Magnetic couplings using DFT in a spin frustrated system

Question

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?

Thanks in advance

P.S.: I’m doing my calculations using the ORCA package.

Answer 1

DFT is fundamentally the wrong tool for a system like this. When you say that the spin 'resonates' between several different states what you are explicitly saying is that the wavefunction is strongly statically correlated. DFT is a single reference method, so any experimental agreement you get from it in a case like this is at worst wrong and at best right for the wrong reasons (and the range of functionals will likely cover that whole spectrum).

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)