A synthetic pseudopotential benchmark for testing production pseudopotentials and constructing pseudopotentials with chemical accuracy.

Norm-conserving pseudopotentials guarantee that the electrostatic monopoles arising from the all-electron and pseudo wavefunctions are identical. We introduce a generalization of this concept, that also guarantees that higher multipoles arising from a hybridization of the orbitals are approximately conserved. By including in addition shallow core states we can achieve errors in the atomization energies within density functional theory that are always smaller than the so-called chemical accuracy of 1 kcal mol-1. To demonstrate the accuracy of our pseudopotentials as well as to assess the accuracy of other pseudopotentials we generated a synthetic benchmark of atomization energies in highly precise all-electron calculations. The data bank contains 669 molecules with 65 chemical elements from the first six periods of the periodic table. In contrast to other databases, ours is designed for calculations with systematic basis sets such as plane waves or wavelets. At the same time our molecular test set contains a much larger structural variety than test sets based on periodic bulk systems. Based on our highly accurate multipole conserving pseudopotentials we introduce a scheme that allows us to disentangle the errors in atomization energies by assigning the energy error contributions from the pseudopotentials of the different elements in a molecule to the individual pseudopotentials of these elements. In this way low quality pseudopotentials for certain elements can easily be detected. Using this approach we tested the default pseudopotentials provided by major codes such as ABINIT or QE and find that the errors for some elements are quite large and are in many cases actually larger than the errors arising from the PBE exchange correlation functional.