We consider an energy operator of four-electron system in the Impurity Hubbard model with a coupling between nearest-neighbors. The spectrum of the systems in the second triplet state in a ν-dimensional lattice is in...We consider an energy operator of four-electron system in the Impurity Hubbard model with a coupling between nearest-neighbors. The spectrum of the systems in the second triplet state in a ν-dimensional lattice is investigated. For investigation the structure of essential spectra and discrete spectrum of the energy operator of four-electron systems in an impurity Hubbard model, for which the momentum representation is convenient. In addition, we used the tensor products of Hilbert spaces and tensor products of operators in Hilbert spaces and described the structure of essential spectrum and discrete spectrum of the energy operator of four-electron systems in an impurity Hubbard model for the second triplet state of the system. The investigations show that the essential spectrum of the system consists of the union of no more than sixteen segments, and the discrete spectrum of the system consists of no more than eleven eigenvalues.展开更多
The β-carotene（β-Car） aggregate was prepared by self-assembly in cetyltrimethylammoniuln bromide （CTAB） micelle. The ground state absorption measurement showed that the aggregate has J-type characteristics and r...The β-carotene（β-Car） aggregate was prepared by self-assembly in cetyltrimethylammoniuln bromide （CTAB） micelle. The ground state absorption measurement showed that the aggregate has J-type characteristics and resonance Raman spectra gave the intrinsic explanation of molecular interaction in aggregate. Upon excitation at the optical allowed S2 state of aggregate, direct generation of triplet state via singlet fission（SF）mechanism was observed. Excitation dynamics was elucidated by fs-transient absorption spectroscopy and ns-flash photolysis, respectively. The triplet state life time of aggregate was found to be independent of the ambient oxygen molecules.展开更多
We consider two-electron systems for the impurity Hubbard Model and investigate the spectrum of the system in a singlet state for the v-dimensional integer valued lattice Z<sup>v</sup>. We proved the essen...We consider two-electron systems for the impurity Hubbard Model and investigate the spectrum of the system in a singlet state for the v-dimensional integer valued lattice Z<sup>v</sup>. We proved the essential spectrum of the system in the singlet state is consists of union of no more then three intervals, and the discrete spectrum of the system in the singlet state is consists of no more then five eigenvalues. We show that the discrete spectrum of the system in the triplet and singlet states differ from each other. In the singlet state the appear additional two eigenvalues. In the triplet state the discrete spectrum of the system can be empty set, or is consists of one-eigenvalue, or is consists of two eigenvalues, or is consists of three eigenvalues. For investigation the structure of essential spectra and discrete spectrum of the energy operator of two-electron systems in an impurity Hubbard model, for which the momentum representation is convenient. In addition, we used the tensor products of Hilbert spaces and tensor products of operators in Hilbert spaces and described the structure of essential spectrum and discrete spectrum of the energy operator of two-electron systems in an impurity Hubbard model.展开更多
We consider the energy operator of six-electron systems in the Hubbard model and investigate the structure of essential spectra and discrete spectrum of the system in the first quintet and first singlet states in the ...We consider the energy operator of six-electron systems in the Hubbard model and investigate the structure of essential spectra and discrete spectrum of the system in the first quintet and first singlet states in the v-dimensional lattice.展开更多
We consider the energy operator of four-electron systems in an impurity Hubbard model and investigated the structure of essential spectra and discrete spectrum of the system in the first triplet state in a one-dimensi...We consider the energy operator of four-electron systems in an impurity Hubbard model and investigated the structure of essential spectra and discrete spectrum of the system in the first triplet state in a one-dimensional lattice. For investigation the structure of essential spectra and discrete spectrum of the energy operator of four-electron systems in an impurity Hubbard model, for which the momentum representation is convenient. In addition, we used the tensor products of Hilbert spaces and tensor products of operators in Hilbert spaces and described the structure of essential spectrum and discrete spectrum of the energy operator of four-electron systems in an impurity Hubbard model. The investigations show that there are such cases: 1) the essential spectrum of the system consists of the union of no more than eight segments, and the discrete spectrum of the system consists of no more than three eigenvalues;2) the essential spectrum of the system consists of the union of no more than sixteen segments, and the discrete spectrum of the system consists of no more than eleven eigenvalues;3) the essential spectrum of the system consists of the union of no more than three segments, and the discrete spectrum of the system is the empty set. Consequently, the essential spectrum of the system consists of the union of no more than sixteen segments, and the discrete spectrum of the system consists of no more than eleven eigenvalues.展开更多
