single point: 0.000 | Number of batches: 499 | Maximal batch size: 141 | Minimal batch size: 50 | Average batch size: 63.431 | Standard deviation of batch sizes: 10.671 Initializing partition tables, free-atom densities, potentials, etc. across the integration grid (initialize_grid_storage). | Net number of integration points: 31652 | of which are non-zero points : 29382 Obtaining max. number of non-zero basis functions in each batch (get_n_compute_maxes). | Maximal number of non-zero basis functions: 28 in task 0

------------------------------------------------------------ Preparing all fixed parts of the calculation.------------------------------------------------------------ Determining machine precision: 2.225073858507201E-308 Setting up grids for atomic and cluster calculations.

Creating wave function, potential, and density for free atoms.

Species: N

List of occupied orbitals and eigenvalues: n l energy [Ha] energy [eV] 1 0 -14.128445 -384.4546 2 0 -0.681395 -18.5417 2 1 -0.260121 -7.0782

Spin-polarized or charged system: Charge density initialized according to selected moments and charges.

------------------------------------------------------------ Preparing all fixed parts of the calculation.------------------------------------------------------------ Determining machine precision: 2.225073858507201E-308 Setting up grids for atomic and cluster calculations.

Creating wave function, potential, and density for free atoms.

Species: N

List of occupied orbitals and eigenvalues: n l energy [Ha] energy [eV] 1 0 -14.128445 -384.4546 2 0 -0.681395 -18.5417 2 1 -0.260121 -7.0782

Spin-polarized or charged system: Charge density initialized according to selected moments and charges.

The main output The FHI-aims output

------------------------------------------------------------ Begin self-consistency loop: Initialization.

Date : 20090608, Time : 145624.781------------------------------------------------------------

Initializing index lists of integration centers etc. from given atomic structure: | Number of centers in hamiltonian partition_tab : 2 | Number of centers in hartree potential : 2 | Number of centers in hartree multipole : 2 | Number of centers in electron density summation: 2 | Number of centers in basis integrals : 2 | Number of centers in integrals : 2 Partitioning the integration grid into batches with maxmin method. | Maximal weight for a single point: 1.000 | Minimal weight for a single point: 0.000 | Number of batches: 499 | Maximal batch size: 141 | Minimal batch size: 50 | Average batch size: 63.431 | Standard deviation of batch sizes: 10.671 Initializing partition tables, free-atom densities, potentials, etc. across the integration grid (initialize_grid_storage). | Net number of integration points: 31652 | of which are non-zero points : 29382 Obtaining max. number of non-zero basis functions in each batch (get_n_compute_maxes). | Maximal number of non-zero basis functions: 28 in task 0

Preparing all fixed parts of the calculation.

geometry-independent preparationsbasis set generation

Page 9: Tutorial: Basics of electronic structure theory Introductionth.fhi-berlin.mpg.de/th/Meetings/.../0623...introduction_basics_v2.pdf · Tutorial: Basics of electronic structure theory

The main output------------------------------------------------------------ Preparing all fixed parts of the calculation.------------------------------------------------------------ Determining machine precision: 2.225073858507201E-308 Setting up grids for atomic and cluster calculations.

Creating wave function, potential, and density for free atoms.

Species: N

List of occupied orbitals and eigenvalues: n l energy [Ha] energy [eV] 1 0 -14.128445 -384.4546 2 0 -0.681395 -18.5417 2 1 -0.260121 -7.0782

Spin-polarized or charged system: Charge density initialized according to selected moments and charges.

The FHI-aims output

------------------------------------------------------------ Begin self-consistency loop: Initialization.

Date : 20090608, Time : 145624.781------------------------------------------------------------

Initializing index lists of integration centers etc. from given atomic structure: | Number of centers in hamiltonian partition_tab : 2 | Number of centers in hartree potential : 2 | Number of centers in hartree multipole : 2 | Number of centers in electron density summation: 2 | Number of centers in basis integrals : 2 | Number of centers in integrals : 2 Partitioning the integration grid into batches with maxmin method. | Maximal weight for a single point: 1.000 | Minimal weight for a single point: 0.000 | Number of batches: 499 | Maximal batch size: 141 | Minimal batch size: 50 | Average batch size: 63.431 | Standard deviation of batch sizes: 10.671 Initializing partition tables, free-atom densities, potentials, etc. across the integration grid (initialize_grid_storage). | Net number of integration points: 31652 | of which are non-zero points : 29382 Obtaining max. number of non-zero basis functions in each batch (get_n_compute_maxes). | Maximal number of non-zero basis functions: 28 in task 0

Begin self-consistency loop: Initialization.

geometry-independent preparationsbasis set generation

geometry-dependent preparationsintegration gridinitialization of charge density

The main output----------------------------------------------------------- Begin self-consistency iteration # 1

Date : 20090608, Time : 145625.136------------------------------------------------------------ Evaluating new KS density. Pulay mixing of updated and previous charge densities.

The FHI-aims output

| --------------------------- | Total energy : -109.38703872 Ha -2976.57276987 eV | Total energy, T -> 0 : -109.38703872 Ha -2976.57276987 eV | Free energy : -109.38703872 Ha -2976.57276987 eV Derived energy quantities: | Kinetic energy : 109.65005028 Ha 2983.72967863 eV | Electrostatic energy : -205.37638266 Ha -5588.57571571 eV | Energy correction for multipole | error in Hartree potential : 0.00062326 Ha 0.01695968 eV | Sum of eigenvalues per atom : -839.30637513 eV | Total energy (T->0) per atom : -1488.28638494 eV | Free energy per atom : -1488.28638494 eV

Self-consistency convergence accuracy: | Change of charge/spin density : 0.2057E+00 0.9030E+00 | Change of sum of eigenvalues : 0.3707E+02 eV | Change of total energy : -.4628E+01 eV

End self-consistency iteration # 1 : max(cpu_time) wall_clock_time(cpu1) Time for this iteration : 0.366 s 0.366 s Charge density update : 0.117 s 0.117 s Density mixing : 0.008 s 0.008 s Hartree multipole update : 0.013 s 0.014 s Hartree multipole summation : 0.072 s 0.072 s Integration : 0.154 s 0.154 s Solution of K.-S. eqns. : 0.001 s 0.001 s Total energy evaluation : 0.000 s 0.000 s------------------------------------------------------------

------------------------------------------------------------ Begin self-consistency iteration # 2

Date : 20090608, Time : 145625.502------------------------------------------------------------

Page 10: Tutorial: Basics of electronic structure theory Introductionth.fhi-berlin.mpg.de/th/Meetings/.../0623...introduction_basics_v2.pdf · Tutorial: Basics of electronic structure theory

The main output----------------------------------------------------------- Begin self-consistency iteration # 1

Date : 20090608, Time : 145625.136------------------------------------------------------------ Evaluating new KS density. Pulay mixing of updated and previous charge densities.

