Foundation of Heisenberg Hamiltonians for systems with several active electrons per centre : acetylene and polyines

Abstract

A non-empirical Heisenberg Hamiltonian had been proposed for conjugated π systems from ab initio calculations on ethylene, and proved to be very efficient. Its theoretical foundation from the full Hamiltonian was evident from the concept of effective Hamiltonian and the use of Quasi-Degenerate-Perturbation Theory (QDPT), as shown by Anderson. When one wants to define a Heisenberg Hamiltonian for systems bearing two active electrons in two orthogonal Atomic Orbitals per centre, as in polyines, one may try to derive it from an accurate calculation on acetylene. The QDPT procedure does not converge, and it is shown that the direct use of the Bloch and des Cloizeaux definitions lead to ill-behaved effective Hamiltonians, which deviate strongly from a Heisenberg structure, and give erroneous results on C3H2 . A modified definition of the effective Hamiltonian is proposed, which recovers the form of a Heisenberg Hamiltonian and proves to give a reasonable spectrum of C3H2