In a parallel development described in chapter 
a new
method for evaluating the expectation value of the Coulomb interaction
was introduced which relies on the short range of the
exchange-correlation hole [3]. This method allows accurate
results to be obtained without summing the interactions over periodic
images of the simulation cell, thereby reducing the computational cost
significantly and leaving the evaluation of the Jastrow factor as the
most time consuming part of the calculation. Therefore, it was decided
to seek a new form for u which is as accurate as the previous form
in Eq.(), yet convenient for optimisation purposes and can
be evaluated rapidly within a QMC calculation.