Properties that are necessarily formulated within pure (symmetric)expectation values are difficult to calculate for projector quantum Monte Carloapproaches, but are critical in order to compute many of the importantobservable properties of electronic systems. Here, we investigate an approachfor the sampling of unbiased reduced density matrices within the FullConfiguration Interaction Quantum Monte Carlo dynamic, which requires onlysmall computational overheads. This is achieved via an independent replicapopulation of walkers in the dynamic, sampled alongside the originalpopulation. The resulting reduced density matrices are free from systematicerror (beyond those present via constraints on the dynamic itself), and can beused to compute a variety of expectation values and properties, with rapidconvergence to an exact limit. A quasi-variational energy estimate derived fromthese density matrices is proposed as an accurate alternative to the projectedestimator for multiconfigurational wavefunctions, while its variationalproperty could potentially lend itself to accurate extrapolation approaches inlarger systems.
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