Spin states of (bio)inorganic systems: Successes and pitfalls


  • Marcel Swart

    Corresponding author
    1. Institució Catalana de Recerca i Estudis Avançats (ICREA), Pg. Lluís Companys 23, 08010 Barcelona, Spain
    2. Institut de Química Computacional and Departament de Química, Universitat de Girona, Campus Montilivi, 17071 Girona, Spain
    • Institució Catalana de Recerca i Estudis Avançats (ICREA), Pg. Lluís Companys 23, 08010 Barcelona, Spain
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The calculation of spin-state splittings of transition-metal complexes is known to be very sensitive to the level of theory and the quality of the basis set. The performance of density functionals is in general understood, with older pure functionals overstabilizing low spin states, and Hartree–Fock and hybrid functionals doing the same for the high spin states. More recent functionals (OLYP/OPBE, TPSSh, SSB-D, M06-L) seem to improve on these, but there are still some systems that prove difficult. This Perspective describes some of the recent successes and pitfalls in the description of spin states and treats both methodology and applications such as metal-oxo complexes, exchange-enhanced reactivity, spin-state catalysis, and spin-crossover compounds. © 2012 Wiley Periodicals, Inc.


Although spin states are present for all elements and all molecules, they are (bio)chemically relevant only for a limited number of organic molecules (e.g., singlet vs. triplet states of carbenes). The situation is completely reversed when transition metals are present, which makes that different spin states are accessible for the majority of these complexes. Of course, this results directly from the d-orbitals of the metals that are close in energy, and which can be occupied in different ways depending on the metal oxidation state, its ligands, and its geometry.

The textbook example is that of a metal in an ideal octahedral (Oh) coordination that leads to a separation of the d-orbitals into two blocks: the triply degenerate (nonbonding) T2g and doubly degenerate (antibonding) Eg orbitals. The energy difference between these T2g and Eg orbitals is then usually referred to as the octahedral splitting (Δoct, or 10Dq). The magnitude of this splitting depends on the “crystal field” strength of the ligands, for example, the Fe(II)(H2O)62+ (d6) complex is high-spin (‘t2g4 ‘eg2) with a Δoct splitting of about 30 kcal mol−1, whereas Fe(II)(CN)64− (d6) is low spin (‘t2g6) with a Δoct splitting of about 94 kcal mol−1.1

Spin states play an important role in enzymatic reactions (e.g., cytochrome P450cam, vide infra), in metal-oxo complexes, in spin-crossover (SCO) compounds and there exists even spin-state catalysis where different reactions take place for different spin states. However, computational studies have shown that a correct description of the spin state is not trivial (vide infra), and a combination of different density functionals and/or ab initio methods may be needed. These aspects are highlighted in this short Perspective that describes recent advances and discusses future directions for spin states in (bio)inorganic chemistry. A very few recent papers are discussed, which are chosen as being representative of current research in spin-state chemistry, and discussed with personal views of the author regarding the future direction of the topic.

Advances in Methodology

Probably one of the first papers to describe the sensitivity of the spin ground-state of transition metal complexes was a study by Trautwein and coworkers2 in 2001, who showed for the first time the intrinsic spin-state preferences of hybrid functionals such as B3LYP (for high spin) and early generalized gradient approximations (GGA) functionals like BLYP/BP86 (for low spin). Since then new density functionals were proposed (B3LYP*, OPBE/OLYP, TPSSh, M06-L, SSB-D) that were shown to perform better (see e.g., Refs. 3, 4 for a more detailed review of the performance of density functionals for spin states). Also, the use of wavefunction methods is not without hazards, with the “gold standard” CCSD(T) proving unreliable for some systems5 due to the intrinsic multiconfigurational character of the wavefunction. More reliable data were obtained with CASPT2,5, 6 but this method is computationally expensive as well, needs specific expertise and much depends on the choice of orbitals to be included in the active space and the basis set used. For instance, for Fe(H2O)62+, CASPT2 with six electrons in five orbitals 6, 5 complete active space (CAS) space with the small 6-31G** basis set gives a ΔELH splitting (ΔELH = ELEH) of 61.8 kcal·mol−1,7 which goes down by about 16 kcal mol−1 (to give 46.3 kcal mol)−1 with 12 electrons in 10 orbitals 12, 10. Using larger basis sets, Pierloot and Vancoillie6 found values of 52.0 (6, 5 CAS) and 47.8 kcal mol−1 (12, 10 CAS), respectively. Similarly, a very recent paper8 on Mn-oxo corrole and corrolazine shows differences of up to 5 kcal mol−1 between CASPT2 and RASPT2 for low-lying states (8–15 kcal mol−1 above the ground state), and up to 10 kcal mol−1 for higher ones (31–42 kcal mol−1 above the ground state). However, one of the most important things to be noted in this latter paper is that even though there are many spin states within a range of 20 kcal mol−1 for the Mn-oxo species,8 both CASPT2/RASPT2 and density functionals (BP86, B3LYP, PBE0, OLYP) agreed very well on the ground-state for Mn-oxo with both the corrole and corrolazine ligands.

