Intermolecular interactions between PH2Cl and Ar–R（R = H,OH,NH2,CH3,Br,Cl,F,CN,NO2） were calculated by using MP2/aug-cc-p VDZ quantum chemical method.It has been shown from our calculations that the aromatic rings ...Intermolecular interactions between PH2Cl and Ar–R（R = H,OH,NH2,CH3,Br,Cl,F,CN,NO2） were calculated by using MP2/aug-cc-p VDZ quantum chemical method.It has been shown from our calculations that the aromatic rings with electron-withdrawing groups represent much weaker binding affinities than those with electron-donating groups.The charge-transfer interaction between PH2Cl and Ar–R plays an important role in the formation of pnicogen bond complexes,as revealed by NBO analysis.Nevertheless,AIM analysis shows that the nature of the interactions between PH2Cl and Ar–R is electrostatic,and the interaction energies of the complexes are correlated positively with the electron densities in the bond critical points（BCPs）.RDG/ELF graphical analyses were performed to visualize the positions and strengths of the pnicogen bonding,as well as the spatial change of the electron localization upon the formation of complexes.The π-type halogen bond was also calculated,and it has been revealed that the π-type pnicogen bond systems are more stable than the halogen bond ones.展开更多
In this paper, we mainly generalize a Maschke type theorem to the setting of a weak Hopf group coalgebra. First we introduce the notion of a weak Hopf group coalgebra as a generalization of Hopf group coalgebra introd...In this paper, we mainly generalize a Maschke type theorem to the setting of a weak Hopf group coalgebra. First we introduce the notion of a weak Hopf group coalgebra as a generalization of Hopf group coalgebra introduced in [7] and a weak Hopf algebra introduced in [2]. And we study some basic properties of weak Hopf group coalgebras. Next we aim at finding some sucient conditions under which an epimorphism of weak （H, A） Hopf π-comodule splits if it splits as an A-module morphism and give an application of our results.展开更多
We prove a Maschke type theorem for Doi-Hopf π-modules. A sufficient condition for having a Maschke type property is that there exists a suitable total integral map for the Doi-Hopf π-modules in question. The applic...We prove a Maschke type theorem for Doi-Hopf π-modules. A sufficient condition for having a Maschke type property is that there exists a suitable total integral map for the Doi-Hopf π-modules in question. The applications of the results are considered. Finally, As an application of the existence of total integral, we prove that α∈π Ca A is a generator in the category π-Cu（H）A.展开更多
基金Supported by the Science and Technology Project of Zhejiang Province(2016C33039)Natural Science Foundation of Zhejiang Province(LY14C030004)+2 种基金National Natural Science Foundation of China(21272211)Project of the Special Foundation for Provincial Research Institutes of Zhejiang Province,China(2017F50002)Science and Technology Planning Project of the Zhejiang Provincial Department of Water Resources(RB1608)
文摘Intermolecular interactions between PH2Cl and Ar–R（R = H,OH,NH2,CH3,Br,Cl,F,CN,NO2） were calculated by using MP2/aug-cc-p VDZ quantum chemical method.It has been shown from our calculations that the aromatic rings with electron-withdrawing groups represent much weaker binding affinities than those with electron-donating groups.The charge-transfer interaction between PH2Cl and Ar–R plays an important role in the formation of pnicogen bond complexes,as revealed by NBO analysis.Nevertheless,AIM analysis shows that the nature of the interactions between PH2Cl and Ar–R is electrostatic,and the interaction energies of the complexes are correlated positively with the electron densities in the bond critical points（BCPs）.RDG/ELF graphical analyses were performed to visualize the positions and strengths of the pnicogen bonding,as well as the spatial change of the electron localization upon the formation of complexes.The π-type halogen bond was also calculated,and it has been revealed that the π-type pnicogen bond systems are more stable than the halogen bond ones.
基金Supported by the Natural Science Foundation of Shandong Province(ZR2012AL02)
文摘In this paper, we mainly generalize a Maschke type theorem to the setting of a weak Hopf group coalgebra. First we introduce the notion of a weak Hopf group coalgebra as a generalization of Hopf group coalgebra introduced in [7] and a weak Hopf algebra introduced in [2]. And we study some basic properties of weak Hopf group coalgebras. Next we aim at finding some sucient conditions under which an epimorphism of weak （H, A） Hopf π-comodule splits if it splits as an A-module morphism and give an application of our results.
文摘We prove a Maschke type theorem for Doi-Hopf π-modules. A sufficient condition for having a Maschke type property is that there exists a suitable total integral map for the Doi-Hopf π-modules in question. The applications of the results are considered. Finally, As an application of the existence of total integral, we prove that α∈π Ca A is a generator in the category π-Cu（H）A.
