Question

Describe a plausible scenario in which a relative error of 10^-6 would be acceptable but any larger error would be unacceptable.

Answer 1

To explain this I would like to take the example of total energy (E_tot) of a solid. If we estimate the E_tot in the unit of Rydberg (Ry) then the error of 10^-6 in Ry between two consecutive iterations will give the error value 0.0000136 eV (since, 1 Ry = 13.6 eV). And also if the given solid is magnetic then the energy difference varies in milli-electron volt (meV).

In the present case 0.0000136 eV = 0.0136 meV (1 eV = 10³ meV). ------> case 1

However, if we consider error as 10^-5 Ry then in meV it is 0.136 meV. -------> case 2

Hence, the diffence in energy between cases 2 and 1 is 0.136 - 0.0136 = 0.1224 meV.

I would like to note that 0.1224 meV can not be simply ignored when the effect of spin-orbit interaction is investigated in the system.