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

结果表明，由时间演化算符计算的时间展开波函数可提取系统任意束缚态的能量特征值和波函数。为了在不逼近电子间相互作用的情况下有效地计算多电子系统的时间发展波函数，将时间演化算符照常展开为切比契夫多项式，并将动力学算符替换为数值微分运算。考虑N个电子系统，原子序数为Z且电子-电子相互作用参数为g的系统的能量通过适当缩放Z和g，与具有不同Z‘和g’的不同系统的能量相关。为了绕过多电子波函数的尖峰条件要求，尝试在电子间库仑相互作用函数中引入一个小参数来抑制其奇异性。如果计算区域网格足够精细，系统能量对参数的变化不敏感。将该方法应用于两个电子原子体系（H^-, He, Li^+, Be^<++>），计算得到的能量与实验结果吻合较好。通过简单的模型计算，定性地理解了基态能量对g的依赖关系。在4-2√<2><g/Z<4的区域，一个电子被束缚，而另一个电子没有被束缚在原子核上。通常的LSDA、GGA、SIC方法不能正确再现激发态之间的能量分裂，也不能描述H^-、Be^<++>的基态和激发态

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^<++>