Another critical component for computational studies on spin-state splittings is the basis set (as already touched upon above). In 2008, we reported spin-state splittings with a series of basis sets using either Slater-type orbitals (STOs), Gaussian-type orbitals (GTOs), and basis sets including effective core potentials (ECPBs).9 Large GTO basis sets were needed to converge to the results from the STO basis sets that converge much faster; standard ECPBs like SDD, LanL2DZ, and LACV3P(++**) were giving systematically different results and therefore were discarded as unreliable for spin-state splittings. The poor results of small GTO basis sets (3-21G*, 6-31G*) were improved by adaptations to include three valence d-functions (s3-21G*, m6-31G*, s6-31G*).10, 11 Since then, the GTO series by Ahlrichs and coworkers (def2-tzvp, def2-qzvp) were found to be reliable for spin-state splittings, whereas the cc-pVTZ-pp ECPB basis set was giving quite good results and getting close to the STO/GTO result (see Table 1).

Table 1. Quartet-sextet splitting[a] (OPBE, kcal mol−1) of FeFHOH with several basis sets.
  • [a]

    ΔEsq = Esextet − Equartet; each splitting obtained with geometries optimized with same basis set.

  • [b]

    From Ref. 9.

  • [c]

    ECP-containing basis set (ECPB), unpublished data (K. Peterson).


In cases where a change in spin-state takes place during a reaction, as is, for example, the case in multistate reactivity or SCO compounds, it may be useful to find the minimum energy crossing point,12 also known as the conical intersection. Furthermore, of interest is also a perspective on the calculation of physical and spectroscopic properties of bioinorganic species that was published recently.13

Metal-Oxo Species and Exchange-Enhanced Reactivity

Heme-containing proteins perform a wide range of functions including electron transfer, oxygen transfer and storage, gas sensing, gene regulation, and catalysis.14 In the case of catalysis, the active complex often involves a metal-oxo (M[DOUBLE BOND]O) species, as is, for example, the case in horse radish peroxidase, catalase, and (probably) cytochrome P450. The latter family of enzymes, with P450cam as prototypical and most studied example,3 shows an intriguing catalytic cycle that includes a number of spin flips. That is, starting from a low-spin ferric (FeIII, doublet) resting state with six water molecules in the active site, the spin state changes to high-spin ferric (sextet) on substrate binding. Only then does the first electron reduction take place giving a high-spin ferrous (FeII, quintet) state, upon which a dioxygen molecule can enter the active site leading to a second spin-flip to give low-spin ferrous (FeII, singlet). Afterward, double protonation of the distal oxygen and a second electron reduction probably leads to compound I (a FeIV[DOUBLE BOND]O iron-oxo species) and the leaving of the distal oxygen as a water molecule.15 This compound I then hydroxylates the substrate involving most likely a rebound mechanism (and two-state reactivity).16

There also exist nonheme iron enzymes in biology that have iron-oxo as the active species, and for which, many biomimetic complexes have been synthesized.17 Intriguingly, whereas the enzymatic species are high-spin (quintet), most biomimetic complexes have intermediate spin (triplet).18, 19 Without any doubt, the protein environment in the enzymes is designed for optimal efficiency of the reaction(s) taking place, and plays a role as well in the spin ground-state of the iron-oxo species. One of the first crystal structures with a terminal FeIV[DOUBLE BOND]oxo indeed was intermediate spin, as indicated by Mössbauer spectroscopy.18 High-spin biomimetic complexes remain rare with very few examples,20–23 the set of which was very recently extended by a complex with a trigonal pyrrolide platform.19 Que and coworkers24 recently also reported a Fe(IV)-oxo-hydroxo species, starting from a high-spin FeII(benzilate) complex.

