Understanding and correcting the self-interaction error in the electrical response of hydrogen chains

Semilocal density functionals such as the local-spin-density and generalized-gradient approximations are known to overestimate the polarizabilities and especially the hyperpolarizabilities of long-chain molecules, the latter by as much as a factor of 10 or more in model hydrogen chains. These quantities are much better predicted by exact-exchange methods such as Hartree-Fock or optimized effective potential. We show here that the semilocal functionals, after full or scaled-down Perdew-Zunger self-interaction correction (SIC), are about as good as the exact-exchange methods for these quantities. As is the case for the exact-exchange methods, SIC is fully nonlocal and exact for all one-electron densities, and (more relevantly to the electrical response) tends to maintain an integer number of electrons on each ${\mathrm{H}}_2$ chain unit to a greater extent than the semilocal functionals do. In this study, the SIC energy is minimized directly, without an optimized effective potential.

Figure 1

(Color online) Hyperpolarizability (in ${10}^{-3}\mathrm{a.u.}$) vs chain length $n$ for hydrogen chains ${\mathrm{H}}_{2n}$. If there were no interaction and no charge transfer between ${\mathrm{H}}_2$ chain units, then the energy, polarizability, and hyperpolarizability would all be proportional to the number of such units, $n$.