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- W1980629447 abstract "The exact Hamiltonian for H2 is averaged over trial functions composed of molecular orbitals which are defined by a model suggested by the authors [J. Chem. Phys. 33, 1803 (1960)]. The three trial functions studied are (a) the single configuration type, (b) a two-configuration type including the σu orbital defined by the model, and (c) a function composed of a product of the lowest σg orbitals multiplied by a correlation function including one term having σu symmetry. The results from the single configuration function indicate that the lowest σg molecular orbital is a good approximation to an SCF orbital. The configuration interaction (CI) calculation indicates that a CI expansion based on these orbitals will converge very slowly to an eigenfunction of H2. Adding a one-term correlation function gave significant improvement, and the construction of a more complicated correlation function, by means of the variation principle, would undoubtedly lead to a good approximation to the exact eigenfunction. Rather than proceed along these lines, analysis of the various average values contributing to the total energy and the corresponding values predicted by the model suggests a different approach. It is found that, at the equilibrium internuclear distance, potential energy terms computed from the model agree with the exact values much better than average values based on the three trial functions, while the kinetic energy is much more poorly represented. This indicates that calculation of the total energy from the potential energy by the virial theorem would give better results than using the less exact kinetic energy term to construct the total energy and, at the same time, provide a means of calculating the total energy without knowledge of the correlation function. A constraint on the average of the exact Hamiltonian is introduced to provide a rigorous foundation for the above observation, and an appropriately modified virial equation is derived. An approximate solution of this equation is investigated. It is found that a complete solution is not possible without knowledge of the exact energy at one point." @default.
- W1980629447 created "2016-06-24" @default.
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- W1980629447 date "1963-05-15" @default.
- W1980629447 modified "2023-09-24" @default.
- W1980629447 title "Molecular Orbitals for H2 Based on Central Potentials. Average Hamiltonian and Correlation Energy" @default.
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- W1980629447 doi "https://doi.org/10.1063/1.1733512" @default.
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