Intermediate Bracketing Theorems for Lower Bounds
- 1 May 1968
- journal article
- research article
- Published by AIP Publishing in The Journal of Chemical Physics
- Vol. 48 (9) , 4131-4133
- https://doi.org/10.1063/1.1669750
Abstract
A set of intermediate resolvents is formed from the truncated Hamiltonians of Bazley and Fox. On replacing the resolvent operator in Löwdin's bracketing theorem by these intermediate resolvents, one obtains lower‐bound expressions suitable for calculations involving molecules. This method is applied to the ground state of H2+ (exact energy ). The results are −1.15029 a.u. for a one‐term and −1.10438 a.u. for a two‐term truncated Hamiltonian.
Keywords
This publication has 11 references indexed in Scilit:
- High-Accuracy Upper and Lower Bounds for Eigenvalues Illustrated withPhysical Review Letters, 1967
- Lower-Bound Procedure for Energy Eigenvalues by the Partitioning TechniqueThe Journal of Chemical Physics, 1966
- Studies in Perturbation Theory. XI. Lower Bounds to Energy Eigenvalues, Ground State, and Excited StatesThe Journal of Chemical Physics, 1965
- Accurate Adiabatic Treatment of the Ground State of the Hydrogen MoleculeThe Journal of Chemical Physics, 1964
- Weinstein Calculation on Hydrogen Molecular IonThe Journal of Chemical Physics, 1964
- Lower bounds for the energy of H2+Proceedings of the Physical Society, 1964
- Lower Bounds for Energy Levels of Molecular SystemsJournal of Mathematical Physics, 1963
- Wave functions of the hydrogen molecular ionPhilosophical Transactions of the Royal Society of London. Series A, Mathematical and Physical Sciences, 1953
- On the Lower Bounds of Weinstein and Romberg in Quantum MechanicsPhysical Review B, 1938
- The theory of Rayleigh's principle as applied to continuous systemsProceedings of the Royal Society of London. Series A, Containing Papers of a Mathematical and Physical Character, 1928