We study the reaction $e^+e^-tobar DD$ near threshold in the $^3P_0$ non-relativistic quark model, including as intermediate states the $J/psi$, $psi(2S)$, $psi(3770)$ and $psi(4040)$ mesons. The work reveals that experimental data strongly favor one
of the two $psi(2S)-psi(3770)$ mixing angles derived by fitting to the $e^-e^+$ partial decay widths of the $psi(2S)$ and $psi(3770)$ mesons. The meson $X(3940)$ as well as the resonance around 3.9 GeV observed by Belle and BaBar Collaborations in the reaction $e^+e^-rightarrow bar DD$ is unlikely to be a $cbar c$ $I^G(J^{PC})=0^-(1^{--})$ state.
