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A DFT computational study of spin crossover in iron(III) and iron(II) tripodal imidazole complexes. A comparison of experiment with calculations Greg Brewer, Myro Joy Olida, Ann M. Schmiedekamp,* Carol Viragh and Peter Y. Zavalij Dalton Trans., 2006 (DOI: 10.1039/b607588f). Amendment published 10th January 2006.

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PAPER | Dalton Transactions

A DFT computational study of spin crossover in iron(III) and iron(II) tripodal imidazole complexes. A comparison of experiment with calculations† Greg Brewer,a Myro Joy Olida,b Ann M. Schmiedekamp,*b Carol Viraghc and Peter Y. Zavalijd Received 30th May 2006, Accepted 14th August 2006 First published as an Advance Article on the web 25th August 2006 DOI: 10.1039/b607588f B3LYP* functionals were used to model the sixteen iron(II) (1 A, LS and 5 T, HS) and iron(III) (2 T, LS and 6 A, HS) complexes of the 1 : 3 Schiff base condensate of tris(2-aminoethyl)amine and imidazole-4-carboxaldehyde, H3 L1 , and its deprotonated forms, [H2 L1 ]1− , [HL1 ]2− , and [L1 ]3− . This ligand system is unusual in that [FeH3 L1 ]3+ , [FeH3 L1 ]2+ and [FeL1 ]− all exhibit a spin crossover between 100–300 K. This makes these complexes ideal for a hybrid DFT computational approach and provides an opportunity to refine the value of the exact exchange admixture parameter, c3 , and to predict properties of partially protonated complexes that are not experimentally available. The accepted value of 0.20 is larger than the value of ∼0.13 that was found to best reproduce experimental data in terms of spin state predictions. With iron(III) B3LYP calculations showed that all of the complexes were low spin at 298 K with the exception of [FeH3 L1 ]3+ which is spin crossover in agreement with experimental results. It was also shown for iron(III) that the ligand field increased as the number of protons decreased. In contrast all of the iron(II) complexes were close to the spin crossover region regardless of protonation state. Experimental structures are fairly well modeled by this system in regard to the key structural indicators of spin state, which are the bite and trans angles. The calculated iron to nitrogen atom distances are always larger in the high spin form than the low spin form but all iron to nitrogen bond distances are larger than the experimental values. In general non-bonded interactions are not well modeled by this methodology.

Introduction The increased interest1 in spin crossover (SC) complexes of d4 – d7 first row transition metal complexes is partly attributed to the potential applications of molecules with two electronic ground states that are interconverted by changes in temperature, pressure, or light as memory devices2 and switches.3 Iron (II) (d6 , 1 A  5 T) and iron(III) (d5 , 2 T  6 A) complexes are the most important systems and activity in this area has been recently reviewed.4 The requirement for SC, that the crystal field splitting parameter (Do ) equals the pairing energy, is met for iron(II) and iron(III) with ligands that have N4 O2 –N6 donor sets. An important class of ligands that can exhibit SC behavior with iron(II) and iron(III) are the 1 : 3 Schiff base condensates of tris(2aminoethyl)amine (tren) and related amines and with imidazole carboxaldehydes (Fig. 1). Recent work in this laboratory5 and others6 has examined the structural and magnetic properties, including SC, of the iron(II) and iron(III) complexes of these and related ligands. The iron complexes of H3 L1 –H3 L4 all contain ionizable imidazole protons and exhibit extensive acid–base chemistry, redox chemistry, and proton coupled electron transfer reactions7 as illustrated in Fig. 2. In addition to the chemistry a Department of Chemistry, Catholic University of America, Washington, DC, 20064 b Penn State University, Abington, Abington, PA, 19001 c Vitreous State Laboratory, Catholic University, Washington, DC, 20064 d Department of Chemistry and Biochemistry, University of Maryland, College Park, MD, 20742-4454 † The HTML version of this article has been enhanced with additional colour images.

This journal is © The Royal Society of Chemistry 2006

Fig. 1 Line drawings of tri-imidazole ligands.

Dalton Trans., 2006, 5617–5629 | 5617

Fig. 2 The acid–base (horizontal level) and redox (vertical) chemistry of iron complexes of H3 L ligands.

