1
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Quiroz M, Lockart MM, Xue S, Jones D, Guo Y, Pierce BS, Dunbar KR, Hall MB, Darensbourg MY. Magnetic coupling between Fe(NO) spin probe ligands through diamagnetic Ni II, Pd II and Pt II tetrathiolate bridges. Chem Sci 2023; 14:9167-9174. [PMID: 37655023 PMCID: PMC10466285 DOI: 10.1039/d3sc01546g] [Citation(s) in RCA: 3] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/23/2023] [Accepted: 08/07/2023] [Indexed: 09/02/2023] Open
Abstract
Reaction of the nitrosylated-iron metallodithiolate ligand, paramagnetic (NO)Fe(N2S2), with [M(CH3CN)n][BF4]2 salts (M = NiII, PdII, and PtII; n = 4 or 6) affords di-radical tri-metallic complexes in a stairstep type arrangement ([FeMFe]2+, M = Ni, Pd, and Pt), with the central group 10 metal held in a MS4 square plane. These isostructural compounds have nearly identical ν(NO) stretching values, isomer shifts, and electrochemical properties, but vary in their magnetic properties. Despite the intramolecular Fe⋯Fe distances of ca. 6 Å, antiferromagnetic coupling is observed between {Fe(NO)}7 units as established by magnetic susceptibility, EPR, and DFT studies. The superexchange interaction through the thiolate sulfur and central metal atoms is on the order of NiII < PdII ≪ PtII with exchange coupling constants (J) of -3, -23, and -124 cm-1, consistent with increased covalency of the M-S bonds (3d < 4d < 5d). This trend is reproduced by DFT calculations with molecular orbital analysis providing insight into the origin of the enhancement in the exchange interaction. Specifically, the magnitude of the exchange interaction correlates surprisingly well with the energy difference between the HOMO and HOMO-1 orbitals of the triplet states, which is reflected in the central metal's contribution to these orbitals. These results demonstrate the ability of sulfur-dense metallodithiolate ligands to engender strong magnetic communication by virtue of their enhanced covalency and polarizability.
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Affiliation(s)
- Manuel Quiroz
- Department of Chemistry, Texas A &M University College Station Texas 77843 USA
| | - Molly M Lockart
- Department of Chemistry & Biochemistry, Samford University Birmingham Alabama 35229 USA
| | - Shan Xue
- Department of Chemistry, Carnegie Mellon University Pittsburgh Pennsylvania 15213 USA
| | - Dakota Jones
- Department of Chemistry, Texas A &M University College Station Texas 77843 USA
| | - Yisong Guo
- Department of Chemistry, Carnegie Mellon University Pittsburgh Pennsylvania 15213 USA
| | - Brad S Pierce
- Department of Chemistry & Biochemistry, University of Alabama Tuscaloosa Alabama 35487 USA
| | - Kim R Dunbar
- Department of Chemistry, Texas A &M University College Station Texas 77843 USA
| | - Michael B Hall
- Department of Chemistry, Texas A &M University College Station Texas 77843 USA
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2
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Uemura K, Ikeda Y, Takamori A, Takeyama T, Iwatsuki S. Asymmetrical Platinum and Rhodium Dinuclear Complex Strongly Bound to Filled d z 2 ${{_{{\rm z}{^{2}}}}}$ Complexes by Unbridged Pt-Metal Bonds: Toward Heterometallic-Extended Metal Atom Chains. Chemistry 2023; 29:e202204057. [PMID: 36585834 DOI: 10.1002/chem.202204057] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/28/2022] [Revised: 12/30/2022] [Accepted: 12/30/2022] [Indexed: 01/01/2023]
Abstract
Heterometallic extended metal atom chains (EMACs) aligned with three types of metal were rationally synthesized by forming unbridged metal-metal bonds based on the interactions between highest occupied and lowest unoccupied molecular orbitals at the d z 2 ${{_{{\rm z}{^{2}}}}}$ orbital. These chains form pentanuclear structures aligned as Rh-Pt-M-Pt-Rh with relatively large formation constants of 5.0×1013 M-2 for M=Pt and 6.3×1011 M-2 for M=Pd, while retaining their backbones in solution. In the case of M=Cu, the original Cu(+2) atoms were reduced to Cu(+1) during the synthetic process. Cu(+1) has an unprecedented trigonal bipyramidal coordination geometry. The reported synthesis based on asymmetrical dinuclear complexes provides a guideline for the synthesis of hetero-EMACs to allow several analogs through judicious combinations realized by tuning the number of metal nuclei and metal species.
