There are examples of non-covalently linked molecular clusters in nature of stunning symmetry and beauty. Two are shown in Figure 1. The 24 individual protein subunits of apoferritin['.21 (the elipsoid-shaped subunits on the left of Fig. 1) cluster Fig. 1. Models of theapoferritin 24-mer (left) and human rhinovirus 60-mer (right). The view of ferritin IS down one of the C, axes. the other two C, axes of the octahedral cluster are horizontal and vertical, respectively. Along the body diagonal (between three of the elipsoid ends marked N) lies the C, axis of the octahedral cluster. The view, of the virus is down the C, axis, and the regions related by symmetry through the C2 axis and the Cj axis are shown in green and blue. respectively.together to form only this polymeric assemblage (symmetry group 0). The approximately spherical cavity can hold over 4000 iron atoms in the form of FeO(OH).['] When the apoprotein is dissociated into the individual protein subunits and then allowed to reassemble only the highly symmetrical 24-mer of apoferritin forms. Something similar happens with many viruses, in which non-covalently linked protein clusters of virus coats are used to protect the viral nucleic acid. The protein cluster coat of the human rhinovirus ( Fig. 1 contains 60 protein subunits, which spontaneously assemble to give an icosahedron (symmetry group I ) . Once again, it is generally true that dissociation and reassembly of the protein coat does not give a random polymer assembly but instead only the highly symmetrical 60-mer.What is it that leads to the high symmetry of such clusters? What is the relationship of this symmetry to the specificity seen in the formation of a single cluster type with unique cavity size and properties? In each case the individual molecular fragments (the protein subunits) are asymmetric units-the order of the pure rotation groups 0 and I are 24 and 60, respectively. Can this process be mimicked by using metal -ligand interactions as the driving force? This paper addresses these questions and shows that highly symmetrical clusters can be systematically designed by using the principles of symmetry-driven reactions deduced from natural structures.In considering the interaction of molecular subunits to make supramolecular assemblages[41 a useful, if extreme, simplification is to consider each intermolecular interaction around the symmetry axis as a molecular lock and key interaction.[5361 Such interactions that require different symmetries are incommensurate-they require different stoichiometries a t the site of interaction. A useful analogy can be made here with the interaction of incommensurate lattices (Fig. 2). As occurs with some natural silicates, the superposition of one layer upon another which has a slightly different lattice spacing soon results in a mismatch of the unit cells due to the incommensurate lattice spacings.171 The two spacings can be kept in register only by curling them, as shown in Figure 2. Similarly, two incommensurate coordination numbers can coexist only by a ...

The bis-hydroxamate ligand isophthal-di-N-(4-methylphenyl)hydroxamate (E) forms tetrahedral clusters of the type M4 E 6 (M = Ga(III), Fe(III)). The syntheses of these and several other tetrahedral metal clusters have illustrated a general approach to the design of supramolecular metal clusters based on incommensurate coordination number interactions. In each case, rigid spacers separate bidentate units and preclude formation of metal coordination species other than the one targeted. For the Ga4 E 6 cluster described here each vertex is a chiral metal center (Δ or Λ) that generates clusters with T (ΔΔΔΔ or ΛΛΛΛ), C 3 (ΔΔΔΛ or ΛΛΛΔ), or S 4 (ΔΔΛΛ) symmetry. The rigid ligand spacer is bimodal, accommodating either mixed or homochiral metal centers at either end, but locks in the chirality of the complex once formed. Therefore all three isomers are seen in solution and their interconversion, although still on the NMR time scale, is significantly slower than isomerization of similar unimolecular hydroxamate complexes. The distribution of the isomers in aqueous solution for the T, C 3, and S 4 isomers is 4, 58, and 38%, respectively. The barrier to the interconversions, which occur through a nondissociative trigonal twist at the metal centers, is 58 kJ mol-1 for each of the isomerization steps. The syntheses of the ligand and corresponding iron and gallium complexes are described. The compound Ga4 E 6·18 DMF (DMF = dimethylformamide) crystallizes in I41/a with Z = 8, a = 24.0738(2) Å, and c = 68.5828(5) Å. Full-matrix refinement of data collected on a CCD detector with 7710 observations and 576 variables gave an R factor (on F) of 0.089. Two crystallographically independent clusters are chemically equivalent, both lying on 4̄ special positions. The Ga-to-Ga distances between metal centers with like and opposite chiralities are 9.0 and 8.8 Å, respectively. Two different ligand conformations are observed:  one bridging homochiral metal centers and the other mixed chiral centers. Their nearly equal stability explains the mix (T, C 3, S 4) of cluster isomers seen. This ligand couples the metal vertices in the cluster so as to increase significantly the transition state free energy for Λ−Δ interconversion but does not couple the chirality for the Λ or Δ ground state.

