Atomic Reference Data for Electronic Structure Calculations, Introduction

The local-density approximation (LDA) and its variants are widely used in ab initio computations of materials properties. They have a demonstrated ability to produce results that, as regards predictive value for ground-state electronic structure, are fully competitive with the best traditional methods of quantum chemistry. In addition, they have superior scaling properties [1], and so can be applied to much larger systems than can the traditional methods. Jones and Gunnarsson have presented a review of this field [2], and Parr and Yang have written a textbook [3].

Although several general-purpose computer codes for LDA-based calculations of molecular and solid structures have recently become commercially available, the writing of such codes remains largely an effort pursued in small research groups, which tend to work independently. Such groups focus on the solution of problems of physics and chemistry, and tend to accord secondary priority to establishing the limits of accuracy of the underlying methods.

As density-functional approaches become more widespread, there will be a need for benchmark data comparable to that which is available for traditional quantum chemistry. Those who are attempting to solve very large problems, utilizing a range of approximations, will want to know how to distinguish the uncertainties that derive from numerical implementation from those that are inherent in the basic formalism. We have therefore initiated a project to generate reference data obtained in well-defined, standard approximations with certified numerical accuracy.

The material presented here is the first set of results of this project. It consists of total energies and orbital energy eigenvalues, for the ground-state configurations of all atoms and singly-charged cations with atomic number Z ≤ 92, as computed in four standard approximations that use the exchange-correlation energy functional of Vosko, Wilk and Nusair [4]: (1) The local-density approximation (LDA); (2) the local-spin-density approximation (LSD); (3) the relativistic local-density approximation (RLDA); (4) the scalar-relativistic local-density approximation (ScRLDA).

These results have been obtained through extensive testing and comparison of results of several independent codes, and were reproduced on several different models of computer to eliminate machine dependence. Our target for absolute accuracy in the total energy was 1 microHartree unit. We have managed to attain consistency between the independent results at a level that allows us to quote the absolute accuracy for the total energies presented here as 1 microHartree. We have found that when this tolerance is imposed on the value of the total energy, a somewhat larger variation is found to occur among the individual orbital energy eigenvalues. Differences between the various results for orbital eigenvalues are below 2 microHartree in all cases.