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

TL;DR

This paper demonstrates that combining explicit correlation with advanced quantum chemistry methods yields near-exact potential energy curves and excitation energies for the beryllium dimer, surpassing previous theoretical and experimental estimates.

Contribution

It introduces a combined approach of explicit correlation with DMRG and i-FCIQMC methods to achieve highly accurate quantum chemical calculations without composite methods.

Findings

Computed a near-exact potential energy curve for Be2

Achieved a well-depth D_e=931.2 cm^{-1} consistent with experiments

Provided benchmark excitation energies for excited states

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, {\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.