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In this work we discuss the cooperative occurrence of instabilities in the Hartree-Fock (HF) approximation and linearized correlation models. Both breakdown phenomena can be analyzed via eigenvalues of characteristic matrices. The well known HF instabilities follow from a quasidegeneracy between the symmetry-adapted mean-field state and singly excited configurations. Quasi-degeneracies between the HF wave function and doubly excited configurations restrict the applicability of linearized correlation models. In the theoretical calculations the method of the local approach (LA) has been employed to derive the correlated ground state. For a system of the general topology XH 2  (X = C, Si, etc.) the bond orbital approximation (BOA) has been used to derive analytic formulae indicating the stability range of linearized correlation schemes. Numerical calculations on the basis of a simple model-Hamiltonian are given for the π systems C 2 H 4  and C 2 H 2 , respectively, which have been studied as a function of the CC bondlength. The comparison of the respective numerical data indicates that both breakdown phenomena are enhanced via coupling terms between strongly correlated bonds.

A Model Study of Instabilities Present in the Mean-Field Description and in Linearized Correlation Schemes