We consider the problem of building an effective Hamiltonian in a subset P of the full Hilbert space in the case where there is an overlap between the states in P and the states in its complement Q. In this case the projectors onto these subspaces are non-Hermitian and one has various possible effective Hamiltonians. We show how these can be constructed directly from the Schrodinger equation and relate them to projections of the Green function operator. In the context of a simple electron-transfer model we discuss the dependence of the matrix elements of the effective Hamiltonians on the distance between orbitals and on the choice of the tunneling energy parameter. We also investigate with what accuracy the effective Hamiltonians estimate the exact eigenenergies of the problem. (C) 2003 American Institute of Physics.