The 6-isoquinolinyl system was incorporated into mechanically interlocked molecules(MIMs)syntheses for comparative analysis of its assembly behavior with 4-pyridyl-based coordination ligands,where a coordination-drive...The 6-isoquinolinyl system was incorporated into mechanically interlocked molecules(MIMs)syntheses for comparative analysis of its assembly behavior with 4-pyridyl-based coordination ligands,where a coordination-driven self-assembly strategy by half-sandwich Cp^(*)Rh units was employed to construct diverse molecular links.The pyridyl ligand,adorned with thiophene moieties,assembles into[2]catenanes(2_(1)^(2)links),whereas the isoquinolinyl ligand produces molecular Borromean links(6_(2)^(3)links).Intriguingly,when utilizing extended bithiophene segments,the pyridyl ligand forms Borromean rings(6_(2)^(3)links),while isoquinolinyl counterparts produced a rare low-symmetry cyclic[3]catenane(6_(3)^(3)topology).The results were confirmed through single-crystal X-ray diffraction analysis,nuclear magnetic resonance(NMR)spectroscopy,and electrospray ionization time-of-flight mass spectrometry(ESI-TOF/MS)experiments.Synergistic π-π stacking,C-H···π interactions,and solvophobic effects governed the complex self-assembly system,with independent gradient model(IGM)analyses and solventaccessible surface area(SASA)calculations providing atomistic insights into the pathway selectivity of distinct topological links.展开更多
We study the limit cycle bifurcations perturbing a class of quartic linear-like Hamiltonian systems having an elementary center at the origin. First, using methods of the qualitative theory, all possible phase portrai...We study the limit cycle bifurcations perturbing a class of quartic linear-like Hamiltonian systems having an elementary center at the origin. First, using methods of the qualitative theory, all possible phase portraits of the unperturbed system are found. Then, using the first order Melnikov function, Hopf bifurcation problem of the perturbed system is investigated, and an upper bound for the function is obtained near the origin.展开更多
基金supported by the Department of Chemistry,Fudan Universitythe National Natural Science Foundation of China(22031003,21720102004)the Shanghai Science Technology Committee(19DZ2270100)。
文摘The 6-isoquinolinyl system was incorporated into mechanically interlocked molecules(MIMs)syntheses for comparative analysis of its assembly behavior with 4-pyridyl-based coordination ligands,where a coordination-driven self-assembly strategy by half-sandwich Cp^(*)Rh units was employed to construct diverse molecular links.The pyridyl ligand,adorned with thiophene moieties,assembles into[2]catenanes(2_(1)^(2)links),whereas the isoquinolinyl ligand produces molecular Borromean links(6_(2)^(3)links).Intriguingly,when utilizing extended bithiophene segments,the pyridyl ligand forms Borromean rings(6_(2)^(3)links),while isoquinolinyl counterparts produced a rare low-symmetry cyclic[3]catenane(6_(3)^(3)topology).The results were confirmed through single-crystal X-ray diffraction analysis,nuclear magnetic resonance(NMR)spectroscopy,and electrospray ionization time-of-flight mass spectrometry(ESI-TOF/MS)experiments.Synergistic π-π stacking,C-H···π interactions,and solvophobic effects governed the complex self-assembly system,with independent gradient model(IGM)analyses and solventaccessible surface area(SASA)calculations providing atomistic insights into the pathway selectivity of distinct topological links.
基金supported by the National Natural Science Foundations of China(12371171)and the Natural Science Foundation of Jiangsu Province(BK20221339).
文摘We study the limit cycle bifurcations perturbing a class of quartic linear-like Hamiltonian systems having an elementary center at the origin. First, using methods of the qualitative theory, all possible phase portraits of the unperturbed system are found. Then, using the first order Melnikov function, Hopf bifurcation problem of the perturbed system is investigated, and an upper bound for the function is obtained near the origin.
