$\rho^{AIM}(\mathbf{r})$ are the CDDs sought, they cannot be used as input. The Hirshfeld method circumvents this problem by using spherically averaged reference state atomic CDDs $\rho_{X}^{\circ}(\mathbf{r})$. In the original paper by Hirshfeld the neutral atomic ground state is used as reference state.[@HirshfeldFL:1977TCA] When summing these isolated atomic CDDs over all AIM, one gets the so-called ‘*promolecular*’ CDD instead of the actual molecular CDD: $$\label{eq:promoldef}
\rho_{promol}(\mathbf{r})=\sum_{B}{\rho^{\circ}_{B}(\mathbf{r})}.$$ It is then assumed that the difference between this promolecular CDD and the actual molecular CDD has only little influence on the Hirshfeld weight . As a result one can write the CDD of an AIM $A$ as: $$\label{eq:Hir_chg_AIM}
\rho^{AIM}_{A}(\mathbf{r})=\frac{\rho^{\circ}_{A}(n_{A}^{\circ},\mathbf{r})}{\rho_{promol}(\mathbf{r})}\rho_{mol}(\mathbf{r})=w^{H}_{A}(\mathbf{r})\rho_{mol}(\mathbf{r}),$$ where the population of the atom $A$ is given by $n_{A}^{\circ}$. In the original Hirshfeld approach, neutral atoms were used as reference. This, however, has been identified by several authors to be a major weakness of the method as changing the choice of the promolecular atom charges can have a highly significant effect on the resulting AIM[@BultinckP:2007JCP_HirRef; @BaderRFWMattaCF:2004JPhysChemA; @BaderRFWMattaCF:2006JPhysChemA; @DavidsonERChakravortyS:1992TheorChimActa; @FranciscoEPendasAM:2007JPhysChemA] From eq. it is easy to understand that the resulting $\rho^{AIM}_{A}(\mathbf{r})$ will tend to be as similar to $\rho^{\circ}_{A}(n_{A}^{\circ},\mathbf{r})$ as possible[@AyersPW:2000JCP; @AyersPW:2002JCP; @BultinckP:2007JCP_HirRef], explaining why the Hirshfeld populations strongly depend on the choice of 