Recently, we proposed an iteration method for solving the eigenvalue problem of the time-independent Schrodinger equation [H. Meissner, E.O. Steinborn, Int. J. Quantum Chem., 61 (1997) 777]. The wave function expansion coefficients (WECs) are matrix elements of the wave operator. They are determined iteratively by utilizing a reference space, the concept of an effective Hamiltonian (in general), and the generalized Bloch equation. Here, in order to test the WEC iteration method, we use a special variant of this iteration method to calculate the (1)A(1) - B-3(1) energy splitting of CH2 and the ground state (1)Sigma(g)(+) potential energy surface of the van der Waals' molecule Be-2. This special variant leads to good results when compared with CI and CC calculations. (C) 1998 Published by Elsevier Science B.V. All rights reserved.