The spin state involved in the activation of H[BOND]H, C[BOND]H, and C[DOUBLE BOND]C bonds by metal-oxo species was recently put into perspective by Shaik et al.,25 who argued for the analog of Hund's rules in transition-metal chemistry. Their principle of exchange-enhanced reactivity (EER) is indeed intuitive, easily applicable and works satisfactorily as shown in another recent contribution.26 The ideas behind it are based on Hund's rule of maximum multiplicity for atoms, which reflects the Pauli-exclusion principle and the corresponding repulsion between like-spins (e.g., α–α or β–β). The avoidance of this repulsion leads to (exchange) stabilization, but only when the electrons are located on the same atom. The extension to transition-metal complexes follows earlier work, which showed that spin ground-states could be understood as resulting from a compromise between exchange-stabilization and the (octahedral) splitting of the d-orbitals. For example, larger exchange-stabilization leads to a stabilization of the high-spin state, whereas larger (octahedral) splitting favors low-spin states. However, the key to the EER-principle is the recognition that the number of exchange interactions on the metal may change during the course of a reaction, which can have a profound effect on the reaction barrier. This is shown in the recent Angewandte paper,26 where Shaik and coworkers illustrate the EER-principle for a H-abstraction reaction. In it, they study a MnV–corrolazinato complex that is able to abstract a hydrogen from dihydroanthracene (DHA). The spin ground-state of the MnVO-oxo complex is either a singlet or triplet, depending on the axial ligand X (X = none, F, CN) and which computational method was used for its determination. More importantly than the spin state of the reactant is, however, the spin state of the transition state and its character (see Fig. 1).

Figure 1.

Molecular orbital occupations of nonenhanced and exchange-enhanced TS.

In the case of the H-abstraction from DHA, there are three possible (viable) electronic states for the transition state (TS). The first one starts from the spin ground-state of the reactant, and follows the singlet state with the transfer of an α-electron from the substrate to the metal; the second one (nonenhanced triplet) starts from the triplet state of the reactant, involving the transfer of a β-electron from the substrate; and finally, the third one, also starting from a triplet state of the reactant and involving the transfer of an α-electron from the substrate. In all three cases does the number of exchange interactions on the metal increase, but it does so the most for the third state that is truly exchange-enhanced. It is in fact obtained by coupling a quartet on the Mn[DOUBLE BOND]O moiety with a doublet on the substrate. The beauty of the EER-principle is that based on the molecular orbitals of the reactant metal-oxo species, one can predict the spin state of the TS that will be followed with concomitant decrease of the reaction barrier. Experience shows that these predictions indeed hold true.25, 26

Spin-State Catalysis

Gibson and coworkers27 reported in 2006 a polymerization reaction using α-diimine-FeII complexes where the spin state correlated with the catalytic reactivity and different pathways were followed for different spin states. The spin state of the reactant depends on the ligands R1 and R2 (see Fig. 2), and those with high spin (R1 = cyclohexyl, tert-butyl; R2 = H) follow the atom-transfer radical polymerization (ATRP) pathway. In contrast, with other ligands (R1 = 2,6-isopropyl2-phenyl, R2 = H) an intermediate spin state was observed for the reactant and the catalytic chain transfer (CCT) pathway was followed.27 Moreover, electron-withdrawing groups at the R3 position favor CCT, whereas electron-donating groups there favor ATRP. It was suggested that the spin state of the iron(III) intermediates A and B would be the deciding factor for which pathway is followed. We have studied these complexes computationally,28 because we are now convinced that the SSB-D functional29 seems to work well for prediction of spin states (ongoing work).

Figure 2.

ATRP versus CCT.

