Consistent Evaluation of Magnetic Exchange Couplings in Multicenter Compounds in KS-DFT: The Recomposition Method

Abstract

The use of broken-symmetry calculations in Kohn− Sham density functional theory has offered an affordable route to study magnetic exchange couplings in transition-metal-based compounds. However, computing this property in compounds exhibiting several couplings is still challenging and especially due to the difficulties to overcome the well-known problem of spin contamination. Here, we present a new and general method to compute magnetic exchange couplings in systems featuring several spin sites. To provide a consistent spin decontamination of J values, our strategy exploits the decomposition method of the magnetic exchange coupling proposed by Coulaud et al. and generalizes our previous work on diradical compounds where the overall magnetic exchange coupling is defined as the sum of its three main and properly extracted physical contributions (direct exchange, kinetic exchange, and spin polarization). In this aim, the generalized extraction of all contributions is presented to systems with multiple spin sites bearing one unpaired electron. This is done by proposing a new paradigm to treat the kinetic exchange contribution, which proceeds through monorelaxations of the magnetic orbitals. This method, so-called the recomposition method, is applied to a compound featuring three Cu(II) ions with a linear arrangement and to a recently synthesized complex containing a Cu 4 O 4 cubane unit presenting an unusual magnetic behavior.

Revisiting magnetic exchange couplings in heterodinuclear complexes through the decomposition method in KS-DFT

“…Some of the present authors recently generalised the decomposition scheme to the context of systems featuring several couplings with one unpaired electron per magnetic centre. 65 We use this strategy here to provide a thinner description of the coupling in extracting the individual electron–electron interactions, considering each magnetic orbital as a site. This allows us to decompose these different electron–electron interactions into their direct and kinetic exchange contributions presented in Table 4.…”

“…The overall magnetic exchange coupling may be evaluated through the recomposition method by taking the sum of these three contributions as 62,65 J Σ = J 0 + Δ J KE + Δ J SP .…”

“…It offers a new affordable route to compute properly spin-decontaminated magnetic exchange couplings in systems featuring more than two magnetic centres, a situation where the spin contamination is almost all the time neglected. 65 However, to date, the decomposition scheme has only been limited to couplings involving one unpaired electron per magnetic centre.…”

The resolution of the weak-exchange limit made rigorous, simple and general in binuclear complexes

“…39 Many seminal studies show the use of configuration interaction schemes to calculate magnetic properties. [40][41][42][43][44][45][46][47] It is worth noting that density functional theory (DFT) is equally involved in rationalizing magnetic data, [48][49][50][51][52][53][54] as well as single-reference spin-flip approaches, [55][56][57] and more recently coupled-cluster methods. [58][59][60] In principle, the low-energy ab initio spectrum offers sufficient detail for calculating anisotropy parameters and spin-orbit correction to the exchange interaction if a SOCI is performed, 22,33 as well as EPR parameters and wT profiles provided that the Zeeman interaction is treated.…”

Natural orbitals and two-particle correlators as tools for the analysis of effective exchange couplings in solids

“…66,67 Unfortunately, such terminology is often misleading since these terms are defined differently in various publications. Such an analysis (sometimes emphasized as an exchange decomposition) has been less rigorously extended to BS-DFT, [68][69][70][71] where such terms are defined through the ''energies'' of various unoptimized, partly optimized, and fully optimized restricted open-shell determinants with approximate spin projections. Besides ambiguity, an apparent limitation of this decomposition is in its strong dependence on a particular family of methods, making it not applicable for the analysis and comparison of magnetic couplings between various electronic structure methods.…”