Symmetry breaking in the Hartree–Fock approximation for binuclear transition metal compounds—a theoretical investigation based on a variable model operator

The validity of the Hartree–Fock ( HF ) approximation in bis(π‐pentadienyl)dinickel ( 1 ) and in cyclopentadienyl‐allyl‐cyclobutadiene‐dinickel ( 2 ) has been investigated by means of the Thouless instability conditions in the computational framework of a variable model Hamiltonian. Singlet, nonsinglet (triplet), and nonreal instabilities in 1 and 2 have been studied as a function of the one‐electron resonance integral β   μ v ABand as a function of the one‐ and two‐center elements of the electron–electron interaction. The one‐center integrals of Coulomb (γ   μ v AA ) and exchange‐type ( K   μ v AA ) have been modified by a multiplicative factor; the two‐center integrals (γ   μ v AB ) have been calculated by means of an exponential interpolation formula with a variable decay amplitude. Additionally the Thouless conditions have been studied for nuclear deformations. The stability domain of the HF solution in the model space spanned by the variable INDO Hamiltonian has been analyzed. The nature of the many‐body interactions in the unstable region depends strongly on the parametrization of the model operator. HF instabilities in the high‐density region (long‐range forces) of 1 have their origin in individual particle–hole fluctuations while negative roots for short‐range forces (low‐density region) are similar to collective excitations in many‐body systems (strong off‐diagonal coupling). The opposite behavior is encountered in the Ni complex 2 . The physical origin of these different types of correlation processes are analyzed in a simple two‐electron two‐orbital model. The nature of the HF fluctuations in 1 and 2 , the importance of spatial and spin correlation, and the coupling of symmetry breaking of the electronic wave function with nuclear deformations are compared with the nature of phase transitions in solid‐state systems.