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, without the use of composite methods. In particular, our direct density matrix renormalization group calculations produce a well-depth of De = 931.2 cm-1 which agrees very well with recent experimentally derived estimates De = 929.7±2 cm-1 [J. M. Merritt, V. E. Bondybey, and M. C. Heaven, Science 324, 1548 (2009)] and De= 934.6 cm-1 [K. Patkowski, V. Špirko, and K. Szalewicz, Science 326, 1382 (2009)], as well the best composite theoretical estimates, D e = 938±15 cm-1 [K. Patkowski, R. Podeszwa, and K. Szalewicz, J. Phys. Chem. A 111, 12822 (2007)] and De=935.1±10 cm-1 [J. Koput, 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 [J. M. Merritt, V. E. Bondybey, and M. C. Heaven, 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 1Σ-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 Schrödinger equation in small molecules. © 2014 AIP Publishing LLC.