First-principles studies on the intrinsic stability of the magic Fe13O8 cluster

Complementary to our previous study [Wang et nl., Phys. Rev. B 59, 12 672 (1999)], the intrinsic stability of the magic Fe13O8 cluster is confirmed by the calculations on the vibrational properties, For all the vibration modes, the frequency is positive, and therefore the structure is dynamically stable. A(1g), B-1g, and B-2g modes are Raman active, A(2g), A(2u), and E-u, modes are infrared active, while the E-g, mode is active both in Raman and in infrared spectroscopy. The intrinsic stability combined:with the relative stability make this cluster to be magic.