-Thus, on the timescale of electronic motion the ions appear at fixed positions and, on the other way round, for the nuclei the electrons appear blurred in space adding an extra term to the ion-ion potential.
-The simplified Schr\"odinger equation is rewritten without the kinetic energy of the ions and its positions enter as fixed parameters.
+Thus, on the timescale of electronic motion the ions appear at fixed positions.
+On the other way round, on the timescale of nuclear motion the electrons appear blurred in space adding an extra term to the ion-ion potential.
+The simplified Schr\"odinger equation no longer contains the kinetic energy of the ions.
+The momentary positions of the ions enter as fixed parameters and, therefore, the ion-ion interaction may be regarded as a constant added to the electronic energies.
+The Schr\"odinger equation describing the remaining electronic problem reads
+\begin{equation}
+\left[-\frac{\hbar^2}{2m}\sum_j\nabla^2_j-
+\sum_{j,l} \frac{Z_le^2}{|\vec{r}_j-\vec{R}_l|}+
+\frac{1}{2}\sum_{j\neq j'}\frac{e^2}{|\vec{r}_j-\vec{r}_{j'}|}
+\right] \Psi = E \Psi
+\text{ ,}
+\end{equation}
+where $Z_l$ are the atomic numbers of the nuclei and $\Psi$ is the many-electron wave function, which depends on the positions and spins of the electrons.
+There is only a parametrical dependence on the ionic coordinates $\vec{R}_l$.