精确计算Be原子SCF水平的电子性质

Accurate Calculation of the Electronic Properties of Beryllium Atom at SCF Level

用基组展开和解析求导的方法精确计算Be原子SCF水平的极化率和超极化率.计算超极化率的基组必须能正确表示无微扰的波函数,又能正确地表示由于外场引起的一阶和二阶微扰波函数.将s,p,d型基函数依次分别对无微扰能量E0,极化率α和超极化率γ进行优化,从而排除了基组选择过程中的任意性,使计算结果可以毫不含糊地随着基组的扩大而无限趋近Hartree-Fock极限值.计算表明,40s17p9d基组是合适的,用这个基组的计算结果是α(SCF)=45.616,γ(SCF)=3.91E4.还对以前的Be原子超极化率的Hartree-Fock水平计算结果进行了讨论.

In the present work the polarizability and the hyperpolarizability of Be atom are obtained at the SCF level with basis-set expansion and analytic derivation method. The basis-set is established with three parts, φ = φ^（0） ＋ φ^（1） ＋ φ^（2）, φ^（0） consists of s-type functions to express the accurate unperturbed wave function, φ^（1） consists of p-type functions and φ^（2） consists of d-type functions to express the first and second perturbed wave functions caused by a uniform electric field respectively, In light of the importance of s, p, and d functions for E0, E2, E4 respectively, exponents for each of these symmetries are optimized for the corresponding property, Eo , α and γ respectively, Our calculations show that 40s17p9d basis set is suitable. According to our calculations with this basis set the Hartree-Foek limit value of the seeond dipole hyperpolarizability （y） for the ground state of the beryllium atom should be 3.91EA. The former hyperpolarizability of the beryllium atom calculated at H-F level has also been diseussed.