A question of balance: Kinetic balance for electrons and positrons

Graphical abstract: Kinetic balance for both electrons and positrons is achieved by applying the correct relation for positive and negative energy states separately and then using the electron and positron eigensolutions from the separate diagonalizations of the Hamiltonian as a dual basis. Highlights: ► Kinetic balance for electrons and positrons is achieved in a dual atomic basis. ► Dual atomic balance alleviates, but does not eliminate, energy prolapse. ► Positron affinities converge quicker with basis set size with dual atomic balance. - Abstract: The kinetic balance criterion used in current relativistic basis set codes is satisfied by the electron solutions of the Dirac equation, but not the positron solutions. A proposal for applying kinetic balance to both sets of solutions is presented. The method is applied along with "normal" kinetic balance to one-electron systems, to investigate its possible relation to prolapse, and to the positron affinity of F−, to investigate the kinetic energy deficiency for positron solutions. The new method reduces but does not eliminate prolapse for energy-optimized basis sets, and provides faster and smoother convergence with basis set size for the positron affinity.