The FHI-aims output

Begin self-consistency iteration # 1

| --------------------------- | Total energy : -109.38703872 Ha -2976.57276987 eV | Total energy, T -> 0 : -109.38703872 Ha -2976.57276987 eV | Free energy : -109.38703872 Ha -2976.57276987 eV Derived energy quantities: | Kinetic energy : 109.65005028 Ha 2983.72967863 eV | Electrostatic energy : -205.37638266 Ha -5588.57571571 eV | Energy correction for multipole | error in Hartree potential : 0.00062326 Ha 0.01695968 eV | Sum of eigenvalues per atom : -839.30637513 eV | Total energy (T->0) per atom : -1488.28638494 eV | Free energy per atom : -1488.28638494 eV

Self-consistency convergence accuracy: | Change of charge/spin density : 0.2057E+00 0.9030E+00 | Change of sum of eigenvalues : 0.3707E+02 eV | Change of total energy : -.4628E+01 eV

End self-consistency iteration # 1 : max(cpu_time) wall_clock_time(cpu1) Time for this iteration : 0.366 s 0.366 s Charge density update : 0.117 s 0.117 s Density mixing : 0.008 s 0.008 s Hartree multipole update : 0.013 s 0.014 s Hartree multipole summation : 0.072 s 0.072 s Integration : 0.154 s 0.154 s Solution of K.-S. eqns. : 0.001 s 0.001 s Total energy evaluation : 0.000 s 0.000 s------------------------------------------------------------

------------------------------------------------------------ Begin self-consistency iteration # 2

Date : 20090608, Time : 145625.502------------------------------------------------------------

The main output----------------------------------------------------------- Begin self-consistency iteration # 1

Date : 20090608, Time : 145625.136------------------------------------------------------------ Evaluating new KS density. Pulay mixing of updated and previous charge densities.

The FHI-aims output

| --------------------------- | Total energy : -109.38703872 Ha -2976.57276987 eV | Total energy, T -> 0 : -109.38703872 Ha -2976.57276987 eV | Free energy : -109.38703872 Ha -2976.57276987 eV Derived energy quantities: | Kinetic energy : 109.65005028 Ha 2983.72967863 eV | Electrostatic energy : -205.37638266 Ha -5588.57571571 eV | Energy correction for multipole | error in Hartree potential : 0.00062326 Ha 0.01695968 eV | Sum of eigenvalues per atom : -839.30637513 eV | Total energy (T->0) per atom : -1488.28638494 eV | Free energy per atom : -1488.28638494 eV

Self-consistency convergence accuracy: | Change of charge/spin density : 0.2057E+00 0.9030E+00 | Change of sum of eigenvalues : 0.3707E+02 eV | Change of total energy : -.4628E+01 eV

End self-consistency iteration # 1 : max(cpu_time) wall_clock_time(cpu1) Time for this iteration : 0.366 s 0.366 s Charge density update : 0.117 s 0.117 s Density mixing : 0.008 s 0.008 s Hartree multipole update : 0.013 s 0.014 s Hartree multipole summation : 0.072 s 0.072 s Integration : 0.154 s 0.154 s Solution of K.-S. eqns. : 0.001 s 0.001 s Total energy evaluation : 0.000 s 0.000 s------------------------------------------------------------

------------------------------------------------------------ Begin self-consistency iteration # 2

Date : 20090608, Time : 145625.502------------------------------------------------------------

Total energyTotal energy, T -> 0Free energy F�E�� S �� ,{ f n}�

E��0�

12�F ����E ����

Page 11: Tutorial: Basics of electronic structure theory Introductionth.fhi-berlin.mpg.de/th/Meetings/.../0623...introduction_basics_v2.pdf · Tutorial: Basics of electronic structure theory

The main output----------------------------------------------------------- Begin self-consistency iteration # 1

Date : 20090608, Time : 145625.136------------------------------------------------------------ Evaluating new KS density. Pulay mixing of updated and previous charge densities.

The FHI-aims output

| --------------------------- | Total energy : -109.38703872 Ha -2976.57276987 eV | Total energy, T -> 0 : -109.38703872 Ha -2976.57276987 eV | Free energy : -109.38703872 Ha -2976.57276987 eV Derived energy quantities: | Kinetic energy : 109.65005028 Ha 2983.72967863 eV | Electrostatic energy : -205.37638266 Ha -5588.57571571 eV | Energy correction for multipole | error in Hartree potential : 0.00062326 Ha 0.01695968 eV | Sum of eigenvalues per atom : -839.30637513 eV | Total energy (T->0) per atom : -1488.28638494 eV | Free energy per atom : -1488.28638494 eV

Self-consistency convergence accuracy: | Change of charge/spin density : 0.2057E+00 0.9030E+00 | Change of sum of eigenvalues : 0.3707E+02 eV | Change of total energy : -.4628E+01 eV

End self-consistency iteration # 1 : max(cpu_time) wall_clock_time(cpu1) Time for this iteration : 0.366 s 0.366 s Charge density update : 0.117 s 0.117 s Density mixing : 0.008 s 0.008 s Hartree multipole update : 0.013 s 0.014 s Hartree multipole summation : 0.072 s 0.072 s Integration : 0.154 s 0.154 s Solution of K.-S. eqns. : 0.001 s 0.001 s Total energy evaluation : 0.000 s 0.000 s------------------------------------------------------------

------------------------------------------------------------ Begin self-consistency iteration # 2

Date : 20090608, Time : 145625.502------------------------------------------------------------

Total energyTotal energy, T -> 0Free energy

Total energy

F�E�� S �� ,{ f n}�

E��0�

12�F ����E ����

clusters !

