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4

For questions like these where the answer is not provided by the Quantum ESPRESSO user guide, it usually pays off to search the source code on the QE gitlab repository. Searching for "freq" turns up find_mode_sym.f90, which shows that this information is stored in the name_rap variable. Searching for "name_rap(1)" turns up PW/src/...


3

Since we are considering the left side of your Eq. 69 as a function of $\mathbf{r}$, it must be the constant function of $\mathbf{r}$ that is 0 everywhere: $0(\mathbf{r})$. If it were any other function, such that the left side of the equation were to be non-zero anywhere, we would not write a 0 there. So it's true that your Eq. 69 is saying that the RHS is ...


5

Yes, the sum of these potentials is zero everywhere with the true ground-state density. But the true ground-state density is generally only expressible when the basis set is complete (if you know the true ground-state density in advance, you can of course construct a finite basis set that reproduces it exactly, but if you don't know the exact density, you ...


8

Roughly speaking and provided that the Hohenberg-Kohn theorem applies, if the $v$-representable ground state density of an interacting system $\rho$ is additionally non-interacting $v$-representable, then by definition there exists a non-interacting system with potential $V$ and $\rho$ as its ground state density. By the virtue of the Hohenberg-Kohn theorem, ...


5

Yes your understanding is correct. It helps to think about BOMD as classical dynamics. The electrons are the springs that hold the masses together and the nuclei are the masses.The two key terms are the internal energy (U) and the kinetic energy of the masses (K). We seek to calculate the positions of the system as a function of time, which we can do ...


6

I explained Car-Parrinello MD here, and a key point is that it approximates BOMD (Born-Oppenheimer Molecular Dynamics) where the electronic state is minimized (i.e. the ground electronic state is found and used) at each step. The reason for the minimization in CPMD at the first step, is the same as the reason in the earlier BOMD method that it approximates. ...


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