Optimization of the orthorhombic structure

The optimization of the orthorhombic structure is to optimize:

- The ration b / a
- The ration c / a
- The volume

There are many ways to do that:

First way: the procedure is cited in this thesis: Procedure 01

Second way: the procedure is cited in this dissertation: Procedure 02

We have adopted the first way and we adapt it to the wien2k code as follows:

 The instruction that allows to optimize the ratio b/a over the garphical interface w2web is "Optimize volume or c / a ratio." We choose "vary b/a with constant c/a ration and  volume "; then we varies the ratio b/a between -6% to 6% of its initial value with a step of 3% and the sign "#" is removed  in front "xdstart" in the shell script "optimize.job".

The shell script produces, based on the files case.struct and case.initial.struct, a series of file structure that differ from the original file by the value of b/a.

The results of the optimization of the report, which is a calculation SCF, are saved in the file ": tmp". We calculate the optimal value of b/a matching the minimum energy after an interpolation to a fourth order equation:


              E (x) = a0 + a1x+ a2x^2 + a3x^3+a4x^4

 with x = b/a and the minimum energy corresponds to the derivative dE/dx = 0 ,ie: 

              a1+a2x+a3x^2+a4x^3 = 0

Then we use this new value of b/a to build a new file structure that will be used to optimize the ratio c/a. We do the same thing for optimization the ratio c/a. We will do the same thing to optimize the c/a ratio and we use the new value to build a new file structure that will be used to optimize the volume. The optimum volume, the bulk modulus and its first derivative are calculated after an interpolation of results obtained using the equation Murnagham.