The main output----------------------------------------------------------- Begin self-consistency iteration # 1

Date : 20090608, Time : 145625.136------------------------------------------------------------ Evaluating new KS density. Pulay mixing of updated and previous charge densities.

The FHI-aims output

| --------------------------- | Total energy : -109.38703872 Ha -2976.57276987 eV | Total energy, T -> 0 : -109.38703872 Ha -2976.57276987 eV | Free energy : -109.38703872 Ha -2976.57276987 eV Derived energy quantities: | Kinetic energy : 109.65005028 Ha 2983.72967863 eV | Electrostatic energy : -205.37638266 Ha -5588.57571571 eV | Energy correction for multipole | error in Hartree potential : 0.00062326 Ha 0.01695968 eV | Sum of eigenvalues per atom : -839.30637513 eV | Total energy (T->0) per atom : -1488.28638494 eV | Free energy per atom : -1488.28638494 eV

Self-consistency convergence accuracy: | Change of charge/spin density : 0.2057E+00 0.9030E+00 | Change of sum of eigenvalues : 0.3707E+02 eV | Change of total energy : -.4628E+01 eV

End self-consistency iteration # 1 : max(cpu_time) wall_clock_time(cpu1) Time for this iteration : 0.366 s 0.366 s Charge density update : 0.117 s 0.117 s Density mixing : 0.008 s 0.008 s Hartree multipole update : 0.013 s 0.014 s Hartree multipole summation : 0.072 s 0.072 s Integration : 0.154 s 0.154 s Solution of K.-S. eqns. : 0.001 s 0.001 s Total energy evaluation : 0.000 s 0.000 s------------------------------------------------------------

------------------------------------------------------------ Begin self-consistency iteration # 2

Date : 20090608, Time : 145625.502------------------------------------------------------------

Change of charge/spin density: 0.2057E+00 0.9030E+00Change of sum of eigenvalues : 0.3707E+02Change of total energy : -.4628E+01

sc_accuracy_rhosc_accuracy_eevsc_accuracy_etot

scf-cycle

Page 12: Tutorial: Basics of electronic structure theory Introductionth.fhi-berlin.mpg.de/th/Meetings/.../0623...introduction_basics_v2.pdf · Tutorial: Basics of electronic structure theory

Self-consistency convergence accuracy: | Change of charge/spin density : 0.3928E-06 0.2390E-06 | Change of sum of eigenvalues : 0.1079E-03 eV | Change of total energy : -.1851E-08 eV

Electronic self-consistency reached - switching on the force computation.

End self-consistency iteration # 10 : max(cpu_time) wall_clock_time(cpu1) Time for this iteration : 0.403 s 0.404 s Charge density & force component update : 0.108 s 0.108 s Density mixing : 0.057 s 0.057 s Hartree multipole update : 0.014 s 0.014 s Hartree multipole summation : 0.072 s 0.072 s Integration : 0.151 s 0.151 s Solution of K.-S. eqns. : 0.001 s 0.001 s Total energy evaluation : 0.000 s 0.001 s------------------------------------------------------------

------------------------------------------------------------ Begin self-consistency iteration # 11

Date : 20090608, Time : 145628.908------------------------------------------------------------

atomic forces [eV/Ang]: ----------------------- atom # 1 Hellmann-Feynman + Multipole : 0.451008E-12 -.102604E-12 -.121793E+02 Pulay + GGA : 0.486819E-13 0.227680E-12 0.106895E+02 ---------------------------------------------------------------- Total forces( 1) : 0.499690E-12 0.125076E-12 -.148978E+01 atom # 2 Hellmann-Feynman + Multipole : -.296693E-12 -.817935E-13 0.121793E+02 Pulay + GGA : 0.464015E-12 0.591618E-13 -.106895E+02 ---------------------------------------------------------------- Total forces( 2) : 0.167322E-12 -.226316E-13 0.148978E+01

Self-consistency convergence accuracy: | Change of charge/spin density : 0.1034E-07 0.6491E-09 | Change of sum of eigenvalues : -.1825E-05 eV | Change of total energy : 0.1701E-10 eV | Change of forces : 0.6537E-06 eV/A

The main output The FHI-aims output

Self-consistency convergence accuracy: | Change of charge/spin density : 0.3928E-06 0.2390E-06 | Change of sum of eigenvalues : 0.1079E-03 eV | Change of total energy : -.1851E-08 eV

Electronic self-consistency reached - switching on the force computation.

End self-consistency iteration # 10 : max(cpu_time) wall_clock_time(cpu1) Time for this iteration : 0.403 s 0.404 s Charge density & force component update : 0.108 s 0.108 s Density mixing : 0.057 s 0.057 s Hartree multipole update : 0.014 s 0.014 s Hartree multipole summation : 0.072 s 0.072 s Integration : 0.151 s 0.151 s Solution of K.-S. eqns. : 0.001 s 0.001 s Total energy evaluation : 0.000 s 0.001 s------------------------------------------------------------

------------------------------------------------------------ Begin self-consistency iteration # 11

Date : 20090608, Time : 145628.908------------------------------------------------------------

atomic forces [eV/Ang]: ----------------------- atom # 1 Hellmann-Feynman + Multipole : 0.451008E-12 -.102604E-12 -.121793E+02 Pulay + GGA : 0.486819E-13 0.227680E-12 0.106895E+02 ---------------------------------------------------------------- Total forces( 1) : 0.499690E-12 0.125076E-12 -.148978E+01 atom # 2 Hellmann-Feynman + Multipole : -.296693E-12 -.817935E-13 0.121793E+02 Pulay + GGA : 0.464015E-12 0.591618E-13 -.106895E+02 ---------------------------------------------------------------- Total forces( 2) : 0.167322E-12 -.226316E-13 0.148978E+01

Self-consistency convergence accuracy: | Change of charge/spin density : 0.1034E-07 0.6491E-09 | Change of sum of eigenvalues : -.1825E-05 eV | Change of total energy : 0.1701E-10 eV | Change of forces : 0.6537E-06 eV/A

The main output The FHI-aims output

0.3928E-06 0.2390E-060.1079E-03 eV-.1851E-08 eV

Page 13: Tutorial: Basics of electronic structure theory Introductionth.fhi-berlin.mpg.de/th/Meetings/.../0623...introduction_basics_v2.pdf · Tutorial: Basics of electronic structure theory

The main output Self-consistency convergence accuracy: | Change of charge/spin density : 0.3928E-06 0.2390E-06 | Change of sum of eigenvalues : 0.1079E-03 eV | Change of total energy : -.1851E-08 eV

Electronic self-consistency reached - switching on the force computation.

