Decomposition of the chemisorption bond by constrained variations: Order of the variations and construction of the variational spaces

Constrained variations provide a way to analyze electronic wave functions and to theoretically decompose the chemical bond into contributions from different bonding mechanisms. The constrained space-orbital variation method has been used extensively to decompose the chemisorption bond for adsorbates on surfaces into, in particular, intraunit polarizations and interunit donations or covalent bonding. The results obtained for different orders of the intraunit and interunit constrained variations are compared for the representative examples of CO/Cu and O/Cu. For CO/Cu, both orders indicate the same dominant bonding mechanism, but for O/Cu they give very different views of the importance of the Cu 3d contribution to the Cu–O covalent bond. When the results for the two orders are not the same, a different division of the variational space for the constrained variations is needed. An appropriate division of the space for the Cu–O bond into contracted orbitals and diffuse orbitals is described.