  By combining density-functional theory (DFT) and wave function theory (WFT)
via the range separation (RS) of the interelectronic Coulomb operator, we
obtain accurate fixed-node diffusion Monte Carlo (FN-DMC) energies with compact
multi-determinant trial wave functions. In particular, we combine here
short-range exchange-correlation functionals with a flavor of selected
configuration interaction (SCI) known as \emph{configuration interaction using
a perturbative selection made iteratively} (CIPSI), a scheme that we label
RS-DFT-CIPSI. One of the take-home messages of the present study is that
RS-DFT-CIPSI trial wave functions yield lower fixed-node energies with more
compact multi-determinant expansions than CIPSI, especially for small basis
sets. Indeed, as the CIPSI component of RS-DFT-CIPSI is relieved from
describing the short-range part of the correlation hole around the
electron-electron coalescence points, the number of determinants in the trial
wave function required to reach a given accuracy is significantly reduced as
compared to a conventional CIPSI calculation. Importantly, by performing
various numerical experiments, we evidence that the RS-DFT scheme essentially
plays the role of a simple Jastrow factor by mimicking short-range correlation
effects, hence avoiding the burden of performing a stochastic optimization.
Considering the 55 atomization energies of the Gaussian-1 benchmark set of
molecules, we show that using a fixed value of $\mu=0.5$~bohr$^{-1}$ provides
effective error cancellations as well as compact trial wave functions, making
the present method a good candidate for the accurate description of large
chemical systems.