shown in Fig. 2 these metal complexes can form Lewis acid base adducts to metal hexafluoroaceylacetonate complexes8 and hydrogen bond adducts to organic substrates9 or themselves. The latter include homo-valence iron(II), {[Fe(II)H3 L][Fe(II)L]}X and mixed valence iron(II) and iron(III), {[Fe(II)H3 L][Fe(III)L]}X2 systems which are very novel self resolving layered structures with possible technological applications.6 The iron complexes of these ligands have recently been the subject of extensive structural and magnetic work and thus offer a timely, unique and important opportunity for a detailed comparison of experimental parameters (structure and spin state) with results of quantum mechanical calculations. However, the reliability of predicting spin state, especially systems near SC, differs among common computational approaches. Ab initio Hartree Fock theory (HF) tends to favor high spin, HS, whereas pure DFT functionals favor low spin, LS. Recently, there have been studies in the literature which compare various DFT functionals in their ability to reproduce spin states of iron(II) and iron(III) but even the best pure DFT functionals generate LS states which are too stable by approximately 54 kJ mol−1 .10 A compromise can be reached with the use of hybrid DFT functionals which include HF exact exchange. B3LYP11 has been one of the most successful and widely used hybrid functionals for transition metal properties and we have applied it to cobalt(II) to understand the basis of spin state change with some biological ligands.12 However, B3LYP has still been shown to favor HS states energetically. And, as noted in some reviews, completely reliable predictions are still not within reach.13 Comparisons of various functionals, both hybrid and pure DFT, to high level ab initio calculations have been reported for small iron(II) complexes as an attempt to identify the best methods.14 Reiher et al.15 have proposed an alternate modification to B3LYP. They have shown that a simple adjustment in the coefficient which controls the fraction of exact exchange contribution in the B3LYP functional can achieve better agreement with experimental SC results. Furthermore, the spin state energy splitting is shown to be linearly dependent on the coefficient of exact exchange admixture and when the exact exchange is reduced from 20% to 15% (B3LYP*) results on Fe(phen)2 (NCS)2 complexes are in better agreement with experiment. But it is recommended that a scan of the coefficient of exact exchange be conducted on small complexes of a specific ligand type when experimental results are available.16 In principle the DFT calculations could be done with any of the ligands in Fig. 1 but it is highly desirable that the fully protonated and fully deprotonated iron(II) and iron(III) complexes of a single ligand which has been experimentally characterized be selected in order to have a number of comparison points between calculation and experiment. This ensures the most reliable calibration of the exact exchange for the B3LYP method. The iron(III) complexes of H3 L3 , H3 L4 , [H3 L5 ]+ , [H3 L6 ]+ , L7 and L8 to date have not been 5618 | Dalton Trans., 2006, 5617–5629

isolated and structurally characterized which reflects the general instability of the iron(III) N6 complexes to reduction to the stable iron(II) complexes.17 In addition the complexes of L7 or L8 have no ionizable protons and are thus less attractive chemically. Lastly to date no iron(II) complexes of [L2 ]3− have been isolated. However, [FeH3 L 1 ]3+ , [FeH3 L1 ]2+ , FeL1 and [FeL1 ]− are all structurally and magnetically characterized and thus this ligand system provides the greatest possible comparison of calculations to experimental data.18 In this work the HS (5 T) and LS (1 A) iron(II) and HS (6 A) and LS (2 T) iron(III) complexes of [H3 L1 ], [H2 L1 ]1− , [HL1 ]2− and [L1 ]3− were examined by B3LYP* methodology resulting in sixteen B3LYP* minimized structures for one ligand in this class. A scan on the coefficient of exact exchange is conducted to determine the best value for predicting SC and therefore also giving an accurate evaluation of the difference between HS and LS states, with the caveat that calculations are done in the gas phase and do not completely mimic the experimental conditions. Not only can the experimental data be used to calibrate the B3LYP results but also the theory may be useful at predicting properties of partially protonated species, e.g., [H2 L1 ]1− and [HL1 ]2− , which are not yet available or too unstable to be isolated. In addition the B3LYP results from this study may yield useful trends for predicting structural and electronic properties in this class of tri-imidazole ligands, Ln , where n = 2–8, that may in fact serve as a guide to the experimentalist as to which systems may exhibit a particular desired structural or electronic feature.

Results and discussion Synthesis and experimental data As part of this work three new complexes of iron(II) and H3 L1 were prepared and characterized to give additional points of comparison of experiment (in addition to those of ref. 5b and 18) to calculations. These are [FeH3 L1 ](ClO4 )2 , [FeH2.39 L1 ](I3 )0.62 (I)0.77 , and {[FeH3 L1 ][FeL1 ]}(ClO4 ). [FeH3 L1 ](ClO4 )2 and [FeH2.39 L1 ](I3 )0.62 (I)0.77 have been characterized by X-ray crystallography (Table 1 and Fig. 3 and 4) and their measured bond distances and angles (Table 3 and Fig. 4) are consistent with the HS B3LYP* calculated ones and are in general agreement with the HS form of the analogous salt, [FeH3 L1 ](BF4 )2 , reported earlier.18 The present report of a second structure of the [FeH3 L1 ]2+ cation (perchlorate vs tetrafluoroborate) points out that there is some variation in the experimentally determined iron to nitrogen bond distances and angles from X-ray analysis attributable to variations in space group, solvates, packing and other forces. Thus, in doing a comparison of experimental and calculated structures it is important to note that the parameters determined from the Xray structure can and do experience variance and should not be regarded as absolute except within the confines of that exact system. The non-stoichiometric compound, [FeH2.39 L1 ](I3 )0.62 (I)0.77 , can be thought of as a mixture of [FeH3 L1 ]2+ (∼39%) and [FeH2 L1 ]+ (∼61%). The total number of uni-negative anions required for this mixture is 1.39 which is met by a combination of iodide and triiodide anions totaling 1.39. The occurrence of mixed iodide triiodide salts has been observed previously with [(C5 H6 N)(I)0.500 (I3 )0.500 ],19 and more recently with the related complex, [FeHL2 ](I3 )0.525 (I)0.475 .20 This journal is © The Royal Society of Chemistry 2006

