We carry out calculations of selected transition metal-oxygen molecules within density functional theory, post-Hartree-Fock, and quantum Monte Carlo (QMC) methods. Transition metal-oxygen systems have competing electron correlation and exchange effects and require accurate treatment of both of these effects. We analyze the biases of the mentioned methods and their impacts on the electronic structure. We evaluate binding energies and compare the accuracy of various approaches including single and multi-reference trial wave functions in QMC. (C) 2003 Elsevier Science B.V. All rights reserved.