A series of homo- and heterotrinuclear complexes containing three face-sharing octahedra has been synthesized by using the pendent arm macrocyclic ligands 1,4,7-tris(3,5-dimethyl-2-hydroxybenzyl)-1,4,7-triazacyclononane, L0H3, and 1,4,7-tris(4-tert-butyl-2-mercaptobenzyl)-1,4,7-triazacyclononane, LH3:  [{L0NiII}2NiII] (1) and [{LCoIII}2CoIII](PF6)3 (2); [{LCoIII}2Ni] n + (n = 2 (3), 3 (4), 4 (5)); [{LNi}2CoIII] n + (n = 1 (6), 2 (7), 3 (8)) and its linkage isomers [{LNi}Ni{CoIIIL}] n + (n = 1 (9), 2 (10), 3 (11)) and, finally, the complexes [{LNi}2Ni] n + (n = 0 (12), 1 (13), 2 (14), 3 (15)). In complex 1 three octahedral NiII ions form a linear array with two terminal [L0NiII]- moieties in a facial N3O3 donor set and a central NiII ion which is connected to the terminal ions via six phenolate bridging pendent arms of L0. In complexes 2−15 the three metal ions are always in the same ligand matrix yielding an N3M(μ-S)3M(μ-S)3MN3 first-coordination sphere regardless of the nature of the metal ions (nickel or cobalt) or their formal oxidation states. From temperature dependent magnetic susceptibility measurements it has been determined that 1 has an S = 3 ground state whereas in 12 it is S = 1. In order to understand this difference in exchange coupling (ferromagnetic in 1 and antiferromagnetic in 12) in two apparently very similar complexes the magnetic properties of 2−15 have been investigated. Complex 3 has an S = 1 and 4 an S = 1/2, and 5 is diamagnetic (S = 0) as is its isoelectronic counterpart 2. This indicates the availability of the oxidation states II, III, and IV of the central NiS6 unit. In the isostructural complexes 6, 7, and 8, two terminal nickel ions are bridged by a central diamagnetic CoIII. The exchange coupling between two terminal paramagnetic nickel ions was studied as a function of their formal oxidation state. In 6 the two NiII ions are ferromagnetically coupled (S = 2); the mixed-valent NiIINiIII species 7 has an S = 3/2 ground state and in 8 most probably two NiIII ions (d7 low spin) give rise to an S = 1 ground state. In contrast, in the series 9, 10, and 11 where two nickel ions are in a position adjacent to each other 9 has an S = 0 (antiferromagnetic coupling), but in the mixed-valent complex 10 an S = 3/2 ground state (ferromagnetic coupling) is observed. In 11 an S = 1 ground state prevails which may be achieved by ferromagnetic coupling between two NiIII ions. For the trinuclear nickel complexes 12−15 an S = 1 ground state has been determined for 12, an S = 3/2 for the mixed valent complex 13, and an S = 2 for 14, and 15 exhibits an S = 3/2 ground state. The Goodenough−Kanamori rules do not provide a consistent explanation for the observed ground states in all cases. The concept of double exchange, originally introduced by Zener in 1951, appears to provide a more appropriate description for the mixed-valent species 7, 10, 13, 14, and 15. This picture is corroborated by the electrochemistry and EPR spectroscopy of complexes.

