  The long-range correlation energies and the off-diagonal interactions are
studied and a general formula for correlation energy $E_c$ of the $\pi$
electron systems is given, which is beyond the nearest-neighbor
electron-electron interactions and includes the off-diagonal interactions. It
is found that the effects of the off-diagonal interactions $W$ and $X$ on the
correlation energies are opposite, but the influence of $X$ on the correlation
energies is much stronger than that of $W$ on the correlation energies, and the
correlation energies decrease with increasing the screening effect.
