From ab initio calculations to model Hamiltonians: The effective Hamiltonian technique as an efficient tool to describe mixed-valence molecules

The excitation spectrum of the Creutz-Taube molecule in slightly modified form, that is, [HCN (NH3)(4) Ru pz Ru (NH3)(4) NCH](5+), where pz = pyrazine, is calculated with wave function-based ab initio methods. An effective matrix is built using Bloch's procedure in a model space generated by the d orbitals of the ruthenium atoms and the lowest pi* orbital of the bridging ligand. A model Hamiltonian is deduced. The effect of the mixing of the orbitals is discussed. A large part of the spectrum (33 states) can be well described in terms of two parameters: t, the transfer integral between a d orbital of the ruthenium and the pi* orbital, and U, the excitation energy from the d orbital to the pi* orbital. These parameters have been estimated at different levels of correlation: the dynamical correlation mostly affects U, which is negative without correlation and becomes almost zero with correlation. This article shows that a two-band Hubbard Hamiltonian is an excellent model for describing bridged mixed-valence molecules and proposes a procedure that allows the determination of the parameters of this model Hamiltonian by wave function-based ab initio calculations.