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Magnetic {Mo72Fe30}-embedded hybrid nanocapsules

“…Müller and coworkers reported that {Mo 72 Fe 30 } was the largest paramagnetic molecule [50]. In this work, magnetic measurements indicate that {Mo 72 Fe 30 }-embedded nanocapsules are paramagnetic (Supporting information, Fig.…”

Magnetic {Mo72Fe30}-embedded hybrid nanocapsules

“…Müller and coworkers reported that {Mo 72 Fe 30 } was the largest paramagnetic molecule [50]. In this work, magnetic measurements indicate that {Mo 72 Fe 30 }-embedded nanocapsules are paramagnetic (Supporting information, Fig.…”

Symmetry and Broken-Symmetry in Molecular Orbital Descriptions of Unstable Molecules. 3. The Nature of Chemical Bonds of Spin Frustrated Systems

“…Muller and his collaborators have synthesized Keplerrate structural-type magnetic molecules abbreviated as Mo 72 M 30 , which has a highly symmetric array of 30 exchange-coupled magnetic ions M m + in an icosidodecahedron cluster, a closed spherical structure consisting of 20 corner-sharing triangles arranged around 12 pentagones. The magnetic ions M m + are Fe(III) with S = 5/2, Cr(III) with S = 3/2, and V(IV) with S = 1/2. − The observed J value between Fe(III) ions was −0.8 K, showing weak antiferromagnetic exchange interaction, while the corresponding interactions for V(IV) ions was found to be relatively strong ( J = −125 K). The numbers of the spin state (2 S + 1) N are variable as follows: (6) 30 = 10 22 for Fe(III) 30 , (4) 30 = 10 18 for Cr(III) 30 , and (2) 30 = 10 9 for V(IV) 30 , respectively.…”

“…The magnetic ions M m+ are Fe(III) with S ) 5/2, Cr(III) with S ) 3/2, and V(IV) with S ) 1/2. [110][111][112][113][114][115][116][117][118][119][120] The observed J value between Fe(III) ions was -0.8 K, showing weak antiferromagnetic exchange interaction, while the corresponding interactions for V(IV) ions was found to be relatively strong (J ) -125 K). The numbers of the spin state (2S + 1) N are variable as follows: (6) 30 ) 10 22 for Fe(III) 30 , (4) 30 ) 10 18 for Cr(III) 30 , and (2) 30 ) 10 9 for V(IV) 30 , respectively.…”

“…Here, exact diagonalization of the Heisenberg spin Hamiltonians was performed for spin clusters illustrated in A−D of Figure . These models, for example, correspond to typical spin frustrated systems, (A) a hexagon cluster for the CoO 2 superconductor, (B) a triangular cluster for the κ-(KEDT−TTF) 2 Cu 2 (CN) 3 and β′-Me 4 P[Pd(dmit) 2 ] 2 superconductors, (C) a triangle−pentagon cluster for a spin polyhedron Mo 72 V(IV) 30 with coners sharing triangle network, − and (D) a kagome lattice cluster for the Cu(II) compounds with a kagome lattice. Figure shows the calculated energy diagrams for A−D clusters with antiferromagnetic interaction ( J ) between the S = 1/2 spin components; note that the energy levels are normalized with J .…”

Magnetic cluster excitations

“…The spin arrangement clearly supports pronounced quantum-spin frustration effects, however, the large s = 5/2 spins also suggest classical or semi-classical approaches (Müller et al, 2001b). The dimension of the Hilbert space in this molecule is a staggering 2.2×10 23 and understanding its magnetic excitation spectrum is obviously challenging.…”

Magnetic {Mo72Fe30}-embedded hybrid nanocapsules

“…Müller and coworkers reported that {Mo 72 Fe 30 } was the largest paramagnetic molecule [50]. In this work, magnetic measurements indicate that {Mo 72 Fe 30 }-embedded nanocapsules are paramagnetic (Supporting information, Fig.…”

Symmetry and Broken-Symmetry in Molecular Orbital Descriptions of Unstable Molecules. 3. The Nature of Chemical Bonds of Spin Frustrated Systems

“…Muller and his collaborators have synthesized Keplerrate structural-type magnetic molecules abbreviated as Mo 72 M 30 , which has a highly symmetric array of 30 exchange-coupled magnetic ions M m + in an icosidodecahedron cluster, a closed spherical structure consisting of 20 corner-sharing triangles arranged around 12 pentagones. The magnetic ions M m + are Fe(III) with S = 5/2, Cr(III) with S = 3/2, and V(IV) with S = 1/2. − The observed J value between Fe(III) ions was −0.8 K, showing weak antiferromagnetic exchange interaction, while the corresponding interactions for V(IV) ions was found to be relatively strong ( J = −125 K). The numbers of the spin state (2 S + 1) N are variable as follows: (6) 30 = 10 22 for Fe(III) 30 , (4) 30 = 10 18 for Cr(III) 30 , and (2) 30 = 10 9 for V(IV) 30 , respectively.…”