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Affiliation(s)
- Kazuhiro Uemura
- Department of Chemistry and Biomolecular Science Faculty of Engineering, Gifu University, Yanagido 1-1, Gifu, 501-1193, Japan
| | - Yuya Ikeda
- Department of Chemistry and Biomolecular Science Faculty of Engineering, Gifu University, Yanagido 1-1, Gifu, 501-1193, Japan
| | - Atsushi Takamori
- Department of Chemistry and Biomolecular Science Faculty of Engineering, Gifu University, Yanagido 1-1, Gifu, 501-1193, Japan
| | - Tomoyuki Takeyama
- Laboratory for Zero-Carbon Energy Institute of Innovative Research, Tokyo Institute of Technology 2-12-1N1-32, O-okayama, Meguro-ku, Tokyo, 152-8550, Japan
| | - Satoshi Iwatsuki
- Department of Chemistry, Konan University, Higashinada-ku, Kobe, 658-8501, Japan
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3
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Wheaton AM, Chipman JA, Roy MD, Berry JF. Metal-Metal Bond Umpolung in Heterometallic Extended Metal Atom Chains. Inorg Chem 2022; 61:15058-15069. [PMID: 36094078 PMCID: PMC9632685 DOI: 10.1021/acs.inorgchem.2c02118] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Abstract
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Understanding the fundamental properties governing metal–metal
interactions is crucial to understanding the electronic structure
and thereby applications of multimetallic systems in catalysis, material
science, and magnetism. One such property that is relatively underexplored
within multimetallic systems is metal–metal bond polarity,
parameterized by the electronegativities (χ) of the metal atoms
involved in the bond. In heterobimetallic systems, metal–metal
bond polarity is a function of the donor–acceptor (Δχ)
interactions of the two bonded metal atoms, with electropositive early
transition metals acting as electron acceptors and electronegative
late transition metals acting as electron donors. We show in this
work, through the preparation and systematic study of a series of
Mo2M(dpa)4(OTf)2 (M = Cr, Mn, Fe,
Co, and Ni; dpa = 2,2′-dipyridylamide; OTf = trifluoromethanesulfonate)
heterometallic extended metal atom chain (HEMAC) complexes that this
expected trend in χ can be reversed. Physical characterization
via single-crystal X-ray diffraction, magnetometry, and spectroscopic
methods as well as electronic structure calculations supports the
presence of a σ symmetry 3c/3e– bond that
is delocalized across the entire metal-atom chain and forms the basis
of the heterometallic Mo2–M interaction. The delocalized
3c/3e– interaction is discussed within the context
of the analogous 3c/3e– π bonding in the vinoxy
radical, CH2CHO. The vinoxy comparison establishes three
predictions for the σ symmetry 3c/3e– bond
in HEMACS: (1) an umpolung effect that causes the
Mo–M interactions to become more covalent as Δχ
increases, (2) distortion of the σ bonding and non-bonding orbitals
to emphasize Mo–M bonding and de-emphasize Mo–Mo bonding,
and (3) an increase in Mo spin population with increasing Mo–M
covalency. In agreement with these predictions, we find that the Mo2···M covalency increases with increasing Δχ
of the Mo and M atoms (ΔχMo–M increases
as M = Cr < Mn < Fe < Co < Ni), an umpolung of the trend predicted in the absence of σ delocalization.
We attribute the observed trend in covalency to the decreased energic
differential (ΔE) between the heterometal orbital and the σ bonding molecular
orbital of the Mo2 quadruple bond, which serves as an energetically
stable, “ligand”-like electron-pair donor to the heterometal
ion acceptor. As M is changed from Cr to Ni, the σ bonding and
nonbonding orbitals do indeed distort as anticipated, and the spin
population of the outer Mo group is increased by at least a factor
of 2. These findings provide a predictive framework for multimetallic
compounds and advance the current understanding of the electronic
structures of molecular heteromultimetallic systems, which can be
extrapolated to applications in the context of mixed-metal surface
catalysis and multimetallic proteins. This
work describes how use of a metal−metal quadruply
bonded metalloligand can reverse expected trends in metal−metal
bond polarity through the preparation and systematic study of a novel
series of Mo2M(dpa)4(OTf)2 (M = Cr,
Mn, Fe, Co, and Ni) heterotrimetallic extended metal atom chain (HEMAC)
complexes. These complexes feature a 3c/3e− metal−metal
bond that is delocalized across the entire metal atom chain and is
compared to the 3c/3e− π bonding in the vinoxyl
radical.
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Affiliation(s)
- Amelia M Wheaton
- Department of Chemistry, University of Wisconsin-Madison, 1101 University Avenue, Madison, Wisconsin 53706, United States
| | - Jill A Chipman
- Department of Chemistry, University of Wisconsin-Madison, 1101 University Avenue, Madison, Wisconsin 53706, United States
| | - Michael D Roy
- Department of Chemistry, University of Wisconsin-Madison, 1101 University Avenue, Madison, Wisconsin 53706, United States
| | - John F Berry
- Department of Chemistry, University of Wisconsin-Madison, 1101 University Avenue, Madison, Wisconsin 53706, United States
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4
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Uemura K, Aoki Y, Takamori A. Paramagnetic one-dimensional chains containing high-spin manganese atoms showing antiferromagnetic interaction through -Pt-Rh-Rh-Pt- bonds. Dalton Trans 2021; 51:946-957. [PMID: 34928286 DOI: 10.1039/d1dt03537a] [Citation(s) in RCA: 3] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/21/2022]
Abstract
To exploit the magnetic interactions of multiple metals, a heterometallic one-dimensional (1D) chain containing three kinds of metals, Rh, Pt, and Mn, where [Rh2(O2CCH3)4] and [Pt2Mn(piam)4(NH3)4]2+ (piam = pivalamidate) are connected through unbridged Rh-Pt bonds to form -Rh-Rh-Pt-Mn-Pt- alignments was successfully synthesized. The Mn atoms are tetrahedrally coordinated by four oxygen atoms of the piam ligands, where the coordination geometries form a zigzag 1D chain. Each Mn atom is linked by -Pt-Rh-Rh-Pt-, with a Mn-Mn separation of 13.9 Å. In parent [Pt2Mn(piam)4(NH3)4](PF6)2, Mn adopts two coordination environments, octahedral and tetrahedral, both of which are Mn(+2) high-spin states. In EtOH, [Rh2(O2CCH3)4] selectively binds tetrahedral Mn to afford a 1D chain. Physical analysis of the 1D chain using electron paramagnetic resonance (EPR) and X-ray photoelectron spectroscopy (XPS) revealed that all metals are divalent, indicating five unpaired spin-localized electrons on the Mn atoms. Magnetic susceptibility measurements indicated antiferromagnetic intra-chain interactions between the Mn atoms in the 1D chain, where χT at 300 K was 5.33 cm3 K mol-1 and gradually decreased to 1.65 cm3 K mol-1 at 2 K. Theoretical fitting of the magnetic behavior showed weak exchange coupling (zJ = -0.43 cm-1) between two high-spin Mn(+2) ions through diamagnetic Pt-Rh-Rh-Pt.
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Affiliation(s)
- Kazuhiro Uemura
- Department of Chemistry and Biomolecular Science, Faculty of Engineering, Gifu University, Yanagido 1-1, Gifu, 501-1193, Japan.
| | - Yusuke Aoki
- Department of Chemistry and Biomolecular Science, Faculty of Engineering, Gifu University, Yanagido 1-1, Gifu, 501-1193, Japan.
| | - Atsushi Takamori
- Department of Chemistry and Biomolecular Science, Faculty of Engineering, Gifu University, Yanagido 1-1, Gifu, 501-1193, Japan.
