Importance sampling

But we have a simple form for the function, namely

$$\Psi_{C}=\prod_{i < j}\exp{f(r_{ij})},$$

and it is easy to see that for particle $k$ we have

$$\frac{\mathbf{\nabla}^2_k \Psi_C}{\Psi_C }= \sum_{ij\ne k}\frac{(\mathbf{r}_k-\mathbf{r}_i)(\mathbf{r}_k-\mathbf{r}_j)}{r_{ki}r_{kj}}f'(r_{ki})f'(r_{kj})+ \sum_{j\ne k}\left( f''(r_{kj})+\frac{2}{r_{kj}}f'(r_{kj})\right)$$

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