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

Long-range correlation energies and off-diagonal interactions for the $\pi$ electronic systems