Computational Quantum Chemistry for Multiple-Site Heisenberg Spin Couplings Made Simple: Still Only One Spin–Flip Required

We provide a simple procedure for using inexpensive ab initio calculations to compute exchange coupling constants, JAB, for multiradical molecules containing both an arbitrary number of radical sites and an arbitrary number of unpaired electrons. For a system comprised of 2M unpaired electrons, one needs only to compute states having the Ŝz quantum number M – 1. Conveniently, these are precisely the states that are accessed by the family of single spin–flip methods. Building an effective Hamiltonian with these states allows one to extract all of the JAB constants in the molecule. Unlike approaches based on density functional theory, this procedure relies on neither spin-contaminated states nor nonunique spin-projection formulas. A key benefit is that it is possible to obtain completely spin-pure exchange coupling constants with inexpensive ab initio calculations. A couple of examples are provided to illustrate the approach, including a 4-nickel cubane complex and a 6-chromium horseshoe complex with 18 entangled electrons.