Our study with three different R2 groups (R2 = PhF, PhOMe, and PhNMe2) indicated that all three reactants have a high-spin (quintet) ground-state, in agreement with experiment.30 Binding of a chloride radical (to give the FeIII complex A in Fig. 2) leads for all three R2 groups to a high-spin (sextet) FeIII state; in contrast, the complexation of an organic radical (to give the FeIII complex B) leads to an intermediate (quartet) spin state. Magnetic moment measurements indicated30 that for complex A only R2 = PhNMe2 should be high spin, whereas the other two should be the rarely seen intermediate spin state. Given that our calculations were clearly indicating a high-spin (by 10–12 kcal mol−1) with only a small variation between the three R2 groups, we found it unlikely that our calculations were in error. Indeed, there were problems experimentally with obtaining meaningful 1H NMR spectra of the FeIII[BOND]Cl3 species. Crystallization attempts also failed, leading in one case to a disproportionation of the complexes with loss of a FeCl3 group. Therefore, we explored a number of pathways: (a) forming only neutral species, (b) forming two charged ferromagnetically coupled Fe-complexes, (c) charged organic radical coupled to FeClmath image, and (d) similar to (c) but including hydrogen abstraction from the solvent. Pathway (b) was clearly favored for R2 = PhNMe2 and would lead to a spin magnetic moment of 5.92 μb (similar to the value observed experimentally for this ligand). For the other R2 ligands, pathway (d) is only slightly less favorable than (b) and would lead to a spin magnetic moment of 4.18 μb, to be compared with the experimentally observed values of 3.9–4.2 μb. Given the approximations used in our calculations, and the experimental problems with 1H NMR spectra and the crystallization of only disproportionated products, it is fair to say that our calculations were indeed correct.

The suggestion that the spin-state of the FeIII species would determine the pathway was, however, wrong. Even though the spin-state of complexes A and B coincides with expectation, high-spin for complex A and intermediate spin for complex B, there is no discrimination between the different R2 ligands. That is, the spin state of complexes A and B does not depend on R2. Therefore, for the differentiation between the ATRP and CCT pathways, one should take the complete reaction (see Fig. 2) into account. Indeed, when doing so ATRP is increasingly more favorable for the series: R2 = PhF < PhOMe < PhNMe2, as observed experimentally as well. We also investigated different density functionals and basis sets and found these to be consistent with the SSB-D results.28

Spin-Crossover Compounds

As mentioned above, Trautwein and coworkers2 reported in 2001 a study on SCO compounds, which were studied with different density functionals. Since then there have been many more studies into the SCO phenomenon, which can be induced by changes in temperature, pressure, and so forth. One of the many SCO compounds is formed by FeII with trispyrazolylborate (Tb) or the related trispyrazolylmethane (Tc) ligands (see Fig. 3).31 Interestingly enough, substitution patterns at the pyrazolyl rings influence the SCO-behavior dramatically, and for the Tc ligands, there was in some cases a dramatic effect of the counter-ion.31 For example, whereas the parent compounds Fe(Tb)2 and Fe(Tc)22+ showed transition temperatures for the low-spin to high-spin switch above room temperature, placing a methyl group at the 3-position leads directly to high spin at low temperatures; instead, placing a methyl group at the 4- or 5-position has hardly an effect. We studied these complexes as well,31 at the OPBE/TZP level,32 and found that in general there was good agreement between the computed spin-state splittings at 0 K and the experimentally observed (or absent) SCO-behavior. Moreover, the computed and experimental Mössbauer parameters agreed well, and based on them, we were able to predict31 that the complex with hydrotris(3-azo-indazol-1-yl)borato ligands (see Fig. 3) does not correspond to a mono-nuclear iron complex, but probably to an oligonuclear or polynuclear structure. In a follow-up study last year,33 we included solvent and performed molecular dynamics simulations using a polarizable force field to have a better approach to obtain the transition temperature. The computed transition temperature of about 290 K was in excellent agreement with experiment.

Figure 3.

Tb, Tc, and hydrotris(3-azo-indazol-1-yl)borato ligands; [BOND](N[BOND]N) represents the third pyrazolyl ring positioned at the back.