End self-consistency iteration # 10 : max(cpu_time) wall_clock_time(cpu1) Time for this iteration : 0.403 s 0.404 s Charge density & force component update : 0.108 s 0.108 s Density mixing : 0.057 s 0.057 s Hartree multipole update : 0.014 s 0.014 s Hartree multipole summation : 0.072 s 0.072 s Integration : 0.151 s 0.151 s Solution of K.-S. eqns. : 0.001 s 0.001 s Total energy evaluation : 0.000 s 0.001 s------------------------------------------------------------

------------------------------------------------------------ Begin self-consistency iteration # 11

Date : 20090608, Time : 145628.908------------------------------------------------------------

The FHI-aims output

atomic forces [eV/Ang]: ----------------------- atom # 1 Hellmann-Feynman + Multipole : 0.451008E-12 -.102604E-12 -.121793E+02 Pulay + GGA : 0.486819E-13 0.227680E-12 0.106895E+02 ---------------------------------------------------------------- Total forces( 1) : 0.499690E-12 0.125076E-12 -.148978E+01 atom # 2 Hellmann-Feynman + Multipole : -.296693E-12 -.817935E-13 0.121793E+02 Pulay + GGA : 0.464015E-12 0.591618E-13 -.106895E+02 ---------------------------------------------------------------- Total forces( 2) : 0.167322E-12 -.226316E-13 0.148978E+01

Self-consistency convergence accuracy: | Change of charge/spin density : 0.1034E-07 0.6491E-09 | Change of sum of eigenvalues : -.1825E-05 eV | Change of total energy : 0.1701E-10 eV | Change of forces : 0.6537E-06 eV/A

0.3928E-06 0.2390E-060.1079E-03 eV-.1851E-08 eV

Electronic self-consistency reached – switching on the force computation.

force terms calculated not untilenergy is converged

save computational time

The main output Self-consistency convergence accuracy: | Change of charge/spin density : 0.3928E-06 0.2390E-06 | Change of sum of eigenvalues : 0.1079E-03 eV | Change of total energy : -.1851E-08 eV

Electronic self-consistency reached - switching on the force computation.

End self-consistency iteration # 10 : max(cpu_time) wall_clock_time(cpu1) Time for this iteration : 0.403 s 0.404 s Charge density & force component update : 0.108 s 0.108 s Density mixing : 0.057 s 0.057 s Hartree multipole update : 0.014 s 0.014 s Hartree multipole summation : 0.072 s 0.072 s Integration : 0.151 s 0.151 s Solution of K.-S. eqns. : 0.001 s 0.001 s Total energy evaluation : 0.000 s 0.001 s------------------------------------------------------------

------------------------------------------------------------ Begin self-consistency iteration # 11

Date : 20090608, Time : 145628.908------------------------------------------------------------

The FHI-aims output

atomic forces [eV/Ang]: ----------------------- atom # 1 Hellmann-Feynman + Multipole : 0.451008E-12 -.102604E-12 -.121793E+02 Pulay + GGA : 0.486819E-13 0.227680E-12 0.106895E+02 ---------------------------------------------------------------- Total forces( 1) : 0.499690E-12 0.125076E-12 -.148978E+01 atom # 2 Hellmann-Feynman + Multipole : -.296693E-12 -.817935E-13 0.121793E+02 Pulay + GGA : 0.464015E-12 0.591618E-13 -.106895E+02 ---------------------------------------------------------------- Total forces( 2) : 0.167322E-12 -.226316E-13 0.148978E+01

Self-consistency convergence accuracy: | Change of charge/spin density : 0.1034E-07 0.6491E-09 | Change of sum of eigenvalues : -.1825E-05 eV | Change of total energy : 0.1701E-10 eV | Change of forces : 0.6537E-06 eV/A

atomic forces [eV/Ang]:

Hellmann-Feynman + MultipolePulay + GGA

force terms calculated not untilenergy is converged

save computational time

Page 14: Tutorial: Basics of electronic structure theory Introductionth.fhi-berlin.mpg.de/th/Meetings/.../0623...introduction_basics_v2.pdf · Tutorial: Basics of electronic structure theory

The main output The FHI-aims output

Total atomic forces (unitary forces cleaned) [eV/Ang]: | 1 0.811297123282653E-28 0.000000000000000E+00 -0.148978313187762E+01 | 2 0.811297123282653E-28 0.202824280820663E-28 0.148978313187762E+01

------------------------------------------------------------ Geometry optimization: Attempting to predict improved coordinates.

Removing unitary transformations (pure translations, rotations) from forces. Before filtering: | Net force on center of mass : 0.162259E-27 0.202824E-28 0.356812E-15 eV/A | Net torque on center of mass: -.111553E-28 0.000000E+00 0.000000E+00 eV After filtering: | Net force on center of mass : 0.360288E-43 0.450360E-44 0.000000E+00 eV/A | Net torque on center of mass: 0.247698E-44 0.000000E+00 0.000000E+00 eV

Net remaining forces (excluding translations, rotations) in present geometry: Maximum force component is 0.148978E+01 eV/A. Present geometry is not yet converged.

Relaxation step number 1: Predicting new coordinates.

Advancing geometry using BFGS. Predicted maximal displacement in this step: 0.153311E-01 A Updated atomic structure: x [A] y [A] z [A] Atom atom 0.00000000 0.00000000 -0.01533115 N atom 0.00000000 0.00000000 1.11533115 N------------------------------------------------------------

The main output The FHI-aims output

Total atomic forces (unitary forces cleaned) [eV/Ang]: | 1 0.811297123282653E-28 0.000000000000000E+00 -0.148978313187762E+01 | 2 0.811297123282653E-28 0.202824280820663E-28 0.148978313187762E+01

------------------------------------------------------------ Geometry optimization: Attempting to predict improved coordinates.

