 |
Atomic Reference Data
for Electronic Structure Calculations |
Results
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 |
|
| LDA |
1 | 2 |
3 | 4 |
4 |
| LSD |
1 | |
3 | 4 |
3 |
| RLDA |
1 | |
3 | 4 |
3 |
| ScRLDA |
|
2 |
3 |
|
2 |
|
Error budget
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 forseeable 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.
Contents |
Introduction |
Procedure |
Results |
Approximations |
References |
Notation