Analyzing the response of exchange-correlation potentials of chain-like molecules to electric fields by Kohn-Sham inversion and evaluation of the response within the random phase approximation

Kohn-Sham inversion based on CCSD(T) (coupled cluster singles doubles with perturbative triples) electron densities is employed to calculate the response of the exchange-correlation (XC) potential to an external electric field for hydrogen chains of varying length with alternating H-H distances of 2 and 3 Bohr in order to provide reference data and to analyze the response of the XC potential. The exchange part of the exact XC potential exhibits an ultra-nonlocal field-counteracting behavior, known from calculations using the exact-exchange-only (EXX) optimized effective potential (OEP) method. The correlation part also counteracts an applied field, but is significantly smaller. The magnitude of the correlation contribution grows with chain length, indicating its increasing importance in the description of the electric response for spatially extended systems. Interestingly, the correlation potential from the random phase approximation (RPA) OEP method, i.e., from a self-consistent RPA method, which closely approximates the exact correlation potential in the absence of an electric field, instead amplifies the applied field. Despite this, the RPA-OEP method substantially outperforms EXX-OEP in predicting optical properties such as polarizability. This improvement is due to the accurate XC potentials and electron densities it yields in the absence of an electric field, as well as its reasonably good response to external field within the interior of the hydrogen chains, which benefits from error cancelations between exchange and correlation. In addition, we analyze the quadratic response of the XC potential to the external field, which exhibits a non-trivial collective behavior, with a magnitude increasing with chain length.