A first encounter with Siesta¶

In this exercise we will get a first acquaintance with SIESTA by studying two simple molecules, CH4 and CH3. We will cover quite a lot of features and concepts, without worrying too much about issues of convergence.

Basic execution. Input and output files¶

Hint

Enter the directory ‘CH4’

You will find an input file named ch4.fdf along with the files C.psf and H.psf containing the information about the pseudopotentials. The ch4.fdf file sets the value of several parameters which specify both the system we want to study and the accuracy of the calculation. We find first the inputs that specify the system:

SystemName          CH4 molecule
SystemLabel         ch4

%block ChemicalSpeciesLabel
 1  6 C   # Species index, atomic number, species label
 2  1 H   # Species index, atomic number, species label
%endblock ChemicalSpeciesLabel

AtomicCoordinatesFormat  Ang

%block AtomicCoordinatesAndAtomicSpecies
  0.000      0.000      0.000   1
  1.219     -0.284     -0.377   2
 -0.284      1.219     -0.377   2
 -0.140     -0.140      1.219   2
 -0.833     -0.833     -0.503   2
%endblock AtomicCoordinatesAndAtomicSpecies

Pay special attention to the block ChemicalSpeciesLabel. In this block you assign an index and a label to each atomic species. The label will allow to recognize the files containing the information about the pseudopotential and the basis set (when provided).

Check the input of the coordinates (they are just some guess coordinates, not the optimized equilibrium ones).

The file ch4.fdf contains also the most important parameters to take into account to perform a molecular calculation. Namely:

Those defining the size and localization of the basis set. Here the number of orbitals per atom is defined by the parameter PAO.BasisSize, and we have set it to select a minimal basis (SZ) for quick, cheap calculation, looking for qualitative results, rather than quantitative results.
The parameter MeshCutoff, controlling the fineness of the real-space grid used to compute the integrals for the matrix elements of the Hamiltonian.
Those that control the self-consistent cycle.

While the parameters specifying the system are mandatory, all other parameters have some default values and, in principle, it is not necessary to explicitly include them in the input file. However, it is important to note that the default values do not always guarantee a converged calculation.

Run the program:

siesta < ch4.fdf > ch4.out           # traditional way

or simply:

siesta ch4.fdf > ch4.out

Take a look at ch4.out once the program has finished. The file contains a human-readable account of the doings of SIESTA for this calculation:

A header with the version and compilation options, and a copy (in the first mode above) or a mention (in the second mode) of the input file.
Details about the pseudopotential read and the basis set generated for each species.
A summary of the values used in the calculation for the most important parameters.
A log of the self-consistent-field (SCF) cycle
A summary of the total energy decomposition, forces, and stress

Hint

You can play with the values of a few parameters and check their effect on the output results:

The basis-set size: Set PAO.Basis-size to any of: DZ, SZP, DZP, TZP. More on this topic in this tutorial.
The fineness of the real-space grid: Use a unreasonable low value for the the parameter MeshCutoff (may be 10-30 Ry) and check the resulting total energy and forces (you can also find the forces in the file ch4.FA). Try to determine the minimum value of the MeshCutoff parameter that gives an energy converged to 0.1 eV. More on this topic in this tutorial.

Periodic boundary conditions¶

You might have wondered about the appearance of this block in the input file:

#Unit cell for the calculation
LatticeConstant 15 Ang
%block LatticeVectors
1.000 0.000 0.000
0.000 1.000 0.000
0.000 0.000 1.000
%endblock LatticeVectors

which does not seem to make sense for a ‘molecule’ calculation. In fact, SIESTA uses periodic boundary conditions (PBC), and this means in this case that we are doing a calculation for an infinite collection of regularly spaced molecules. If we want to simulate an isolated molecule it is important to have enough distance between the molecule and its neighboring images. At the very minimum, there should not be overlap between the orbitals on different image molecules. This can be actually automatically checked by the program, so the block is not strictly necessary. However, in the general case it might be important to have more control over the separation. (This is quite important for molecules with a dipole, for example, which will have a long-range interaction with their images in PBC.)

Hint

You can play with the size of the lattice parameters to go from ‘interacting’ molecules to effectively isolated ones. Look at the variation in the total energy as a function of the cell size, to see how the interaction between molecules decreases with increasing distance between images. For this non-polar molecule, the interaction should be very small. (But see the case of the water molecule here.

