Many transition metals, including lanthanides and actinides, form C-H(X) insertion products and also high oxidation-state complexes with a carbon-metal multiple bond via following H(X) migration in reactions with small hydrocarbons and halomethanes.1,2 These new breed of metal complexes, small cousins of metal complexes with large ligands, often show unique structures and photochemical properties. Particularly the methylidene complexes often show markedly distorted structures for one of the hydrogen atoms to position close to the metal atom (agostic structure).2,3 These small complexes are more amenable to higher level of theoretical investigations and, therefore, considered as ideal systems to investigate the distinct structures and ligand effects of the transition-metal complexes with larger ligands.While many transition-metal complexes with large ligands are often agostic, the experimental evidences are often elusive particularly in IR spectra.1-3 Recently CH2=ZrH2, the smallest possible methylidene hydride complex, is generated from reactions of laser-ablated Zr atoms and methane isotopomers in excess neon and argon. 6 The strong symmetric and antisymmetric stretching ZrH 2 absorptions, along with the deuterium counterparts, are observed along with other lower frequency absorptions. More importantly the two sets of Zr-H as well as Zr-D stretching absorptions of the half deuterated species are observed between the strong symmetric and anti-symmetric stretching bands, a strong IR evidence for the agostic structure.6 Normally the decoupled M-H stretching bands appear at the middle of the symmetric and anti-symmetric stretching bands if the two M-H bonds are identical. The two sets of strong absorptions observed between the symmetric and anti-symmetric ZrH 2 and ZrD 2 stretching absorptions, therefore, indicate that the molecule is markedly distorted such that the decoupled M-H stretching frequencies differ as large as 16.5 cm -1 in a Ne matrix. 6 Furthermore, electronic structure calculations show that CH2=ZrH2 has a highly distorted C1 structure, where the methylene group is considerably distorted, and the Zr atom is located at the apex of the trigonal pyramid structure. 2,3,6 The 8 possible isotopomers with C1 symmetry shown in Scheme 1 are grouped into four sets (1-2, 3-5, 4-6, and 7-8), the two configurations in each set having essentially the same hydrogen stretching frequencies. 6 Calculations with the planar C 2V symmetry constraint generate two imaginary frequencies (the ZrH 2 wagging and CH 2 rocking modes).In this study we have carried out a theoretical investigation at various levels in an effort to properly understand the details of the agostic interactions, which often play an important role for the structures of high oxidation-state transition-metal complexes. Density functional theory (DFT) calculations were carried out using the Gaussian 03 package, 7 the B3LYP density functional, 6-311++G(3df,3pd) basis sets for C, H, and SDD pseudopotential and basis for Zr (28 electron core). BPW91 functional...