In this study, we obtained previously existing codes, and modified them to implement the same density functional, improve numerical accuracy, and regularize input and output. One code was originally written as a Hartree-Fock atomic structure program, and so required more substantial modifications. The codes had different functionality, and so different subsets were used to treat each case, as indicated in the table below.
|codes used||number of codes|
The goal of this project was to obtain total energies accurate to 1 microHartree across the periodic table (compared to an RLDA total energy of -28 001 Hartree for U), a value which seems thoroughly adequate for all foreseeable needs of materials science and chemistry (1 microHartree = 0.03 meV = 0.0006 kcal/mole).
Obviously, this goal could only be attained by performing complex numerical calculations, for which it is difficult to state an error budget in rigorous quantitative terms. The only exact analytical results available to us are the total energies (equal to orbital energy eigenvalues) of one-electron atoms, as given by solution of the Schrödinger equation. We found that, in all cases, these energies were reproduced to the numerical accuracy of the computer for radial grid parameters similar to those used in our production runs.
Thus, our basis for quoting the absolute numerical accuracies given here derives from
- establishing the accuracy of one-electron calculations, and
- observing consensus of the results of independent calculations (quantified in the following figures), which were seen to improve systematically as the numerical grids were refined.