Removing unitary transformations (pure translations, rotations) from forces. Before filtering: | Net force on center of mass : 0.162259E-27 0.202824E-28 0.356812E-15 eV/A | Net torque on center of mass: -.111553E-28 0.000000E+00 0.000000E+00 eV After filtering: | Net force on center of mass : 0.360288E-43 0.450360E-44 0.000000E+00 eV/A | Net torque on center of mass: 0.247698E-44 0.000000E+00 0.000000E+00 eV

Net remaining forces (excluding translations, rotations) in present geometry: Maximum force component is 0.148978E+01 eV/A. Present geometry is not yet converged.

Relaxation step number 1: Predicting new coordinates.

Advancing geometry using BFGS. Predicted maximal displacement in this step: 0.153311E-01 A Updated atomic structure: x [A] y [A] z [A] Atom atom 0.00000000 0.00000000 -0.01533115 N atom 0.00000000 0.00000000 1.11533115 N------------------------------------------------------------

Total atomic forces (unitary forces cleaned) [eV/Ang]:

Page 15: Tutorial: Basics of electronic structure theory Introductionth.fhi-berlin.mpg.de/th/Meetings/.../0623...introduction_basics_v2.pdf · Tutorial: Basics of electronic structure theory

The main output The FHI-aims output

Total atomic forces (unitary forces cleaned) [eV/Ang]: | 1 0.811297123282653E-28 0.000000000000000E+00 -0.148978313187762E+01 | 2 0.811297123282653E-28 0.202824280820663E-28 0.148978313187762E+01

------------------------------------------------------------ Geometry optimization: Attempting to predict improved coordinates.

Removing unitary transformations (pure translations, rotations) from forces. Before filtering: | Net force on center of mass : 0.162259E-27 0.202824E-28 0.356812E-15 eV/A | Net torque on center of mass: -.111553E-28 0.000000E+00 0.000000E+00 eV After filtering: | Net force on center of mass : 0.360288E-43 0.450360E-44 0.000000E+00 eV/A | Net torque on center of mass: 0.247698E-44 0.000000E+00 0.000000E+00 eV

Net remaining forces (excluding translations, rotations) in present geometry: Maximum force component is 0.148978E+01 eV/A. Present geometry is not yet converged.

Relaxation step number 1: Predicting new coordinates.

Advancing geometry using BFGS. Predicted maximal displacement in this step: 0.153311E-01 A Updated atomic structure: x [A] y [A] z [A] Atom atom 0.00000000 0.00000000 -0.01533115 N atom 0.00000000 0.00000000 1.11533115 N------------------------------------------------------------

Relaxation step number 1: Predicting new coodinates.

Updated atomic structure:

relaxation step

The main output The FHI-aims output

Net remaining forces (excluding translations, rotations) in present geometry: Maximum force component is 0.390021E-02 eV/A. Present geometry is converged.

------------------------------------------------------------ Final atomic structure: x [A] y [A] z [A] Atom atom 0.00000000 0.00000000 -0.00505130 N atom 0.00000000 0.00000000 1.10505130 N------------------------------------------------------------

------------------------------------------------------------ Leaving FHI-aims. Date : 20090608, Time : 145641.881

Computational steps: | Number of self-consistency cycles : 36 | Number of relaxation steps : 3

Detailed time accounting : max(cpu_time) wall_clock_time(cpu1) | Total time : 17.321 s 17.330 s | Preparation time : 0.229 s 0.229 s | Grid partitioning : 0.205 s 0.208 s | Preloading free-atom quantities on grid : 0.170 s 0.170 s | Free-atom superposition energy : 0.188 s 0.188 s | Total time for integrations : 5.780 s 5.781 s | Total time for solution of K.-S. equations : 0.036 s 0.038 s | Total time for EV reorthonormalization : 0.000 s 0.001 s | Total time for density & force components : 5.907 s 5.906 s | Total time for mixing : 0.830 s 0.834 s | Total time for Hartree multipole update : 0.493 s 0.497 s | Total time for Hartree multipole sum : 3.444 s 3.445 s | Total time for total energy evaluation : 0.002 s 0.009 s

Have a nice day.------------------------------------------------------------

Page 16: Tutorial: Basics of electronic structure theory Introductionth.fhi-berlin.mpg.de/th/Meetings/.../0623...introduction_basics_v2.pdf · Tutorial: Basics of electronic structure theory

The main output The FHI-aims output

Net remaining forces (excluding translations, rotations) in present geometry: Maximum force component is 0.390021E-02 eV/A. Present geometry is converged.

------------------------------------------------------------ Final atomic structure: x [A] y [A] z [A] Atom atom 0.00000000 0.00000000 -0.00505130 N atom 0.00000000 0.00000000 1.10505130 N------------------------------------------------------------

------------------------------------------------------------ Leaving FHI-aims. Date : 20090608, Time : 145641.881

Computational steps: | Number of self-consistency cycles : 36 | Number of relaxation steps : 3

Detailed time accounting : max(cpu_time) wall_clock_time(cpu1) | Total time : 17.321 s 17.330 s | Preparation time : 0.229 s 0.229 s | Grid partitioning : 0.205 s 0.208 s | Preloading free-atom quantities on grid : 0.170 s 0.170 s | Free-atom superposition energy : 0.188 s 0.188 s | Total time for integrations : 5.780 s 5.781 s | Total time for solution of K.-S. equations : 0.036 s 0.038 s | Total time for EV reorthonormalization : 0.000 s 0.001 s | Total time for density & force components : 5.907 s 5.906 s | Total time for mixing : 0.830 s 0.834 s | Total time for Hartree multipole update : 0.493 s 0.497 s | Total time for Hartree multipole sum : 3.444 s 3.445 s | Total time for total energy evaluation : 0.002 s 0.009 s

Have a nice day.------------------------------------------------------------

Maximum force component is 0.390021E-02 eV/A.Present geometry is converged.

The main output The FHI-aims output

Net remaining forces (excluding translations, rotations) in present geometry: Maximum force component is 0.390021E-02 eV/A. Present geometry is converged.

