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Theoretical study on the mechanism of reaction between 3-hydroxy-3-methyl-2-butanone and malononitrile catalyzed by lithium ethoxide

100%

Hu Q.-S. , Li L.-C. , Wang X.

Open Chemistry

2008

tom 6

nr 2

304-309

The The mechanism of reaction between 3-hydroxy-3-methyl-2-butanone and malononitrile for the synthesis of 2-dicyanomethylene-4, 5, 5-trimethyl-2,5-dihydrofuran-3-carbonitrile catalyzed by lithium ethoxide was investigated by density functional theory (DFT). The geometries and the frequencies of reactants, intermediates, transition states and products were calculated at the B3LYP/6-31G(d) level. The vibration analysis and the IRC analysis verified the authenticity of transition states. The reaction processes were confirmed by the changes of charge density at the bond-forming critical point. The results indicated that lithium ethoxide is an effective catalyst in the synthesis of 2-dicyanomethylene-4, 5, 5-trimethyl-2, 5-dihydrofuran-3-carbonitrile from malononi-trile and 3-hydroxy-3-methyl-2-butanone. The activation energy of the reaction with lithium ethoxide was 115.86 kJ·mol−1 less than the uncatalyzed reaction. The mechanism of the lithium ethoxide catalyzed reaction differed from the mechanism of the uncatalyzed reaction.

$L^{p}(ℝⁿ)$ bounds for commutators of convolution operators

100%

Hu G. , Sun Q. , Wang X.

Colloquium Mathematicum

2002

tom 93

nr 1

11-20

The $L^{p}(ℝⁿ)$ boundedness is established for commutators generated by BMO(ℝⁿ) functions and convolution operators whose kernels satisfy certain Fourier transform estimates. As an application, a new result about the $L^{p}(ℝⁿ)$ boundedness is obtained for commutators of homogeneous singular integral operators whose kernels satisfy the Grafakos-Stefanov condition.