The authors provided a simple method for calculating Wiener numbers of molecular graphs with symmetry in 1997.This paper intends to further improve on it and simplifies the calculation of the Wiener numbers of the mol...The authors provided a simple method for calculating Wiener numbers of molecular graphs with symmetry in 1997.This paper intends to further improve on it and simplifies the calculation of the Wiener numbers of the molecular graphs.展开更多
In the electron or x-ray scattering experiment,the measured spectra at larger momentum transfer are dominated by the electric dipole-forbidden transitions,while the corresponding selection rules for triatomic molecule...In the electron or x-ray scattering experiment,the measured spectra at larger momentum transfer are dominated by the electric dipole-forbidden transitions,while the corresponding selection rules for triatomic molecules have not been clearly elucidated.In this work,based on the molecular point group,the selection rules for the electric multipolarities of the electronic transitions of triatomic molecules are derived and summarized into several tables with the variation of molecular geometry in the transition process being considered.Based on the summarized selection rules,the electron energy loss spectra of H2O,CO2,and N2O are identified,and the momentum transfer dependence behaviors of their valence-shell excitations are explained.展开更多
The knowledge of the energy level structures of atoms and molecules is mainly obtained by spectroscopic experiments. Both photoabsorption and photoemission spectra are subject to the electric dipole selection rules （...The knowledge of the energy level structures of atoms and molecules is mainly obtained by spectroscopic experiments. Both photoabsorption and photoemission spectra are subject to the electric dipole selection rules （also known as optical selection rules）. However, the selection rules for atoms and molecules in the scattering experiments are not identical to those in the optical experiments. In this paper, based on the theory of the molecular point group, the selection rules are derived and summarized for the electric monopole, electric dipole, electric quadrupole, and electric octupole transitions of diatomic molecules under the first Born approximation in scattering experiments. Then based on the derived selection rules, the electron scattering spectra and x-ray scattering spectra of H2, N2, and CO at different momentum transfers are explained, and the discrepancies between the previous experimental results measured by different groups are elucidated.展开更多
A novel method which makes full use of point groups including Abeian and nonAbelian groups is presented. The key point for this method is the definition of a kind of newsymmetry moecular orbitals (SMOs). Any group ele...A novel method which makes full use of point groups including Abeian and nonAbelian groups is presented. The key point for this method is the definition of a kind of newsymmetry moecular orbitals (SMOs). Any group element in a moecular point group willtransform one SMO to another equlvalent SMO and no mixture among SMCh exists. The unique feature will be kept for one or two - electron integrals as well as the Slater determinantsconstructed using SMCh. Consequently, the character integrals and character detendnants(CDs) can be selected according to some simple rules. Based on this method, a preliminarycharacter single and doubly excited single reference CI (CD - SR - CISD) program is developed, and pilot calculations are performed and compared with GAUSSIAN - 94.For thehigh symmetry point group models and linear molecules our CD - CISD program costs lessCPU - time than G94 - CISD and the storage demand of CD - CISD is also remarkably alleviated.展开更多
文摘The authors provided a simple method for calculating Wiener numbers of molecular graphs with symmetry in 1997.This paper intends to further improve on it and simplifies the calculation of the Wiener numbers of the molecular graphs.
基金Project supported by the National Key Research and Development Program of China(Grant No.2017YFA0402300)the National Natural Science Foundation of China(Grant No.U1732133)the Science Fund from Chinese Academy of Sciences(Grant No.11320101003)
文摘In the electron or x-ray scattering experiment,the measured spectra at larger momentum transfer are dominated by the electric dipole-forbidden transitions,while the corresponding selection rules for triatomic molecules have not been clearly elucidated.In this work,based on the molecular point group,the selection rules for the electric multipolarities of the electronic transitions of triatomic molecules are derived and summarized into several tables with the variation of molecular geometry in the transition process being considered.Based on the summarized selection rules,the electron energy loss spectra of H2O,CO2,and N2O are identified,and the momentum transfer dependence behaviors of their valence-shell excitations are explained.
基金Project supported by the National Natural Science Foundation of China(Grant Nos.U1332204,11274291,and 11320101003)
文摘The knowledge of the energy level structures of atoms and molecules is mainly obtained by spectroscopic experiments. Both photoabsorption and photoemission spectra are subject to the electric dipole selection rules （also known as optical selection rules）. However, the selection rules for atoms and molecules in the scattering experiments are not identical to those in the optical experiments. In this paper, based on the theory of the molecular point group, the selection rules are derived and summarized for the electric monopole, electric dipole, electric quadrupole, and electric octupole transitions of diatomic molecules under the first Born approximation in scattering experiments. Then based on the derived selection rules, the electron scattering spectra and x-ray scattering spectra of H2, N2, and CO at different momentum transfers are explained, and the discrepancies between the previous experimental results measured by different groups are elucidated.
文摘A novel method which makes full use of point groups including Abeian and nonAbelian groups is presented. The key point for this method is the definition of a kind of newsymmetry moecular orbitals (SMOs). Any group element in a moecular point group willtransform one SMO to another equlvalent SMO and no mixture among SMCh exists. The unique feature will be kept for one or two - electron integrals as well as the Slater determinantsconstructed using SMCh. Consequently, the character integrals and character detendnants(CDs) can be selected according to some simple rules. Based on this method, a preliminarycharacter single and doubly excited single reference CI (CD - SR - CISD) program is developed, and pilot calculations are performed and compared with GAUSSIAN - 94.For thehigh symmetry point group models and linear molecules our CD - CISD program costs lessCPU - time than G94 - CISD and the storage demand of CD - CISD is also remarkably alleviated.
