Abstract: The structural parameters of Eu@C₆₀ isomers and thesquared electron spin <Ŝ²> have been calculatedusing the quantum-chemical DFT (U)PBE0 method with variable quantum numbersM_S. The (C_2v) isomer (M_S = 7/2,<Ŝ²> = 15.76 a. u.) includes a triatomicEuC₂ fragment with a degraded C=C bond (2.565 Å),common for two 6-atom cycles. Two (C_3v) isomers (M_S = 7/2±1,<Ŝ²> = 17.76±7.01 a. u.) include thehexagonal pyramid EuC₆. The energies of the isomersdiffer by no more than 0.046 eV. The energy barriers allow pseudo-rotation ofthe molecule. The Eu endo atom increases the reactivity of the carbon shell ofC₆₀ and stabilizes the(Eu@C₆₀)₂ nano-dumbbell. The<Ŝ²> values are 56 and 90 a. u. for thestructures of similar energy, (C_i)-(Eu@η²-C₆₀)₂and (C_i)-(Eu@η⁶-C₆₀)₂,with Eu∙∙∙Eu distances of 10.35 and 10.08 Å, respectively.