The suitability of calculating atomic multipole moments from AM1 wave functions by cumulative potential-derived method has been investigated. It is shown that this method has a faster convergence of the fitting proces...The suitability of calculating atomic multipole moments from AM1 wave functions by cumulative potential-derived method has been investigated. It is shown that this method has a faster convergence of the fitting process and gives a better description of the charge distribution than the original PD method. Atomic charges obtained in this way are of comparable quality with 6-31G* data and the calculated dipole moments are closer to the experimental data than the values computed directly from the AM1 charges. The results demonstrate that the atomic multipole moments higher than monopole moment can be used to supplement the atomic charge to obtain a more accurate description of charge distribution. For the sake of comparison, both the Williams fitting potential surface and the Connolly one are used in the calculation.展开更多
The multipole moment method not only conduces to the understanding of the deformation of the space-time, but also serves as an effective tool to approximately solve the Einstein field equation with. However, the usual...The multipole moment method not only conduces to the understanding of the deformation of the space-time, but also serves as an effective tool to approximately solve the Einstein field equation with. However, the usual multipole moments are recursively determined by a sequence of symmetric and trace-free tensors, which is inconvenient for practical resolution. In this paper, we develop a simplified procedure to generate the series solutions to the metric of the stationary vacuum with axisymmetry, and show its validity. In order to understand the free parameters in the solution, we propose to take the Schwarzschild metric as a standard ruler, and some well- known examples are analysed and compared with the series solutions in detail.展开更多
文摘The suitability of calculating atomic multipole moments from AM1 wave functions by cumulative potential-derived method has been investigated. It is shown that this method has a faster convergence of the fitting process and gives a better description of the charge distribution than the original PD method. Atomic charges obtained in this way are of comparable quality with 6-31G* data and the calculated dipole moments are closer to the experimental data than the values computed directly from the AM1 charges. The results demonstrate that the atomic multipole moments higher than monopole moment can be used to supplement the atomic charge to obtain a more accurate description of charge distribution. For the sake of comparison, both the Williams fitting potential surface and the Connolly one are used in the calculation.
文摘The multipole moment method not only conduces to the understanding of the deformation of the space-time, but also serves as an effective tool to approximately solve the Einstein field equation with. However, the usual multipole moments are recursively determined by a sequence of symmetric and trace-free tensors, which is inconvenient for practical resolution. In this paper, we develop a simplified procedure to generate the series solutions to the metric of the stationary vacuum with axisymmetry, and show its validity. In order to understand the free parameters in the solution, we propose to take the Schwarzschild metric as a standard ruler, and some well- known examples are analysed and compared with the series solutions in detail.
