Accuracy limits on the description of the lowest S excitation in the Li atom using explicitly correlated Gaussian basis functions

We have performed very accurate quantum-mechanical calculations for the two lowest S states of the lithium atom in order to determine the transition energy. In the nonrelativistic part of the calculations performed using the variational method, we explicitly included the nuclear motion. The nonrelativistic wave function was expanded in terms of explicitly correlated Gaussian functions. Next, this wave function was used to calculate the leading α2 relativistic correction (α is the fine-structure constant) and the α3 QED correction. We also estimated the α4 QED correction by calculating its dominating component. The results obtained with Gaussians are compared with the most accurate results obtained recently with the Hylleraas-type basis functions.