A computational study for the [2 + 1] addition of the lithium carbenoids LiCH₂X (X = Cl, Br, I) with ketene have been investigated by means of the B3LYP hybrid density functional method. All the reactions examined displayed similar concerted mechanisms for the cyclopropanation of these reagents. The lithium carbenoids react with ketene via an asynchronous attack on one CH₂ or C group of ketene with relatively low barrier to reaction in the range of 25.34-33.74 kJ/mol in THF solvent. The trend of the lithium carbenoids reaction barrier with ketene is LiCH₂Cl < LiCH₂Br < LiCH₂I. The results show that the reactions could be highly chemical reactivity with low barriers and could be favoured in experiment. The reactions could proceed easily at lower temperature. The computational results are briefly compared to other carbenoid reactions and related species.

The mechanism of palladium(II)-catalysed carboxylation of acetanilide with CO has been investigated using density functional theory calculation done at the B3LYP/6-31G(d, p)(SDD for Pd) level of theory. Solvent effects on these reactions have been explored by calculation that included a polarizable continuum model (PCM) for the solvent. Two plausible pathways which led to the formation of anhydride or benzoxazinone intermediate structure were proposed. Our calculated results suggested that the steps of forming the anhydride or benzoxazinone intermediate became the rate-determining one in the whole catalytic cycle. The process of forming benzoxazinone is more favoured kinetically with a barrier of 16.6 kcal/mol versus 22.9 kcal/mol for the pathway of forming anhydride structure. Subsequent hydrolysis process of these intermediates then provide the corresponding product ortho-acetaminobenzoic acid. The computational results are consistent with the experimental observations of Yu et al. for palladium(II)-catalysed synthesis of acetanilide based on carbon monoxide.

The reaction mechanisms of palladium-catalyzed divergent reactions of 1,6-enyne carbonates have been investigated using DFT calculations at the B3LYP/6-31G(d,p) (LanL2DZ for Pd) level. Solvent effects on these reactions have been considered by the polarizable continuum model (PCM) for the solvent (DMF). The formation of vinylidenepyridines and vinylidenepyrrolidines were generated through 5-exo-dig cyclization or 6-endo-dig cyclization. Our calculation results suggested the following: (i) The first step of the whole cycle is the rate-determining step, which causes allenic palladium intermediate through two plausible pathways. This intermediate provides the corresponding products and releases the palladium catalyst by a subsequent hydrogen transfer and elimination process. (ii) For the catalyst CH₃OPdH, the reaction could occur through two possible pathways, but 5-exo-dig cyclization is favoured over 6-endo-dig cyclization. However, when the hydrogen atom is substituted with a phenyl group, the energy barriers for 5-exo-dig cyclization or 6-endo-dig cyclization become relatively high, 18.0–28.5 kcal/mol. The computational results provide good explanation for the experimental observations.

Density functional theory calculations at the M06-2X level were done to study the reaction mechanism and regioselectivity for the [2+2] cycloaddition of allyltrimethylsilane with alkynones using InBr₃ as the catalyst. The solvent effect was described by the single-point calculations with SMD model in 1,2-dichloroethane. The calculation results prove that the InBr₃-catalyzed cycloaddition of allyltrimethylsilane to alkynones takes place through two possible pathways and get selective cyclobutenone products. The reaction involves two main steps: attack of unsaturated carbon atoms of the alkynone by the π electrons of allyltrimethylsilane and a closed-loop process. The process of forming cyclobutenone product of silicon in the 2-position of the ketone group is more favored and the barrier is 15.5 kcal/mol, while the energies for the cyclobutenone of 3-position product are relatively high of 21.2 kcal/mol. In addition, we calculated the catalytic activity of the InX₃(X=Cl, Br, I) catalyst for this cycloaddition. This is a good explanation for the experimental data thatInBr₃ and InI₃ would be the most effective catalysts.