“…The magnetic ions M m+ are Fe(III) with S ) 5/2, Cr(III) with S ) 3/2, and V(IV) with S ) 1/2. [110][111][112][113][114][115][116][117][118][119][120] The observed J value between Fe(III) ions was -0.8 K, showing weak antiferromagnetic exchange interaction, while the corresponding interactions for V(IV) ions was found to be relatively strong (J ) -125 K). The numbers of the spin state (2S + 1) N are variable as follows: (6) 30 ) 10 22 for Fe(III) 30 , (4) 30 ) 10 18 for Cr(III) 30 , and (2) 30 ) 10 9 for V(IV) 30 , respectively.…”

“…Here, exact diagonalization of the Heisenberg spin Hamiltonians was performed for spin clusters illustrated in A−D of Figure . These models, for example, correspond to typical spin frustrated systems, (A) a hexagon cluster for the CoO 2 superconductor, (B) a triangular cluster for the κ-(KEDT−TTF) 2 Cu 2 (CN) 3 and β′-Me 4 P[Pd(dmit) 2 ] 2 superconductors, (C) a triangle−pentagon cluster for a spin polyhedron Mo 72 V(IV) 30 with coners sharing triangle network, − and (D) a kagome lattice cluster for the Cu(II) compounds with a kagome lattice. Figure shows the calculated energy diagrams for A−D clusters with antiferromagnetic interaction ( J ) between the S = 1/2 spin components; note that the energy levels are normalized with J .…”

Magnetic cluster excitations

“…The spin arrangement clearly supports pronounced quantum-spin frustration effects, however, the large s = 5/2 spins also suggest classical or semi-classical approaches (Müller et al, 2001b). The dimension of the Hilbert space in this molecule is a staggering 2.2×10 23 and understanding its magnetic excitation spectrum is obviously challenging.…”

Magnetic {Mo72Fe30}-embedded hybrid nanocapsules

“…Müller and coworkers reported that {Mo 72 Fe 30 } was the largest paramagnetic molecule [50]. In this work, magnetic measurements indicate that {Mo 72 Fe 30 }-embedded nanocapsules are paramagnetic (Supporting information, Fig.…”

Symmetry and Broken-Symmetry in Molecular Orbital Descriptions of Unstable Molecules. 3. The Nature of Chemical Bonds of Spin Frustrated Systems

“…Muller and his collaborators have synthesized Keplerrate structural-type magnetic molecules abbreviated as Mo 72 M 30 , which has a highly symmetric array of 30 exchange-coupled magnetic ions M m + in an icosidodecahedron cluster, a closed spherical structure consisting of 20 corner-sharing triangles arranged around 12 pentagones. The magnetic ions M m + are Fe(III) with S = 5/2, Cr(III) with S = 3/2, and V(IV) with S = 1/2. − The observed J value between Fe(III) ions was −0.8 K, showing weak antiferromagnetic exchange interaction, while the corresponding interactions for V(IV) ions was found to be relatively strong ( J = −125 K). The numbers of the spin state (2 S + 1) N are variable as follows: (6) 30 = 10 22 for Fe(III) 30 , (4) 30 = 10 18 for Cr(III) 30 , and (2) 30 = 10 9 for V(IV) 30 , respectively.…”

“…The magnetic ions M m+ are Fe(III) with S ) 5/2, Cr(III) with S ) 3/2, and V(IV) with S ) 1/2. [110][111][112][113][114][115][116][117][118][119][120] The observed J value between Fe(III) ions was -0.8 K, showing weak antiferromagnetic exchange interaction, while the corresponding interactions for V(IV) ions was found to be relatively strong (J ) -125 K). The numbers of the spin state (2S + 1) N are variable as follows: (6) 30 ) 10 22 for Fe(III) 30 , (4) 30 ) 10 18 for Cr(III) 30 , and (2) 30 ) 10 9 for V(IV) 30 , respectively.…”

“…Here, exact diagonalization of the Heisenberg spin Hamiltonians was performed for spin clusters illustrated in A−D of Figure . These models, for example, correspond to typical spin frustrated systems, (A) a hexagon cluster for the CoO 2 superconductor, (B) a triangular cluster for the κ-(KEDT−TTF) 2 Cu 2 (CN) 3 and β′-Me 4 P[Pd(dmit) 2 ] 2 superconductors, (C) a triangle−pentagon cluster for a spin polyhedron Mo 72 V(IV) 30 with coners sharing triangle network, − and (D) a kagome lattice cluster for the Cu(II) compounds with a kagome lattice. Figure shows the calculated energy diagrams for A−D clusters with antiferromagnetic interaction ( J ) between the S = 1/2 spin components; note that the energy levels are normalized with J .…”

Magnetic cluster excitations

“…The spin arrangement clearly supports pronounced quantum-spin frustration effects, however, the large s = 5/2 spins also suggest classical or semi-classical approaches (Müller et al, 2001b). The dimension of the Hilbert space in this molecule is a staggering 2.2×10 23 and understanding its magnetic excitation spectrum is obviously challenging.…”