  We present a generalization of the recently proposed variational cluster
perturbation theory to extended Hubbard models at half filling with repulsive
nearest neighbor interaction. The method takes into account short-range
correlations correctly by the exact diagonalisation of clusters of finite size,
whereas long-range order beyond the size of the clusters is treated on a
mean-field level. For one dimension, we show that quantum Monte Carlo and
density-matrix renormalization-group results can be reproduced with very good
accuracy. Moreover we apply the method to the two-dimensional extended Hubbard
model on a square lattice. In contrast to the one-dimensional case, a first
order phase transition between spin density wave phase and charge density wave
phase is found as function of the nearest-neighbor interaction at onsite
interactions U>=3t. The single-particle spectral function is calculated for
both the one-dimensional and the two-dimensional system.