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Uemura K, Yasuda E, Sugiyama Y. Improving the Solubility of Hexanuclear Heterometallic Extended Metal Atom Chain Compounds in Nonpolar Solvents by Introducing Alkyl Amine Moieties. ACS OMEGA 2021; 6:18487-18503. [PMID: 34308079 PMCID: PMC8296546 DOI: 10.1021/acsomega.1c02634] [Citation(s) in RCA: 3] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Received: 05/19/2021] [Accepted: 06/24/2021] [Indexed: 06/13/2023]
Abstract
The highest occupied molecular orbital-lowest unoccupied molecular orbital (HOMO-LUMO) interaction at the d z 2 orbital between two kinds of metal complex is useful for obtaining heterometallic one-dimensional (1D) chains as well as heterometallic metal string compounds (HMSCs). Platinum dinuclear complexes, [Pt2(piam)2(NH2R)4]X2 (piam = pivalamidate, R = CH3, C2H5, C3H7, or C4H9, X = anion), comprising σ* as HOMO were mixed with [Rh2(O2CCH3)4] comprising σ* as LUMO in solvents to afford single crystals of [{Rh2(O2CCH3)4}{Pt2(piam)2(NH2R)4}2]X4 (2-5). Single-crystal X-ray analyses revealed that 2-5 are hexanuclear complexes that are one-dimensionally aligned as Pt-Pt-Rh-Rh-Pt-Pt with metal-metal bonds, where the alkyl moieties at end Pt atoms obstruct further 1D extension. Complexes 2-5 appear as if they are cut off from an infinite chain [{Rh2(O2CCH3)4}{Pt2(piam)2(NH3)4}2] n (PF6)4n ·6nH2O (1) aligned as -{Pt-Pt-Rh-Rh-Pt-Pt} n -. The diffuse reflectance spectrum of 1 depicts broad shoulder bands, which are not present in the spectra of 2-5, proving that the infinite chain 1 forms a band structure. Compounds 4 and 5 with propyl or butyl moieties at amine ligands, respectively, are soluble in nonpolar solvents, such as CH2Cl2, without the dissociation of their hexanuclear structures. Taking advantage of their solubility, measurement of cyclic voltammetry in CH2Cl2 become possible, which shows the quasi-reversible oxidation and reduction waves at 4: E ox = 0.86 V and E red = 0.69 V and 5: E ox = 0.87 V and E red = 0.53 V.
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6
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Nicolini A, Affronte M, SantaLucia DJ, Borsari M, Cahier B, Caleffi M, Ranieri A, Berry JF, Cornia A. Tetrairon(II) extended metal atom chains as single-molecule magnets. Dalton Trans 2021; 50:7571-7589. [PMID: 33983354 PMCID: PMC8214398 DOI: 10.1039/d1dt01007g] [Citation(s) in RCA: 6] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/21/2022]
Abstract
Iron-based extended metal atom chains (EMACs) are potentially high-spin molecules with axial magnetic anisotropy and thus candidate single-molecule magnets (SMMs). We herein compare the tetrairon(ii), halide-capped complexes [Fe4(tpda)3Cl2] (1Cl) and [Fe4(tpda)3Br2] (1Br), obtained by reacting iron(ii) dihalides with [Fe2(Mes)4] and N2,N6-di(pyridin-2-yl)pyridine-2,6-diamine (H2tpda) in toluene, under strictly anhydrous and anaerobic conditions (HMes = mesitylene). Detailed structural, electrochemical and Mössbauer data are presented along with direct-current (DC) and alternating-current (AC) magnetic characterizations. DC measurements revealed similar static magnetic properties for the two derivatives, with χMT at room temperature above that for independent spin carriers, but much lower at low temperature. The electronic structure of the iron(ii) ions in each derivative was explored by ab initio (CASSCF-NEVPT2-SO) calculations, which showed that the main magnetic axis of all metals is directed close to the axis of the chain. The outer metals, Fe1 and Fe4, have an easy-axis magnetic anisotropy (D = -11 to -19 cm-1, |E/D| = 0.05-0.18), while the internal metals, Fe2 and Fe3, possess weaker hard-axis anisotropy (D = 8-10 cm-1, |E/D| = 0.06-0.21). These single-ion parameters were held constant in the fitting of DC magnetic data, which revealed ferromagnetic Fe1-Fe2 and Fe3-Fe4 interactions and antiferromagnetic Fe2-Fe3 coupling. The competition between super-exchange interactions and the large, noncollinear anisotropies at metal sites results in a weakly magnetic non-Kramers doublet ground state. This explains the SMM behavior displayed by both derivatives in the AC susceptibility data, with slow magnetic relaxation in 1Br being observable even in zero static field.
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Affiliation(s)
- Alessio Nicolini
- Department of Chemical and Geological Sciences, University of Modena and Reggio Emilia & INSTM, I-41125 Modena, Italy. and Department of Physics, Informatics and Mathematics, University of Modena and Reggio Emilia, I-41125 Modena, Italy
| | - Marco Affronte
- Department of Physics, Informatics and Mathematics, University of Modena and Reggio Emilia, I-41125 Modena, Italy
| | - Daniel J SantaLucia
- Department of Chemistry, University of Wisconsin-Madison, 1101 University Avenue, Madison, Wisconsin 53706, USA
| | - Marco Borsari
- Department of Chemical and Geological Sciences, University of Modena and Reggio Emilia & INSTM, I-41125 Modena, Italy.
| | - Benjamin Cahier
- Max-Planck-Institut für Kohlenforschung, Kaiser-Wilhelm-Platz 1, 45470 Mülheim an der Ruhr, Germany
| | - Matteo Caleffi
- Department of Physics, Informatics and Mathematics, University of Modena and Reggio Emilia, I-41125 Modena, Italy
| | - Antonio Ranieri
- Department of Life Sciences, University of Modena and Reggio Emilia, I-41125 Modena, Italy
| | - John F Berry
- Department of Chemistry, University of Wisconsin-Madison, 1101 University Avenue, Madison, Wisconsin 53706, USA
| | - Andrea Cornia
- Department of Chemical and Geological Sciences, University of Modena and Reggio Emilia & INSTM, I-41125 Modena, Italy.
