Hyperfine Splittings in Spin-Frustrated Trinuclear Cu3 Clusters

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Abstract
The hyperfine structures of the EPR spectra of the spin-frustrated and distorted Cu(II) trimers were calculated in the spin-coupling model. The correlations between the hyperfine structures of the EPR spectra and geometry of the Cu3 clusters (equilateral, isosceles, and scalene triangles) were found. For the EPR spectrum of the spin-frustrated ground state 2(S = 1/2) of an equilateral triangle Cu3 cluster (J12 = J13 = J23 = J), the calculated hyperfine structure represents the complicated spectrum of the 24 hyperfine lines, of total length 5a, where a is the hyperfine constant of the mononuclear Cu center. For an isosceles Cu3 cluster (J12 ≠ J13 = J23), the hyperfine splittings of the EPR spectra of the two split S = 1/2 levels with intermediate spins S12 = 0 and S12 = 1 are essentially different. The EPR signal of the |(S12 = 0)S = 1/2〉 level is characterized by the four equally spaced hyperfine lines (interval A = a) with the same relative spectral amplitudes 16:16:16:16 and total length 3a. For the |(S12 = 1)S = 1/2〉 level, the calculated hyperfine structure represents the spectrum of the 16 hyperfine lines with equal spacing (interval A‘ = a/3), the spectral intensity distribution 1:1:3:3:5:5:7:7:7:7:5:5:3:3:1:1 and total length 5a. These hyperfine spectra differ from the hyperfine structure (10 lines with interval a/3) of the EPR signals of the excited S = 3/2 level of the Cu3 cluster. The quartet hyperfine structure, characteristic of a single Cu2+ nucleus, which was observed experimentally for the doublet ground state of the spin-frustrated Cu3(II) clusters, corresponds to the hyperfine structure of the EPR signal of the |(S12 = 0)S = 1/2〉 level. This hyperfine structure is evidence of the lowering of the Cu3 cluster symmetry from trigonal to orthorhombic and the small splitting of the spin-frustrated 2(S = 1/2) ground state.