Ab initio calculation of the pair potentials of MgB2

Ab initio calculations on model clusters of MgB2 are presented to estimate the pairing potentials of superconductivity. The total energies of the clusters for the restricted Hartree–Fock (RHF) type and unrestricted Hartree–Fock (UHF) type singlet ground states and the triplet state are calculated by the hybrid DFT method of Gaussian G03 program. The energy difference between the UHF singlet state and the triplet state is correlated to the superconducting energy gap 2Δ. The highest occupied molecular orbital (HOMO) and the next HOMO are composed of mostly the 2pσ and the 3s orbitals of boron and 3pσ orbitals of magnesium. These orbitals constitute the spin polarized singlet state which represent the superconducting state. The vibrational frequencies of the singlet and the triplet states are calculated on a model cluster, Mg8B16H10, to find vibrational frequencies, and the results are used to interpret the isotope effects of 10B and 11B for the transition temperatures.