Polarizabilities of Polyacetylene from a Field-Counteracting Semilocal Functional

Predicting the polarizabilities of extended conjugated molecules with semilocal functionals has been a long-standing problem in density functional theory. These difficulties are due to the absence of a term in the typical semilocal Kohn-Sham exchange potentials that has been named "ultranonlocal". Such a term should develop in extended systems when an external electric field is applied, and it should counteract the field. We calculate the polarizabilities of polyacetylene molecules using the recently developed extended Becke-Johnson functional. Our results show that this functional predicts the polarizabilities with much better accuracy than typical semilocal functionals. Thus, the field-counteracting term in this functional, which is semilocal in the Kohn-Sham orbitals, can realistically describe real molecules. We discuss approaches of constructing an energy functional that corresponds to this potential functional, for example, via the Levy-Perdew virial relation.