The reaction of mononuclear [LFeIII] where L represents the trianionic ligand 1,4,7-tris(4-tert-butyl-2-mercaptobenzyl)-1,4,7-triazacyclononane with CrSO4·5H2O, CoCl2·6H2O, or Fe(BF4)2·6H2O and subsequent oxidation with ferrocenium hexafluorophosphate or NO(BF4) or reduction with [(tmcn)Mo(CO)3] (tmcn = 1,4,7-trimethyl-1,4,7-triazacyclononane) produced an isostructural series of [LFeMFeL] n + complexes, the following salts of which were isolated as crystalline solids:  (i) [LFeCrFeL](PF6) n with n = 1 (1a), n = 2 (1b), and n = 3 (1c); (ii) [LFeCoFeL]X n with X = BPh4 and n = 2 (2b) and X = PF6 and n = 3 (2c); (iii) [LFeFeFeL](BPh4) n with n = 2 (3b) and n = 3 (3c). All compounds contain linear trinuclear cations (face-sharing octahedral) with an N3Fe(μ-SR)3M(μ-SR)3FeN3 core structure. The electron structure of all complexes has been studied by Fe and M K-edge X-ray absorption near edge structure (XANES), UV−vis, and EPR spectroscopy, variable-temperature, variable-field susceptibility measurements, and Mössbauer spectroscopy (in zero and applied field). The following electronic structures have been established:  (1a) FeII(ls)CrIIIFeII(ls) (ls = low-spin) with a spin ground state of S t = 3/2; (1c) FeIII(ls)CrIIIFeIII(ls) with an S t = 1/2 ground state; (2c) FeIII(ls)CoIII(ls)FeIII(ls) with an S t = 1 ground state; (3c) FeIII(ls)FeIII(ls)FeIII(ls) with an S t = 1/2 ground state. For 1b (S t = 2) it is found that the two iron ions are spectroscopically equivalent (Fe2.5) and, therefore, the excess electron is delocalized (class III):  [LFe2.5CrIIIFe2.5L]2+. For 2b clearly two different iron sites prevail at low temperatures (4.2 K); at higher temperatures (>200 K) they become equivalent on the Mössbauer time scale. Thus, 2b is class II with temperature-dependent electron hopping between the FeII and FeIII ions. 3b is again fully delocalized (class III) with an S t = 1 ground state; the excess electron is delocalized over all three iron sites. The electronic structure of all complexes is discussed in terms of double exchange and superexchange mechanisms.

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The hexadentate, pendant arm macrocycle 1,4,7-tris(4-tert-butyl-2-mercaptobenzyl)-1,4,7-triazacyclononane (H(3)L) has been synthesized and isolated as its trihydrochloride, H(3)L.3HCl, or sodium salt, Na(3)L, and its coordination chemistry with first-row transition metals has been studied. Mononuclear complexes of the type [LM(III)] (M = Ga (1), In (2), V (3), Cr (4), Mn (5), Fe,Co (6)) have been isolated as have the one-electron-oxidized forms [LM]PF(6) (M = V(IV) (3a), Mn(IV) (5a)). The crystal structure of 6 has been determined by single-crystal X-ray crystallography. Complex 6 crystallizes in the orthorhombic space group Iba2, with cell constants a = 14.206(8) Å, b = 22.53(1) Å, c = 26.07(1) Å, V = 8344.0(3) Å(3), and Z = 8. The cobalt(III) ion is in a distorted octahedral fac-N(3)S(3) donor set. The reaction of L with divalent metal chlorides in a 1:2 ratio in methanol affords the homodinuclear complexes [LM(II)(2)Cl] (M = Mn (7), Co (8), Ni (9), Zn (10), Cd (11)) where one metal is six- (N(3)MS(3)) and the other is four-coordinate (S(3)MCl); the two polyhedra are linked by three &mgr;(2)-thiolato bridges. Heterodinuclear complexes of the type [LM(1)M(2)Cl] have been obtained from [LM(2)Cl] species by abstraction of the four-coordinate metal ion and replacement by a different metal ion. The complexes [LZn(II)M(II)Cl] (M = Fe (12), Co (13), Ni (14)), [LNi(II)M(II)Cl] (M = Co (15), Zn (16)), and [LMn(II)M(II)Cl] (M = Fe (17), Co (18), Ni (19), Zn (20), Cd (21), Hg (22)) have been isolated as solid materials. The crystal structure of 14 has been determined by X-ray crystallography. Complex 14 crystallizes in the orthorhombic space group P2(1)2(1)2(1), with cell constants a = 15.45(1) Å, b = 17.77(1) Å, c = 17.58(1) Å, V = 4826.5(4) Å(3), and Z = 4. The linkage isomers 14 and 16 show characteristic electronic spectra for octahedrally and tetrahedrally coordinated Ni(II), respectively. The electronic structures of new complexes have been investigated by UV-vis spectroscopy; their magnetochemistry and electrochemistry are reported.

