How Accurately Does the Free Complement Wave Function of a Helium Atom Satisfy the Schrodinger Equation?
How Accurately Does the Free Complement Wave Function of a Helium Atom Satisfy the Schrodinger Equation?
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DOI：
10.1103/physrevlett.101.240406
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发表时间：
2008-12-12
影响因子：
8.6
通讯作者：
Nakatsuji, Hiroshi
中科院分区：
文献类型：
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作者：
Nakashima, Hiroyuki;Nakatsuji, Hiroshi
由H psi/psi定义的局部能量必须等于原子或分子在任何坐标处的精确能量E，只要所考虑的psi是精确的。这个量与E的差异是对所计算的波函数的准确性的严格检验。标准化psi的H平方误差（由sigma（2）定义，相当于）也是对精度的严格测试。使用这些量，我们已经检查了我们的波函数的准确性的氦原子计算使用的自由补充方法，开发解决薛定谔方程。与变分上限一起，使用修改的Temple公式计算的精确能量的下限确保氦固定核基态能量的绝对正确值为-2.9037243770341195983111592451944a.u.，这是正确的32位数。
The local energy defined by H psi/psi must be equal to the exact energy E at any coordinate of an atom or molecule, as long as the psi under consideration is exact. The discrepancy from E of this quantity is a stringent test of the accuracy of the calculated wave function. The H-square error for a normalized psi, defined by sigma(2)equivalent to , is also a severe test of the accuracy. Using these quantities, we have examined the accuracy of our wave function of a helium atom calculated using the free complement method that was developed to solve the Schrodinger equation. Together with the variational upper bound, the lower bound of the exact energy calculated using a modified Temple's formula ensured the definitely correct value of the helium fixed-nucleus ground state energy to be -2.903 724 377 034 119 598 311 159 245 194 4 a.u., which is correct to 32 digits.