Table 1 Crystallographic data for [FeH3 L1 ](ClO4 )2 ·EtOH·0.817H2 O and [FeH2.39 L1 ](I3 )0.62 (I)0.77

Empirical formula Formula weight/g mol−1 Temperature/K ˚ k/A Crystal system Space group ˚ a/A ˚ b/A ˚ c/A a/◦ b/◦ c /◦ ˚3 Volume/A Z Dc /Mg m−3 Absorption coefficients/mm−1 F(000) Crystal size/mm3 Theta range/◦ Index ranges Reflections collected Independent reflections R1 wR2 Rint Goodness of fit

[FeH3 L1 ](ClO4 )2 ·EtOH·0.817H2 O

[FeH2.39 L1 ](I3 )0.62 (I)0.77

C20 H31.64 Cl2 FeN10 O9.82 696.11 223(2) 0.71073 Monoclinic P21 13.5488(6) 12.3949(6) 18.2340(8) 90 100.7830(10) 90 3008.1(2) 4 1.537 0.746

C18 H23.39 FeI2.63 N10 768.82 223(2) 0.71073 Trigonal P32 21 11.9397(5) 11.9397(5) 35.951(2) 90 90 120 4438.4(4) 6 1.726 3.271

1441 0.42 × 0.40 × 0.27 1.14–27.50 −17 ≤ h ≤ 17 −16 ≤ k ≤ 15 −23 ≤ l ≤ 23 38532 13657 0.0329 0.0762 0.0312 1.030

2199 0.33 × 0.22 × 0.19 1.1–25◦ −14 ≤ h ≤ 14 −14 ≤ k ≤ 14 −42 ≤ l ≤ 42 36811 5180 0.0744 0.1732 0.0435 0.978

Fig. 3 ORTEP26,27 of the two independent [FeH3 L1 ]2+ cation sites in [FeH3 L1 ](ClO4 )2 ·EtOH·0.817H2 O. The counteranions and solvates have been omitted for clarity. Selected bond distances and angles are given in Table 3.

Reaction of a methanol solution of [FeH3 L1 ]3+ (generated in situ) with excess sodium iodide results in the isolation of a small amount of [FeH2.39 L1 ](I3 )0.62 (I)0.77 . The formation of this species is likely to be somewhat similar to that reported for [FeHL2 ](I3 )0.525 (I)0.475 as shown below except that an iron(II) complex is isolated rather than an iron(III) species. 2[FeH3 L1 ]3+ + 2I− → 2[FeH3 L1 ]2+ + I2

4[FeH3 L1 ]2+ + O2 → 4[FeH2 L1 ]2+ + 2H2 O 2[FeH2 L1 ]2+ + 2I− → 2[FeH2 L1 ]+ + I2 This journal is © The Royal Society of Chemistry 2006

The mixed iron(II) complexes [FeH3 L1 ]2+ and [FeH2 L1 ]+ produced in the first and third reactions co-precipitate (39 : 61%) as the mixed iodide and triiodide salt, the former anion being present in excess and the latter produced by the reaction of iodine with iodide. The factors that favored the crystallization of [FeH2.39 L1 ](I3 )0.62 (I)0.77 over other compositions are not understood and it is possible that there are composition differences both in terms of level of protonation and the triiodide to iodide ratio between individual crystals and the bulk material. Elemental analysis does not distinguish between iodide and triiodide as both species are converted to iodate in the analysis and the result is presented as total percent iodine. Thus, the X-ray results are the most reliable for determining the amount of iodide and triiodide present with the significant limitation that it applies to the crystal examined Dalton Trans., 2006, 5617–5629 | 5619

˚ ) and angles (◦ ) for iron(III) complexes of Hx L1 (x = 0–3), c3 = 0.15. Bold script indicates Table 2 Experimental and calculated bond distances (A measured X-ray bond lengths and italic font indicates that the imidazole associated with that part of the ligand is protonated. Iron to nitrogen bond distances are given individually as trans pairs and all other parameters are given as an average of equivalent arms Iron(III) Expta



Formula Spin Multiplicity Charge Fe–Nimine Fe–Nimid Fe–Nimine Fe–Nimid Fe–Nimine Fe–Nimid Fe–Nap C=N (imine) C =N (imine) C–Nap –C Nimid –Fe–Nimid Nimine –Fe–Nimine Bite angle Trans angle

FeL1 1/2 2 0 1.988 1.939 1.988 1.939 1.988 1.939 3.257 1.286

FeL1 1/2 2 0 2.022 1.948 2.023 1.947 2.023 1.948 3.416 1.308

119.0 92.8 98.1 81.0 173.7

119.8 93.4 96.6 81.6 174.8

Formula Spin Multiplicity Charge Fe–Nimine Fe–Nimid Fe–Nimine Fe–Nimid Fe–Nimine Fe–Nimid Fe–Nap C=N (imine) C =N (imine) C–Nap –C Nimid –Fe–Nimid Nimine –Fe–Nimine Bite angle Trans angle


