Speaker
Description
The no-pair Dirac--Coulomb(--Breit) equation is solved with high-accuracy \cite{allorder,DiracCoulomb,Breit,LScoupling} to provide a starting point for a new alternative theoretical method in relation with high-resolution atomic and molecular spectroscopy \cite{QEDcorr}. The sub-parts-per-billion convergence of the energy is achieved by considering the relativistic symmetry with an $LS$ coupling scheme and expanding the relativistic wave function with an explicitly correlated Gaussian (ECG) basis set. The ECG significantly improves the description of the electron correlation compared to {\it e.g.,} a determinant basis set, but the positive-energy projection is more complicated due to the lack of the underlying one-electron picture. Therefore, several positive-energy projectors are examined to achieve and justify the parts-per-billion convergence of the energy. The no-pair Dirac--Coulomb energy is compared with perturbative results for atomic and molecular systems with small nuclear charge numbers and it reproduces the perturbative expressions \cite{SucherPHD} up to $\alpha^3 E_\text{h}$ order.
