Error Bounds to Expectation Values of One-Electron Operators Using Hartree–Fock Wavefunctions
- 15 December 1969
- journal article
- conference paper
- Published by AIP Publishing in The Journal of Chemical Physics
- Vol. 51 (12) , 5650-5658
- https://doi.org/10.1063/1.1671994
Abstract
The properties of Hartree–Fock wavefunctions are used to derive a number of new expressions for upper and lower bounds to the true expectation value of an arbitrary one‐electron operator. These expressions depend on the prior knowledge of upper and lower bounds to the overlap between the Hartree–Fock and true wavefunctions. A new extrapolation method is presented to obtain accurate bounds to these overlaps. A critical study is made of the effectiveness and accuracy of these new error bounds as applied to the systems He, He2, LiH, and Be.Keywords
This publication has 50 references indexed in Scilit:
- Upper and lower bounds to polarizabilities and van der Waals forces I. General theoryInternational Journal of Quantum Chemistry, 1968
- Error Bounds for the Long-Range Forces between AtomsThe Journal of Chemical Physics, 1968
- Upper Bounds for Errors of Expectations in the Few-Body ProblemPhysical Review B, 1967
- Electronic Structure of the First Excited State of CO. I. SCF Wavefunction Calculated in the Restricted Hartree—Fock FormalismThe Journal of Chemical Physics, 1966
- Use of Numerical Integration in the Computation of the Expectation Value of H2 with Applications to H2The Journal of Chemical Physics, 1966
- Electronic Structure of Diatomic Molecules. III. A. Hartree—Fock Wavefunctions and Energy Quantities for N2(X1Σg+) and N2+(X2Σg+, A2Πu, B2Σu+) Molecular IonsThe Journal of Chemical Physics, 1966
- Electronic Structure of CO and BFThe Journal of Chemical Physics, 1965
- Error estimates for atomic and molecular quantitiesProceedings of the Physical Society, 1965
- Error bounds in the Rayleigh-Ritz approximation of eigenvectorsJournal of Research of the National Bureau of Standards Section B Mathematics and Mathematical Physics, 1960
- Note on an Approximation Treatment for Many-Electron SystemsPhysical Review B, 1934