This is in cartesian coordinates, so |k|=sqrt(kx^2+ky2). On the other hand if you start from the general definition that the length of a vector is the square root of the scalar product of the vector with itself, you can work out the general formula even if the basis vectors are not orthogonal.

Roberto D'Agosta

Hi Professor,

I am using yambo for my research to calculate dielectric function for every q point (wave vector). So, there is an exponential term, exp(2*|q|*d),where q is the so called q point in DFT and d is the separation distance between two materials(graphene).

For example, one of the q point in yambo as follows:

0.450530976 0.780342519 0.000000000 (unit: 1/a.u.)

so, what i did, i simply apply this formulae |q|=sqrt(qx^2+qy^2) and then insert it in the exponential factor. However, my result very close to the other study (though not perfect, there is small discrepancy). I email the author and discuss about the issue. And he mentioned as follows:

"I think your q-point set is correct. Please also check the value of |q| used in Eq. 9. The lattice is a parallelogram so that |q| does NOT simply equal to sqrt(qx^2+qy^2)."

That's why I posted here, professor.

This changes things obviously. In your question, the k point is reported in cartesian coordinates, and thus the simple formula applies. In the case of Yambo, if the q vectors are reported in non-orthogonal coordinates you need to change something. In this case, assume you have q= a v1+ b v2 then

|q|^2 = a^2 v1^2 + b^2 v^2 + 2 a b v1.v2

where v1.v2 is the scalar product of these two vectors. As i said, there is nothing magical here, you simply need to apply a little geometry and algebra. Clearly, if v1.v2 is small this |q| would be close to the value obtained by neglecting it.