28.6 FCIQMC output

The estimate of the energy is extracted from the simulation in various ways. Once in variable shift phase of the calculation, where the walker number is stabilised (column 5 in output and FCIQMCStats file), the shift parameter (column 2) should vary about the correlation energy ($S$ in Eq. 56) after equilibration. Alternatively, a projected energy estimate can be obtained through the projection of the walker distribution onto a reference configuration (column 9, 11 and 23 – see below for details), as

$\displaystyle E_{{\textrm proj}}$ $\textstyle =$ $\displaystyle \frac{\langle D_0 \vert H \vert \Psi_{\textrm FCIQMC} \rangle}{\langle D_0 \vert \Psi_{\textrm FCIQMC} \rangle}$ (55)
  $\textstyle =$ $\displaystyle E_0 + \sum_j \frac{n_j}{n_0} \langle D_0 \vert H \vert D_j \rangle$ (56)

It is clear that this estimate is sensitive to the number of walkers on the reference configuration ($D_0$), which is why the use of the PROJE-CHANGEREF option is encouraged if it is unclear which the most highly weighted configuration is from the outset of calculation. Initially, this reference will be chosen as the Hartree–Fock determinant, or the configuration resulting from the occupation of the highest weighted orbitals in the case of a prior CASSCF/MCSCF calculation. Unless the system is very strongly correlated and no dominant single reference exists, the projected energy estimate will usually have smaller errorbars, while at convergence the two values should provide relatively independent energy estimates which should agree to within random errors.

The output file contains the following columns of data every INTERVAL iterations from the calculation, unless the NOMCOUTPUT option is given.

  1. Iteration number
  2. Current shift value
  3. Walker change from previous interval
  4. Walker growth rate
  5. Total walkers
  6. Total annihilated walkers over last interval
  7. Total walkers that died over last interval
  8. Total spawned walkers over last interval
  9. Averaged projected correlation energy estimate from beginning of calculation $\left( \sum_j \frac{\langle n_j H_{0j} \rangle}{\langle n_0 \rangle} \right)$
  10. Averaged shift correlation energy estimate from 1000 iterations after entry into variable shift mode
  11. Instantaneous projected correlation energy estimate averaged only over last INTERVAL iterations
  12. Number of walkers currently residing on reference configuration
  13. Number of walkers currently residing on single or double excitations of reference configuration (that contribute to the sum in Eq. 58)
  14. Fraction of spawning attempts which are successful
  15. Total number of currently occupied configurations
  16. Time taken for last iteration

    The end of the output also contains a summary of the most highly weighted configurations at the end of the simulation.
    The FCIQMCStats file also contains this data, in a way that can easily be plotted, and also contains additional diagnostic information, detailed below
  17. Fraction of successful spawning events to single, rather than double excitations
  18. Range of occupied configuration number over between MPI processes – a measure of the parallel load-balancing of the simulation
  19. Total imaginary-time which has elapsed in the calculation
  20. Ignore column
  21. Expected shift value obtained in fixed shift mode calculated from rate of growth of reference configuration
  22. Expected shift value obtained in fixed shift mode calculated from rate of growth of total walker number
  23. Projected total energy estimate averaged only over last INTERVAL iterations (col. 11 + reference energy)
  24. Denominator of projected energy estimate averaged only over last INTERVAL iterations
  25. Numerator of projected energy estimate averaged only over last INTERVAL iterations
  26. Instantaneous normalised weight of reference configuration in FCIQMC wavefunction
  27. Instantaneous normalisation factor of FCIQMC wavefunction

In addition to the FCIQMCStats file, unless the full scheme is being used, a file called INITIATORStats is created. Of interest in this file are column 7: the number of `initiator' configurations, column 9: the number of walkers residing on `initiator' configurations and column 11: the number of spawned walkers which were aborted due to the initiator approximation in the last INTERVAL iterations. A NodeFile file is also created for each MPI process. Generally, these files will contain nothing that is not mirrored in the output file, however if the calculation terminates unexpectedly, these files will often contain information on the process-specific reason for this, and should be checked in this instance. At the end of a calculation, the output will print the highest weighted configurations in the calculation, as well as attempting an automatic error analysis on the final energies, which is discussed in the next section.

Especially for initial investigations into a new system, it can be instructive to graphically view the progress of the simulation as it proceeds, to determine whether the simulation can enter the variable shift phase, whether the population on the reference configuration is sufficient, or whether any other parameters should be adjusted via the CHANGEVARS facility. Examples of typical plots starting from a single walker are shown in Fig. 1 and 2.

Figure 1: Growth in total walker population (column 5), and population on the reference configuration (column 12), obtained from the working directory of the calculation with the GNUPLOT package and the command set logscale y; plot 'FCIQMCStats' u 1:5 w l, ” u 1:12 w l.
Figure 2: Instantaneous total energy estimate from column 23 of the FCIQMCStats file.

molpro@molpro.net 2020-04-18