In our bulk Silicon calculation we had a rigid supercell shape and the starting atomic positions of the silicon atoms
were those known to be correct. What effect will a variable cell calculation have?

In the cell file

`FIX_ALL_CELL : FALSE`

In the .param file our keywords are;

`finite_basis_corr : 2`

which ensures that an automatic finite basis set correction is made

The complete output is in the link. We see that the first three steps are indeed
singlepoint energy calculations

Calculating finite basis set correction with 3 cut-off energies. Calculating total energy with cut-off of 270.000eV. ------------------------------------------------------------------------ <-- SCF SCF loop Energy Energy gain Timer <-- SCF per atom (sec) <-- SCF ------------------------------------------------------------------------ <-- SCF Initial 0.00000000E+000 4.05 <-- SCF 1 -2.07999179E+002 1.03999590E+002 15.06 <-- SCF 2 -2.16644967E+002 4.32289377E+000 25.37 <-- SCF 3 -2.16547612E+002 -4.86773393E-002 35.44 <-- SCF 4 -2.16472419E+002 -3.75966977E-002 45.52 <-- SCF 5 -2.16473346E+002 4.63609274E-004 51.23 <-- SCF 6 -2.16473342E+002 -2.09197016E-006 55.58 <-- SCF 7 -2.16473343E+002 7.21451053E-007 59.95 <-- SCF 8 -2.16473343E+002 1.95459391E-008 64.28 <-- SCF ------------------------------------------------------------------------ <-- SCF Final energy = -216.4733431455 eV (not corrected for finite basis set) Calculating total energy with cut-off of 275.000eV. ------------------------------------------------------------------------ <-- SCF SCF loop Energy Energy gain Timer <-- SCF per atom (sec) <-- SCF ------------------------------------------------------------------------ <-- SCF Initial -2.16473343E+002 65.79 <-- SCF 1 -2.16474422E+002 5.39545221E-004 72.46 <-- SCF 2 -2.16474423E+002 2.77186149E-007 76.73 <-- SCF 3 -2.16474423E+002 2.10512829E-007 81.13 <-- SCF ------------------------------------------------------------------------ <-- SCF Final energy = -216.4744232114 eV (not corrected for finite basis set) Calculating total energy with cut-off of 280.000eV. ------------------------------------------------------------------------ <-- SCF SCF loop Energy Energy gain Timer <-- SCF per atom (sec) <-- SCF ------------------------------------------------------------------------ <-- SCF Initial -2.16474423E+002 82.48 <-- SCF 1 -2.16475528E+002 5.52276233E-004 89.09 <-- SCF 2 -2.16475528E+002 3.59413754E-007 93.47 <-- SCF 3 -2.16475529E+002 2.76001709E-007 97.85 <-- SCF ------------------------------------------------------------------------ <-- SCF Final energy = -216.4755290347 eV (not corrected for finite basis set) For future reference: finite basis dEtot/dlog(Ecut) = -0.061086eV Total energy corrected for finite basis set = -216.475512 eV

With the finite basis set correction in place the calculation can proceed as normal. The calculation completes and we have a silicon bond length of 2.328 Å which is 0.17% out and an improvement of about 1.7% on our fixed cell calculation.

We get a bonus. The calculation of the finite basis set correction provides information that can be used to estimate the bulk modulus of silicon based upon the energy changes as the cell size changes.

The known bulk modulus of silicon is 98.8 GPa at room temperature (Kittel page 59 [5]) and our zero temperature estimation is only 1 % out. A more rigorous way to calculate this quantity would be to plot energy versus cell volume for a variety of cell volumes (perhaps individually done as fixed cell calculations) and to fit a curve to this plot. The bulk modulus B can then be calculated from

(1) |

In summary the user should become more inclined to a finite basis set correction whenever there is uncertainty about whether the final expected configuration of the supercell might be very different from the initial configuration.