Spin states in biochemistry and inorganic chemistry
University of Zaragoza, Spain
The electrons surrounding the nuclei of all matter around and within us can be in two different states, denoted the electron spin. This effect, although being purely quantum-chemical, has profound implications for real-world, large-scale systems like, for example, living tissue. In most cases, electrons of different spin pair up, effectively cancelling the spin-effect. In some cases, however, electrons prefer not to pair up, which leads to an excess of one type of electrons in a system. Depending on the exact conditions and surroundings, the number of these unpaired electrons can vary, leading to different spin-states not only for the individual electrons, but for much larger molecular species. In many cases, the spin-state has been found to be a key factor governing the behaviour of the system. Elucidating the role and effect of different spin states on the properties of a system, even deciding which spin-state occurs naturally, is presently one of the most challenging endeavours both from an experimental and theoretical point-of-view.
Reactivity patterns in organometallic and bioinorganic chemistry often depend critically on the spin state, e.g., on the spin-state preferences of reactants, products, intermediates and transition states [1,2]. For heme-proteins, this has been acknowledged for decades , and recently, spin-state controlled reactions have been proposed to be important also outside the realm of biomolecules, that is, in industrial catalysis . As a specific, intriguing example of this, merely one of a myriad, we consider the catalytic cycle of cytochrome P450cam that catalyzes the hydroxylation of R-camphor to 5-exo camphorol . In the catalytic cycle , a low-spin doublet is observed for the resting state which goes to a high-spin sextet after substrate binding [7-12]. This spin-flip in the first step seems to be determined primarily by the presence or absence of water molecules in the active site, and is vital for the specificity of the reaction taking place. Another key factor is a tyrosine residue that serves as an anchor for the natural substrate (R-camphor) and prepares it maximally for the subsequent hydroxylation [13-15]. For instance, a previous study  showed that upon binding to Tyr96, the substrate is found to be distorted, especially at the atom (C5) where the reaction takes place. The replacement of the Tyr96 residue by phenylalanine indeed reduces the regio- and stereo-specificity dramatically .
Another intriguing aspect of the catalytic cycle of P450cam is related to the step after the substrate has entered the active site . The cycle continues with an electron transfer from a reducing agent, in the natural system putidaredoxin [17,18]. to give a quintet state after the transfer. This electron transfer takes place only when substrate is present, that is, only for the high spin state. Moreover, it seems that only when the electron transfer has taken place, that dioxygen can enter the active site. In this process of dioxygen binding, there is a second spin-flip present. The paramagnetic dioxygen molecule (with a triplet ground-state) on its own already induces a change of the spin-state, which would have lead to a triplet. Instead, it goes to a singlet state. The subsequent steps to product formation probably follow a rebound mechanism involving “compound I”, but there are also studies that suggest other mechanisms [19-23].
In order to help understand these subtleties and explain the missing steps in the reaction mechanism that occur too fast for experiments to follow, theoretical chemistry can play an important role. However, theory is not without its own problems (see State of the art section). At present, the situation is such that it is advisable to always include the results from a number of different quantum-chemical methods, to ensure the results are consistent. In practice, when large molecular systems are of interest, the density functional theory (DFT) approach is the only viable alternative. There are, however, many different functionals that are proposed by different research groups (B3LYP*, TPSSh, OPBE/OLYP, SSB-D, M06-L, B3LYP, B2PLYP, …), without a clear consensus on which should be used (and why). The motivation for proposing this workshop is to be able to get together important players in the field and discuss this unfortunate situation thoroughly. The aim is to reach consensus on the current situation at hand, and more importantly, discuss best practices on how to deal with the problem in future scientific research.
The focus of the workshop will not be limited only to theory; many of the assumptions about spin-state preferences are based on experimental data, which may not be not conclusive in each and every case. For instance, different complications may occur in the experiments, such as dimerization, ligand exchange, or disproportionation, which make that the system studied theoretically does not correspond to the one for which experimental data are observed. Likewise, there may be metal impurities present in the sample that might interfere with the observation of magnetic moments. Recent examples of “failures” of DFT in our research group in Girona turned out to be most likely due to inconsistencies in the experiments (e.g., disproportionation as described in ref. [24,25]). In order to resolve this, and get a clear discussion about these effects, we have also invited several experimentalists (Mayer, Que, Ghosh, Costas) to share their experiences and insights on this.
The most popular method for studying (bio)inorganic catalysis is presented by Density Functional Theory (DFT) [26-28], due to its efficiency that enables to treat large systems of up to several hundreds, even thousands of atoms in a reasonable time. Also wave-function based methods can be used (for example, CASPT2), such as done by, e.g., de Graaf or Pierloot, with the significant draw-back that only much smaller systems can be treated. Almost all DFT studies in the literature so far have either used the B3LYP [29-30] or BP86 [31-32] functionals, which for most simple cases both give good results. This is no longer true when spin-states with energy levels in close proximity are involved [33,34], that is, when a transition metal like chrome, manganese, iron, cobalt or nickel is present. Previous studies [35-37] have shown that both of these functionals are unable to correctly predict the spin ground-state of these transition-metal complexes. Early GGA functionals like BP86 tend to overstabilize the low-spin state, while hybrid functionals like B3LYP tend to overstabilize the high-spin state (due to the inclusion of a portion of Hartree-Fock exchange) [34, 38]. Several remedies have been proposed, such as lowering the amount of Hartree-Fock exchange in B3LYP to 15% (B3LYP*) , mixing the Becke88 and PW91x [39,40] exchange functionals (XLYP, X3LYP) , or introducing a Hubbard U parameter , but none one of these was really satisfactory for all situations. In fact, it was suggested to always calculate the spin-state energies with a number of functionals. An important step forward was made by the application of Handy and Cohen’s optimized exchange (OPTX) functional (abbreviated as O in combination with other functionals, as in OPBE or OLYP) . Previous validation studies have shown the validity of the OPBE [33, 44] and OLYP [45-51] functional for the spin-state splittings of iron complexes. While for the vertical spin-state splittings a number of DFT functionals could be trusted to give the correct spin ground-state , this picture changed for relaxed splittings [25, 34]. The experience with the OPBE and PBE functionals for spin-states and (SN2) reaction barriers has led to the development of an improved GGA functional (SSB-D), which like OPBE works well for spin states. Other groups have advocated other functionals such as B3LYP* (Reiher, Siegbahn), OLYP (Ghosh), TPSSh (Jensen), or B2PLYP (Neese).
Note also the EuroBic conference that is being held the week before the CECAM workshop in Granada:
Mikael P. Johansson ( Girona University ) - Organiser
Marcel Swart ( ICREA and Univ. Girona ) - Organiser & speaker