How Accurately Does the Free Complement Wave Function of a Helium Atom Satisfy the Schroedinger Equation?

Journal Article · Fri Dec 12 04:00:00 EST 2008 · Physical Review Letters

DOI:https://doi.org/10.1103/PHYSREVLETT.101.240406· OSTI ID:21179972

Nakashima, Hiroyuki; Nakatsuji, Hiroshi ^[1]

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1. Quantum Chemistry Research Institute, JST, CREST, Kyodai Katsura Venture Plaza 106, Goryo Oohara 1-36, Nishikyo-ku, Kyoto 615-8245 (Japan)

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}{sup 2}{identical_to}<{psi}|(H-E){sup 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 Schroedinger 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.

• OSTI ID: 21179972
• Journal Information: Physical Review Letters, Journal Name: Physical Review Letters Journal Issue: 24 Vol. 101; ISSN 0031-9007; ISSN PRLTAO
• Country of Publication: United States
• Language: English

Related Subjects

71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
GROUND STATES
HELIUM
SCHROEDINGER EQUATION
VARIATIONAL METHODS
WAVE FUNCTIONS