Geometries, stabilities, NBO, vibrational spectroscopy and NICS of (BN)₂₅ clusters were optimized in the framework of density functional theory (DFT) through the use of B3LYP hybrid functional associated with 6-31G(d) basis sets. We found that (BN)₂₅ clusters is stable due to its large average binding energy and energy gap. Charge transfer and s, p hybridization between adjacent B and N atoms are confirmed by NBO analysis. Many vibration peaks are found in infrared spectrum and Raman spectra. Negative nucleus independent chemical shifts(NICS) indicate that BN clusters have aromatic properties.

Geometrical optimizations of (OsH₂)_n(n=1-⁵) clusters are carried out by using density functional calculation with generalized gradient approximation (GGA) in which electronic spin multiplicities are adequately considered.Ground-state structures of clusters are obtained with optimized geometries' total energy and frequency.For each ground state structure,average binding energy,second-order differences of total energies,magnetic moment and density of states are investigated.It shows that (OsH₂)_n(n=1-⁵) clusters tend to form three-dimensional structures.Interaction between H and Os is strong and (OsH₂)₄ is more stable than its neighbors.Only ground-state geometry of (OsH₂)₅ displays anti-ferromagnetic coupling.Magnetic moment is mainly provided by osmium atoms and is dominant from contributions of d orbitals.

Geometric structure of W_mB_n(m+n≤7) clusters are optimized by using density functional theory at B3LYP/LANL2DZ level. For ground state configurations, average binding energies, second order differential energies, energy gaps and WIB bond orders are analyzed. It shows that ground state structures of WB_n clusters are flat structures; as m≥2 and m+n≥4, all clusters are cube structure except W₃B cluster. Stability of clusters is getting better and better as W atoms increase. The bonding strength of W-W is significantly higher than those of W-B and B-B key. W atom plays a leading role in stability of clusters. Stability of W₂B₂ and W₃B cluster is the best.

Possible equilibrium geometries of W_mC_n clusters are optimized by using density functional theory at B3LYP/LANL2DZ level.For ground-state structures,average binding energy,second difference in energy,HOMO-LOMO gaps and the Wiberg bond index are analyzed.With increasing tungsten atoms,structures of clusters transform from linear into planar,and then become three-dimensional structures.All spin multiplicity is not more than 5.Hybridization of carbon atoms enhanced stability of the clusters,but reduced chemical activity.And Wiberg of W-C is much stronger than that of W-W and C-C,so it is easier to form W-C bond in W_mC_n clusters.

NBO,vibrational spectrum,aromatic characteristics and polarizability of ground state PtIr_n^0,±(n=1~5)clusters are analyzed by using density functional theory(b31yp).It shows that platinum atom gains charges during cluster growth,while some iridium atoms gain charges and others lose.They are transferred to platinum atom and other iridium atoms.More vibration peaks appear in IR and Raman sDectrums as more atoms are added. Vibration peaks of IR and Raman spectrum of Ptlr₄^- cluster are the strongest. PtIrl₃、Ptlr₅、PtIr₅⁺ clusters are aromatic.Bond interactions between atoms present a rising tendency with the increase of atomic number-Electronic structures of PtIr₃、Ptlrs₅⁺ clusters are relatively unstable, and delocalization effects are strong. With the increase of atomic number,stability of electronic structure of anionic clusters presents a rising tendency,and delocalization effect decreases gradually.

Possible equilibrium geometries of W_nNi_m(n+m=8) clusters are optimized with density functional theory at B3LYP/LANL2DZ level.For ground state structures,molecular orbital energy level,HOMO level,LUMO level,aromaticity and thermodynamics are analyzed.It shows that molecular orbits between Alpha and Beta in clusters W₅Ni₃ and W₆Ni₂ are completely degenerate,and all electrons are strictly paired.W₂Ni₆ cluster,with low energy gap,has strong chemical activity.Its component for frontier orbital are basically the same.W₆Ni₂cluster,with high energy gap,has weak chemical activity;Clusters W₁Ni₇,W₅Ni₃,W₆Ni₂,W₇Ni₁ have aromaticity,while W₂Ni₆ cluster has antiaromaticity.Formation enthalpy of all clusters W_nNi_m(n+m=8) are negative.They are stable Oil thermodynamics.

Possible geometrical configurations of PtIr_n^0,± (n=1~5) clusters are optimized with density functional theory(b3lyp) at lanl2dz level.For ground state structures of PtIr_n^0,± (n=1~5) clusters,stability is calculated and analyzed.It shows that there are many isomerides in PtIr_n^0,± (n=1~5) clusters.Clusters with less atoms are two-dimensional graphic structures,while clusters with more atoms are three-dimensional graphic structures.With increase of atoms,thermodynamics stability of clusters is better.And stability of PtIr₃⁺ cluster is the best.Compared with pure iridium clusters,it is easier for PtIr_n(n=1~5) clusters to get an electron,Nonmetallicity of PtIr_n(n=1~5) clusters is stronger.iridium atoms play a dominant action in stability of PtIr_n^0,± (n=1~5) clusters.

Possible equilibrium geometries of W_nC^0,±(n=1,…,6) clusters are optimized with density functional theory at B3LYP/LANL2DZ level.Stability and electronic properties of ground state structures are analyzed.It shows that as n > 3 cluster undergoes a transition from a two-dimensional structure to a three-dimensional structure,and carbon atom remains on the surface of cluster.Stability of W_n cluster is increased with doped carbon atom.Moreover W₃C is the most stable one among W_nC^0,±(n=1,…,6) clusters,and it is taken as a basic structure.Electronic properties of W_nC^0,±(n=1,…,6) clusters are characterized by analyzing energy gaps,vertical electron affinities(VEA) and vertical ionization potentials(VIP) of W_nC with pure Wnclusters.W_nC clusters get electron easily and shows higher nonmetallicity than W_n clusters.