Choose $n$ points $p_1,\ldots,p_n$ in the unit square $[0,1]^2\subset\mathbb{R}^2$ arbitrarily such that $D:=\mathop{\sum}\limits_{1\le i,j\le n}\frac{1}{dist(p_i,p_j)}$ is of the minimum value, where $dist(p_i,p_j)$ is the Euclidean distance between $p_i$ and $p_j$. The what's the magnitude of $D$ in $n$?

I have work out that $D\le\Omega(n\log(n))$ by construction.

Choose $n$ points $p_1,\ldots,p_n$ in the unit square $[0,1]^2\subset\mathbb{R}^2$ such that $D:=\mathop{\sum}\limits_{1\le i<j\le n}\frac{1}{dist(p_i,p_j)}$ is minimized, where $dist(p_i,p_j)$ is the Euclidean distance between $p_i$ and $p_j$. What is the magnitude of $D$ in $n$?

I have worked out that $D\le\Omega(n\log(n))$ by construction.