FeL1 5/2 6 0 2.199 2.093 2.200 2.090 2.199 2.092 3.347 1.306 117.9 92.5 96.1 77.4 167.6

[FeHL1 ]+ 1/2 2 1 2.060 1.902 1.979 1.999 2.029 1.946 3.319 1.316 1.291 119.2 92.4 98.0 81.3 173.7

[FeH2 L1 ]2+ 1/2 2 2 2.056 1.929 2.014 1.989 2.023 1.986 3.282 1.314 1.293 119.1 92.3 98.7 81.1 173.4

[FeH3 L1 ]3+ 1/2 2 3 2.022 2.016 2.023 2.017 2.023 2.017 3.341

[FeH3 L1 ]3+ 1/2 2 3 1.974 1.941 1.982 1.962 1.990 1.955 3.170

1.298 119.4 93.3 97.8 80.6 173.9

1.287 118.4 93.1 99.2 80.8 173.9

[FeHL1 ]+ 5/2 6 1 2.140 2.125 2.098 2.286 2.252 2.101 2.955 1.313 1.286 115.0 86.2 103.6 76.2 162.0

[FeH2 L1 ]2+ 5/2 6 2 2.222 2.120 2.104 2.240 2.220 2.240 3.265 1.321 1.291 118.3 90.4 99.6 76.4 166.0

[FeH3 L1 ]3+ 5/2 6 3 2.192 2.237 2.192 2.236 2.193 2.241 3.315

[FeH3 L1 ]3+ 5/2 6 3 2.060 2.118 2.088 2.090 2.077 2.112 2.762

1.296 118.7 92.6 98.7 75.8 166.9

1.279 113.7 87.4 106.3 76.5 163.4

Ref. 5b, no HS analogue of this species is known. b Ref. 18.

and that differences with other crystals and/or the bulk are quite possible. The ORTEP of [FeH2.39 L1 ](I3 )0.62 (I)0.77 is pictured in Fig. 4 along with selected structural parameters. There is only one iron site crystallographically observed in [FeH2.39 L1 ](I3 )0.62 (I)0.77 which indicates that the protonation differences between the [FeH3 L1 ]2+ and [FeH2 L1 ]+ species are averaged out in the solid state. It is clear from the structural parameters (discussed later) given in Fig. 4 that the iron(II) atom is HS in this environment. The {[FeH3 L1 ][FeL1 ]}(ClO4 ) salt was prepared by a reaction of [FeH3 L1 ](ClO4 )2 in methanol with an excess of triethylamine on a Schlenk line under nitrogen and resulted in the immediate precipitation of a bright red insoluble powder, analyzed as {[FeH3 L1 ][FeL1 ]}(ClO4 ). Evidence that this species is a homovalent hydrogen bound pseudo dimer comes from the IR which shows bands at 2700 and 2000 cm−1 which are consistent with this type of adduct.21 This complex on exposure to air gradually darkens to a deep blue corresponding to LS iron(III) suggesting an oxidative instability. Since {[FeH3 L1 ][FeL1 ]}(ClO4 ) is an insoluble 5620 | Dalton Trans., 2006, 5617–5629

powder, and therefore not suitable for structural characterization, ¨ it was electronically characterized by Mossbauer spectroscopy. ¨ The Mossbauer spectra in Fig. 5 detail the initial characterization of {[FeH3 L1 ][FeL1 ]}(ClO4 )(s) and its aerial oxidation. The initial spectrum (a) was recorded at 77 K within hours of preparation of the complex to minimize any oxidation. At 77 K the spectrum consists of a single LS iron(II) signal. At RT both LS (59.3%) and HS (40.7%) iron(II) signals are observed. Thus the complex is SC between 77 and 295 K in agreement with DFT calculations presented later. The analogous complex, {[FeH3 L1 ][FeL1 ]}(BF4 )(s),18 exhibits similar spectra except that the species was contaminated with LS iron(III) even in its initial spectrum whereas the present species is much less prone to oxidation which is most likely due to its insolubility. Since the tetrafluoroborate salt is soluble it experiences some oxidation (∼7%) to give the LS iron(III) species, FeL1 , prior to isolation of the product. This oxidation product contaminates the initial sample and affects all subsequent measurements. The present complex avoids this complication due This journal is © The Royal Society of Chemistry 2006

˚ ) and angles (◦ ) for iron(II) complexes of Hx L1 (x = 0–3), c3 = 0.15. Bold script indicates measured Table 3 Experimental and calculated bond distances (A X-ray bond lengths and italic font indicates that the imidazole associated with that part of the ligand is protonated. Iron to nitrogen bond distances are given individually as trans pairs and all other parameters are given as an average of equivalent arms Iron(II) Expta Formula Charge Spin Multiplicity Fe–Nimine Fe–Nimid Fe–Nimine Fe–Nimid Fe–Nimine Fe–Nimid Fe–Nap C=N (imine) C =N (imine) C–Nap –C Nimid –Fe–Nimid Nimine –Fe–Nimine Bite angle Trans angle


