Abstract
Spin-state energetics of exchange-coupled copper complexes pose a persistent challenge for applied quantum chemistry. Here, we provide a comprehensive comparison of all available theoretical approaches to the problem of exchange coupling in two antiferromagnetically coupled bis-μ-hydroxo Cu(II) dimers. The evaluated methods include multireference methods based on the density matrix renormalization group (DMRG), multireference methods that incorporate dynamic electron correlation either perturbatively, such as the N-electron valence state perturbation theory, or variationally, such as the difference-dedicated configuration interaction. In addition, we contrast the multireference results with those obtained using broken-symmetry approaches that utilize either density functional theory or, as demonstrated here for the first time in such systems, a local implementation of coupled cluster theory. The results show that the spin-state energetics of these copper dimers are dominated by dynamic electron correlation and represent an impossible challenge for multireference methods that rely on brute-force expansion of the active space to recover correlation energy. Therefore, DMRG-based methods even at the limit of their applicability cannot describe quantitatively the antiferromagnetic exchange coupling in these dimers, in contrast to dinuclear complexes of earlier transition metal ions. The convergence of the broken-symmetry coupled cluster approach is studied and shown to be a limiting factor for the practical application of the method. The advantages and disadvantages of all approaches are discussed, and recommendations are made for future developments.
Highlights
Local spins in inorganic and bioinorganic systems with multiple open-shell transition metals couple to a multitude of total spin states whose energy is a function of the total spin S
To assess the performance of BS-density functional theory (DFT) for predicting the exchange coupling constant J of the selected copper complexes 1 and 2, we present a series of calculations using the generalized-gradient-approximation (GGA) functionals BLYP, [47, 79] PBE, [80, 81] and BP86 [82], the metaGGA TPSS, [38] hybrid GGA B3LYP, [47, 48] B1LYP, [48] PBE0 [83] and B3PW91 [48, 80] and meta-hybrid GGA functionals TPSSh [65] and TPSS0 [63, 64]
We showed that DFT is a computationally accessible approach yet unreliable as a predictive tool, and that density matrix renormalization group (DMRG)-based CI and NEVPT2 fall short even with relatively large active spaces
Summary
Local spins in inorganic and bioinorganic systems with multiple open-shell transition metals couple to a multitude of total spin states whose energy is a function of the total spin S. A number of previous studies of magnetic couplings relied on a minimal active space that comprises only the partially occupied metal d-orbitals [5, 12,13,14] Since this active space does not capture all of the essential physics of magnetic exchange coupling, sophisticated and computationally demanding approaches to dynamic electron correlation such as the difference-dedicated CI (DDCI) are needed to obtain qualitatively and quantitatively accurate results [15, 16]. A different strategy to compute magnetic exchange couplings based on large active spaces has been explored This conceptual shift was triggered by the development of techniques that allow for large active spaces in CASSCF-type calculations on the order of 20–50 orbitals at considerably reduced computational cost. We assess the performance of all four
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