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7
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Spivak M, de Graaf C, Arcisauskaite V, López X. Gating the conductance of extended metal atom chains: a computational analysis of Ru 3(dpa) 4(NCS) 2 and [Ru 3(npa) 4(NCS) 2]. Phys Chem Chem Phys 2021; 23:14836-14844. [PMID: 34212973 DOI: 10.1039/d1cp02429a] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/21/2022]
Abstract
The effects of a gate potential on the conductance of two members of the EMAC family, Ru3(dpa)4(NCS)2 and its asymmetric analogue, [Ru3(npa)4(NCS)2]+, are explored with a density functional approach combined with non-equilibrium Green's functions. From a computational perspective, the inclusion of an electrochemical gate potential represents a significant challenge because the periodic treatment of the electrode surface resists the formation of charged species. However, it is possible to mimic the effects of the electrochemical gate by including a very electropositive or electronegative atom in the unit cell that will effectively reduce or oxidize the molecule under study. In this contribution we compare this approach to the more conventional application of a solid-state gate potential, and show that both generate broadly comparable results. For two extended metal atom chain (EMAC) compounds, Ru3(dpa)4(NCS)2 and [Ru3(npa)4(NCS)2], we show that the presence of a gate potential shifts the molecular energy levels in a predictable way relative to the Fermi level, with distinct peaks in the conductance trace emerging as these levels enter the bias window.
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Affiliation(s)
- Mariano Spivak
- Department of Chemistry, University of Oxford, South Parks Road, Oxford OX1 3QZ, UK and Universitat Rovira I Virgili, Departament de Química Física i Inorgànica, Marcel·lí Domingo 1, 43007 Tarragona, Spain.
| | - Coen de Graaf
- Universitat Rovira I Virgili, Departament de Química Física i Inorgànica, Marcel·lí Domingo 1, 43007 Tarragona, Spain. and Institució Catalana de Recerca i Estudis Avançats (ICREA), Passeig Lluís Companys 23, 08010 Barcelona, Spain
| | - Vaida Arcisauskaite
- Department of Chemistry, University of Oxford, South Parks Road, Oxford OX1 3QZ, UK
| | - Xavier López
- Universitat Rovira I Virgili, Departament de Química Física i Inorgànica, Marcel·lí Domingo 1, 43007 Tarragona, Spain.
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8
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Cheng MC, Lee GH, Lin TS, Liu YC, Chiang MH, Peng SM. A new series of heteronuclear metal strings, MRhRh(dpa)4Cl2 and MRhRhM(dpa)4X2, from the reactions of Rh2(dpa)4 with metal ions of group 7 to group 12. Dalton Trans 2021; 50:520-534. [DOI: 10.1039/d0dt03311a] [Citation(s) in RCA: 4] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/19/2023]
Abstract
A new series of trinuclear and tetranuclear HMSCs, MRhRh(dpa)4Cl2 and MRhRhM(dpa)4X2, from the reactions of Rh2(dpa)4 and metal ions were synthesized.
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Affiliation(s)
- Ming-Chuan Cheng
- Department of Chemistry
- National Taiwan University
- Taipei
- Republic of China
- Institute of Chemistry
| | - Gene-Hsiang Lee
- Department of Chemistry
- National Taiwan University
- Taipei
- Republic of China
| | - Tien-Sung Lin
- Department of Chemistry
- National Taiwan University
- Taipei
- Republic of China
| | - Yu-Chiao Liu
- Institute of Chemistry
- Academia Sinica
- Taipei
- Republic of China
| | - Ming-Hsi Chiang
- Institute of Chemistry
- Academia Sinica
- Taipei
- Republic of China
| | - Shie-Ming Peng
- Department of Chemistry
- National Taiwan University
- Taipei
- Republic of China
- Institute of Chemistry
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9
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Abstract
Significant progress has been made in the past 10-15 years on the design, synthesis, and properties of multimetallic coordination complexes with heterometallic metal-metal bonds that are paramagnetic. Several general classes have been explored including heterobimetallic compounds, heterotrimetallic compounds of either linear or triangular geometry, discrete molecular compounds containing a linear array of more than three metal atoms, and coordination polymers with a heterometallic metal-metal bonded backbone. We focus in this Review on the synthetic methods employed to access these compounds, their structural features, magnetic properties, and electronic structure. Regarding the metal-metal bond distances, we make use of the formal shortness ratio (FSR) for comparison of bond distances between a broad range of metal atoms of different sizes. The magnetic properties of these compounds can be described using an extension of the Goodenough-Kanamori rules to cases where two magnetic ions interact via a third metal atom. In describing the electronic structure, we focus on the ability (or not) of electrons to be delocalized across heterometallic bonds, allowing for rationalizations and predictions of single-molecule conductance measurements in paramagnetic heterometallic molecular wires.
