Tutorial:Hydrogen atom
From OctopusWiki
The objective of this tutorial is to give a basic idea of how octopus works.
Contents |
Generating the input file
With a text editor, create a text file called inp containing the following text:
CalculationMode= gs %Coordinates'H' | 0 | 0 | 0 %
This is the simplest example of an Octopus input file:
-
CalculationMode= gs
- %
Coordinates: The entry is not just the definition of a variable, but rather of a full set of them -- a "block" of variables. The beginning of a block is marked by the %identifier line, and ended by a % line. In this case the identifier is %Coordinates, where we list the atoms or species in our calculation and its coordinates, one per line. In this case, we put a single hydrogen atom in the center of our simulation box.
The reason this input file can be so simple is that Octopus comes with default values for the simulation parameters, and a set of default pseudopotentials for several elements (for properly converged calculations you might need to adjust these parameters, though).
To get a general idea of the format of the Octopus input file, go and read the page about the Input file in the manual.
Running Octopus
Once you have written your input file, run the octopus command. If everything goes correctly, you should see several lines of output in the terminal (if you don't, there must be a problem with your installation). As this is probably the first time you run Octopus, we will examine the most important parts of the output:
- First there is an octopus drawn in ASCII art, the copyright notice and some information about the octopus version you are using and the system where you are running:
<><><><><><><><><><><><><><><><><><><><><><><><><><><><><><><>
___
.-' `'.
/ \
| ;
| | ___.--,
_.._ |0) ~ (0) | _.---'`__.-( (_.
__.--'`_.. '.__.\ '--. \_.-' ,.--'` `""`
( ,.--'` ',__ /./; ;, '.__.'` __
_`) ) .---.__.' / | |\ \__..--"" """--.,_
`---' .'.''-._.-'`_./ /\ '. \ _.-~~~````~~~-._`-.__.'
| | .' _.-' | | \ \ '. `~---`
\ \/ .' \ \ '. '-._)
\/ / \ \ `=.__`~-.
jgs / /\ `) ) / / `"".`\
, _.-'.'\ \ / / ( ( / /
`--~` ) ) .-'.' '.'. | (
(/` ( (` ) ) '-;
` '-; (-'
This program is free software; you can redistribute it and/or modify
it under the terms of the GNU General Public License as published by
the Free Software Foundation; either version 2, or (at your option)
any later version.
This program is distributed in the hope that it will be useful,
but WITHOUT ANY WARRANTY; without even the implied warranty of
MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
GNU General Public License for more details.
You should have received a copy of the GNU General Public License
along with this program; if not, write to the Free Software
Foundation, Inc., 59 Temple Place - Suite 330, Boston, MA
<><><><><><><><><><><><><><><><><><><><><><><><><><><><><><><>
Running octopus
Version : 3.2.0
Revision : 6135
Build time : Fri Nov 27 16:16:18 CET 2009
Configuration options : max-dim=3
Optional libraries :
Architecture : x86_64
C compiler : gcc-4.4
C compiler flags : -march=native -funroll-loops -O3 -ffast-math
Fortran compiler : gfortran-4.4
Fortran compiler flags : -march=native -funroll-loops -O3 -ffast-math
The octopus is swimming in lascar (Linux)
Calculation started on 2009/11/27 at 16:38:10
- The type of calculation it was asked to perform:
************************** Calculation Mode ************************** Input: [CalculationMode = gs] **********************************************************************
- The species and pseudopotentials it is using:
****************************** Species *******************************
Reading pseudopotential from file:
'/home/xavier/share/octopus/PP/PSF/H.psf'
Calculating atomic pseudo-eigenfunctions for specie H ....
Done.
