cusp is defined by the equation (see, e.g., [@cusp]) $$\begin{aligned}
  \nu_{ab} = \frac{\langle \delta({\bf r}_{ab}) \frac{\partial}{\partial r_{ab}} \rangle}{\langle \delta({\bf r}_{ab}) \rangle} \label{cusp}.\end{aligned}$$ Numerical coincidence of the $\nu_{ab}$ and $\overline{\nu}_{ab}$ values is a good test for the overall quality of the wave functions constructed for different atomic and molecular systems.

It should be mentioned that the ‘classical’ definition of the cusp (or cusp-condition) given by Eq.(\[cusp\]) can be generalized to quantum mechanics in a number of different ways. To explain this let us introduce the following cusp-operator $$\begin{aligned}
  \hat{\nu}_{ab} = \frac{1}{\langle \delta({\bf r}_{ab}) \rangle} \delta({\bf r}_{ab}) \frac{\partial}{\partial r_{ab}} \label{cusp2}\end{aligned}$$ For the expectation values one finds $\nu_{ab} = \langle \Psi \mid \hat{\nu}_{ab} \mid \Psi \rangle$. Formally, we can consider the quantity $\langle \Psi_i 
\mid \hat{\nu}_{ab} \mid \Psi_j \rangle$, where $\Psi_i$ and $\Psi_j$ are the two different wave functions from the bound state spectrum. The last expression, however, is not symmetric upon the $i \leftrightarrow j$ substitution. Such a symmetry can be restored with the following redefinition of the cusp operator, Eq.(\[cusp2\]): $$\begin{aligned}
 \hat{\nu}_{ab} = \frac{1}{2 \langle \delta({\bf r}_{ab}) \rangle} \Bigl[ {}_{\leftarrow}\Bigl( \frac{\partial}{\partial r_{ab}}\Bigr) \delta({\bf r}_{ab}) 
 + \delta({\bf r}_{ab}) \Bigl(\frac{\partial}{\partial r_{ab}}\Bigr)_{\rightarrow} \Bigr] \label{cusp3}\end{aligned}$$ where the differential operator with the index ‘$\rightarrow$’ acts on 