[QE-users] derivative of the conduction orbitals with respect to k

[Wang, Xiaoming]

Hi all,

I would like to calculate the derivative of the KS orbitals with respect to k for the conduction states. The derivative of the occupied orbitals can be calculated using the linear response routine cgsolve_all.f90 in LR_Modules, which solves the Equation 30 of the paper Rev. Mod. Phys., 73, 515-562. For the conduction states, I refer to Eq. 25 of the same paper and adapt to the k derivative (with v the velocity operator):

( H - e_n ) dpsi_n/dk = -( 1 - |psi_n><psi_n| ) v |psi_n>

I replaced d0psi of cgsolve_all with the right-hand side vector of the above equation and remove the alpha*Pv term. I managed to get the CG iterations converged but with much more steps (~100) than the default implementation for the occupied states. To check whether the obtained first order wave functions are correct or not, I calculated some properties (orbital magnetization in my case) which only needs occupied orbitals. However, the method using the above equation produced different results compared with the QE default implementation which agrees with literature. So, here is my question: is there anything wrong to use the above equation to calculate the wave function derivative?

Best,
--------------------------------------------
Xiaoming Wang
Postdoctoral Research Associate
Department of Physics and Astronomy
University of Toledo
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