Pseudopotentials

Pseudopotentials are effective potentials used in quantum simulations of atoms, molecules, and solids to replace the influence of core electrons and the nucleus on valence electrons. By smoothing the strong Coulomb field near the nucleus, they reduce the oscillatory behavior of core states and allow calculations to be carried out with a smaller basis set, typically plane waves. This simplification enables efficient treatment of large systems and high-throughput studies.

Construction and varieties: Pseudopotentials are generated from reference calculations on isolated atoms. Norm-conserving pseudopotentials preserve the norm of the pseudo-wavefunction inside a chosen core radius; they are generally transferable but require higher plane-wave cutoffs. Ultrasoft pseudopotentials relax norm conservation to achieve smaller cutoffs, at the cost of introducing augmentation charges and a generalized overlap operator. The projector augmented wave (PAW) method is an all-electron reconstruction technique that combines the efficiency of a pseudopotential with the ability to recover all-electron wavefunctions. In practice, pseudopotentials are nonlocal, with projectors for different angular momentum channels, and are usually decomposed into a local part and a nonlocal part.

Relativistic and spin-orbit effects: For heavy elements, scalar-relativistic corrections or fully relativistic pseudopotentials are used, sometimes including spin-orbit coupling. Transferability: Pseudopotentials must be tested across chemical environments; inaccuracies may arise in ionic compounds, extreme pressures, or where core–valence coupling is significant. Limitations include neglect of explicit core–valence correlation and potential failures in strongly correlated systems.

Usage: They are central to plane-wave density functional theory codes and other electronic structure methods, enabling efficient simulations of solids, surfaces, and large molecules. The choice of pseudopotential affects accuracy and convergence, and researchers often compare different sets or generate system-specific potentials.