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Affiliation(s)
- Jill A Chipman
- Department of Chemistry, University of Wisconsin-Madison, 1101 University Avenue, Madison Wisconsin 53706, United States
| | - John F Berry
- Department of Chemistry, University of Wisconsin-Madison, 1101 University Avenue, Madison Wisconsin 53706, United States
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10
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Cornia A, Barra AL, Bulicanu V, Clérac R, Cortijo M, Hillard EA, Galavotti R, Lunghi A, Nicolini A, Rouzières M, Sorace L, Totti F. The Origin of Magnetic Anisotropy and Single-Molecule Magnet Behavior in Chromium(II)-Based Extended Metal Atom Chains. Inorg Chem 2020; 59:1763-1777. [PMID: 31967457 PMCID: PMC7901656 DOI: 10.1021/acs.inorgchem.9b02994] [Citation(s) in RCA: 21] [Impact Index Per Article: 5.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 02/08/2023]
Abstract
Chromium(II)-based extended metal atom chains have been the focus of considerable discussion regarding their symmetric versus unsymmetric structure and magnetism. We have now investigated four complexes of this class, namely, [Cr3(dpa)4X2] and [Cr5(tpda)4X2] with X = Cl- and SCN- [Hdpa = dipyridin-2-yl-amine; H2tpda = N2,N6-di(pyridin-2-yl)pyridine-2,6-diamine]. By dc/ac magnetic techniques and EPR spectroscopy, we found that all these complexes have easy-axis anisotropies of comparable magnitude in their S = 2 ground state (|D| = 1.5-1.8 cm-1) and behave as single-molecule magnets at low T. Ligand-field and DFT/CASSCF calculations were used to explain the similar magnetic properties of tri- versus pentachromium(II) strings, in spite of their different geometrical preferences and electronic structure. For both X ligands, the ground structure is unsymmetric in the pentachromium(II) species (i.e., with an alternation of long and short Cr-Cr distances) but is symmetric in their shorter congeners. Analysis of the electronic structure using quasi-restricted molecular orbitals (QROs) showed that the four unpaired electrons in Cr5 species are largely localized in four 3d-like QROs centered on the terminal, "isolated" Cr2+ ion. In Cr3 complexes, they occupy four nonbonding combinations of 3d-like orbitals centered only on the two terminal metals. In both cases, then, QRO eigenvalues closely mirror the 3d-level pattern of the terminal ions, whose coordination environment remains quite similar irrespective of chain length. We conclude that the extent of unpaired-electron delocalization has little impact on the magnetic anisotropy of these wire-like molecular species.
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Affiliation(s)
- Andrea Cornia
- Department of Chemical and Geological Sciences , University of Modena and Reggio Emilia & INSTM , 41125 Modena , Italy
| | - Anne-Laure Barra
- Laboratoire National des Champs Magnétiques Intenses-CNRS , Université Grenoble-Alpes , 38042 Grenoble Cedex 9 , France
| | - Vladimir Bulicanu
- Univ. Bordeaux, CNRS, Centre de Recherche Paul Pascal, CRPP, UMR 5031 , 33600 Pessac , France
| | - Rodolphe Clérac
- Univ. Bordeaux, CNRS, Centre de Recherche Paul Pascal, CRPP, UMR 5031 , 33600 Pessac , France
| | - Miguel Cortijo
- Univ. Bordeaux, CNRS, Centre de Recherche Paul Pascal, CRPP, UMR 5031 , 33600 Pessac , France
| | - Elizabeth A Hillard
- Univ. Bordeaux, CNRS, Centre de Recherche Paul Pascal, CRPP, UMR 5031 , 33600 Pessac , France
| | - Rita Galavotti
- Department of Chemical and Geological Sciences , University of Modena and Reggio Emilia & INSTM , 41125 Modena , Italy
| | - Alessandro Lunghi
- School of Physics and CRANN Institute , Trinity College Dublin , Dublin 2 , Ireland
| | - Alessio Nicolini
- Department of Chemical and Geological Sciences , University of Modena and Reggio Emilia & INSTM , 41125 Modena , Italy.,Department of Physics, Informatics, and Mathematics , University of Modena and Reggio Emilia , 41125 Modena , Italy
| | - Mathieu Rouzières
- Univ. Bordeaux, CNRS, Centre de Recherche Paul Pascal, CRPP, UMR 5031 , 33600 Pessac , France
| | - Lorenzo Sorace
- Department of Chemistry "Ugo Schiff" , University of Florence & INSTM , 50019 Sesto Fiorentino (FI) , Italy
| | - Federico Totti
- Department of Chemistry "Ugo Schiff" , University of Florence & INSTM , 50019 Sesto Fiorentino (FI) , Italy
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11
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Yoshida T, Ninomiya Y, Higuchi M. Reversible four-color electrochromism triggered by the electrochemical multi-step redox of Cr-based metallo-supramolecular polymers. RSC Adv 2020; 10:10904-10909. [PMID: 35492949 PMCID: PMC9050427 DOI: 10.1039/d0ra00676a] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/22/2020] [Accepted: 02/28/2020] [Indexed: 12/12/2022] Open
Abstract
Four color electrochromism (yellow, magenta, blue, and navy) has been achieved in Cr(iii)-based metallo-supramolecular polymers (polyCr), which were synthesized by 1 : 1 complexation of Cr ions and 1,4-di[[2,2′:6′,2′′-terpyridin]-4′-yl]benzene (L).
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Affiliation(s)
- Takefumi Yoshida
- Electronic Functional Macromolecules Group
- National Institute for Materials Science (NIMS)
- Tsukuba 305-0044
- Japan
| | - Yoshikazu Ninomiya
- Electronic Functional Macromolecules Group
- National Institute for Materials Science (NIMS)
- Tsukuba 305-0044
- Japan
| | - Masayoshi Higuchi
- Electronic Functional Macromolecules Group
- National Institute for Materials Science (NIMS)
- Tsukuba 305-0044
- Japan
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12
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Uemura K, Miyake R. Paramagnetic One-Dimensional Chain Complex Consisting of Three Kinds of Metallic Species Showing Magnetic Interaction through Metal-Metal Bonds. Inorg Chem 2019; 59:1692-1701. [PMID: 31877032 DOI: 10.1021/acs.inorgchem.9b02844] [Citation(s) in RCA: 12] [Impact Index Per Article: 2.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/18/2023]
Abstract
A heterometallic and paramagnetic one-dimensional (1-D) chain (3) aligned as -Rh(+2)-Rh(+2)-Pt(+2)-Co(+2)-Pt(+2)- with direct metal-metal bonds was obtained by HOMO-LUMO interactions at the σ* (dz2) orbital between two kinds of complexes. The 1-D chains in 3 have relatively straight backbones because the raw material complexes, [Rh2(O2CCH3)4] and [Pt2Co(piam)4(NH3)4], are connected and stacked in a face-to-face fashion, where Co---Co are separated by about 13.3 Å with four different metals. Physical measurements revealed that 3 has a band gap between the σ-type conduction and valence bands, where d-orbitals of the Co ion with three unpaired electrons are laid among them. The magnetic behavior of 3 was investigated and found to be consistent with a complex interaction involving both zero-field splitting and Pauli paramagnetism attributed to band formation superimposed on relatively strong exchange coupling (zJ = -22.2 cm-1) between two high-spin Co(+2) ions separated by the diamagnetic Pt-Rh-Rh-Pt.
