Lagrange网格法计算双电子离子的核临界电荷
Nuclear critical charge for two-electron ion in Lagrange mesh method
摘要：
用拉格朗日网格法求解了两个电子在带电固定中心$Z$场中的薛定谔方程，计算了接近临界电荷$Z_{cr}$的电荷。我们确认了Estienne等人最近计算的核临界电荷$Z_{cr}$的值。{ \em Phys. Rev. Lett. \bf 112}，173001（2014）中描述的方法，使用大小为$70 \times 70 \times 20$的非均匀（非均匀）三维晶格将数据转换为11个十进制数字。我们表明，与Nakashima-Nakatsuji，{ \it J. Chem. Phys. \bf 127}，224104（2007）的高度精确的结果相比，H $^-$的基态能量在晶格$50 \times 50 \times 40$上精确到14位小数。
英文摘要：
The Schroedinger equation for two electrons in the field of a charged fixed center $Z$ is solved with the Lagrange mesh method for charges close to the critical charge $Z_{cr}$. We confirm the value of the nuclear critical charge $Z_{cr}$ recently calculated in Estienne et al. {\em Phys. Rev. Lett. \bf 112}, 173001 (2014) to 11 decimal digits using an inhomogeneous (non-uniform) three-dimensional lattice of size $70 \times 70 \times 20$. We show that the ground state energy for H$^-$ is accurate to 14 decimals on the lattice $50 \times 50 \times 40$ in comparison with the highly accurate result by Nakashima-Nakatsuji, {\it J. Chem. Phys. \bf 127}, 224104 (2007).
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