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We introduce here a new partitioning of the Hamiltonian in calculating pair-correlation energies using many-body perturbation theory, by which we are able to eliminate the off-diagonal particle-hole (p-h) ladders exactly to all orders in the perturbation expansion. In this formulation, the particle states turn out to be different for each distinct pair of hole states in the correlation energy calculation. We have also included the contributions of the diagonal particle-particle (p-p) and hole-hole ladders exactly to all orders. The effect of the off-diagonal p-p ladders has been estimated for each pair by computing the third-, foruth- and fifth-order energies. For highly symmetric systems the present partitioning yields in general symmetry-broken orbitals. Here one may use an average kind of partitioning for all the partners of the degenerate sets, which restores the symmetry and at the same time ensures cancellation of the p-h ladders exactly at the lowest order and approximately at the higher orders. Results are presented for a selection of 6π-electron conjugated systems. The correlation energy for each pair is in excellent agreement with that obtained from a partial CI calculation involving all double excitations from this pair. The advantages of implementing the present scheme in larger systems has been discussed.

In this communication we discuss a method of incorporating corrections to the coupled Hartree–Fock (CHF) formalism by introducing the so-called “rearrangement effect.” In this we take account of the relaxation of the core orbitals when excitations from a starting Hartree–Fock wave function occur. The magnitude of this correction numerically is found to be quite significant for the polarizabilities of two-electron atomic systems, results for which are reported.

In this paper we present a non-perturbative approach to the calculation of correlation energies of open-shell systems. The formulation utilizes an Ursell-type expansion about a multi-determinant starting wavefunction. We have proved a theorem which enables us to derive an effective hamiltonian for the system consisting entirely of linked terms. In the symmetry-degenerate case this effective hamiltonian acts within the subspace of a set of symmetry-degenerate functions, and generates the energy eigenvalues of the system. The present theory has been cast in a diagrammatic language which facilitates the analysis of the correlation problem. The workability of the theory has been tested on a 4 π electron problem, transbutadiene, for which we have calculated the lowest π-π* singlet and triplet energies. The agreement between the results of the present theory and that found from a full CI calculation is excellent. The desirable feature of the theory is that the effective hamiltonian is energy-independent. We hav...

In this paper we explore the feasibility of widening the scope of the non-perturbative open-shell many-body formalism recently developed by us [1], which utilizes an Ursell type of cluster expansion about certain starting wavefunctions spanning a model space. We show that, by generalizing the definition of the cluster expansion operator, we can incorporate into the model space (a) determinants differing widely in energy and (b) determinants differing in their number of electrons. This flexibility is useful for the calculation of difference energies of interest, like transition energies and ionization potentials of atomic and molecular systems. The generalized scheme has been tested on the 4π-electron problem trans-butadiene for which, by choosing a very general model space, we have calculated the energies of the ground, the lowest π-π* singlet and triplet and the first ionization potential by choosing a single composite cluster expansion operator for all states. Results for some more restricted choice of ...

In this paper a fully coupled variation-perturbation theory has been introduced for handling open-shell atomic systems in the presence of static perturbations. The static dipolar and quadrupolar polarizabilities and shielding factors for Li, Be+, B2+, B, C+, Na and Al have been calculated and compared with available results. Important sources of discrepancies in previous calculations of shielding factors have been noticed and critically examined. The dipolar shielding factors calculated in this paper show satisfactory agreement with the theoretical N/Z ratio. In the absence of any theoretical test for the quadrupolar shielding factor, the accuracy of the calculations of γ∞, should be judged in the light of the accuracy of the corresponding β∞ values.

A variational formulation of the Hartree–Fock–Roothaan (HFR) theory for open shell ions in presence of time dependent perturbations is presented. The theory has been used to calculate the dynamic polarizabilities of the first three ions of the Li sequence. The polarizability values, extrapolated to zero frequency, show good shell by shell agreement with the corresponding static results. The polarizability graphs display resonance behaviour at the transition frequencies of the ions, and a study of these points leads to analytic HF wave functions for their low lying excited states. The calculated transition frequencies are in excellent accord with the experimental values. The calculated oscillator strengths for the 2s → np transitions are in reasonable agreement with the extensive multiconfiguration calculations of Weiss and the available experimental results.

The quadrupolar and octupolar distortion of the ions in the He-sequence caused by an external electro–magnetic field has been studied by a variation–perturbation method in the Hartree–Fock scheme. For certain frequencies singularities appear in the response of the system to the perturbation. Approximate representations for the excited d and f states have been obtained from a study of these resonances. Such a perturbation calculation has the advantage that representations of the different excited states are obtained independently. The orthogonality to all the lower lying levels of the same symmetry is not required. The only source of inaccuracy implicit in the procedure lies in the improper consideration of the inter-electronic interaction. This is corrected for by an independent calculation, which is again formulated in terms of a perturbation treatment. The resulting wave functions for the excited states are accurate in the Hartree–Fock model. Expectation values of several operators have been calculated with these corrected wave functions.

In this note, the authors’ recently developed non-perturbative open-shell theory is adapted for direct calculation o f ionisation potential and excitation energy of m any-electron systems. The H -F ground state is used as the “vacuum ” or “ core” in order to achieve a transparent separation o f the ground state energy. An application to a simple 4 π-electron system is discussed as an illustration o f the workability of the theory.