A differential approach for exact fixed-node quantum Monte Carlo calculation was proposed in this paper. This new algorithm can be used to directly compute the energy differential between two systems in exact fixed-node quantum Monte Carlo process, making the statistical error of calculation reduce to order of 10^-2 kJ/mol and recover about more than 90% of the correlation energy. The approach was employed to set up a potential energy surface of a molecule, through a model of rigid move, and Jacobi transformation utilized to make energy calculation for two configurations of a molecule having good positive correlation. So, an accurate energy differential could be obtained, and the potential energy surface with good quality depicted. This novel algorithm was used to study the potential energy curve of the ground state of BH and the potential energy surface of H3, and could be also applied to study other related fields such as molecular spectroscopy and the energy variation of chemical reactions.
We substituted several environmentally friendly catalysts which included HY and H- β zeolites, various cation-exchanged β zeolites, and solid-supported ferric chloride for conventional catalysts for the synthesis of 3-(1-cyclohexenyl)-2-butanone from the reaction of ethylidenecyclohexane with acetic anhydride at room temperature. HY zeolite was found to be the most effective for this reaction, and gave the acylated product in a 72% yield under the conditions of n (ethylidenecyclohexane)/ n (acetic anhydride)/ m (HY zeolite)=1 mmol/10 mmol/0 100 g, reaction temperature 25 ℃ and reaction time 2 h. The used HY zeolite can be recovered, regenerated and gave almost the same yield as the fresh one. The lifetime of the HY zeolite is over 80 h. The effect of different factors on the reaction has also been investigated.