[FeL1 ]− −1 0 1 2.014 1.993 2.014 1.993 2.014 1.993 3.424 1.307

[FeL1 ]− −1 0 1 2.035 2.000 2.034 2.001 2.034 2.000 3.582 1.307

119.9 89.6 97.5 81.1 170.6

119.9 93.8 94.9 80.8 173.1

FeHL1 0 0 1 2.019 1.984 2.04 1.989 2.004 1.984 3.523 1.308 1.298 120.0 92.2 96.1 81.0 172.7

[FeH2 L1 ]+ 1 0 1 2.027 1.989 2.028 1.975 2.013 2.013 3.499 1.310 1.295 120.0 92.6 96.2 81.1 173.1

[FeH3 L1 ]2+ 2 0 1 2.032 2.023 2.033 2.022 2.034 2.022 3.475

[FeH3 L1 ]2+ 2 0 1 1.989 1.981 1.989 1.981 1.989 1.981 3.522

1.294 119.9 94.1 96.0 80.6 173.8

1.297 119.9 91.2 95.9 81.1 171.6

Expta Formula Charge Spin Multiplicity Fe–Nimine Fe–Nimid Fe–Nimine Fe–Nimid Fe–Nimine Fe–Nimid Fe–Nap C=N (imine) C =N (imine) C–Nap –C Nimid –Fe–Nimid Nimine –Fe–Nimine Bite angle Trans angle a

[FeL1 ]− −1 4/2 5 2.110 2.106 2.110 2.106 2.110 2.106 3.012 1.284

[FeL1 ]− −1 4/2 5 2.301 2.193 2.315 2.165 2.281 2.184 3.569 1.299

116.6 87.7 101.6 77.5 165.1

118.9 97.9 91.9 75.9 166.0

FeHL1 0 4/2 5 2.345 2.119 2.284 2.172 2.199 2.268 3.331 1.303 1.283 117.2 92.3 96.1 75.7 165.0

[FeH2 L1 ]+ 1 4/2 5 2.288 2.101 2.248 2.232 2.192 2.304 3.321 1.304 1.286 118.0 90.9 97.8 75.9 164.6




[FeH3 L1 ]2+ 2 4/2 5 2.225 2.301 2.225 2.284 2.239 2.317 2.975

[FeH3 L1 ]2+ 2 4/2 5 2.195 2.189 2.195 2.189 2.195 2.189 2.888

[FeH3 L1 ]2+ 2 4/2 5 2.173 2.217 2.188 2.204 2.188 2.232 2.858

[FeH3 L1 ]2+ 2 4/2 5 2.174 2.187 2.155 2.187 2.176 2.195 3.000

1.287 114.4 89.2 103.0 74.8 163.2

1.264 113.9 86.8 103.5 75.8 162.5

1.271 113.4 87.0 104.1 75.3 162.1

1.268 114.8 89.2 101.5 76.2 165.1

Ref. 18. b This work.

to its great insolubility, which results in rapid isolation prior to any significant oxidation. An additional unanticipated result was that the aerial oxidation reaction of this species could be followed ¨ by Mossbauer spectroscopy, which provides new information on the role of spin state in this proton coupled electron transfer reaction. On exposure to air over time at RT the LS iron(II) signal is depleted preferentially to the HS iron(II) species while the LS iron(III) signal grows. After several weeks the conversion is complete and the spectrum simplifies to exhibit only HS iron(II) and LS iron(III) in a 1 : 3 ratio which is consistent with ¨ the equation shown below. It is possible to fit the Mossbauer parameters of Fig. 5 to two iron sites, [FeH3 L1 ]2+ and [FeL1 ]− , rather than one as was done. However this is not experimentally justified since the compound is not structurally characterized and the analogous complex, {[FeH3 L1 ][FeL1 ]}(BF4 ), which is structurally characterized has only a single iron site represented as [FeH1.5 L1 ](BF4 )0.5 This journal is © The Royal Society of Chemistry 2006

The aerial oxidation of iron(II) to iron(III) in {[FeH3 L1 ][FeL1 ]}(ClO4 ) cannot be complete if the only source of protons, needed in the conversion of dioxygen to water, is the [FeH3 L1 ]2+ cation as is shown in the following overall equation. 4{[FeH3 L1 ][FeL1 ]}(ClO4 )(s) + 3/2O2 (g) → 3H2 O + 2[FeH3 L1 ](ClO4 )2 (s) + 6FeL1 (s) It is likely that the iron product(s) of the above reaction is not simply a mixture of the two species indicated but rather some adduct such as {[FeH3 L1 ]2 [FeL1 ]6 }](ClO4 )4 (s) or 2{[FeH3 L1 ][FeL1 ]3 }](ClO4 )2 (s). This is indicated by the fact that both [FeH3 L1 ](ClO4 )2 (s) and FeL1 (s) are soluble in methanol but the product of the aerial oxidation is not. Not surprisingly addition of aqueous sodium hydroxide to a methanol slurry of this product results in conversion to the indigo blue methanol soluble FeL1 . Dalton Trans., 2006, 5617–5629 | 5621

Fig. 4 ORTEP26,27 of [FeH2.39 L1 ](I3 )0.62 (I)0.77 with selected bond dis˚ ) and angles (◦ ). Fe–N1 2.863, Fe–N17 2.156(10), Fe–N27 tances (A 2.161(9), Fe–N37 2.234(10), Fe–N11 2.247(11), Fe–N21 2.211(11), Fe N31 2.230(11), aver. C=N(imine) 1.254, aver. C–N1–C 112.5, aver. Nimid –Fe–Nimid 85.8, aver. Nimine –Fe–Nimine 104.4, aver. bite angle 75.5, and aver. trans angle 161.3.