------------------------------------------------------------ Final atomic structure: x [A] y [A] z [A] Atom atom 0.00000000 0.00000000 -0.00505130 N atom 0.00000000 0.00000000 1.10505130 N------------------------------------------------------------

------------------------------------------------------------ Leaving FHI-aims. Date : 20090608, Time : 145641.881

Computational steps: | Number of self-consistency cycles : 36 | Number of relaxation steps : 3

Detailed time accounting : max(cpu_time) wall_clock_time(cpu1) | Total time : 17.321 s 17.330 s | Preparation time : 0.229 s 0.229 s | Grid partitioning : 0.205 s 0.208 s | Preloading free-atom quantities on grid : 0.170 s 0.170 s | Free-atom superposition energy : 0.188 s 0.188 s | Total time for integrations : 5.780 s 5.781 s | Total time for solution of K.-S. equations : 0.036 s 0.038 s | Total time for EV reorthonormalization : 0.000 s 0.001 s | Total time for density & force components : 5.907 s 5.906 s | Total time for mixing : 0.830 s 0.834 s | Total time for Hartree multipole update : 0.493 s 0.497 s | Total time for Hartree multipole sum : 3.444 s 3.445 s | Total time for total energy evaluation : 0.002 s 0.009 s

Have a nice day.------------------------------------------------------------

Final atomic structure: x[A] y[A] z[A] Atom atom 0.00000000 0.00000000 -0.00505130 Natom 0.00000000 0.00000000 1.10505130 N

to be used for post-processing by

copy and paste

Page 17: Tutorial: Basics of electronic structure theory Introductionth.fhi-berlin.mpg.de/th/Meetings/.../0623...introduction_basics_v2.pdf · Tutorial: Basics of electronic structure theory

The main output The FHI-aims output

Net remaining forces (excluding translations, rotations) in present geometry: Maximum force component is 0.390021E-02 eV/A. Present geometry is converged.

------------------------------------------------------------ Final atomic structure: x [A] y [A] z [A] Atom atom 0.00000000 0.00000000 -0.00505130 N atom 0.00000000 0.00000000 1.10505130 N------------------------------------------------------------

------------------------------------------------------------ Leaving FHI-aims. Date : 20090608, Time : 145641.881

Computational steps: | Number of self-consistency cycles : 36 | Number of relaxation steps : 3

Detailed time accounting : max(cpu_time) wall_clock_time(cpu1) | Total time : 17.321 s 17.330 s | Preparation time : 0.229 s 0.229 s | Grid partitioning : 0.205 s 0.208 s | Preloading free-atom quantities on grid : 0.170 s 0.170 s | Free-atom superposition energy : 0.188 s 0.188 s | Total time for integrations : 5.780 s 5.781 s | Total time for solution of K.-S. equations : 0.036 s 0.038 s | Total time for EV reorthonormalization : 0.000 s 0.001 s | Total time for density & force components : 5.907 s 5.906 s | Total time for mixing : 0.830 s 0.834 s | Total time for Hartree multipole update : 0.493 s 0.497 s | Total time for Hartree multipole sum : 3.444 s 3.445 s | Total time for total energy evaluation : 0.002 s 0.009 s

Have a nice day.------------------------------------------------------------

| Number of self-consistency cycles : 36| Number of relaxation steps : 3

# “ “

# “ “# “ “

The main output The FHI-aims output

Net remaining forces (excluding translations, rotations) in present geometry: Maximum force component is 0.390021E-02 eV/A. Present geometry is converged.

------------------------------------------------------------ Final atomic structure: x [A] y [A] z [A] Atom atom 0.00000000 0.00000000 -0.00505130 N atom 0.00000000 0.00000000 1.10505130 N------------------------------------------------------------

------------------------------------------------------------ Leaving FHI-aims. Date : 20090608, Time : 145641.881

Computational steps: | Number of self-consistency cycles : 36 | Number of relaxation steps : 3

Detailed time accounting : max(cpu_time) wall_clock_time(cpu1) | Total time : 17.321 s 17.330 s | Preparation time : 0.229 s 0.229 s | Grid partitioning : 0.205 s 0.208 s | Preloading free-atom quantities on grid : 0.170 s 0.170 s | Free-atom superposition energy : 0.188 s 0.188 s | Total time for integrations : 5.780 s 5.781 s | Total time for solution of K.-S. equations : 0.036 s 0.038 s | Total time for EV reorthonormalization : 0.000 s 0.001 s | Total time for density & force components : 5.907 s 5.906 s | Total time for mixing : 0.830 s 0.834 s | Total time for Hartree multipole update : 0.493 s 0.497 s | Total time for Hartree multipole sum : 3.444 s 3.445 s | Total time for total energy evaluation : 0.002 s 0.009 s

Have a nice day.------------------------------------------------------------

Have a nice day.

Page 18: Tutorial: Basics of electronic structure theory Introductionth.fhi-berlin.mpg.de/th/Meetings/.../0623...introduction_basics_v2.pdf · Tutorial: Basics of electronic structure theory

Overview The exercises

� the nitrogen dimerbinding curve, binding energy, spin polarizationpbe vs. pw-lda

� the silicon trimerlocal structural relaxationvibrational analysischarge density plots, HOMO plotsvisualization

� small X(+)Si3 – clusters, X=Sc,Ti,V,Cr“sampling” of cluster structuresdensity of states plots

14:30 - 15:15 (45 min)

15:15 - 16:00 (45 min)

16:00 - 18:00 (120 min)

The nitrogen dimer The exercises

/usr/local/aimsfiles/tutorial1/N2� general part of control.in file:

� species-dependent part:/usr/local/aimsfiles/species_defaults/light/07_N_default

� geometry.in file simple (just two atoms) Eb�E tot �N 2��2 E tot �N �

control.in.basic

xc xxspin xxrelativistic xx

0.8 -2962.767360.9 -2972.908881.0 -2977.15015

xmgrace, gnuplot

xmgrace, gnuplot, awk,...

d [Å]

Page 19: Tutorial: Basics of electronic structure theory Introductionth.fhi-berlin.mpg.de/th/Meetings/.../0623...introduction_basics_v2.pdf · Tutorial: Basics of electronic structure theory

The nitrogen dimer The exercises

the free atom� spin-polarized

� enhanced cutoff radius: 3.5 Å ��5.0 Å

spin collinear

cut_pot 5.0 1.5 1.0

The nitrogen dimer The exercises

the free atom� spin-polarized

� enhanced cutoff radius: 3.5 Å ��5.0 Å

spin collinear

cut_pot 5.0 1.5 1.0

Page 20: Tutorial: Basics of electronic structure theory Introductionth.fhi-berlin.mpg.de/th/Meetings/.../0623...introduction_basics_v2.pdf · Tutorial: Basics of electronic structure theory

