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 =
10^{3} 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.

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