DFT calculations In order to determine the computed spin state difference in energy, energy optimized geometries were computed for the iron(II) and iron(III) HS and LS cases for each of the four ligand protonation states: H3 L1 , [H2 L1 ]− , [HL1 ]2− and [L1 ]3− . The hybrid B3LYP functional was used throughout all calculations and the coefficient of exact exchange, c3 , was changed from the standard value of 0.2 to 0.15, to give a 15% exact exchange contribution to the energy. When the value of c3 is changed from the standard 0.2, we denote the method as B3LYP*. To compare calculations to experimental spin states determined at 0, 100 and 298 K, it is necessary to compute thermodynamic corrections at the equilibrium geometries. Since the B3LYP* energies determined for the equilibrium geometries are for structures that are not vibrating, the normal mode vibrational frequencies were calculated using B3LYP*(c3 = 0.15) at the equilibrium geometries for each spin state. The free energy difference, DGHS–LS (T) = GHS (T) − GLS (T) was determined based on these computed vibrational frequencies. The energies and gas phase optimized geometry results of the B3LYP* calculations are given below for iron(III) and iron(II). If DGHS−LS , is positive, the complex is LS and if the difference is negative, the complex is HS. A value of zero would indicate a 50 : 50 mixture of HS and LS and a small value (∼5–10 kJ) (positive or negative) would indicate that both spin states were present in significant quantities. Comparisons of these energies with the experimentally known spin states of the various iron complexes of H3 L1 allows for at least a partial calibration of the c3 parameter. Selected bond distances and angles for the optimized equilibrium geometries of all sixteen complexes of HS and LS iron(III) and iron(II) of [H3 L1 ], [H2 L1 ]1− , [HL1 ]2− and [L1 ]3− are given in Tables 2 5622 | Dalton Trans., 2006, 5617–5629

¨ Fig. 5 Mossbauer spectra of {[FeH3 L1 ][FeL1 ]}(ClO4 )(s). (a) 77 K, IS = 0.296 mm s−1 , QS = 0.127 mm s−1 ; (b) 295 K, doublet 1, IS = 0.240 mm s−1 , QS = 0.00 mm s−1 , 59.3%; doublet 2, IS = 0.978 mm s−1 , QS = 1.83 mm s−1 , 40.7%; (c) 295 K after prolonged standing in air, doublet 1, IS = − 0.01 mm s−1 , QS = 1.87 mm s−1 , 75.0%; doublet 2, IS = 0.964 mm s−1 , QS = 1.84 mm s−1 , 25.0%.

and 3 respectively. Comparison of B3LYP* values to those of structurally characterized systems is made where possible. Energies compared to experiment: iron(III) The B3LYP* (c3 = 0.15) DG5/2−1/2 , which denotes the difference between the calculated high spin and low spin for the series of structures [FeH3 L1 ] 3+ , [FeH2 L1 ]2+ , [FeHL1 ]+ , [FeL1 ] are shown in Fig. 6. The results for 0 and 100 K are almost the same but at 298 K the difference between spin states is reduced by at least 10 kJ mol−1 for all four ligand protonation conditions. At both T = 100 K and T = 298 K, FeL1 , is predicted to be LS in agreement with experiment.5 For [FeHL1 ]+ the calculation clearly shows that the LS form is the preferred one at room temperature by 20 kJ mol−1 . Unfortunately to date [FeHL1 ]+ has not been prepared and therefore it is not possible to do a direct comparison to experiment. However, the closely related [FeHL2 ]+ has recently been prepared and structurally and magnetically characterized as a pure LS species20 in agreement with the computational predictions. For [FeH2 L1 ]2+ the difference in spin states is decreased This journal is © The Royal Society of Chemistry 2006

Energies compared to experiment: iron(II)

Fig. 6 DG5/2−1/2 vs T for iron(III) complexes with c3 = 0.15.

