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In a previous paper, we have avoided an infinite order perturbation expansion and obtained a closed expression which consists of the second-order Møller-Plesset energy component together with a remainder term. The applicabilty of second-order many-body perturbation theory with a Møller-Plesset reference hamiltonian then rests upon the magnitude of this remainder term rather than the behaviour of the higher order terms on the perturbation series. In the present work, we show how this remainder term can be estimated by limited configuration interaction.

Many-body perturbation theory with a Møller-Plesset reference hamiltonian is the most widely used approach to the correlation problem in atomic and molecular systems. Second-order theory, which is often designated

By employing a hybrid partitioning scheme based on both the Rayleigh-Schrödinger and the generalized Brillouin-Wigner approaches, it has been shown [

In this work we obtain an estimate of the remainder term, ℜ, from limited configuration inter-action and, in particular, from the method most often designated CISD, configuration interaction with single and double excitations. In

Let the time-independent Schrödinger equation be written in the form
_{1} is the perturbation operator and

In our previous work [

Employing both the Rayleigh-Schrodinger choice for

The approximation to the total energy of an atomic or molecular system given by

In this paper, we consider the use of limited configuration interaction in obtaining an estimate for _{0} is the Brillouin-Wigner resolvent

In order to recover an approximation for the total energy in the form given in (22), we use the identity

The first and second terms on the left-hand-side of (44) are just the Møller-Plesset series through second order in the energy and so we have

Now we expect one- and two-body effects to be most significant and we, therefore, make the approximation
_{0} in equation (42), then equations (40), (41) and (42) provide a computational scheme which realizes the limited configuration interaction method in its CISD form. In this approximation the evalua-tion of the remainder term

In previous work [

In the present work, an analysis of the limited configuration interaction CISD method using the Brillouin-Wigner expansion has been used to obtain an estimate of the remainder term in

We note that the Brillouin-Wigner coupled cluster expansion could also be used to obtain an estimate of the remainder term

References

This work was carried out under the auspices of the EU COST D9/0001/97 and EU COST D23 programmes. IH acknowledges support under 1/4197/97 VEGA. SW acknowledges the support of EPSRC under Research Grant GR/M74627.