We study the quasinormal modes（QNMs） of massless scalar perturbations to probe the van der Waals like SBH/LBH phase transition of anti-de Sitter black holes in five-dimensional（5D） Gauss–Bonnet gravity. It is fou...We study the quasinormal modes（QNMs） of massless scalar perturbations to probe the van der Waals like SBH/LBH phase transition of anti-de Sitter black holes in five-dimensional（5D） Gauss–Bonnet gravity. It is found that the signature of this SBH/LBH phase transition is detected when the slopes of the QNMs frequency change drastically and differently in small and large black holes near the critical point. The obtained results further support that the QNMs can be a dynamic probe to investigate the thermodynamic properties in black holes.展开更多
Various bond modes of the M-C（C5 ring） exist in metallocene compounds of group 14 heavier elements,mostly due to an intricate interaction between the lone electron pairs at the M center and the 6 p-electrons of the ...Various bond modes of the M-C（C5 ring） exist in metallocene compounds of group 14 heavier elements,mostly due to an intricate interaction between the lone electron pairs at the M center and the 6 p-electrons of the C5 ring.The tin（Ⅱ） metallocene complexes LSn R（L = HC[CMe（N-2,6-iPr2C6H3）]2,R = cyclopentadienyl,C5H5（1）; indenyl,C9H7（2）; fluorenyl,C（13）H9（3）） stabilized by the β-diketiminato ligand were prepared and utilized in the study on their solid and solution state structures.X-ray single-crystal diffraction data revealed an η~1-mode of the Sn-C（C5 ring） bond in each 1~3.However,the room temperature ~1H NMR spectral studies disclosed such a fluxional bonding mode in solution.The 119 Sn NMR studies suggested a quadruple coordination nature of the Sn center in 1 while the triple coordination manner was for the Sn atom in both 2 and 3.Then the variable-temperature（25~–75 ℃） ~1H NMR spectral studies for each 1~3 were performed,which detected the relaxation state structures of 1~3 at lower temperature.All of these results indicate a stereochemical activity of the lone electron pairs at the tin（Ⅱ） atom that definitely has an electronic interaction with the 6 p-electrons of the C5 ring.The observed Sn-C（C5 ring） bond modes appear influenced by either the metallocene size or the compound state existed.展开更多
基金Supported by the National Natural Science Foundation of China under Grant Nos 11647050,11675139 and 51575420the Scientific Research Program Funded by Shaanxi Provincial Education Department under Grant No 16JK1394
文摘We study the quasinormal modes（QNMs） of massless scalar perturbations to probe the van der Waals like SBH/LBH phase transition of anti-de Sitter black holes in five-dimensional（5D） Gauss–Bonnet gravity. It is found that the signature of this SBH/LBH phase transition is detected when the slopes of the QNMs frequency change drastically and differently in small and large black holes near the critical point. The obtained results further support that the QNMs can be a dynamic probe to investigate the thermodynamic properties in black holes.
基金supported by the National Natural Science Foundation of China(21473142 and 21673191)the National Innovative Research Team of China(IRT_14R31 and J1310024)
文摘Various bond modes of the M-C（C5 ring） exist in metallocene compounds of group 14 heavier elements,mostly due to an intricate interaction between the lone electron pairs at the M center and the 6 p-electrons of the C5 ring.The tin（Ⅱ） metallocene complexes LSn R（L = HC[CMe（N-2,6-iPr2C6H3）]2,R = cyclopentadienyl,C5H5（1）; indenyl,C9H7（2）; fluorenyl,C（13）H9（3）） stabilized by the β-diketiminato ligand were prepared and utilized in the study on their solid and solution state structures.X-ray single-crystal diffraction data revealed an η~1-mode of the Sn-C（C5 ring） bond in each 1~3.However,the room temperature ~1H NMR spectral studies disclosed such a fluxional bonding mode in solution.The 119 Sn NMR studies suggested a quadruple coordination nature of the Sn center in 1 while the triple coordination manner was for the Sn atom in both 2 and 3.Then the variable-temperature（25~–75 ℃） ~1H NMR spectral studies for each 1~3 were performed,which detected the relaxation state structures of 1~3 at lower temperature.All of these results indicate a stereochemical activity of the lone electron pairs at the tin（Ⅱ） atom that definitely has an electronic interaction with the 6 p-electrons of the C5 ring.The observed Sn-C（C5 ring） bond modes appear influenced by either the metallocene size or the compound state existed.