to less than 10 kJ mol−1 at 298 K, predicting that this structure is approaching the SC point, but unfortunately there is no comparable experimental structure for comparison. At c3 = 0.15 [FeH3 L1 ]3+ is predicted to be HS at 298 K while at low temperatures the difference in free energy of the two spin states is near zero, predicting a mixed spin complex. Experimentally [FeH3 L1 ]3+ is in fact SC, entirely LS at 93 K and ∼75% HS and ∼25% LS at 298 K.18 Thermodynamic corrections at 298 K are approximately −23 kJ mol−1 relative to the enthalpy differences between spin states DH 5/2−1/2 . With some reservations the experimental spin states for [FeH3 L1 ]3+ can be used to calibrate the exact exchange parameter c3 of the B3LYP* functional. Fig. 7 shows the dependence of DG5/2−1/2 for [FeH3 L1 ]3+ on c3 in the B3LYP* functional. The thermodynamic corrections applied are those calculated from the vibrational frequencies of the c3 = 0.15 geometry. The standard value of 0.2 clearly predicts HS at all temperatures and this is not in agreement with experiment. With c3 = 0.125, this modified B3LYP functional predicts the structure barely reaching HS at T = 298 K. Therefore 0.15 > c3 > 0.125 brackets agreement with experiment for [FeH3 L1 ]3+ . A probable value is 0.13 but there is not enough experimental evidence to determine c3 more precisely. Agreement between experiment and calculation for FeL1 and [FeH3 L1 ]3+ strongly indicates that [FeH2 L1 ]2+ and [FeHL1 ]+ , not accessible by experiment to date, are LS at all temperatures up to T = 298 K. Experimentally and theoretically only [FeH3 L1 ]3+ is SC between 77 and 298 K. Regardless of the value of c3 the calculations show that Do for the ligands follows the following order which is predicted on the basis of simple electrostatics, [H3 L1 ] < [H2 L1 ]1− < [HL1 ]2− < [L1 ]3− .

Fig. 7

DG5/2−1/2 vs T for [FeH3 L1 ]3+ at selected values of c3 .

This journal is © The Royal Society of Chemistry 2006

The free energy difference between the quintet and singlet states, DG2−0 , calculated by B3LYP* hybrid functional (c3 = 0.15) for all protonation levels, [FeL1 ]− , FeHL1 , [FeH2 L1 ]+ and [FeH3 L1 ]2+ , are shown in Fig. 8 on the same scale as that in Fig. 6 to allow for an easier comparison of DGHS–LS of iron(III) and iron(II). Thermodynamic corrections at 293 K for DGHS–LS among all protonation states fall within a 1 kJ mol−1 standard deviation of 23 kJ mol−1 , which is the same correction as for iron(III). However, for iron(III) the corrections for the range of protonation state only fell to within a 3.5 kJ mol−1 standard deviation of 23 kJ mol−1 . Nevertheless these ranges are narrow enough to provide a realistic estimate of DGHS–LS if only the enthalpy DH HS–LS is calculated.

Fig. 8 DG2−0 vs T for iron(II) complexes with c3 = 0.15. The scale is the same as Fig. 6, iron(III), to show the compression of energy differences between different protonation states.

Fig. 8, which shows DG2−0 vs T when c3 = 0.15, predicts that all complexes except [FeH3 L1 ]2+ would be SC with the transition region at ∼100 K. This stands in stark contrast to the iron(III) computational results which predicted LS ground state for all but [FeH3 L1 ]3+ . Another point of contrast with iron(III) is that the energy differences between different protonation states is fairly small and less than computational accuracy for all but [FeH3 L1 ]2+ . Both the [FeH3 L1 ]2+ and [FeL1 ]− structures provide guidelines for estimation of the c3 parameter as described below. Experimentally [FeH3 L1 ](BF4 )2 ·3H2 O exhibits a gradual spin transition between 110–270 K.18 At 300 K the complex is essentially pure HS. B3LYP* calculations of the free energy difference DG2−0 between spin states, for c3 ranging from 0.2 to 0.125, are shown for [FeH3 L1 ]2+ in Fig. 9. A value for c3 slightly less than

Fig. 9

DG2−0 vs T for [FeH3 L1 ]2+ at selected values of c3 .

Dalton Trans., 2006, 5617–5629 | 5623

0.125 would fit the experimental data if a linear scaling of this parameter is assumed. A similar analysis for [FeL1 ]− is shown in Fig. 10. The spin transition temperature for [FeL1 ]− based on the {[FeH3 L1 ][FeL1 ]}(ClO4 ) (see Fig. 5) and {[FeH3 L1 ][FeL1 ]}(BF4 )18 is about 300 K. A value of c3 of ∼0.132 is consistent with the experimental data. A more precise estimation of c3 is not warranted due to complications in the experimental structures of the [FeL]− anions as discussed below. The [FeL]− anions are not isolated as a simple salt but as the more complicated homovalent iron(II) species, {[FeH3 L1 ][FeL1 ]}(X) (X = ClO4 − or BF4 − ), and the analogous {[FeH3 L3 ][FeL3 ]}(X) (X = NO3 − or PF6 − ).6 These homovalent iron(II) complexes can alternately be formulated as {[FeH3 L][FeL]}(X) or [FeH1.5 L](X)0.5 . The difference between the {[FeH3 L][FeL]}(X) (two distinct iron sites) and [FeH1.5 L](X)0.5 (one iron site) formulations is very subtle and depends on the location of the imidazole hydrogen atoms. {[FeH3 L3 ][FeL3 ]}(X) (X = NO3 − or PF6 − ) has two iron sites but the iron to nitrogen bond distances at several temperatures for both sites are nearly identical, which indicates that in effect the bond distances are averaged. {[FeH3 L1 ][FeL1 ]}(BF4 − ) gave satisfactory solutions in two closely related space groups, P3 and P321, which require two and one iron sites respectively. However since the imidazole hydrogen atoms could not be located in P3 but were in P321 the latter was taken as the better solution and the complex formulated as [FeH1.5 L1 ](BF4 )0.5 which requires a single iron site. Clearly the distinction between the {[FeH3 L][FeL]}(X) (two distinct iron sites) and [FeH1.5 L](X)0.5 (one iron site) formulations is complex and ultimately rests on the extent of hydrogen transfer from one iron imidazole complex to its neighbor and the experimental ability to determine the location of the imidazole protons. The DFT calculations (Fig. 8) show that there is no significant difference in DG2–0 among the [FeL1 ]− , [FeHL1 ], and [FeH2 L1 ]+ species. Thus, the error introduced in comparing the experimental structure of [FeH1.5 L1 ](BF4 )0.5 to the DFT calculated structure of [FeL1 ]− is regarded as rather small based both on Fig. 8 and the experimental fact that when [FeH1.5 L1 ](BF4 )0.5 was solved in P3 as {[FeH3 L1 ][FeL1 ]}(BF4 − ) the two iron sites were essentially identical.18 In addition a further complication is that these species have an extensive hydrogen bonding network, which have been shown to have an impact on spin state for iron(II)22 but are not considered in the present computational model. The data presented in figure 10 suggests that 0.15 > c3 > 0.125 for [FeL1 ]− .

