How to Calculate Cohesive Energy
The energy for bonding can be
calculated using the difference between a bonded structure and a
dissociated one. This energy, which is necessary to separate an atom
from the solid, is called cohesive energy. [1]
It can be calculated by getting the total energy of the bulk structure
and the single atom, and their difference with the plane-wave DFT.
First, prepare silicon unit cells for the calculation of bulk. In Manipulator Crystal → Preset Structure, select Silicon (unit cell) for easy modeling.
First, prepare silicon unit cells for the calculation of bulk. In Manipulator Crystal → Preset Structure, select Silicon (unit cell) for easy modeling.
To use the previous convergence
conditions, set the scripting option to General, and set the input
parameters. The previous result was obtained with the energy convergence
input parameter set of single crystal silicon, cutoff energy of 40–240
Ry, and 63 k-points.
It takes about several seconds or
minutes to make an SCF calculation that has a good symmetry structure
such as silicon single crystal. The progress of the submitted job is
displayed in the dashboard of the menu bar on the upper section. Once
the calculation is complete, refresh the page to check whether the end
message is normally displayed.
Once the green finish message is
displayed, add the energy module, and check the final energy value. This
energy is for eight atoms.
Next, we need to prepare a structure
to calculate the single atom. A new structure builder can be added, but
another structure can be added by opening the Structure List(
) on the upper right of the visualizer of the existing structure builder. Click to add a new structure(
), and create a cell with only one atom in the crystal builder menu.
) on the upper right of the visualizer of the existing structure builder. Click to add a new structure(), and create a cell with only one atom in the crystal builder menu.
It is important to set the length of
the cell to a large value. In the periodic-boundary cell, it is assumed
that the structure seen in the structure builder is repeated infinitely.
Thus, a vacuum should be created to separate the repeating nearby atoms
and prevent them from interfering with each other. If there is much
vacuum, the interaction between atoms decreases, but the calculation
time increases. Thus, it tends to set the vacuum width to as much as the
distance between gas molecules 10–15 â„«. This example uses 12 â„«.
For the energy calculation, add a new
QE module. For cutoff energy, 40–240, which is decided for a convergence
setting, needs to be used. However, as the single atomic energy is not
related to k-points, gamma (one k-point) can be set for a fast
calculation. Note that, in case of a single atom, a spin needs to be
considered according to the Hund’s rule to get a more correct energy.
Once the calculation is complete,
refresh the page, and check if the calculation is normally finished. If
so, add an energy module to check the energy.
Add a memo module, and paste the final
energy value of the silicon bulk and the atom to compare the data
easily. Calculate the energy for each atom, and find the difference to
get the Ecoh/atom of the silicon.
The cohesive energy calculated is 4.59 eV/atom, and the experimental value is 4.63 eV/atom. [2]
This shows a difference of about 0.04 eV. If the spin is not
considered, the calculation will have much error. Thus, it is good to
consider the spin polarization when calculating the energy of a single
atom.
https://blog.virtuallab.co.kr/en/2019/05/23/3-1-how-to-calculate-cohesive-energy/?fbclid=IwAR3l07RiwKcpX2tHDhAnpN5QTxbA3MfEhTypYr7XE6A8L0OtsZNq8ECeJxQ
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