Origin of the field-counteracting term of the Kohn-Sham exchange-correlation potential of molecular chains in an electric field

The origin and the mechanisms responsible for an ultranonlocal field-counteracting term in the Kohn-Sham exchange-correlation potential ${\nu }_{\mathrm{xc}}$ of molecular chains in an external electric field are established for prototype systems. Using various analysis tools—conditional probability amplitude analysis, construction of the (nearly) exact ${\nu }_{\mathrm{xc}},$ one-electron perturbation theory, and Krieger-Li-Iafrate (KLI) calculations—it is shown that a field-counteracting term emerges in the “response” part ${\nu }_{\mathrm{resp}}$ of ${\nu }_{\mathrm{xc}}.$ For systems $A_2$ of two open-shell units A, with ${\mathrm{H}}_2$ as a prototype, the left-right electron Coulomb correlation generates a step in ${\nu }_{\mathrm{resp}},$ which effectively compensates for an electric field in the limit of large interatomic distances. For systems $A_n$ of closed-shell units A, with ${\mathrm{He}}_2$ and ${\mathrm{H}}_2{+\mathrm{H}}_2$ as prototypes, a field-counteracting term is generated in ${\nu }_{\mathrm{resp}}$ by the Pauli repulsion of electrons in the occupied Kohn-Sham orbitals. An analytical estimate of the field-counteracting step is obtained for ${\mathrm{He}}_2$ with the exchange-only KLI model of ${\nu }_{\mathrm{resp}},$ and the existence of an ultranonlocal linear term in ${\nu }_{\mathrm{resp}}$ is established with KLI calculations on the prototype molecular chain ${\mathrm{H}}_{18}.$