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We combine explicit correlation via the canonical transcorrelation approachwith the density matrix renormalization group and initiator full configurationinteraction quantum Monte Carlo methods to compute a near-exact beryllium dimercurve, {\it without} the use of composite methods. In particular, our directdensity matrix renormalization group calculations produce a well-depth of$D_e$=931.2 cm$^{-1}$ which agrees very well with recent experimentally derivedestimates $D_e$=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 compositetheoretical 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 formof the potential used at shorter bond lengths to fit the experimental data[Science, 324, 1548 (2009)]. With the density matrix renormalization group wealso compute near-exact vertical excitation energies at the equilibriumgeometry. These provide non-trivial benchmarks for quantum chemical methods forexcited states, and illustrate the surprisingly large error that remains for1$^1\Sigma^-_g$ state with approximate multi-reference configurationinteraction and equation-of-motion coupled cluster methods. Overall, wedemonstrate that explicitly correlated density matrix renormalization group andinitiator full configuration interaction quantum Monte Carlo methods allow usto fully converge to the basis set and correlation limit of thenon-relativistic Schr\"odinger equation in small molecules.

Spectroscopic accuracy directly from quantum chemistry: application to ground and excited states of beryllium dimer