Orbital structure of the Kohn-Sham exchange potential and exchange kernel and the field-counteracting potential for molecules in an electric field

Exchange-only Kohn-Sham (KS) theory is developed based on a physically motivated common energy denominator approximation for the orbital Green's function G₈. An explicit expression for the exchange potential vₗ in terms of the occupied KS orbitals is obtained via the analytical inverse of the resulting density response function ₒ, with vₗ being subdivided into the Slater potential vₒ and the ``response'' potential vₑ₄ₒ₏. The latter exhibits a characteristic orbital structure with ``diagonal'' contributions from the densities |₈|^2 of the occupied KS orbitals as well as ``off-diagonal'' ones from the occupied-occupied orbital products ₈₉^*. An expression for the response part fₑ₄ₒ₏ of the exchange kernel is derived. It is established for the case of a symmetric molecular chain in an applied electric field that the kernel derived from the Krieger-Li-Iafrate potential with the Sharp-Horton approximation for G₈ fails to produce the field-counteracting potential vₑ₄ₒ₏, which is lacking in local-density and generalized-gradient approximations but which is required to obtain realistic (hyper) polarizabilities. On the contrary, as is shown in the case of He₂, the present kernel fₑ₄ₒ₏ generates a field-counteracting potential vₑ₄ₒ₏^ (fc). The field-counteracting exchange effect is seen to arise from the spatial dependence of the cross product ₆ₔ^-1 of the symmetric and antisymmetric orbitals which is coupled with an integral over itself times. Similar ``self-coupling'' terms are indicated in the general case of a symmetric molecular chain.