Tsallis-q entanglement is a well-known entanglement measures which obeys a tighter monogamy inequality with q∈[2,3]. We extend the range of q for analytic formula of Tsallis-q entanglement to q∈[(5-√13)/2,(5+√13)/2], and prove that it is a tighter monogamy inequality of quantum entanglement in terms of squared Tsallis-q entanglement. It is tighter than existing ones,and the range of q become broader than tighter monogamy inequality using Tsallis-q entanglement.

Electronic structures of unsaturated and H saturated GaN nanowires with diameters of 9.5Å, 15.9Å and 22.5Å are studied with generalized gradient approximation (GGA) of density functional theory (DFT). Results show that unsaturated and H saturated GaN nanowires have direct band gaps. Band gaps of unsaturated GaN nanowires decrease with the increase of nanowire diameter, but not significantly. Band gaps of H saturated GaN nanowires decrease with the increase of nanowire diameter as well. They are more apparent than unsaturated ones. 2p electrons of N atoms in surface of unsaturated GaN nanowires locate at top of valence band, and 4p electrons of Ga atoms in surface locate at bottom of conduction band. These two kinds of electrons are local which decide the band gap. Surface effect of surface atoms can be eliminated by saturating with hydrogen atoms.

The B3LYP method of density functional theory(DFT) is used to optimize geometry configuration,stability and frequency calculation of Ga_nN⁺(n=2~8) and Ga_nN₂⁺(n=1~7) cation clusters at the level of 6-31G^*.Ground state of Ga_nN⁺(n=2~8) and Ga_nN₂⁺(n=1~7) clusters are obtained.The geometry of clusters transforms from a planar structure to a spacial structure as cluster sizes of Ga_nN⁺(n=2~8) and Ga_nN₂⁺(n=1~7) are increased to 6 and 7,respectively.Among Ga_nN⁺(n=2~8) and Ga_nN₂⁺(n=1~7) cation clusters,Ga₄N⁺,Ga₆N⁺,Ga₃N₂⁺ and Ga₅N₂⁺ are stabler.