Spectroscopic accuracy directly from quantum chemistry: application to ground and excited states of beryllium dimer
Abstract
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 [Science, 324, 1548 (2009)] and De=934.6~cm-1 [Science, 326, 1382 (2009)]], as well the best composite theoretical estimates, De=938 15~cm-1 [J. Phys. Chem. A, 111, 12822 (2007)] and De=935.1 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 11-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.
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