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 νxc 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 νxc, one-electron perturbation theory, and Krieger-Li-Iafrate (KLI) calculations---it is shown that a field-counteracting term emerges in the ``response'' part νᵣₑₛₚ of νxc. For systems A₂ of two open-shell units A, with H₂ as a prototype, the left-right electron Coulomb correlation generates a step in νᵣₑₛₚ, which effectively compensates for an electric field in the limit of large interatomic distances. For systems Aₙ of closed-shell units A, with He₂ and H₂+H₂ as prototypes, a field-counteracting term is generated in νᵣₑₛₚ by the Pauli repulsion of electrons in the occupied Kohn-Sham orbitals. An analytical estimate of the field-counteracting step is obtained for He₂ with the exchange-only KLI model of νᵣₑₛₚ, and the existence of an ultranonlocal linear term in νᵣₑₛₚ is established with KLI calculations on the prototype molecular chain H₁₈.