Systematic Correction of Kohn–Sham-Derived Excitation Energies via a Quantum Monte Carlo Approach

Developing and applying accurate methods for the calculation of excitation spectra remains an outstanding problem in electronic structure. Here, we present the first application of auxiliary boson-corrected diffusion Monte Carlo (ABCDMC) to ab initio systems of atoms and ions in the second row of the periodic table and molecules. In ABCDMC, the many-body electron–electron correction to the density functional theory (DFT) exchange-correlation energy is captured statistically via an auxiliary boson ground state obtained with diffusion Monte Carlo. Moreover, the kinetic-energy contribution to correlation is included up to the limit of a finite active-space expansion. The excitations are described as a product of a linear combination of Fermionic functions derived from DFT and the auxiliary boson state. The corrections to the DFT-derived excitation spectra are obtained by statistically sampling an observable on the auxiliary boson state. We benchmark ABCDMC on the experimental excitation spectra of second-row neutral atoms (Li–F), cations (Be+–Ne+), dications (B2+–Na2+), and the carbon dimer against full configuration interaction (FCI). For the atomic set (96 excitations), ABCDMC improves local density approximation excitation energies for low-lying single excitations up to the n = 3 shell, reducing the mean signed error from −0.059 to less than 0.001 Ha and the root-mean-square deviation (RMSD) from 0.102 to 0.037 Ha using at most 25 determinants per species. An O+ convergence study shows systematic improvement as the determinant space is enlarged and double excitations are included. For the carbon dimer, ABCDMC matches FCI within 9 mHa RMSD for 11 low-lying excitations using 16 determinants. Overall, these results indicate that ABCDMC is particularly promising for the calculation of low-energy excitations with very small active spaces. However, the method is not designed to correct basis-set errors associated with diffuse wave functions and the cusp condition errors at the core in atomic systems using Gaussian bases which are also present in the underlying DFT. The compact determinant expansions used here suggest that ABCDMC may be useful for larger systems and, in future work, for correcting DFT band structures of solids, provided a sparse multireference basis can be constructed.