The age structure of harvested animals provides the basis for many demographic analyses. Ages of harvested white-tailed deer (Odocoileus virginianus) and other ungulates often are estimated by evaluating replacement and wear patterns of teeth, which is subjective and error-prone. Few previous studies however, examined age-and sex-specific error rates. Counting cementum annuli of incisors is an alternative, more accurate method of estimating age, but factors that influence consistency of cementum annuli counts are poorly known. We estimated age of 1,261 adult (!1.5 yr old) white-tailed deer harvested in Wisconsin and Illinois (USA; 2005-2008) using both wear-and-replacement and cementum annuli. We compared cementum annuli with wear-and-replacement estimates to assess misclassification rates by sex and age. Wear-and-replacement for estimating ages of white-tailed deer resulted in substantial misclassification compared with cementum annuli. Age classes of females were consistently underestimated, while those of males were underestimated for younger age classes but overestimated for older age classes. Misclassification resulted in an impression of a younger age-structure than actually was the case. Additionally, we obtained paired age-estimates from cementum annuli for 295 deer. Consistency of paired cementum annuli ageestimates decreased with age, was lower in females than males, and decreased as age estimates became less certain. Our results indicated that errors in the wear-and-replacement techniques are substantial and could impact demographic analyses that use age-structure information. Ó 2014 The Wildlife Society.

The reaction of mononuclear [LFe(III)] where L represents the trianionic ligand 1,4,7-tris(4-tert-butyl-2-mercaptobenzyl)-1,4,7-triazacyclononane with NiCl(2).6H(2)O and subsequent oxidations with [Ni(III)(tacn)(2)](ClO(4))(3) (tacn = 1,4,7-triazacyclononane) and PbO(2)/methanesulfonic acid produced an isostructural series of complexes [LFeNiFeL](n)()(+) (n = 2 (1), n = 3 (2), n = 4 (3)), which were isolated as PF(6)(-) (1, 3) or ClO(4)(-) salts (2). The molecular structures were established by X-ray crystallography for [LFeNiFeL](ClO(4))(2).5CH(3)CN (1), C(88)H(123)Cl(2)Fe(2)N(11)NiO(8)S(6), and [LFeNiFeL](ClO(4))(3).8acetone (2), C(102)H(156)Cl(3)Fe(2)N(6)NiO(20)S(6). Both compounds crystallize in the triclinic space group P&onemacr; with a = 13.065(2) Å (13.155(2) Å), b = 13.626(3) Å (13.747(3) Å), c = 14.043(3) Å (16.237(3) Å), alpha = 114.47(3) degrees (114.20(2) degrees ), beta = 97.67(3) degrees (96.57(2) degrees ), gamma = 90.34(3) degrees (98.86(2) degrees ), Z = 1(1) (values in parentheses refer to 2). The cations in 1, 2, and 3 have been determined to be isostructural by Fe and Ni K-edge extended X-ray absorption fine structure (EXAFS) spectroscopy. All compounds contain linear trinuclear cations (face-sharing octahedral) with an N(3)Fe(&mgr;-SR)(3)Ni(&mgr;-SR)(3)FeN(3) core structure. The electronic structures of 1, 2, and 3 have been studied by Fe and Ni K-edge X-ray absorption near edge (XANES), UV-vis, EPR, and Mössbauer spectroscopy as well as by temperature-dependent magnetic susceptibility measurements. Complexes 1 and 3 possess an S(t)() = 0 whereas 2 has an S(t)() = (1)/(2) ground state. It is shown that the electronic structures cannot be described by using localized valences (oxidation states). Delocalized models invoking the double-exchange mechanism are appropriate; i.e., spin-dependent delocalization via a double-exchange mechanism yields the correct ground state in each case. 1, 2, and 3 represent the first examples where double exchange stabilizes a ground state of minimum spin multiplicity.