# Magnetic couplings using DFT in a spin frustrated system

I’m working with a trimeric copper system that have the classic triangular shape and experiences spin frustration. This is my first time dealing with such system and, so far, from what I’m reading, I know that the spins resonate between ↑↑↑ ↔ ↑↓↑ ↔ ↑↑↓ and that the triangle have couplings $$J1_{ab}$$, $$J2_{bc}$$ and $$J3_{ca}$$.

My question is: how it is possible, using DFT, to obtain the three magnetic couplings ($$J1_{ab}$$, $$J2_{bc}$$, $$J3_{ca}$$)? I’m supposing that the strategy of breaking the molecule in three dimers and calculating a broken-symmetry is not going to work, right?

If we knew the exact density functional DFT would, of course, be exact. Unfortunately, real functionals are parametrized for mostly organic compounds and the occasional single metal, but certainly nothing as correlated as a spin frustrated Cu$$_3$$ cluster. If you want a result which is believable, you need to use a real multireference method. (It's not going to be a quick calculation, but you only need a single point so it's not too bad)