Within the framework of the Poggio-Schnitzer flavor-independent static-potential model with long-distance vacuum-polarization correction, we analyze the Lorentz-Dirac structure of the confinement potential with reference to the charmonium hyperfine splittings. In view of the questionable existence and/or doubtful identity of the $X(2830)$ and $\ensuremath{\chi}(3455)$ states, we give preference to the Lorentz-Dirac character of the confinement potential in the form of an approximately equal admixture of scalar and vector components with no anomalous moment. This in turn predicts the $^{1}S_{0}$ partners of $\ensuremath{\psi}$ and ${\ensuremath{\psi}}^{\ensuremath{'}}$ to be near the 3.0- and 3.6-GeV mass regions, respectively. This also suggests the $^{1}P_{1}$ state of charmonium is to be found above the $^{3}P_{0}$ state near the mass region of 3.48 GeV.