  We combine explicit correlation via the canonical transcorrelation approach
with the density matrix renormalization group and initiator full configuration
interaction quantum Monte Carlo methods to compute a near-exact beryllium dimer
curve, {\it without} the use of composite methods. In particular, our direct
density matrix renormalization group calculations produce a well-depth of
$D_e$=931.2 cm$^{-1}$ which agrees very well with recent experimentally derived
estimates $D_e$=929.7$\pm 2$~cm$^{-1}$ [Science, 324, 1548 (2009)] and
$D_e$=934.6~cm$^{-1}$ [Science, 326, 1382 (2009)]], as well the best composite
theoretical estimates, $D_e$=938$\pm 15$~cm$^{-1}$ [J. Phys. Chem. A, 111,
12822 (2007)] and $D_e$=935.1$\pm 10$~cm$^{-1}$ [Phys. Chem. Chem. Phys., 13,
20311 (2011)]. Our results suggest possible inaccuracies in the functional form
of the potential used at shorter bond lengths to fit the experimental data
[Science, 324, 1548 (2009)]. With the density matrix renormalization group we
also compute near-exact vertical excitation energies at the equilibrium
geometry. These provide non-trivial benchmarks for quantum chemical methods for
excited states, and illustrate the surprisingly large error that remains for
1$^1\Sigma^-_g$ state with approximate multi-reference configuration
interaction and equation-of-motion coupled cluster methods. Overall, we
demonstrate that explicitly correlated density matrix renormalization group and
initiator full configuration interaction quantum Monte Carlo methods allow us
to fully converge to the basis set and correlation limit of the
non-relativistic Schr\"odinger equation in small molecules.