The in silico design of new SCO and light-induced excited spin state trapped (LIESST) materials is a new area, with great interest for molecular electronics, data storage, and so forth.34 As the discovery of new transition-metal complexes with potential for either SCO or LIESST would require conformational averaging and molecular dynamics for any candidate, the use of quantum-mechanics is prohibitive. Therefore, Deeth et al.35 explored the use of ligand field molecular mechanics (LFMM) for a number of FeII complexes with a FeN6 motif. Their LFMM data agreed very well with reliable density functional theory (DFT) data, which allowed them to explore molecular discovery with LFMM. Based on it, they found a number of modified versions of SCO complexes, whose LFMM spin-state splittings were subsequently proven to be correct by DFT calculations. In a more recent paper,36 the LFMM force field was further optimized leading to a reduction of errors in Fe[BOND]N distances and spin-state energies. Now, these latter energies show root mean squared deviation (RMSD) errors between DFT and LFMM of only 0.2 kcal mol−1, although for some systems still differences of up to 7 kcal mol−1 were found.36

Spin Ground States

Currently, there exists the situation that different research groups recommend the use of different density functionals for studying spin-state splittings. Therefore, the recommended strategy is to compute spin-state splittings with a number of density functionals (B3LYP(*), BP86, OLYP/OPBE, TPSSh, SSB-D, M06-L) and a number of basis sets (s6-31G*/m6-31G*, def2-tzvp, def2-qzvp). This enables a rigorous check on the importance of both the functional and the basis set for the spin-state splittings. Furthermore, a CECAM workshop will be held in September 2012 (Zaragoza), where this situation will be discussed in more detail, and which will hopefully lead to a more general recommendation to end the uncertainty about which functional and basis set to use.

Moreover, new density functionals are being proposed every year, which is why we set up an annual DFT popularity poll (www.marcelswart.eu/dft-poll) to probe the preferences of the computational chemistry community. Its results may serve as an indication of what the community considers to be reliable density functionals. Note that this reliability is for the general case, not specifically for spin-state splittings, although without any doubt these will play a role in the preferences of the community.

Conclusions and Outlook

Having a reliable and accurate method for determining spin ground states will be beneficial for studying a variety of systems, be it of organometallic, inorganic, or bioinorganic nature. This is why it is promising that Deeth's LFMM method seems to work quite well, but may need some further improvement. To do so, it may be worthwhile to compile a set of difficult systems, for which the spin ground states are known decisively. For example, sometimes the experimental conditions (contaminants, disproportionation, oligo/polymerization, and ligand/solvent exchange) can make that the signal being measured (magnetic moment, Mössbauer spectra) does not actually correspond to the system that one is after. A combined experimental and theoretical endeavor (e.g., CECAM workshop) is needed to bring forward such a database of complicated systems. A number of systems are already known such as, for example, the spin states of FeII–porphyrin with an axial histidine (or models for it);3 the structurally similar monopyridylmethylamine FeII(amp)2Cl2 and dipyridylmethylamine FeII(dpa)22+ complexes with opposite spin ground-states;32 FeIII–aryl porphyrins with different halide substitutions and different spin states;37 Mn-oxo corrole and corrolazine.8 However, until these are combined into a general database of complicated spin-state systems, the field does not advance and it will be difficult to value and validate new computational methods such as Deeth's LFMM method or new density functionals, let alone to give a rigorous estimate of the viability/validity of results obtained for a particular system.


Kirk Peterson (Washington State University) is greatly acknowledged for providing early access to the cc-pVTZ-pp ECP basis set for iron.

Biographical Information

original image

Marcel Swart obtained his PhD (Groningen, 2002) for a thesis on copper proteins. He then moved to Amsterdam as post doc to work on cytochrome P450s, and later DNA, for which he was given the Young Scientist award in 2005. In 2006, he was awarded the prestigious ICREA-Júnior research position at the Catalan research institute (ICREA). In 2009, he obtained a permanent position as ICREA Research Professor. He is member of the Editorial Board of international scientific journals, and has (co-)authored about 100 scientific papers. He recently was awarded the MGMS Silver Jubilee Prize 2012. [Color figure can be viewed in the online issue, which is available at wileyonlinelibrary.com.]