We adopt the Lorentz gauge to derive the non-local two-gluon vacuum expectation value (VEV) with translational invariance. By means of the obtained non-local two-gluon VEV, the leading nonperturbative QCD corrections to one gluon exchange quark-quark, quark-antiquark and qq-bar pair-excitation potentials are given by employing non-vanishing vacuum condensates of quarks and gluons to modify the free gluon propagator. The linear, cubic and Yukawa-type terms in quark-quark potential appear automatically. In the qq-bar pair-excitation potential with #omega#_q=0, the linear, square and cubic terms arise from the nonzero quark and gluon condensates.
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