Study of the electronic correlation effect of surface atom by a time evolution operator

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It was shown that an energy eigenvalue and a wavefunction of any bound state of a system were extracted from the time developping wavefunction, which was calculated by a time evolution operator. In order to calculate efficiently a time developping wavefunction of a many electron system without any approximation of the interaction between electrons, the time evolution operator was expanded by a Chebychev polynomial as usual and a kinetic operator was replaced by a numerical differential operation. Considering N electron systems, an energy of a system with an atomic number Z and an electron-electron interaction parameter g was related with that of a different system with different Z' and g' by scaling Z and g properly. In order to bypass a requirement of a cusp condition on a many electron wavefunction, it was attempted to introduce a small parameter into the inter-electron Coulomb interaction function to suppress its singular behavior. If a mesh of calculating region was fine enough, the energy of the system was not sensitive to the change of the parameter. This method was applied to two electrons atom systems (H^-, He, Li^+, Be^<++>), and the calculated energies reprodeced the experimental results well. The g dependence of the grond state energy was understood qualitatively by a simple model calculation. In the region of 4-2√<2><g/Z<4, one electron was bounded but the other was not bounded to the nucleus. Usual LSDA,GGA,SIC mehods could not reproduce the energy splitting between the excited states correctly and could not describe the groud states and excited states of H^-, Be^<++>