The nitrogen dimer The exercises

the free atom� spin-polarized

� enhanced cutoff radius: 3.5 Å ��5.0 Å

spin collinear

cut_pot 5.0 1.5 1.0

################################ "First tier" hydro 2 p 1.8 hydro 3 d 6.8 hydro 3 s 5.8# "Second tier"# hydro 4 f 10.8# hydro 3 p 5.8# hydro 1 s 0.8# hydro 5 g 16# hydro 3 d 4.9# "Third tier" # hydro 3 s 16# ionic 2 p auto# hydro 3 d 6.6# hydro 4 f 11.6

The nitrogen dimer The exercises

the free atom� spin-polarized

� enhanced cutoff radius: 3.5 Å ��5.0 Å

spin collinear

cut_pot 5.0 1.5 1.0

basis set convergence

############################# "First tier" hydro 2 p 1.8 hydro 3 d 6.8 hydro 3 s 5.8# "Second tier" hydro 4 f 10.8 hydro 3 p 5.8 hydro 1 s 0.8 hydro 5 g 16 hydro 3 d 4.9# "Third tier" # hydro 3 s 16# ionic 2 p auto# hydro 3 d 6.6# hydro 4 f 11.6

tier1 tier2

Page 21: Tutorial: Basics of electronic structure theory Introductionth.fhi-berlin.mpg.de/th/Meetings/.../0623...introduction_basics_v2.pdf · Tutorial: Basics of electronic structure theory

The nitrogen dimer The exercises

pw-lda, light: d0 = 1.1 Å, Eb = -11.35 eV

d [Å]

pbe, tight: d0 = 1.1 Å, Eb = -10.31 eV

exp.: d0 = 1.1 Å, Eb = -9,8 eV 1

1 K. Huber and G. Herzberg, Molecular Spectra and Molecular Structure. IV. Constants of Diatomic Molecules (Van Nostrand, Princeton, 1979)

reasonable bond distances overestimation of binding energy

The silicon trimer The exercises

� create_relax_movie.pl Si3.prerelax.out > Si3.prerelax.irc

/usr/local/aimsfiles/tutorial1/Si3

� create_geometry.x dmin D Si 3 > geometry.in

Local structural relaxation

� molden -m Si3.prerelax.irc

Page 22: Tutorial: Basics of electronic structure theory Introductionth.fhi-berlin.mpg.de/th/Meetings/.../0623...introduction_basics_v2.pdf · Tutorial: Basics of electronic structure theory

The silicon trimer The exercises

Visualization of local relaxation

Run through relaxation steps

Bond distancesangles

output style(balls & sticks)

The silicon trimer The exercises

Vibrational analysis:

/usr/local/aimsfiles/tutorial1/Si3/Si3_pw-lda /usr/local/aimsfiles/tutorial1/Si3/Si3_pbe

� aims.vibrations.pl Si3_pw-lda (0.005)

default value for finite displacement

Si3_pw-lda.mol

Si3_pw-lda.xyz

(molden)

(jmol)� molden Si3_pw-lda.mol

d F

d R�

�F �R� , 0����F �R� , 0���

2�d Pd R�

�P �R

�, 0����P�R� , 0���

2�

I�� d PdQ�2

IR-intensity

Page 23: Tutorial: Basics of electronic structure theory Introductionth.fhi-berlin.mpg.de/th/Meetings/.../0623...introduction_basics_v2.pdf · Tutorial: Basics of electronic structure theory

The silicon trimer The exercises

visualization of vibrations

The silicon trimer The exercises

Cube files:

total_density.cube

output cube total_densitycube origin 0.0 0.0 0.0cube edge 50 0.2 0.0 0.0cube edge 50 0.0 0.2 0.0cube edge 50 0.0 0.0 0.2

50 x 50 x 50 “voxels” with a volume of 0.2 x 0.2 x 0.2 Å3

see e.g. http://local.wasp.uwa.edu.au/~pbourke/dataformats/cube/

Page 24: Tutorial: Basics of electronic structure theory Introductionth.fhi-berlin.mpg.de/th/Meetings/.../0623...introduction_basics_v2.pdf · Tutorial: Basics of electronic structure theory

The silicon trimer The exercises

Enter densitymode

The silicon trimer The exercises

Read cube files

Page 25: Tutorial: Basics of electronic structure theory Introductionth.fhi-berlin.mpg.de/th/Meetings/.../0623...introduction_basics_v2.pdf · Tutorial: Basics of electronic structure theory

The silicon trimer The exercises

The silicon trimer The exercises

Enter contour values for isosurfaces

Page 26: Tutorial: Basics of electronic structure theory Introductionth.fhi-berlin.mpg.de/th/Meetings/.../0623...introduction_basics_v2.pdf · Tutorial: Basics of electronic structure theory

The silicon trimer The exercises

X(+)Si3 , X=Sc,Ti,V,Cr The exercises

� create_geometry.x dmin D Si 3 Sc 1 > geometry.in.struct1

geometry.in.struct1geometry.in.struct2geometry.in.struct3geometry.in.struct4geometry.in.struct5

control.in.prerelax

~/tutorial1/X(+)Si3/XSi3_pw-lda ~/tutorial1/X(+)Si3/XSi3_pbe~/tutorial1/X(+)Si3/X+Si3_pw-lda ~/tutorial1/X(+)Si3/X+Si3_pbe

combi_run.pl

aims.struct1.prerelax.outaims.struct2.prerelax.outaims.struct3.prerelax.outaims.struct4.prerelax.outaims.struct5.prerelax.out

� create_relax_movie.pl aims.struct1.prerelax.out > relax.1.irc

� molden -m relax.1.irc

� KS_DOS_total_raw.dat, KS_DOS_total.dat ASCII-file � xmgrace

unshifted DOS shifted w.r.t. EF

Page 27: Tutorial: Basics of electronic structure theory Introductionth.fhi-berlin.mpg.de/th/Meetings/.../0623...introduction_basics_v2.pdf · Tutorial: Basics of electronic structure theory

The exercises

energetic order

PBE vs PW-LDAScSi3

E = 0.0 N = 1

ΔE = 0.08 eV N = 1

ΔE = 0.64 eV N = 2.3 � = 0.2 eV !

