Structural stability and electronic state of transition metal trimers

Ground state geometries were searched for transition metal trimers Sc3, Y3, La3, Lu3, Ti3, Zr3, and Hf3 by density functional methods. For all the studied trimers, our calculation indicates that the ground state geometries are either equilateral triangle (Zr3 and Hf3) or near equilateral triangle (Ti3, Sc3, Y3, La3, and Lu3). For rare earth trimers Sc3, Y3, La3, and Lu3, isosceles triangle (near equilateral triangle) at quartet state is the ground state. Isosceles triangle at doublet state is the competitive candidate for the ground state. For Zr3 and Hf3, equilateral triangle at singlet state is the most stable. For Ti3, isosceles triangle (near equilateral triangle) at quintet state gives the ground state. For Sc3, Zr3, and Hf3, where experimental results are available, the predicted geometries are in agreement with experiment in which the ground state is equilateral triangle (Zr3) or fluxional (Sc3 and Hf3). For Y3, the calculated geometry is in agreement with experimental observation and previous theoretical study that Y3 is a bent molecule for the ground state. For La3, our calculation is in excellent agreement with previous theoretical study based on density functional methods.