If the non-local energy is strongly coupled to the expectation values of other observables via the trial/guiding wavefunction, then even though the non-local potential energy itself is a small fraction of the total energy, it is necessary to include it in the variance minimisation procedure. This can be achieved by storing all the information required to evaluate the change in the ratio of the wavefunction as the variational parameters change, at each of the grid points on which the original value of the non-local energy is stored. Schematically, one can write the total non-local energy for a single configuration as
All the other electrons in the ratio have been dropped from the notation and are assumed to be kept fixed. Eq.() can be simplified by using the fact that the non-local pseudopotential is relatively short ranged. Each electron only feels the effect of the non-local pseudopotential from one or two ions. The first two summations can therefore be replaced with a summation over hits. A hit is the event where an electron in the configuration is close enough to an ion to feel the effect of its non-local pseudopotential:
In a similar approach to that of Eq.() the contribution to the ratio for each grid point of each hit in each configuration from the function, u function and determinant are stored at the start of the optimisation procedure. For example, the contribution to each ratio of functions can summed over all the vectors in each star, s, such that
The ratio of the function at the points and can then be quickly reconstructed for each set of trial parameters from
A similar method of storage is adopted for the u function and the Slater determinant.