N = N� - N�

E = 0.0 N = 1

ΔE = 0.02 eV N = 1

energetic orderchanged !

TiSi3 vs. Ti+Si3PW-LDA

E = 0.0 N = 2

ΔE = 0.81 eV N = 2

E = 0.0 N = 1

ΔE = 0.28 eV N = 1.3

The exercises

Distribution of tasks

ScSi3 PW-LDA 01,02,03

PBE 04,11,12

PW-LDA 18,19,20

PBE 09,10,17

Sc+Si3

TiSi3 PW-LDA 25,26,27

PBE 28,35,36

PW-LDA 42,43,44

PBE 33,34,41

Ti+Si3

VSi3 PW-LDA 05,06,07

PBE 08,15,16

PW-LDA 22,23,24

PBE 13,14,21

V+Si3

CrSi3 PW-LDA 29,30,31

PBE 32,39,40

PW-LDA 37,38,45

PBE 46,47,48

Cr+Si3

desktop machines: aimsXX

Page 28: Tutorial: Basics of electronic structure theory Introductionth.fhi-berlin.mpg.de/th/Meetings/.../0623...introduction_basics_v2.pdf · Tutorial: Basics of electronic structure theory

Sc(+)Si3PW-LDA PBE

cationic cationicneutral neutral

N = N� - N�

A B C D E F

????

Sc(+)Si3PW-LDA PBE

cationic cationicneutral neutral

N = 1

N = N� - N�

A B C D E F

???

Page 29: Tutorial: Basics of electronic structure theory Introductionth.fhi-berlin.mpg.de/th/Meetings/.../0623...introduction_basics_v2.pdf · Tutorial: Basics of electronic structure theory

Sc(+)Si3PW-LDA PBE

cationic cationicneutral neutral

N = 1

N = N� - N�

N = 0

A B C D E F

??

Sc(+)Si3PW-LDA PBE

cationic cationicneutral neutral

N = 1

N = N� - N�

N = 1N = 0

A B C D E F

?

Page 30: Tutorial: Basics of electronic structure theory Introductionth.fhi-berlin.mpg.de/th/Meetings/.../0623...introduction_basics_v2.pdf · Tutorial: Basics of electronic structure theory

Sc(+)Si3PW-LDA PBE

cationic cationicneutral neutral

N = 1

N = N� - N�

N = 1N = 0 N = 0

A B C D E F

Ti(+)Si3PW-LDA PBE

cationic cationicneutral neutral

N = N� - N�

A B C D E F

????

Page 31: Tutorial: Basics of electronic structure theory Introductionth.fhi-berlin.mpg.de/th/Meetings/.../0623...introduction_basics_v2.pdf · Tutorial: Basics of electronic structure theory

Ti(+)Si3PW-LDA PBE

cationic cationicneutral neutral

N = 2

N = N� - N�

A B C D E F

???

Ti(+)Si3PW-LDA PBE

cationic cationicneutral neutral

N = 2

N = N� - N�

N = 1

A B C D E F

??

Page 32: Tutorial: Basics of electronic structure theory Introductionth.fhi-berlin.mpg.de/th/Meetings/.../0623...introduction_basics_v2.pdf · Tutorial: Basics of electronic structure theory

Ti(+)Si3PW-LDA PBE

cationic cationicneutral neutral

N = 2

N = N� - N�

N = 2N = 1

A B C D E F

?

Ti(+)Si3PW-LDA PBE

cationic cationicneutral neutral

N = 2

N = N� - N�

N = 2N = 1 N = 1

A B C D E F

Page 33: Tutorial: Basics of electronic structure theory Introductionth.fhi-berlin.mpg.de/th/Meetings/.../0623...introduction_basics_v2.pdf · Tutorial: Basics of electronic structure theory

V(+)Si3PW-LDA PBE

cationic cationicneutral neutral

N = N� - N�

A B C D E F

????

V(+)Si3PW-LDA PBE

cationic cationicneutral neutral

N = 1

N = N� - N�

A B C D E F

???

Page 34: Tutorial: Basics of electronic structure theory Introductionth.fhi-berlin.mpg.de/th/Meetings/.../0623...introduction_basics_v2.pdf · Tutorial: Basics of electronic structure theory

V(+)Si3PW-LDA PBE

cationic cationicneutral neutral

N = 1

N = N� - N�

N = 2

A B C D E F

??

V(+)Si3PW-LDA PBE

cationic cationicneutral neutral

N = 1

N = N� - N�

N = 1N = 2

A B C D E F

?

Page 35: Tutorial: Basics of electronic structure theory Introductionth.fhi-berlin.mpg.de/th/Meetings/.../0623...introduction_basics_v2.pdf · Tutorial: Basics of electronic structure theory

V(+)Si3PW-LDA PBE

cationicneutral neutral

N = 1

N = N� - N�

N = 1N = 2 N = 2

A B C D E F

cationic

Cr(+)Si3PW-LDA PBE

cationic cationicneutral neutral

N = N� - N�

A B C D E F

? ? ? ?

Page 36: Tutorial: Basics of electronic structure theory Introductionth.fhi-berlin.mpg.de/th/Meetings/.../0623...introduction_basics_v2.pdf · Tutorial: Basics of electronic structure theory

Cr(+)Si3PW-LDA PBE

cationic cationicneutral neutral

N = N� - N�

A B C D E F

? ?N = 0

?

Cr(+)Si3PW-LDA PBE

cationic cationicneutral neutral

N = N� - N�

A B C D E F

??N = 3N = 0

Page 37: Tutorial: Basics of electronic structure theory Introductionth.fhi-berlin.mpg.de/th/Meetings/.../0623...introduction_basics_v2.pdf · Tutorial: Basics of electronic structure theory

Cr(+)Si3PW-LDA PBE

cationic cationicneutral neutral

N = N� - N�

N = 0N = 3

A B C D E F

?N = 0

Cr(+)Si3PW-LDA PBE

cationic cationicneutral neutral

N = 0

N = N� - N�

N = 0N = 3 N = 3

A B C D E F

Page 38: Tutorial: Basics of electronic structure theory Introductionth.fhi-berlin.mpg.de/th/Meetings/.../0623...introduction_basics_v2.pdf · Tutorial: Basics of electronic structure theory

Very well done!!