antoine-levitt
commented
1 year ago So in general if you want a new term that isn't covered by the existing ones you have to implement it yourself: look at hartree.jl for instance. If you don't have an energy functional, you can set it to an arbitrary value; it might break things in DFTK (like the default heuristics for the SCF) but that can be fixed. The issue I see here is that your potential function is not a simple form in the density, because the kernel K(r,r') = fxc(r-r', n0)/fxch(n0') looks like a general nonseparable function of r and r' (not of r-r'). You can implement it directly, but it will probably be pretty expensive. I'd start by getting and idea of how costly (in flops and in ram) it is to form the matrix K(r,r') for all r,r' in the grid (of size basis.fft_size), for the system of interest. If it's doable you can try, but you will very likely be limited to very small systems.
aouinaayoub
mfherbst
I would like to use a new xc potential in the Kohn-Sham Hamiltonian for a given system. This xc potential does not have an energy functional, it reads:
$v{\rm xc}({\bf r},[n]) = v^{\rm LDA}{\rm xc} (n^c_r )$
where: $n({\bf r})$ is the electronic density,
$v^{\rm LDA}_{\rm xc}(n)$ is the LDA xc potential function,
$n^c{\bf r} = \int d {\bf r}' \frac{f{\rm xc}( |{\bf r}-{\bf r}'|, n0) }{f^h{\rm xc}(n'_0)} n({\bf r}')$,
with $f_{\rm xc}(|\mathbf{r}-\mathbf{r}'|,n0)=\left.\delta v{\rm xc}(\mathbf{r},[ n])/\delta n(\mathbf{r}')\right|{n=n_0}$ is the static non local xc kernel of the homogeneous electron gas with density $n0$, and $f^h{\rm xc}(n'_0)$ is its limit of zero wave-vector. Both functions are parameterized and available,
$n0=\frac{n({\bf r})+n^c{\bf r}}{2}$ and $n'_0=\frac{n({\bf r})+n({\bf r'})}{2}$.
Could you provide me with guidelines to implement and use this functional?