Orbital forces and chemical bonding in density-functional theory: Application to first-row dimers

The local-density-functional description of chemical bonding in first-row homonuclear dimers is analyzed in terms of both static and dynamic orbital forces. The dynamic orbital force of the i-italicth molecular orbital is equal to the negative of the derivative of the one-electron energy epsilon-c/sub i-italic/ with respect to the p-italicth nuclear coordinate, i.e., -partialepsilon-c/sub i-italic//partialX/sub p/. The static orbital force is also equal to a derivative of the one-electron energy, but the differentiation is carried out with the orbital held fixed, i.e., (-partialepsilon-c/sub i-italic//partialX/sub p/)psi. It is shown that the static force is the orbital's contribution to the total Hellmann-Feynman force, whereas the dynamic force describes the change in the total force due to change in the orbital's occupation number. The chemical bond force in the first-row dimers is observed to be a delicate balance between bonding and antibonding orbital forces. Most of the bond force comes from the 2sigma/sub g-italic/ orbital and to a lesser extent from the 1..pi../sub u-italic/ state. The polarization of the core orbitals in N/sub 2/, O/sub 2/, and F/sub 2/ is found to originate indirectly through their interaction with the 3sigma/sub g-italic/ orbital. The dynamic orbital force gives accurate predictions about the change of equilibriummore » bond distances accompanying electronic ionization and excitation. The formalism and results are related to earlier Hartree-Fock studies.« less