  By performing a stochastic dynamic in a space of Slater determinants, the
Full Configuration Interaction Quantum Monte Carlo (FCIQMC) method has been
able to obtain energies which are essentially free from systematic error to the
basis set correlation energy, within small and systematically improvable
errorbars. However, the weakly exponential scaling with basis size makes
converging the energy with respect to basis set costly and in larger systems,
impossible. To ameliorate these basis set issues, here we use perturbation
theory to couple the FCIQMC wave function to an explicitly correlated strongly
orthogonal basis of geminals, following the [2]_{\textrm{R12}} approach of
Valeev {\em et al.}. The required one- and two-particle density matrices are
computed on-the-fly during the FCIQMC dynamic, using a sampling procedure which
incurs relatively little additional computation expense. The F12 energy
corrections are shown to converge rapidly as a function of sampling, both in
imaginary time, and number of walkers. Our pilot calculations on the binding
curve for carbon dimer, which exhibits strong correlation effects as well as
substantial basis set dependence, demonstrate that the accuracy of the
FCIQMC-F12 method surpasses that of all previous FCIQMC calculations, and that
the F12 correction improves accuracy equivalent to increasing the quality of
the one-electron basis by two cardinal numbers.
