The geometries of azobenzene compounds are optimized with B3LYP/6-311G* method, and analyzed with nature bond orbital, then their visible absorption maxima are calculated with TD-DFT method and ZINDO/S method respecti...The geometries of azobenzene compounds are optimized with B3LYP/6-311G* method, and analyzed with nature bond orbital, then their visible absorption maxima are calculated with TD-DFT method and ZINDO/S method respectively. The results agree well with the observed values. It was found that for the calculation of visible absorption using ZINDO/S method could rapidly yield better results by adjusting OWFπ-π (the relationship between π-π overlap weighting factor) value than by the TD-DFT method. The method of regression showing the linear relationship between OWFπ-π and BLN-N (nitrogen-nitrogen bond lengths) as OWFπ-π=?8.1537+6.5638BLN-N, can be explained in terms of quantum theory, and also be used for prediction of visible absorption maxima of other azobenzne dyes in the same series. This study on molecules’ orbital geometry indicates that their visible ab- sorption maxima correspond to the electron transition from HOMO (the highest occupied molecular orbital) to LUMO (the lowest unoccupied molecular orbital).展开更多
Based on finite element method and finite strip method, a simplified approach was presented to analyze high rise frame tube structures. The generalized strip element is introduced and then the generalized stiffness ma...Based on finite element method and finite strip method, a simplified approach was presented to analyze high rise frame tube structures. The generalized strip element is introduced and then the generalized stiffness matrices for beam and column line are derived by using the displacement functions that describe the nodal displacements and displacement transforms. Furthermore, the formulas for the generalized stiffness matrix of generalized strip element and load arrays corresponding to the displacement parameters were developed. It is shown through a series of numerical computation that the nodal angular displacements at the same floor in a generalized strip element are approximately identical. A comparison of the finite element method and the finite strip method shows that the simplified approach not only is accurate, but also reduces the number of basic unknown quantities.展开更多
The nature and origin of a fundamental quantum QSPR （QQSPR） equation are discussed. In principle, as any molecular structure can be associated to quantum mechanical density functions （DF）, a molecular set can be r...The nature and origin of a fundamental quantum QSPR （QQSPR） equation are discussed. In principle, as any molecular structure can be associated to quantum mechanical density functions （DF）, a molecular set can be reconstructed as a quantum multimolecular polyhedron （QMP）, whose vertices are formed by each molecular DF. According to QQSPR theory, complicated kinds of molecular properties, like biological activity or toxicity, of molecular sets can be calculated via the quantum expectation value of an approximate Hermitian operator, which can be evaluated with the geometrical information contained in the attached QMP via quantum similarity matrices. Practical ways of solving the QQSPR problem from the point of view of QMP geometrical structure are provided. Such a development results into a powerful algorithm, which can be implemented within molecular design as an alternative to the current classical QSPR procedures.展开更多
This paper is concerned with solving some structured multi-linear systems, which are called tensor absolute value equations. This kind of absolute value equations is closely related to tensor complementarity problems ...This paper is concerned with solving some structured multi-linear systems, which are called tensor absolute value equations. This kind of absolute value equations is closely related to tensor complementarity problems and is a generalization of the well-known absolute value equations in the matrix case. We prove that tensor absolute value equations are equivalent to some special structured tensor complementary problems. Some sufficient conditions are given to guarantee the existence of solutions for tensor absolute value equations. We also propose a Levenberg-Marquardt-type algorithm for solving some given tensor absolute value equations and preliminary numerical results are reported to indicate the efficiency of the proposed algorithm.展开更多
文摘The geometries of azobenzene compounds are optimized with B3LYP/6-311G* method, and analyzed with nature bond orbital, then their visible absorption maxima are calculated with TD-DFT method and ZINDO/S method respectively. The results agree well with the observed values. It was found that for the calculation of visible absorption using ZINDO/S method could rapidly yield better results by adjusting OWFπ-π (the relationship between π-π overlap weighting factor) value than by the TD-DFT method. The method of regression showing the linear relationship between OWFπ-π and BLN-N (nitrogen-nitrogen bond lengths) as OWFπ-π=?8.1537+6.5638BLN-N, can be explained in terms of quantum theory, and also be used for prediction of visible absorption maxima of other azobenzne dyes in the same series. This study on molecules’ orbital geometry indicates that their visible ab- sorption maxima correspond to the electron transition from HOMO (the highest occupied molecular orbital) to LUMO (the lowest unoccupied molecular orbital).
基金Fund of Science and Technology Develop-ment of Shanghai ( No.0 2 ZF14 0 5 6)
文摘Based on finite element method and finite strip method, a simplified approach was presented to analyze high rise frame tube structures. The generalized strip element is introduced and then the generalized stiffness matrices for beam and column line are derived by using the displacement functions that describe the nodal displacements and displacement transforms. Furthermore, the formulas for the generalized stiffness matrix of generalized strip element and load arrays corresponding to the displacement parameters were developed. It is shown through a series of numerical computation that the nodal angular displacements at the same floor in a generalized strip element are approximately identical. A comparison of the finite element method and the finite strip method shows that the simplified approach not only is accurate, but also reduces the number of basic unknown quantities.
文摘The nature and origin of a fundamental quantum QSPR （QQSPR） equation are discussed. In principle, as any molecular structure can be associated to quantum mechanical density functions （DF）, a molecular set can be reconstructed as a quantum multimolecular polyhedron （QMP）, whose vertices are formed by each molecular DF. According to QQSPR theory, complicated kinds of molecular properties, like biological activity or toxicity, of molecular sets can be calculated via the quantum expectation value of an approximate Hermitian operator, which can be evaluated with the geometrical information contained in the attached QMP via quantum similarity matrices. Practical ways of solving the QQSPR problem from the point of view of QMP geometrical structure are provided. Such a development results into a powerful algorithm, which can be implemented within molecular design as an alternative to the current classical QSPR procedures.
基金supported by National Natural Science Foundation of China (Grant Nos. 11671220, 11401331, 11771244 and 11271221)the Nature Science Foundation of Shandong Province (Grant Nos. ZR2015AQ013 and ZR2016AM29)the Hong Kong Research Grant Council (Grant Nos. PolyU 501913,15302114, 15300715 and 15301716)
文摘This paper is concerned with solving some structured multi-linear systems, which are called tensor absolute value equations. This kind of absolute value equations is closely related to tensor complementarity problems and is a generalization of the well-known absolute value equations in the matrix case. We prove that tensor absolute value equations are equivalent to some special structured tensor complementary problems. Some sufficient conditions are given to guarantee the existence of solutions for tensor absolute value equations. We also propose a Levenberg-Marquardt-type algorithm for solving some given tensor absolute value equations and preliminary numerical results are reported to indicate the efficiency of the proposed algorithm.
