The transformation of CO_(2)into cyclic carbonates via atom-economical cycloadditions with epoxides has recently attracted tremendous attention.On one hand,though many heterogeneous catalysts have been developed for t...The transformation of CO_(2)into cyclic carbonates via atom-economical cycloadditions with epoxides has recently attracted tremendous attention.On one hand,though many heterogeneous catalysts have been developed for this reaction,they typically suffer from disadvantages such as the need for severe reaction conditions,catalyst loss,and large amounts of soluble co-catalysts.On the other hand,the development of heterogeneous catalysts featuring multiple and cooperative active sites,remains challenging and desirable.In this study,we prepared a series of porous organic catalysts(POP-PBnCl-TPPMg-x)via the copolymerization metal-porphyrin compounds and phosphonium salt monomers in various ratios.The resulting materials contain both Lewis-acidic and Lewis-basic active sites.The molecular-level combination of these sites in the same polymer allows these active sites to work synergistically,giving rise to excellent performance in the cycloaddition reaction of CO_(2)with epoxides,under mild conditions(40℃ and 1 atm CO_(2))in the absence of soluble co-catalysts.POP-PBnCl-TPPMg-12 can also efficiently fixate CO_(2)under low-CO_(2)-concentration(15%v/v N2)conditions representative of typical CO_(2)compositions in industrial exhaust gases.More importantly,this catalyst shows excellent recyclability and can easily be separated and reused at least five times while maintaining its activity.In view of their heterogeneous nature and excellent catalytic performance,the obtained catalysts are promising candidates for the transformation of industrially generated CO_(2)into high value-added chemicals.展开更多
The photodetachment of a negative molecular ion is studied theoretically using a two-center model. The detached electron wave function is obtained as a superposition of two coherent waves originating from each center....The photodetachment of a negative molecular ion is studied theoretically using a two-center model. The detached electron wave function is obtained as a superposition of two coherent waves originating from each center. The photo-detached electron flux is evaluated on a screen placed at a large distance from the negative molecular ion. The electron flux on the screen displays strong interferences, the peak positions are related to the distance between the two centers in the negative molecular ion. We a/so obtained a simple analytical formula for the total photodetachment cross section. It approaches one and two times of the cross section for the one-center system in the high and lowphoton energy limits respectively.展开更多
Under the necessary conditions for a double pyramidal central configuration with a diamond base to exist in the real number space, the existence and uniqueness of such configurations were studied by employing combined...Under the necessary conditions for a double pyramidal central configuration with a diamond base to exist in the real number space, the existence and uniqueness of such configurations were studied by employing combinedly the algebraic method and numerical calculation. It is found that there exists a planar curl triangle region G in a square Q such that any point in G and given by the ratio of the two diagonal lengths of the diamond base and the ratio of one diagonal length of the base to the height of the double pyramid configuration determines a unique double pyramid central configuration, while all points in Q-G have no referance to any central configuration.展开更多
文摘The transformation of CO_(2)into cyclic carbonates via atom-economical cycloadditions with epoxides has recently attracted tremendous attention.On one hand,though many heterogeneous catalysts have been developed for this reaction,they typically suffer from disadvantages such as the need for severe reaction conditions,catalyst loss,and large amounts of soluble co-catalysts.On the other hand,the development of heterogeneous catalysts featuring multiple and cooperative active sites,remains challenging and desirable.In this study,we prepared a series of porous organic catalysts(POP-PBnCl-TPPMg-x)via the copolymerization metal-porphyrin compounds and phosphonium salt monomers in various ratios.The resulting materials contain both Lewis-acidic and Lewis-basic active sites.The molecular-level combination of these sites in the same polymer allows these active sites to work synergistically,giving rise to excellent performance in the cycloaddition reaction of CO_(2)with epoxides,under mild conditions(40℃ and 1 atm CO_(2))in the absence of soluble co-catalysts.POP-PBnCl-TPPMg-12 can also efficiently fixate CO_(2)under low-CO_(2)-concentration(15%v/v N2)conditions representative of typical CO_(2)compositions in industrial exhaust gases.More importantly,this catalyst shows excellent recyclability and can easily be separated and reused at least five times while maintaining its activity.In view of their heterogeneous nature and excellent catalytic performance,the obtained catalysts are promising candidates for the transformation of industrially generated CO_(2)into high value-added chemicals.
基金The project supported by National Natural Science Foundation of China under Grant No. 90403028
文摘The photodetachment of a negative molecular ion is studied theoretically using a two-center model. The detached electron wave function is obtained as a superposition of two coherent waves originating from each center. The photo-detached electron flux is evaluated on a screen placed at a large distance from the negative molecular ion. The electron flux on the screen displays strong interferences, the peak positions are related to the distance between the two centers in the negative molecular ion. We a/so obtained a simple analytical formula for the total photodetachment cross section. It approaches one and two times of the cross section for the one-center system in the high and lowphoton energy limits respectively.
文摘Under the necessary conditions for a double pyramidal central configuration with a diamond base to exist in the real number space, the existence and uniqueness of such configurations were studied by employing combinedly the algebraic method and numerical calculation. It is found that there exists a planar curl triangle region G in a square Q such that any point in G and given by the ratio of the two diagonal lengths of the diamond base and the ratio of one diagonal length of the base to the height of the double pyramid configuration determines a unique double pyramid central configuration, while all points in Q-G have no referance to any central configuration.
