| Iron cluster as representative of 3d transition-metal clusters has become a focus due to its use in the magnetic, catalytic industry and nanotechnologies. Furthermore, the knowledge about it could obtain the resolution of the controversy on the binding rule. The dramatic size-dependent character of the iron cluster is observed by a variety of experiments. That is, the properties of the clusters are strongly size- dependent, giving rise to the quantum size effect. The electronic structure or chemical bond of cluster dominate geometric configuration, contrariwise, geometric configuration reflects electronic structure. Therefore, unambiguous assignment of the ground state geometric configuration is a principal task. On the theoretical side, the difficulties associated with small iron cluster arise from partly filled d-shells and narrowly spaced d levels, thus, possess a number of nearly degenerate states with varying spin multiplicities that are energetically very close. The potential energy surface is complexity at these reasons, therefore, post-self-consistent-field treatment is required. Density functional theory (DFT) is a good alternative. DFT take the electron exchange effect into account adequately, so exactness is improved, while it has become possible that the theoretical investigations are performed including large system such as transition-metal clusters by electron density is used as variable of the functional unlike ab initio method which focus single electron.In practice, there is a controversy about a large number of iron clusters except that Fe2 has been studied systematically with several different functionals in DFT and agreement has been attained. However the lack of a detailed computational section in studies on transition-metal clusters does not allow a fair comparison between them and explains why differences are observed among results from different programs. To deal with this difficulty, many methods are conceived as G..L.Gutsev, S.N.Khanna, and P.Jena's method is a example applied to iron clusters in this paper.Dennis R. Salshub and Charles W. Bauschliche, Jr., the two group have proved LSDA,B3LYP,BLYP unsuitable for iron clusters by theoretical research on anion and cation of iron clusters with many functionals in DFT, so we avoid these methods . In this paper mPW1PW91(modific-ation of the exchange functional introduced by Perdew and Wang, the correlation functional introduced by Perdew and Wang)in DFT of quantum chemistry is used . The basis set used is LanL2dz which adopt effective core potentials (ECP) to replace the innermost core electron for third-row(k-Cu) by explicitly treating the outmost core orbits (3s,3p) along with the valence orbits (3d,4s,4p).Applications of this method begin with Fe2. Results that the state with spin multiplicity of 2S+1=7 is the ground state while the state with 2S+1=9 is higher in energy by 1.5674eV agree with the other's results. Definitive identification of the ground state of Fe3,Fe4, however, is problematic because of nearly degenerate isomers. So, original method is used as mentioned above. Limited by computer's ability, high symmetry confine is imposed upon two initial structure of Fe5,Fe6,Fe7. Adiabatic electron affinities (Aad) and adiabatic ionization potentials (IP) of the neutral clusters are computed after the equilibrium geometries are confirmed. Our calculations on Fe3 suggest that the triangle as consequence of the initial structure for a given Fe3 without symmetry constrain is the ground state. The bond lengths are R12=2.753?,R23=2.410? and R13=2.497?, respectively. Our calculated Aad and IP of 0.2258hartree = 6.1444eV and 0.0512hartree = 1.3932eV is in excellent agreement with the experimental value of 1.47±0.08eV. For Fe4, our calculated Aad and IP is 0.002hartree = 0.0544eV, 0.2657hartree = 7.2301eV, respectively, but experimental value is 1.78±0.06eV and 6.4±0.1eV. Such discrepancy according to our analysis is the consequence of as the referred three below:(1) The present way of determining the grou...
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