DFT functional¶

Up to now we have been implicitly using LDA for our calculations. However, it is also possible to use other functionals, such as those of GGA type. Edit the ch4.fdf file to include this block:

#Density functional (Notice that Xc.authors and XC.functional
#are both needed and must be consistent)
XC.functional GGA
XC.authors  PBE

Note the use of ‘#’ to mark comments, and, once again, the fact that Siesta uses defaults (in this case an LDA functional) for certain parameters if they are not specified in the input.

Run the program again and look for possible lines with ‘WARNING’ or ‘ERROR’ in them. You will see that there is a warning. The code does not like that you are using a GGA functional with a pseudopotential generated using LDA, as this is not consistent!. Fortunately, we have produced also the pseudopotentials using GGA for you. They are in the files C.gga.psf and H.gga.psf. You can modify the input file again to use these files by simply changing the ‘species’ strings:

%block ChemicalSpeciesLabel
1  6 C.gga   # Species index, atomic number, species label
2  1 H.gga   # Species index, atomic number, species label
%endblock ChemicalSpeciesLabel

Run the program again and check whether the warning disappears from the output.

Structural optimization¶

Now add to ch4.fdf the following lines:

#Geometrical optimization
MD.TypeOfRun CG
MD.NumCGsteps 50
MD.MaxCGDispl         0.1 Bohr
MD.MaxForceTol        0.04d0 eV/Ang

to instruct Siesta to perform a structural optimization using the conjugate gradient algorithm (you can check the manual to understand the meaning of the lines added). If you run the program again you will notice that the output file contains several new sections, each corresponding to a different structure, in a series that should converge to an optimal configuration with zero forces. There are defaults for the tolerance in convergence. (We will cover relaxation in more detail in this tutorial.

Hint

Relax the structure for various basis set sizes (SZ, DZ, DZP) and check the differences on geometry and total energy.

Note

The file ch4.ANI contains all the structures generated during the relaxation in XYZ format. It can be processed by various graphical tools, such as XCrysden , VMD or Ovito .

Spin polarization in the CH3 molecule¶

Hint

Enter the directory ‘CH3’

Now we are going to perform calculations for the molecule CH3. If you look at the input file ch3.fdf` you should realize that we are requesting, within the LDA, the optimized geometry of the molecule, using an automatically generated unit-cell.

However, this molecule contains an unpaired electron. Therefore the system should show some spin polarization. We can request a spin-polarized calculation by including the line:

Spin polarized

If you compare the results of this calculation with those of the previous one you will see that there is extra output regarding the total spin moment during the scf cycle. The final energy should be lower than for the calculation without spin.

Note

To obtain spin polarization we need to break the symmetry between the up and down spins. If spin symmetry is somehow imposed or assumed in the initial configuration the results will not be spin-polarized. You can check this by adding the block:

%block DM.InitSpin
 1 0.0
 2 0.0
 3 0.0
 4 0.0
%endblock DM.InitSpin

which will set the initial spins to zero on all atoms (check the manual to see the meaning of the block contents). When not using the block, the built-in Siesta heuristics prepared an initial density-matrix with a spin imbalance.

Plotting densities¶

You might have noticed the lines:

SaveRho .true.                 # -- Output of charge density
%block LocalDensityOfStates    # -- LDOS ('charge' for an energy window)
-6.00  -3.00 eV
%endblock LocalDensityOfStates

In response to these lines, SIESTA produced two extra files:

ch3.RHO: contains the values of the self-consistent electronic density on the real-space mesh.
ch3.LDOS: contains the ‘charge density’ associated only to the HOMO of the molecule. We had to specify an energy window (-6 to -3 eV) in which we know that there is only this state. (We can get this information by looking at the ch3.EIG file).

Hint

You can modify the block LocalDensityOfStates to plot the ‘density’ associated with different molecular orbitals lying in different energy windows.

More details on how to visualize the charge density and other quantities represented on the real-space grid are given in this how-to. For this tutorial we will use Xcrysden. Execute:

rho2xsf < rho2xsf.inp

to generate a ‘ch3.XSF’ file that contains both the total charge density and the LDOS information.

Then:

xcrysden --xsf ch3.XSF

will open the Xcrysden window. You need to go into the ‘Grid’ section and set the options to select the data-set (ch3.RHO or ch3.LDOS). For the charge density, you can select your preferred combination of the ‘up’ and ‘down’ charge densities. If you give them factors of ‘+1’ and ‘-1’ you will get the spin-density, showing in essence the ‘unpaired electron’.