Computation of Exchange Couplings by Means of an Exchange-Dedicated Perturbation Theory

The accurate computation of high-spin/low-spin gaps remains a challenging task in computational chemistry, with significant implications for both theoretical studies and experimental applications. In this work, we present an exchange-dedicated perturbation theory (EDPT2) that allows an efficient calculation of exchange couplings in magnetic systems. Our approach builds on a previously developed second-order perturbative scheme based on de Loth's formalism but refines the treatment of singlet wave functions by explicitly incorporating ionic determinants in the zeroth-order description. The EDPT2 method is derived from a two-electron-two-center model and can be applied to multispin systems using minimal CAS-generated orbitals. A key advantage of EDPT2 lies in its computational efficiency, with a scaling of N⁴, where N is the number of basis functions. Benchmark calculations on diverse test systems demonstrate that EDPT2 achieves high-spin/low-spin gaps with accuracy comparable to the commonly used FIC-NEVPT2 method. Beyond its efficiency, EDPT2 provides valuable information on the mechanisms that govern magnetic exchange. The method allows for a detailed decomposition of second-order contributions, facilitating the identification of dominant exchange pathways. This is exemplified on two bis(nitronyl nitroxide) biradicals, where dynamic spin polarization emerges as the key exchange mechanism. Furthermore, using the example of a trisnitroxide triradical, we demonstrate how the insights from EDPT2 can be used to prepare selective multireference CI approaches. A combined DDCI1 approach with EDPT2-derived corrections is shown to successfully reproduce the experimental doublet-quartet gap.