How accurately does the free complement wave function of a helium atom satisfy the Schrödinger equation?
The local energy defined by Hpsi/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 sigma2 identical with psi|(H-E)2|psi, 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 Schrödinger 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.
Nakashima
Hiroyuki
H
Quantum Chemistry Research Institute, JST, CREST, Kyodai Katsura Venture Plaza 106, Goryo Oohara 1-36, Kyoto 615-8245, Japan.
Nakatsuji
Hiroshi
H