K q w d Transition meLal mnonitrides, density functional theory, band structure, density of state (DOS), & states, elastic CnllSLants Introduction Transition-metal m o n d i d e s , mononitrides and monoxides (MX, M = metal, X = C, N, 0) have at-tracted a great deal of attention for a long time because of the very interesting physical propetties these materials exhibited, especially for nitrides and &ides.?hey possess high hardness, high melting point, and metallic conductivity (Table 1 ) .'-3 These nmadcable propeaies lead them to be used as coatings for cutting tools, wear resistant surfaces, refractory materials, and conducting banien in the electric industry. Although these compounds m t l y crystallize in the rock salt structure, which is typical of materials with ionic c'ystals, they also show pmpetties of compounds of covalent bonding.According to these properties they exhibit that three kinds of chemical bonding, ionic, covalent and metallic bonding might exist in these compounds, and three dep e a of the bonding are varied with the types of X atom, which results in the different properties. For example, the hardness of Tic is greater than Ti and Ti, as well as the melting points (Table 1 ) . Table 1 Some physical properties of metal ' l i , Tic and Ti Species -(Wnmt') Melting point (t) Electrical mistivity (pa-cm) TI 200 1600 42 Tic 3Ooo 3140 200 TLV rn 2930 20 Many investigations for MX compounds have sought to the 'vial *tions between pmperties and the electronic structures. Experimentally, intensive spectnscopic studies have been performed on these cM"p0U"ds to obtain the band structures and the density of states (DOS) of their valence band,"" such as X-ray and ultraviolet photoelectron spectrr>scopy (XPS and Ups), angle resolved photoemission ( ARPES ) , and electron SP-OPY ( E m ) e&* ; Roject supported by the National Nahnal science Foundation of China (NO. 2%73010) and granta h the State Key Labomtory of sbuctural chermetry ( N o . 990018).