We have presented the synthesis and characterization of three new bromo substituted stilbene derivatives, p-3,4,5-trimethoxy-p′- 2,3,4,5,6-pentabromostilbene （C1）, p-N,N-dimethylamino-p′-2,3,4,5,6-pentabromostilbe...We have presented the synthesis and characterization of three new bromo substituted stilbene derivatives, p-3,4,5-trimethoxy-p′- 2,3,4,5,6-pentabromostilbene （C1）, p-N,N-dimethylamino-p′-2,3,4,5,6-pentabromostilbene （C2） and p-N,N-diphenylamino-p′- 2,3,4,5,6-pentabromostilbene （C3） in this letter. The UV/vis absorption and photoluminescence were investigated in various solvents. The maximal absorption wavelength of C1 exhibited blue-shift to those of C2 and C3 in different solvents. No florescence emission could be detected for these compounds at room temperature. Singlet oxygen could be efficiently produced with these sensitizers under near-ultraviolet and visible light irradiation.展开更多
The research results of the excited-state properties of asymmetric pentaazadentate ex-panded-porphyrins are reported. The results show that the emission spectra appear in the 770-820 nm region in accord with the diffe...The research results of the excited-state properties of asymmetric pentaazadentate ex-panded-porphyrins are reported. The results show that the emission spectra appear in the 770-820 nm region in accord with the different substituents on the benzene ring. The quantum yield of fluorescence is less than 0.02, and the lifetime of the first singlet excited state (S1) is shorter than 1ns. There are excellent linear relationships between the energy of the S1 and the Hammett constants as well as the quantum yield of fluorescence and the electrophilic substituent constants σ+. The energies of the lowest excited triplet state (T1) of the complexes are in the range of 94 -130kJ/mol. The lifetime of T 1 is as long as tens of microseconds. The T1-Tn transient absorption spectra appear in 450-550 nm region. And the quantum yield of title compounds for generating singlet oxygen is as high as 0.9.展开更多
基金This work was supported by the National Key R&D Program of China(No.2017YFA0303500 to Guo-qing Zhang)the National Natural Science Foundation of China(No.21975238 to Guo-qing Zhang)the University of Science and Technology of China startup funds(No.KY2340000139 to Xue-peng Zhang).
基金supported by the National Natural Science Foundation of China(No.11774233)Anhui Province College Student Innovation and Entrepreneurship Training Program(No.S202010359212).
文摘We consider an energy operator of four-electron system in the Impurity Hubbard model with a coupling between nearest-neighbors. The spectrum of the systems in the second triplet state in a ν-dimensional lattice is investigated. For investigation the structure of essential spectra and discrete spectrum of the energy operator of four-electron systems in an impurity Hubbard model, for which the momentum representation is convenient. In addition, we used the tensor products of Hilbert spaces and tensor products of operators in Hilbert spaces and described the structure of essential spectrum and discrete spectrum of the energy operator of four-electron systems in an impurity Hubbard model for the second triplet state of the system. The investigations show that the essential spectrum of the system consists of the union of no more than sixteen segments, and the discrete spectrum of the system consists of no more than eleven eigenvalues.
基金Supported by the National Natural Science Foundation of China（Nos.21673289, 21273282, 21673288）.
文摘The β-carotene（β-Car） aggregate was prepared by self-assembly in cetyltrimethylammoniuln bromide （CTAB） micelle. The ground state absorption measurement showed that the aggregate has J-type characteristics and resonance Raman spectra gave the intrinsic explanation of molecular interaction in aggregate. Upon excitation at the optical allowed S2 state of aggregate, direct generation of triplet state via singlet fission（SF）mechanism was observed. Excitation dynamics was elucidated by fs-transient absorption spectroscopy and ns-flash photolysis, respectively. The triplet state life time of aggregate was found to be independent of the ambient oxygen molecules.
