  Although selected configuration interaction (SCI) algorithms can tackle much
larger Hilbert spaces than the conventional full CI (FCI) method, the scaling
of their computational cost with respect to the system size remains inherently
exponential. Additionally, inaccuracies in describing the correlation hole at
small interelectronic distances lead to the slow convergence of the electronic
energy relative to the size of the one-electron basis set. To alleviate these
effects, we show that the non-Hermitian, transcorrelated (TC) version of SCI
significantly compactifies the determinant space, allowing to reach a given
accuracy with a much smaller number of determinants. Furthermore, we note a
significant acceleration in the convergence of the TC-SCI energy as the basis
set size increases. The extent of this compression and the energy convergence
rate are closely linked to the accuracy of the correlation factor used for the
similarity transformation of the Coulombic Hamiltonian. Our systematic
investigation of small molecular systems in increasingly large basis sets
illustrates the magnitude of these effects.