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Affiliation(s)
- Kazuhiro Uemura
- Department of Chemistry and Biomolecular Science, Faculty of Engineering , Gifu University , Yanagido 1-1 , Gifu , 501-1193 , Japan
| | - Rika Miyake
- Department of Chemistry and Biomolecular Science, Faculty of Engineering , Gifu University , Yanagido 1-1 , Gifu , 501-1193 , Japan
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13
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Lin G, Cheng M, Liou S, Tsao H, Lin C, Lin YR, Lee G, Chen C, Peng S. Revisit of trinickel metal string complexes [Ni
3
L
4
X
2
] (L = dipyridylamido, diazaphenoxazine; X = NCS, CN) for quantum transport. J CHIN CHEM SOC-TAIP 2019. [DOI: 10.1002/jccs.201900229] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/20/2022]
Affiliation(s)
- Geng‐Min Lin
- Department of Chemistry and Center for Emerging Material and Advanced DeviceNational Taiwan University Taipei Taiwan
| | | | - Shun‐Jie Liou
- Department of Chemistry and Center for Emerging Material and Advanced DeviceNational Taiwan University Taipei Taiwan
| | - Ho‐Sung Tsao
- Department of Chemistry and Center for Emerging Material and Advanced DeviceNational Taiwan University Taipei Taiwan
| | - Chih‐Hsun Lin
- Department of Chemistry and Center for Emerging Material and Advanced DeviceNational Taiwan University Taipei Taiwan
| | - Yi R. Lin
- Department of Chemistry and Center for Emerging Material and Advanced DeviceNational Taiwan University Taipei Taiwan
| | - Gene‐Hsiang Lee
- Department of Chemistry and Center for Emerging Material and Advanced DeviceNational Taiwan University Taipei Taiwan
| | - Chun‐hsien Chen
- Department of Chemistry and Center for Emerging Material and Advanced DeviceNational Taiwan University Taipei Taiwan
| | - Shie‐Ming Peng
- Department of Chemistry and Center for Emerging Material and Advanced DeviceNational Taiwan University Taipei Taiwan
- Institute of Chemistry, Academia Sinica Taipei Taiwan
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14
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Coste SC, Pearson TJ, Freedman DE. Magnetic Anisotropy in Heterobimetallic Complexes. Inorg Chem 2019; 58:11893-11902. [DOI: 10.1021/acs.inorgchem.9b01459] [Citation(s) in RCA: 9] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Affiliation(s)
- Scott C. Coste
- Department of Chemistry, Northwestern University, Evanston, Illinois 60208, United States
| | - Tyler J. Pearson
- Department of Chemistry, Northwestern University, Evanston, Illinois 60208, United States
| | - Danna E. Freedman
- Department of Chemistry, Northwestern University, Evanston, Illinois 60208, United States
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15
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Chen L, Song J, Zhao W, Yi G, Zhou Z, Yuan A, Song Y, Wang Z, Ouyang ZW. A mononuclear five-coordinate Co(ii) single molecule magnet with a spin crossover between the S = 1/2 and 3/2 states. Dalton Trans 2018; 47:16596-16602. [PMID: 30417917 DOI: 10.1039/c8dt03783c] [Citation(s) in RCA: 28] [Impact Index Per Article: 4.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/21/2022]
Abstract
Although a great number of single-ion magnets (SIMs) and spin-crossover (SCO) compounds have been discovered, multifunctional materials with the combination of SCO and SIM properties are extremely scarce. Here magnetic studies have been carried out for a mononuclear, five-coordinate cobalt(ii) complex [Co(3,4-lut)4Br]Br (1) with square pyramidal geometry. Direct-current magnetic measurement confirms the spin transition between the S = 1/2 and 3/2 states in the range of 150-290 K with a small hysteresis loop. Frequency- and temperature-dependent alternating-current magnetic susceptibility reveals slow magnetization relaxation under an applied dc field of 3000 Oe. The work here presents the first instance of the five-coordinate mononuclear cobalt(ii)-based SIM exhibiting the thermally induced complete SCO.
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Affiliation(s)
- Lei Chen
- School of Environmental and Chemical Engineering, Jiangsu University of Science and Technology, Zhenjiang 212003, P. R. China.