文摘We consider two-electron systems for the impurity Hubbard Model and investigate the spectrum of the system in a singlet state for the v-dimensional integer valued lattice Z<sup>v</sup>. We proved the essential spectrum of the system in the singlet state is consists of union of no more then three intervals, and the discrete spectrum of the system in the singlet state is consists of no more then five eigenvalues. We show that the discrete spectrum of the system in the triplet and singlet states differ from each other. In the singlet state the appear additional two eigenvalues. In the triplet state the discrete spectrum of the system can be empty set, or is consists of one-eigenvalue, or is consists of two eigenvalues, or is consists of three eigenvalues. For investigation the structure of essential spectra and discrete spectrum of the energy operator of two-electron systems in an impurity Hubbard model, for which the momentum representation is convenient. In addition, we used the tensor products of Hilbert spaces and tensor products of operators in Hilbert spaces and described the structure of essential spectrum and discrete spectrum of the energy operator of two-electron systems in an impurity Hubbard model.
文摘We consider the energy operator of six-electron systems in the Hubbard model and investigate the structure of essential spectra and discrete spectrum of the system in the first quintet and first singlet states in the v-dimensional lattice.
文摘We consider the energy operator of four-electron systems in an impurity Hubbard model and investigated the structure of essential spectra and discrete spectrum of the system in the first triplet state in a one-dimensional lattice. For investigation the structure of essential spectra and discrete spectrum of the energy operator of four-electron systems in an impurity Hubbard model, for which the momentum representation is convenient. In addition, we used the tensor products of Hilbert spaces and tensor products of operators in Hilbert spaces and described the structure of essential spectrum and discrete spectrum of the energy operator of four-electron systems in an impurity Hubbard model. The investigations show that there are such cases: 1) the essential spectrum of the system consists of the union of no more than eight segments, and the discrete spectrum of the system consists of no more than three eigenvalues;2) the essential spectrum of the system consists of the union of no more than sixteen segments, and the discrete spectrum of the system consists of no more than eleven eigenvalues;3) the essential spectrum of the system consists of the union of no more than three segments, and the discrete spectrum of the system is the empty set. Consequently, the essential spectrum of the system consists of the union of no more than sixteen segments, and the discrete spectrum of the system consists of no more than eleven eigenvalues.
基金support from National Natural Science Foundation of China(Nos. 20776165,20702065,20872184)Key Foundation of Chongqing Science and Technology Commission"(No.CSTC 2008BA4020)+1 种基金"A Foundation for the Author of National Excellent Doctoral Dissertation of PR China(200735)"for financial supportsponsored by the Scientific Research Foundation for the Returned Overseas Chinese Scholars,State Education Ministry as well(Nos.20071108-1, 20071108-5).
文摘We have presented the synthesis and characterization of three new bromo substituted stilbene derivatives, p-3,4,5-trimethoxy-p′- 2,3,4,5,6-pentabromostilbene （C1）, p-N,N-dimethylamino-p′-2,3,4,5,6-pentabromostilbene （C2） and p-N,N-diphenylamino-p′- 2,3,4,5,6-pentabromostilbene （C3） in this letter. The UV/vis absorption and photoluminescence were investigated in various solvents. The maximal absorption wavelength of C1 exhibited blue-shift to those of C2 and C3 in different solvents. No florescence emission could be detected for these compounds at room temperature. Singlet oxygen could be efficiently produced with these sensitizers under near-ultraviolet and visible light irradiation.
基金Project supported by the National Natural Science Foundation of China
文摘The research results of the excited-state properties of asymmetric pentaazadentate ex-panded-porphyrins are reported. The results show that the emission spectra appear in the 770-820 nm region in accord with the different substituents on the benzene ring. The quantum yield of fluorescence is less than 0.02, and the lifetime of the first singlet excited state (S1) is shorter than 1ns. There are excellent linear relationships between the energy of the S1 and the Hammett constants as well as the quantum yield of fluorescence and the electrophilic substituent constants σ+. The energies of the lowest excited triplet state (T1) of the complexes are in the range of 94 -130kJ/mol. The lifetime of T 1 is as long as tens of microseconds. The T1-Tn transient absorption spectra appear in 450-550 nm region. And the quantum yield of title compounds for generating singlet oxygen is as high as 0.9.
