Argon matrix effect on the geometry and infrared spectrum of H2Cdouble bond; length as m-dashMH2 (M = Ti, Zr, Hf): A theoretical study

Within the framework of polarizable continuum model with integral equation formalism (IEF-PCM), an argon matrix effect on the geometry and infrared frequencies of the agostic H2Cdouble bond; length as m-dashMH2 (M = Ti, Zr, Hf) methylidene complexes was investigated at B3LYP level of theory with the 6-311++G(3df,3pd) basis set for C, H, and Ti atoms and Stuttgart/Dresden ECPs MWB28 and MWB60 for the Zr and Hf atoms. At the B3LYP/IEF-PCM level of theory, H2Cdouble bond; length as m-dashTiH2 was optimized to an energy minimum having a pyramidal structure. The calculated dipole moment of this structure is 3.06 D. The B3LYP/IEF-PCM simulations gave the three complexes’ agostic angle ∠HCM (°), distance r(H⋯M) (Å), and Cdouble bond; length as m-dashM bond length r(Cdouble bond; length as m-dashM) (Å) as follows: ∠HCTi = 87.4, r(H⋯Ti) = 2.079, r(Cdouble bond; length as m-dashTi) = 1.803; ∠HCZr = 89.3, r(H⋯Zr) = 2.243, r(Cdouble bond; length as m-dashZr) = 1.956; ∠HCHf = 94.7, r(H⋯Hf) = 2.343, r(Cdouble bond; length as m-dashHf) = 1.972. As a comparison, the B3LYP simulations gave the values as follows: ∠HCTi = 91.5, r(H⋯Ti) = 2.150, r(Cdouble bond; length as m-dashTi) = 1.811; ∠HCZr = 92.9, r(H⋯Zr) = 2.299, r(Cdouble bond; length as m-dashZr) = 1.955; ∠HCHf = 95.6, r(H⋯Hf) = 2.352, r(Cdouble bond; length as m-dashHf) = 1.967. As far as the MH2 symmetric and asymmetric stretching and CH2 wagging frequencies are concerned, the IEF-PCM calculated values are in better agreement with the experimental argon matrix ones than those calculated based on a gas phase model.