Details of the FCIQMC algorithm are best obtained from various publications on the method, which include:

Briefly, the FCIQMC method involves discretizing the wavefunction amplitudes over the full Slater
determinant space into a number of signed `walkers'. These walkers represent a coarse-grained
snapshot of the wavefunction at any given instant. Through a population dynamics of these
walkers evolving in imaginary-time, the ground-state energy and wavefunction can be resolved to arbitrary
accuracy (in principle FCI quality), in a time-averaged fashion, without the need for any explicit
diagonalization steps. The
master equations which are stochastically realized and govern this dynamic, are given by

However, in a modification to the algorithm which allows for a generally smooth convergence to the FCIQMC result with
increasing walker number, the sum in Eq. 56 is truncated, such that when considering a configuration whose population
is zero, this sum then only runs over those configurations who are deemed `initiator' configurations. These initiator configurations
are ones which have an instantaneous population of above a parameter , or are the chosen `reference' configuration.
This modification to the algorithm rigorously converges to the full FCIQMC result in the limit of a large number of
walkers, or as
, and is dubbed `-FCIQMC'. This is the default algorithm used in the
`FCIQMC` module.

Note that the choice of reference configuration, or indeed orbital space, should be independent of the final energy obtained, and the method thus constitutes a multiconfigurational correlation treatment, suitable for strongly-correlated problems. However, the choice of reference configuration and orbital space may affect rate of convergence and random error decay.

molpro@molpro.net 2018-10-21