I was reading and (still) trying to understand Hartree-Fock Theory. I read that exchange interaction only occurred between particles with parallel spin, and not the opposite spin, which is why there is no exchange in Helium, but there are in Carbon. Can someone please explain to me why that is?...

In the original paper of Jahn et Teller (https://royalsocietypublishing.org/doi/pdf/10.1098/rspa.1937.0142, section I-Two Examples) are described two examples: a linear molecule and one with square planar configuration of nuclei. I don't understand this part: There is a similarity between the tw...

I am modeling a metabolic network of signaling pathways through a system of ordinary differential equations $$ \frac{dX}{dt} = F(X) = S v $$ where $X$ is the vector of molecules (121 in my case) involved in the system, $(F_i)_i$ is the vector right hand side (production of $X_i$ - consumption of ...