# CP2K Open Source Molecular Dynamics

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exercises:2016_uzh_cmest:bulk_modulus_calculation

# Calculating the bulk modulus of Silicon

Many times when doing an analysis of a (novel) material, you have to validate your model against values from real experiments. One of those values is the bulk modulus of a material which we are going to calculate for bulk silicon.

If you are looking at a crystal with a well known structure, the simulation study gets particularly easy since you can specify the atomic coordinates in terms of an irreducible cell (note the SCALED keyword in the &COORD section):

silicon.inp
&GLOBAL
PROJECT silicon
RUN_TYPE ENERGY
PRINT_LEVEL MEDIUM
&END GLOBAL
&FORCE_EVAL
METHOD Quickstep
STRESS_TENSOR ANALYTICAL
&DFT
BASIS_SET_FILE_NAME  BASIS_SET
POTENTIAL_FILE_NAME  POTENTIAL
&POISSON
PERIODIC XYZ
&END POISSON
&SCF
SCF_GUESS ATOMIC
EPS_SCF 1.0E-6
MAX_SCF 500
&END SCF
&XC
&XC_FUNCTIONAL PBE
&END XC_FUNCTIONAL
&END XC
&END DFT
&SUBSYS
&KIND Si
ELEMENT   Si
BASIS_SET DZVP-GTH-PBE
POTENTIAL GTH-PBE
&END KIND
&CELL
ABC 5.430697500 5.430697500 5.430697500
PERIODIC XYZ
&END CELL
&COORD
SCALED
Si    0    0    0
Si    0    2/4  2/4
Si    2/4  2/4  0
Si    2/4  0    2/4
Si    3/4  1/4  3/4
Si    1/4  1/4  1/4
Si    1/4  3/4  3/4
Si    3/4  3/4  1/4
&END COORD
&END SUBSYS
&END FORCE_EVAL
• By scaling the lattice constant (for example between $0.97 \cdot a$ and $1.1 \cdot a$) you can now run the simulation for different volumes and get a volume-energy curve. You may want to use and adapt the script from the previous exercise
• Fit this curve to the Birch–Murnaghan equation of state to recover the bulk modulus $B_0$