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

时间演化算子研究表面原子电子关联效应

• 批准号: 10640314
• 负责人: SHIMA Nobuyuki
• 金额: $ 0.9万
• 依托单位: Himeji Institute of Technology
• 依托单位国家: 日本
• 项目类别: Grant-in-Aid for Scientific Research (C)
• 财政年份: 1998
• 资助国家: 日本
• 起止时间: 1998 至 2000
• 项目状态: 已结题
• 来源: https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-10640314/
• 关键词: time evolution operator; electronic state; many electrons; electronic correlation; 時間発展演算子

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^<++>

结果表明，由时间演化算符计算出的随时间发展的波函数，可以提取出系统任意束缚态的能量本征值和波函数。为了有效地计算多电子系统的时间发展波函数，在不对电子间相互作用作任何近似的情况下，将时间演化算符按通常的Chebychev多项式展开，并将动力学算符用数值微分运算代替.考虑N个电子系统，通过适当地标度Z和g，将原子序数为Z和电子-电子相互作用参数为g的系统的能量与具有不同Z'和g'的不同系统的能量联系起来。为了绕过对多电子波函数的尖点条件的要求，尝试在电子间库仑相互作用函数中引入小参数以抑制其奇异行为。如果计算区域的网格足够细，系统的能量对参数的变化不敏感。将该方法应用于H^-，He，Li^+，Be^<++>等双电子原子体系，计算的能量与实验结果符合较好。通过一个简单的模型计算定性地理解了基态能量与g的关系。在4-2 π <2>&lt;g/Z&lt;4的范围内，一个电子与原子核结合，另一个电子与原子核不结合。传统的LSDA、GGA、SIC方法不能准确地再现激发态之间的能量分裂，不能描述H^-、Be^++的基态和激发态