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16
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Nicolini A, Galavotti R, Barra AL, Borsari M, Caleffi M, Luo G, Novitchi G, Park K, Ranieri A, Rigamonti L, Roncaglia F, Train C, Cornia A. Filling the Gap in Extended Metal Atom Chains: Ferromagnetic Interactions in a Tetrairon(II) String Supported by Oligo-α-pyridylamido Ligands. Inorg Chem 2018; 57:5438-5448. [PMID: 29668273 DOI: 10.1021/acs.inorgchem.8b00405] [Citation(s) in RCA: 10] [Impact Index Per Article: 1.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Abstract
The stringlike complex [Fe4(tpda)3Cl2] (2; H2tpda = N2, N6-bis(pyridin-2-yl)pyridine-2,6-diamine) was obtained as the first homometallic extended metal atom chain based on iron(II) and oligo-α-pyridylamido ligands. The synthesis was performed under strictly anaerobic and anhydrous conditions using dimesityliron, [Fe2(Mes)4] (1; HMes = mesitylene), as both an iron source and a deprotonating agent for H2tpda. The four lined-up iron(II) ions in the structure of 2 (Fe···Fe = 2.94-2.99 Å, Fe···Fe···Fe = 171.7-168.8°) are wrapped by three doubly deprotonated twisted ligands, and the chain is capped at its termini by two chloride ions. The spectroscopic and electronic properties of 2 were investigated in dichloromethane by UV-vis-NIR absorption spectroscopy, 1H NMR spectroscopy, and cyclic voltammetry. The electrochemical measurements showed four fully resolved, quasi-reversible one-electron-redox processes, implying that 2 can adopt five oxidation states in a potential window of only 0.8 V. Direct current (dc) magnetic measurements indicate dominant ferromagnetic coupling at room temperature, although the ground state is only weakly magnetic. On the basis of density functional theory and angular overlap model calculations, this magnetic behavior was explained as being due to two pairs of ferromagnetically coupled iron(II) ions ( J = -21 cm-1 using JŜ i·Ŝ j convention) weakly antiferromagnetically coupled with each other. Alternating-current susceptibility data in the presence of a 2 kOe dc field and at frequencies up to 1.5 kHz revealed the onset of slow magnetic relaxation below 2.8 K, with the estimated energy barrier Ueff/ kB = 10.1(1.3) K.
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Affiliation(s)
- Alessio Nicolini
- Department of Chemical and Geological Sciences , University of Modena and Reggio Emilia & INSTM , I-41125 Modena , Italy.,Department of Physics, Informatics and Mathematics , University of Modena and Reggio Emilia , I-41125 Modena , Italy
| | - Rita Galavotti
- Department of Chemical and Geological Sciences , University of Modena and Reggio Emilia & INSTM , I-41125 Modena , Italy
| | - Anne-Laure Barra
- Laboratoire National des Champs Magnétiques Intenses-CNRS , Université Grenoble-Alpes , F-38042 Grenoble Cedex 9 , France
| | - Marco Borsari
- Department of Chemical and Geological Sciences , University of Modena and Reggio Emilia & INSTM , I-41125 Modena , Italy
| | - Matteo Caleffi
- Department of Chemical and Geological Sciences , University of Modena and Reggio Emilia & INSTM , I-41125 Modena , Italy
| | - Guangpu Luo
- Department of Physics , Virginia Tech , Blacksburg , Virginia 24061 , United States
| | - Ghenadie Novitchi
- Laboratoire National des Champs Magnétiques Intenses-CNRS , Université Grenoble-Alpes , F-38042 Grenoble Cedex 9 , France
| | - Kyungwha Park
- Department of Physics , Virginia Tech , Blacksburg , Virginia 24061 , United States
| | - Antonio Ranieri
- Department of Life Sciences , University of Modena and Reggio Emilia , I-41125 Modena , Italy
| | - Luca Rigamonti
- Department of Chemical and Geological Sciences , University of Modena and Reggio Emilia & INSTM , I-41125 Modena , Italy
| | - Fabrizio Roncaglia
- Department of Chemical and Geological Sciences , University of Modena and Reggio Emilia & INSTM , I-41125 Modena , Italy
| | - Cyrille Train
- Laboratoire National des Champs Magnétiques Intenses-CNRS , Université Grenoble-Alpes , F-38042 Grenoble Cedex 9 , France
| | - Andrea Cornia
- Department of Chemical and Geological Sciences , University of Modena and Reggio Emilia & INSTM , I-41125 Modena , Italy
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17
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Dirvanauskas A, Galavotti R, Lunghi A, Nicolini A, Roncaglia F, Totti F, Cornia A. Solution structure of a pentachromium(ii) single molecule magnet from DFT calculations, isotopic labelling and multinuclear NMR spectroscopy. Dalton Trans 2018; 47:585-595. [DOI: 10.1039/c7dt03931j] [Citation(s) in RCA: 7] [Impact Index Per Article: 1.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/21/2022]
Abstract
Solution NMR spectroscopy on isotopically-labelled samples of [Cr5(tpda)4Cl2] unveils a D4 symmetric molecule, implying fast shuttling between the two unsymmetric ground configurations over NMR timescale.
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Affiliation(s)
- Aivaras Dirvanauskas
- Department of Chemical and Geological Sciences
- University of Modena and Reggio Emilia & INSTM
- I-41125 Modena
- Italy
- Department of Chemistry
| | - Rita Galavotti
- Department of Chemical and Geological Sciences
- University of Modena and Reggio Emilia & INSTM
- I-41125 Modena
- Italy
| | - Alessandro Lunghi
- Department of Chemistry ‘Ugo Schiff’
- University of Florence & INSTM
- I-50019 Sesto Fiorentino (FI)
- Italy
| | - Alessio Nicolini
- Department of Chemical and Geological Sciences
- University of Modena and Reggio Emilia & INSTM
- I-41125 Modena
- Italy
| | - Fabrizio Roncaglia
- Department of Chemical and Geological Sciences
- University of Modena and Reggio Emilia & INSTM
- I-41125 Modena
- Italy
| | - Federico Totti
- Department of Chemistry ‘Ugo Schiff’
- University of Florence & INSTM
- I-50019 Sesto Fiorentino (FI)
- Italy
| | - Andrea Cornia
- Department of Chemical and Geological Sciences
- University of Modena and Reggio Emilia & INSTM
- I-41125 Modena
- Italy
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18
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Chipman JA, Berry JF. Extraordinarily Large Ferromagnetic Coupling (J≥150 cm -1 ) by Electron Delocalization in a Heterometallic Mo≣Mo-Ni Chain Complex. Chemistry 2017; 24:1494-1499. [PMID: 29124828 DOI: 10.1002/chem.201704588] [Citation(s) in RCA: 24] [Impact Index Per Article: 3.4] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/27/2017] [Indexed: 12/22/2022]
Abstract
The new heterometallic chain compounds Mo2 Ni(dpa)4 Cl2 (1) and [Mo2 Ni(dpa)4 Cl2 ]OTf (2) (dpa=2,2'-dipyridylamine) have been prepared and studied by crystallography and magnetic susceptibility, among other methods. Oxidation of 1 to 2 removes an electron from the multiply bonded Mo2 unit, consistent with the formulation of 2 containing a (Mo2 )5+ ⋅⋅⋅(Ni)2+ core. While 1 contains an S=1, pseudo-octahedral NiII ion, 2 has an S=3/2 ground state, in which the two NiII unpaired electrons, one in a localized δ-orbital and one in a heavily delocalized σnb -orbital are joined by an unpaired electron in a Mo-Mo δ-orbital. The S=3/2 ground state is persistent to 300 K, evidencing strong ferromagnetic coupling of the Mo2 and Ni spins with J≥150 cm-1 . This ferromagnetic interaction occurs via delocalization of a σnb -electron across all three metal atoms, forcing ferromagnetic alignment of electrons in orthogonal Ni and Mo2 δ-symmetry orbitals. We anticipate that this new means of coupling spins can be used as a design principle for the preparation of new compounds with high spin ground states.
