Analytical Second Derivatives for Effective Core Potential. Application to Transition Structures of Cp₂Ru₂(μ-H)₄ and to the Mechanism of Reaction Cu + CH₂N₂

Routines for calculation of analytical second derivatives for the effective core potential have been developed. The present version allows for spdf basis sets with spdfg projection operators for HF, DFT, and MP2 methods and has been incorporated into the Gaussian package. Analytical frequency analysis has been applied to the characterization of a critical structure of Cp 2 Ru 2 (μ-H) 4 and to the study of the mechanism of reaction between Cu and CH 2 N 2 . Frequency analysis demonstrates that the structure previously found as the transition state of H 2 dissociation of Cp 2 Ru 2 (μ-H) 4 actually is a third-order stationary point. For various species of the system of Cu + CH 2 N 2, DFT and MP2 second derivatives gave reasonable frequencies (∼5% average error) compared to the experimental in most cases, except that the N−N stretch was very poor at the MP2 level because of spin contamination in N 2 CuCH 2 . On the basis of vibrational frequencies, assignment has been made for adducts found experimentally between Cu and CH 2 N 2. The energetics was also studied with the PCI-80 method and compared with DFT and ab initio results. The best estimated binding energy for Cu−CH 2 is 60.8 kcal/mol. The end-on isomer is the only stable N 2 ·CuCH 2 species, and the side-on N 2 ·CuCH 2 isomerizes to the end-on form without barrier. The best estimate of binding energy for N 2 −CuCH 2 is 19.4 kcal/mol for the end-on complex. The overall reaction for Cu + CH 2 N 2 → CuCH 2 + N 2 is 34.9 kcal/mol exothermic. The reaction is found to take place without substantial barrier. The effect of recontraction of the ECP-associated basis set in DFT calculations is also briefly discussed.