A general formula of the long-range correlation energy Ec for the π electron systems is given, which includes diagonal interactions and off-diagonal interactions and we put forward to a correlation Hamiltonian at the first time. It is found that the effects of the off-diagonal interactions W and X on the correlation energies are opposite. The effect of W is to increase the correlation energies, but the effect of X is being counteracted by the integral term J due to |X|～|J |. The long-range correlation energies decrease with increasing the screening effect. At normal screening, the influence of W on the correlation energies can be neglected.