For c3 = 0.15 (Fig. 8) both FeHL1 and [FeH2 L1 ]+ are predicted to be SC, LS below 100 K and HS at RT. However, the nonstoichiometric compound, [FeH2.39 L1 ](I3 )0.62 (I)0.77 , reported here (Fig. 4) contains ∼61% [FeH2 L1 ]+ and is HS at RT, which is consistent with the DFT c3 = 0.15 predictions. In addition the isomeric FeHL4 has long Fe–N bond distances23 at RT that are consistent with a HS iron(II) which is also in agreement with the general trends predicted by these calculations. However, if one uses c3 = 0.125 which agrees better with Fe(II)L− and Fe(II)H3L+2 spin crossover results, then DG2–0 would be 13–14 kJ mol−1 higher than calculated at c3 = 0.15. This would predict that FeHL1 and [FeH2 L1 ]+ are LS at all temperatures. However, since the partially protonated complexes of L1 have not been isolated in pure form to date, a true optimization of c3 for these species is not possible. Experimental geometries: general comments Some general features that are applicable to this class of complex are mentioned below prior to discussion of the DFT minimized structures. The iron atom is bound in a facial manner to the three Nimid atoms and the three Nimine atoms. The apical nitrogen atom of the tripodal amine, Nap , caps the imine face in a symmetric fashion and can exhibit the four conformations illustrated in Fig. 11. The “N bound” conformation has a pyramidal geometry with Nap pointed toward the metal atom and within bonding distance, ˚ and is illustrated by HS [FeH3 L2 ](ClO4 )3 .20 The “N in” ∼2.8 A conformation refers to cases where Nap is also pyramidal with Nap pointed toward the metal atom but Fe · · · Nap is beyond the ˚ ) and is illustrated ˚ < Fe–Nap < 3.2 A bonding distance (2.8 A 2 24 by HS [FeH3 L ](ClO4 )2 . The “P” conformation, found in LS [FeH3 L2 ](ClO4 )2 ,24 has a trigonal planar geometry for Nap and ˚ . Lastly exhibits a Fe · · · Nap distance is in the range 3.2–3.5 A the “N out” conformation, illustrated by LS [FeH3 L5 ](ClO4 )3 ,24 exhibits a pyramidal geometry about Nap but inverted from the “N in” conformation so that Nap is pointed away from the metal ˚. atom with a Fe · · · Nap distance greater than 3.5 A

Fig. 11 Conformations of Nap in tripodal iron imidazole complexes. ˚ ); “Nin ” (2.8 A ˚ < Fe · · · Nap < 3.2 A ˚ , “P” “Nbound ” (Fe · · · Nap < 2.8 A ˚ ), “Nout ” (Fe · · · Nap > 3.5 A ˚ ). Nap is positioned ˚ < Fe · · · Nap < 3.5 A (3.2 A directly above the iron atom.

Fig. 10 DG2−0 vs T for [FeL1 ]− at selected values of c3 .

5624 | Dalton Trans., 2006, 5617–5629

There are several structural signatures of HS and LS iron in these tripodal imidazole complexes. These are (1) the Fe–Nimid and Fe–Nimine bond distances; (2) the Nimid –Fe–Nimine bite angle; (3) the Nimid –Fe–Nimine trans angle; (4) the Fe–Nap distance and (5) the Nap conformation. In general the HS state correlates with ˚ ), Nimid –Fe– long Fe–Nimid and Fe–Nimine bond distances (>2.10 A Nimine bite angles of ∼76◦ , Nimid –Fe–Nimine trans angles of ∼166◦ , This journal is © The Royal Society of Chemistry 2006

˚ ) and “N in” or “N bound” Nap short Fe–Nap distances (