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The di-electron widths of $\psi(4040)$, $\psi(4160)$, and $\psi(4415)$, andtheir ratios are shown to be in good agreement with experiment, if in all casesthe $S-D$ mixing with a large mixing angle $\theta\approx 34^\circ$ is taken.Arguments are presented why continuum states give small contributions to thewave functions at the origin. We find that the Y(4360) resonance, considered asa pure $3 {}^3D_1$ state, would have very small di-electron width,$\Gamma_{ee}(Y(4360))=0.060$ keV. On the contrary, for large mixing between the$4 {}^3S_1$ and $3 {}^3D_1$ states with the mixing angle $\theta=34.8^\circ$,$\Gamma_{ee}(\psi(4415))=0.57$ keV coincides with the experimental number,while a second physical resonance, probably Y(4360), has also a rather large$\Gamma_{ee} (Y(\sim 4400))=0.61$ keV. For the higher resonance Y(4660),considered as a pure $5 {}^3S_1$ state, we predict the di-electron width$\Gamma_{ee}(Y(4660))=0.70$ keV, but it becomes significantly smaller, namely0.31 keV, if the mixing angle between the $5 {}^3S_1$ and $4 {}^3D_1$ states$\theta=34^\circ$. The mass and di-electron width of the $6 {}^3S_1$ charmoniumstate are calculated.

The $\mathbf{S}-\mathbf{D}$ mixing and di-electron widths of higher charmonium $\mathbf{1^{--}}$ states