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Affiliation(s)
- Jill A Chipman
- Department of Chemistry, University of Wisconsin Madison, 1101 University Avenue, Madison, WI 53706, USA
| | - John F Berry
- Department of Chemistry, University of Wisconsin Madison, 1101 University Avenue, Madison, WI 53706, USA
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19
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Li GL, Wu SQ, Zhang LF, Wang Z, Ouyang ZW, Ni ZH, Su SQ, Yao ZS, Li JQ, Sato O. Field-Induced Slow Magnetic Relaxation in an Octacoordinated Fe(II) Complex with Pseudo-D2d Symmetry: Magnetic, HF-EPR, and Theoretical Investigations. Inorg Chem 2017; 56:8018-8025. [DOI: 10.1021/acs.inorgchem.7b00765] [Citation(s) in RCA: 16] [Impact Index Per Article: 2.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Affiliation(s)
- Guo-Ling Li
- Institute for Materials Chemistry and Engineering & IRCCS, Kyushu University, 744 Motooka Nishi-ku, 819-0395 Fukuoka, Japan
- School of Chemical Engineering and Technology, China University of Mining and Technology, Xuzhou 221116, People’s Republic of China
| | - Shu-Qi Wu
- Institute for Materials Chemistry and Engineering & IRCCS, Kyushu University, 744 Motooka Nishi-ku, 819-0395 Fukuoka, Japan
| | - Li-Fang Zhang
- School of Chemical Engineering and Technology, China University of Mining and Technology, Xuzhou 221116, People’s Republic of China
| | - Zhenxing Wang
- Wuhan National High Magnetic
Field Center, Huazhong University of Science and Technology, Wuhan 430074, People’s Republic of China
| | - Zhong-Wen Ouyang
- Wuhan National High Magnetic
Field Center, Huazhong University of Science and Technology, Wuhan 430074, People’s Republic of China
| | - Zhong-Hai Ni
- School of Chemical Engineering and Technology, China University of Mining and Technology, Xuzhou 221116, People’s Republic of China
| | - Sheng-Qun Su
- Institute for Materials Chemistry and Engineering & IRCCS, Kyushu University, 744 Motooka Nishi-ku, 819-0395 Fukuoka, Japan
| | - Zi-Shuo Yao
- Institute for Materials Chemistry and Engineering & IRCCS, Kyushu University, 744 Motooka Nishi-ku, 819-0395 Fukuoka, Japan
| | - Jun-Qiu Li
- Institute for Materials Chemistry and Engineering & IRCCS, Kyushu University, 744 Motooka Nishi-ku, 819-0395 Fukuoka, Japan
| | - Osamu Sato
- Institute for Materials Chemistry and Engineering & IRCCS, Kyushu University, 744 Motooka Nishi-ku, 819-0395 Fukuoka, Japan
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20
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Corcos AR, Berry JF. Anilinopyridinate-supported Ru2x+ (x = 5 or 6) paddlewheel complexes with labile axial ligands. Dalton Trans 2017; 46:5532-5539. [DOI: 10.1039/c6dt04328c] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/18/2023]
Abstract
Five new metal–metal bonded Ru2 amidinate compounds with labile axial ligands are presented and discussed.
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Affiliation(s)
- Amanda R. Corcos
- Department of Chemistry
- University of Wisconsin-Madison
- Madison
- USA
| | - John F. Berry
- Department of Chemistry
- University of Wisconsin-Madison
- Madison
- USA
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21
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Rej S, Majumdar M, Kando S, Sugino Y, Tsurugi H, Mashima K. Mixed Ligated Tris(amidinate)dimolybdenum Complexes as Catalysts for Radical Addition of CCl4 to 1-Hexene: Leaving Ligand Lability Controls Catalyst Activity. Inorg Chem 2016; 56:634-644. [DOI: 10.1021/acs.inorgchem.6b02525] [Citation(s) in RCA: 18] [Impact Index Per Article: 2.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/13/2023]
Affiliation(s)
- Supriya Rej
- Department of Chemistry, Graduate School of Engineering Science, Osaka University, Toyonaka, Osaka 560-8531, Japan
| | - Moumita Majumdar
- Department of Chemistry, Graduate School of Engineering Science, Osaka University, Toyonaka, Osaka 560-8531, Japan
| | - Shun Kando
- Department of Chemistry, Graduate School of Engineering Science, Osaka University, Toyonaka, Osaka 560-8531, Japan
| | - Yoshitaka Sugino
- Department of Chemistry, Graduate School of Engineering Science, Osaka University, Toyonaka, Osaka 560-8531, Japan
| | - Hayato Tsurugi
- Department of Chemistry, Graduate School of Engineering Science, Osaka University, Toyonaka, Osaka 560-8531, Japan
| | - Kazushi Mashima
- Department of Chemistry, Graduate School of Engineering Science, Osaka University, Toyonaka, Osaka 560-8531, Japan
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