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Error bound for the Hartree-Fock energy of atoms and molecules. (English) Zbl 0771.46038

The ground state energy \(E_ Q\) of the Hamiltonian \[ H_ N(\underline {Z},\underline {R})=\sum_{i=1}^ N \left(-\Delta_ i-\sum_{j=1} ^ K {{Z_ j} \over {| x_ j-R_ j|}}\right)+ \sum_{1\leq i<j}^ N {1\over {| x_ i-x_ j|}} \] where \(\underline {Z}=[Z_ 1,\dots,Z_ K],\;\underline {R}=[R_ 1,\dots,R_ k]\), is investigated. The error of the Hartree-Fock energy \(E_{HF}\) is estimated when \(Z\to \infty\), \(N\approx Z\), \(\underline{Z}/Z\) fixed, \(\min| R_ i-R_ j| \geq CZ^{-2/3+\varepsilon}\) \((Z=\sum_{j=1}^ K Z_ j)\). For any \(0<\delta< 2/21\) there exists a \(C_ \delta>0\) such that \(| E_ Q-E_{HF}|\leq C_ \delta Z^{5/3-\delta}\).

MSC:

46N50 Applications of functional analysis in quantum physics
81V45 Atomic physics
81V55 Molecular physics
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