Hyperfine splittings in spin-frustrated trinuclear Cu3 clusters

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 Cu-3 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 Cu-3 cluster (J(12) = J(13) = J(23) = 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 Cu-3 cluster (J(12) not equal J(13) = J(23)), the hyperfine splittings of the EPR spectra of the two split S = 1/2 levels with intermediate spins S-12 = 0 and S-12 = 1 are essentially different. The EPR signal of the \(S-12 = O)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 (S-12 = 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 Cu-3 cluster. The quartet hyperfine structure, characteristic of a single Cu2+ nucleus, which was observed experimentally for the doublet ground state of the spin-frustrated Cu-3(II) clusters, corresponds to the hyperfine structure of the EPR signal of the \(S12 = O)S = 1/2> level. This hyperfine structure is evidence of the lowering of the Cu-3 cluster symmetry from trigonal to orthorhombic and the small splitting of the spin-frustrated 2(S = 1/2) ground state.