Direct Calculation of Approximate Natural Orbitals and Natural Expansion Coefficients of Atomic and Molecular Electronic Wavefunctions. II. Decoupling of the Pair Equations and Calculation of the Pair Correlation Energies for the Be and LiH Ground States

Starting from the integro‐differential equations satisfied by the natural orbitals (NO's) in the framework of the antisymmetrized‐product‐of‐strongly‐orthogonal‐geminals (APSG) approximation, a set of decoupled equations for the different electron pairs is derived, which corresponds to the physical model of independent electron pairs in the Hartree‐Fock field of the other electrons. These simplified equations lead to an easily practicable computational scheme which furnishes directly the correlation energy of the different pairs and a wavefunction, which is an antisymmetrized product of geminals which are, however, no longer strongly orthogonal in the rigorous sense. The total intrapair correlation energy, which is defined as the energy expectation value (with respect to this wavefunction) minus the Hartree‐Fock energy, differs from the sum of the pair correlation energies by a correction term, the magnitude of which depends on the highest occupation number of a weakly occupied NO. In the Be ground state,...

[1]  M. Krauss,et al.  Pair Correlations in Closed‐Shell Systems , 1964 .

[2]  H. Levine,et al.  Many‐Electron‐Theory ab Initio Calculation for the Be Atom , 1965 .

[3]  Klaus Ruedenberg,et al.  Localized Atomic and Molecular Orbitals , 1963 .

[4]  W. Brown,et al.  Perturbation theory of constraints - Application to a lithium hydride calculation , 1966 .

[5]  O. Sǐnanoğlu,et al.  Many‐Electron Theory of Atoms and Molecules. II , 1962 .

[6]  Enrico Clementi,et al.  Correlation Energy in Atomic Systems. IV. Degeneracy Effects , 1966 .

[7]  A. C. Wahl,et al.  Extended Hartree—Fock Wavefunctions: Optimized Valence Configurations for H2 and Li2, Optimized Double Configurations for F2 , 1966 .

[8]  A. Weiss.  Configuration Interaction in Simple Atomic Systems , 1961 .

[9]  H. Shull,et al.  Approximate Natural Orbitals for Four‐Electron Systems , 1965 .

[10]  R. Brout.  VARIATIONAL METHODS AND THE NUCLEAR MANY-BODY PROBLEM , 1958 .

[11]  Darwin W. Smith,et al.  Natural Orbitals and Geminals of the Beryllium Atom , 1965 .

[12]  W. Kutzelnigg,et al.  On the solution of the quantum mechanical two-electron problem by direct calculation of the natural orbitals , 1966 .

[13]  C. Edmiston.  Relation of Sinanoğlu's Theory of ``Exact Pairs'' to the First Iteration, beyond SCF, in Separated-Pair Theory , 1963 .

[14]  Darrell D. Ebbing,et al.  Separated‐Electron‐Pair Model: Application to the π‐Electronic Structure of the Ground State of Benzene , 1966 .

[15]  M. Krauss,et al.  Pseudonatural Orbitals as a Basis for the Superposition of Configurations. I. He2 , 1966 .

[16]  Werner Kutzelnigg,et al.  Direct Determination of Natural Orbitals and Natural Expansion Coefficients of Many‐Electron Wavefunctions. I. Natural Orbitals in the Geminal Product Approximation , 1964 .