  We calculate the linear and non-linear susceptibilities of periodic
longitudinal chains of hydrogen dimers with different bond-length alternations
using a diffusion quantum Monte Carlo approach. These quantities are derived
from the changes in electronic polarization as a function of applied finite
electric field - an approach we recently introduced and made possible by the
use of a Berry-phase, many-body electric-enthalpy functional. Calculated
susceptibilities and hyper-susceptibilities are found to be in excellent
agreement with the best estimates available from quantum chemistry - usually
extrapolations to the infinite-chain limit of calculations for chains of finite
length. It is found that while exchange effects dominate the proper description
of the susceptibilities, second hyper-susceptibilities are greatly affected by
electronic correlations. We also assess how different approximations to the
nodal surface of the many-body wavefunction affect the accuracy of the
calculated susceptibilities.
