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The Bethe-Salpeter equation (BSE) based on GW quasiparticle levels is asuccessful approach for calculating the optical gaps and spectra of solids andalso for predicting the neutral excitations of small molecules. We here presentan all-electron implementation of the GW+BSE formalism for molecules, usingnumeric atom-centered orbital (NAO) basis sets. We present benchmarks forlow-lying excitation energies for a set of small organic molecules, denoted inthe literature as "Thiel's set". Literature reference data based onGaussian-type orbitals are reproduced to about one meV precision for themolecular benchmark set, when using the same GW quasiparticle energies andbasis sets as the input to the BSE calculations. For valence correlationconsistent NAO basis sets, as well as for standard NAO basis sets for groundstate density-functional theory with extended augmentation functions, wedemonstrate excellent convergence of the predicted low-lying excitations to thecomplete basis set limit. A simple and affordable augmented NAO basis setdenoted "tier2+aug2" is recommended as a particularly efficient formulation forproduction calculations. We finally demonstrate that the same convergenceproperties also apply to linear-response time-dependent density functionaltheory within the NAO formalism.

Ab Initio Bethe-Salpeter Equation Approach to Neutral Excitations in Molecules with Numeric Atom-Centered Orbitals