With closed form formulae we can speed up the computation of the correlation. In our case we write it as $$ \Psi_C= \exp{\left\{\sum_{i < j}\frac{ar_{ij}}{1+\beta r_{ij}}\right\}}, $$ which means that the gradient needed for the so-called quantum force and local energy can be calculated analytically. This will speed up your code since the computation of the correlation part and the Slater determinant are the most time consuming parts in your code.

We will refer to this correlation function as \( \Psi_C \) or the linear Pade-Jastrow.