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.