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