Ab Initio Pseudopotentials (Extending Ab Initio QM Throughout the Periodic Table)

Abstract

In the 1960s, no serious calculations were done on transition metals or even the Si row of the periodic table because the core electrons had to be present, adding substantially to the cost (state-of-the-art computers were about 0.1 mips and memory was 36 K words, including operating system). To get around this problem, the concept of a pseudopotential that cancels the deep potential in the core region was introduced by Phillips, Kleinman, Cohen, Heine, and Ziman as a way to think about bonding in metals such as Li. As formulated, their pseudopotential had serious problems. 1. The pseudopotential was not unique; there are an infinite number of different pseudopotentials each of which leads to a different pseudo-orbitals, but with the same E. 2. Second, the new Hamiltonian is not Hermitian, leading to complications when considering scattering. 3. Third, the pseudopotential was an integral operator; not a local potential, causing problems when considering scattering. The Goddard group (Carl Melius and Luis Kahn) solved this problem by introducing the Effective Core Potential (ECP). Adding in core orbital character to make the valence orbital nodeless while going smoothly to zero as the distance from the nucleus goes to 0 led a pseudo-orbital that leads to a unique ECP (or pseudopotential). Most importantly, the ECP depended dramatically on symmetry. It was very different for s states than p states then d states, etc. This led to the concept of writing the ECP in terms of angular momentum projection operators. We showed that the excited states of each symmetry are well described with the same ECP. This was completed by 1974. The final refinement (1977) was restricting the form of the smooth pseudo-orbital so that the long range size was not changed (norm conserving). This concept of ECP with angular momentum projection operators extracted from ab initio atomic wavefunctions has been the basis of the enormous progress in the last 50 years for treating materials for the full periodic table.