Info: l = 0 component used as local potential
**********************************************************************
- After some other output, Octopus prints information about the grid: as we didn't say anything in the input file, Octopus used the parameters recommended for this pseupopotential:
******************************** Grid ******************************** Simulation Box: Type = around nuclei Radius [b] = -1.000 Octopus will run in 3 dimension(s). Octopus will treat the system as periodic in 0 dimension(s). Main mesh: Spacing [b] = ( 0.435, 0.435, 0.435) volume/point [b^3] = 0.08211 # inner mesh = 22119 # total mesh = 52127 Grid Cutoff [H] = 26.123 **********************************************************************
- The level of theory and, in the case of (TD)DFT, the approximation to the exchange-correlation term:
**************************** Theory Level ****************************
Input: [TheoryLevel = dft]
Exchange and correlation:
Exchange
Slater exchange (LDA)
[1] PAM Dirac, Proceedings of the Cambridge Philosophical Society 26, 376 (1930)
[2] F Bloch, Zeitschrift fuer Physik 57, 545 (1929)
Correlation
Perdew & Zunger (Modified) (LDA)
[1] Perdew and Zunger, Phys. Rev. B 23, 5048 (1981)
[2] Modified to improve the matching between the low and high rs parts
Input: [SICCorrection = sic_none]
**********************************************************************
- At this point, Octopus tries to read the wave-functions from a previous calculation. As there are none, it will give a warning.
** Warning: ** Could not load wavefunctions from 'restart/gs/' ** Starting from scratch!
- Now Octopus commences the calculation. To get a reasonable starting point for the DFT calculation, the initial wavefunctions are calculated as a Linear Combination of Atomic Orbitals (LCAO).
Info: Performing initial LCAO calculation with 1 orbitals. Eigenvalues [H] #st Spin Eigenvalue Occupation 1 -- -0.231981 1.000000
- After the LCAO, the real DFT calculation starts. For each self-consistency step some information is printed. When SCF converges, the calculation is done.
*********************** SCF CYCLE ITER # 1 ************************
etot = -4.44578403E-01 abs_ev = 6.30E-04 rel_ev = 2.71E-03
abs_dens = 7.46E-04 rel_dens = 7.46E-04
Matrix vector products: 27
Converged eigenvectors: 0
Eigenvalues [H]
#st Spin Eigenvalue Occupation Error
1 -- -0.232610 1.000000 (9.1E-05)
Elapsed time for SCF step: 0.10
**********************************************************************
...
********************** SCF CYCLE ITER # 4 ************************
etot = -4.44579903E-01 abs_ev = 1.00E-05 rel_ev = 4.32E-05
abs_dens = 5.82E-06 rel_dens = 5.82E-06
Matrix vector products: 15
Converged eigenvectors: 1
Eigenvalues [H]
#st Spin Eigenvalue Occupation Error
1 -- -0.231962 1.000000 (9.9E-07)
Elapsed time for SCF step: 0.15
**********************************************************************
Info: SCF converged in 4 iterations
Analyzing the results
The detailed results of the ground-state calculation can be found in the static/info file. If you open that file, first you will see some parameters of the calculations (that we already got from the output) and then the calculated energies and eigenvalues:
Eigenvalues [H]
#st Spin Eigenvalue Occupation
1 -- -0.231962 1.000000
Energy:
Total = -0.44457606
Ion-ion = 0.00000000
Eigenvalues = -0.23196234
Hartree = 0.28315896
Int[n*v_xc] = -0.30327009
Exchange = -0.19303436
Correlation = -0.03969050
Kinetic = 0.41347550
External = -0.90848938
Since by default Octopus does a spin-unpolarized density-functional-theory calculation with the local-density approximation, our results differ from the exact total energy of 0.5 [Ha].
Extra
If you want to improve the LDA results, you can try to repeat the calculation with spin-polarization:
SpinComponents = spin_polarized
And if you want to obtain the exact result (something possible only for very simple systems like this one) you have to remove the self-interaction error (a problem of the LDA). Since we only have one electron the simplest way to do it for this case is to use independent electrons:
TheoryLevel = independent_particles
A more general way would be to include self-interaction correction.
