Strong bonds

The electrostatic energy reads $V = \frac{1}{4 \pi \varepsilon} \sum_{j = 1}^n \frac{q_0 q_j}{|\vec r_0 - \vec r_j|} = \frac{e^2}{4 \pi \varepsilon d} \underbrace{ \left[ \sum_{j = 1}^{n-1} \frac{1}{r_{0j}} - n \right] }_{z_n}$ with the bond lenght $d$ , elemental charge $e$ , the coordination number $n$ and the relative distance $r_{0j}$ (in units of $d$ ). We evaluate the dimensionless factor $z_n$ for each molecule: $\begin{aligned} z_1 &= -1 \\ z_2 &= \frac{1}{2} - 2 = -1.5 \\ z_3 &= \frac{1}{\sqrt{3}} + \frac{1}{\sqrt{3}} - 3 \approx -1.85 \\ z_4 &= \frac{1}{\sqrt{2}} + \frac{1}{\sqrt{2}} + \frac{1}{2} - 4 \approx -2.59 \\ z_5 &= \frac{1}{2 \sin(36^\circ)} + \frac{1}{2 \sin(36^\circ)} + \frac{1}{2 \sin(72^\circ)} + \frac{1}{2 \sin(72^\circ)} - 5 \approx - 2.25 \end{aligned}$ Therefore, the case $n = 4$ is energetically most favourable.