Multiple helicenes display distinct aromatic cores characterized by highly twisted rings that are shared or fused with constituent helicene moieties.Diversifying these aromatic cores unlocks avenues for creating multi...Multiple helicenes display distinct aromatic cores characterized by highly twisted rings that are shared or fused with constituent helicene moieties.Diversifying these aromatic cores unlocks avenues for creating multiple helicenes with distinct properties and topologies.Herein we report the synthesis of a quadruple[6]helicene featuring pyrene as the aromatic core.The synthesis involved key steps of the annulativeπ-extension reaction and Scholl reaction.By extending multiple helicenes along the axial direction,the degree of contortion of the aromatic core can be controlled from nearly flat to highly twisted.Notably,quadruple[6]-helicene exhibits a significant red-shift of 0.49 eV compared to quadruple[4]-helicenes,of which the red-shift arises from bothπ-extension and augmented effective conjugation due to enhanced twisting.Quantum chemical calculations demonstrate that the degree of contortion in the pyrene core adeptly governs the energy levels of the HOMO and LUMO,which offers an alternative strategy beyond mere enlargement of theπbackbone.An intriguing serendipitous finding reveals the formation of one-molecule-thick supramolecular homochiral nanosheets through selfinterlocking interactions of enantiomers in single crystals,a rare packing motif for multiple helicenes.展开更多
The twistor kinematic-energy model of the space-time and the kinematic-energy tensor as the energy-matter tensor in relativity are considered to demonstrate the possible behavior of gravity as gravitational waves that...The twistor kinematic-energy model of the space-time and the kinematic-energy tensor as the energy-matter tensor in relativity are considered to demonstrate the possible behavior of gravity as gravitational waves that derive of mass-energy source in the space-time and whose contorted image is the spectrum of the torsion field acting in the space-time. The energy of this field is the energy of their second curvature. Likewise, it is assumed that the curvature energy as spectral curvature in the twistor kinematic frame is the curvature in twistor-spinor framework, which is the mean result of this work. This demonstrates the lawfulness of the torsion as the indicium of the gravitational waves in the space-time. A censorship to detect gravitational waves in the space-time is designed using the curvature energy.展开更多
The tension between the Hubble constant values obtained from local measurements and cosmic microwave background(CMB)measurements has motivated us to consider the cosmological model beyondΛCDM.We investigate the cosmo...The tension between the Hubble constant values obtained from local measurements and cosmic microwave background(CMB)measurements has motivated us to consider the cosmological model beyondΛCDM.We investigate the cosmology in the large scale Lorentz violation model with a non-vanishing spatial curvature.The degeneracy among spatial curvature,cosmological constant,and cosmological contortion distribution makes the model viable in describing the known observational data.We obtain some constraints on the spatial curvature by comparing the relationship between measured distance modulus and red-shift with the predicted one,the evolution of matter density over time,and the evolution of effective cosmological constant.The implications of the large scale Lorentz violation model with the non-vanishing spatial curvature under these constrains are discussed.展开更多
基金supported by Deutsche Forschungsgemeinschaft(DFG)through RTG 2591“Template-Designed Organic Electronics”the Manchot Foundation for a doctoral scholarship.
文摘Multiple helicenes display distinct aromatic cores characterized by highly twisted rings that are shared or fused with constituent helicene moieties.Diversifying these aromatic cores unlocks avenues for creating multiple helicenes with distinct properties and topologies.Herein we report the synthesis of a quadruple[6]helicene featuring pyrene as the aromatic core.The synthesis involved key steps of the annulativeπ-extension reaction and Scholl reaction.By extending multiple helicenes along the axial direction,the degree of contortion of the aromatic core can be controlled from nearly flat to highly twisted.Notably,quadruple[6]-helicene exhibits a significant red-shift of 0.49 eV compared to quadruple[4]-helicenes,of which the red-shift arises from bothπ-extension and augmented effective conjugation due to enhanced twisting.Quantum chemical calculations demonstrate that the degree of contortion in the pyrene core adeptly governs the energy levels of the HOMO and LUMO,which offers an alternative strategy beyond mere enlargement of theπbackbone.An intriguing serendipitous finding reveals the formation of one-molecule-thick supramolecular homochiral nanosheets through selfinterlocking interactions of enantiomers in single crystals,a rare packing motif for multiple helicenes.
文摘The twistor kinematic-energy model of the space-time and the kinematic-energy tensor as the energy-matter tensor in relativity are considered to demonstrate the possible behavior of gravity as gravitational waves that derive of mass-energy source in the space-time and whose contorted image is the spectrum of the torsion field acting in the space-time. The energy of this field is the energy of their second curvature. Likewise, it is assumed that the curvature energy as spectral curvature in the twistor kinematic frame is the curvature in twistor-spinor framework, which is the mean result of this work. This demonstrates the lawfulness of the torsion as the indicium of the gravitational waves in the space-time. A censorship to detect gravitational waves in the space-time is designed using the curvature energy.
基金Supported by the National Natural Science Foundation of China (11775080, 11865016)。
文摘The tension between the Hubble constant values obtained from local measurements and cosmic microwave background(CMB)measurements has motivated us to consider the cosmological model beyondΛCDM.We investigate the cosmology in the large scale Lorentz violation model with a non-vanishing spatial curvature.The degeneracy among spatial curvature,cosmological constant,and cosmological contortion distribution makes the model viable in describing the known observational data.We obtain some constraints on the spatial curvature by comparing the relationship between measured distance modulus and red-shift with the predicted one,the evolution of matter density over time,and the evolution of effective cosmological constant.The implications of the large scale Lorentz violation model with the non-vanishing spatial curvature under these constrains are discussed.
