Accurate Energies of Electrons on Spheres

DIPC Seminars

Peter M. W. Gill, Australian National University, Canberra
Donostia International Physics Center
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Accurate Energies of Electrons on Spheres Density functional theory (DFT) has become the most popular approach within quantum chemistry but even the most sophisticated functionals suffer from certain well-documented weaknesses [1]. In a systematic attempt to improve this situation, we have been led to re-investigate the fundamental model on which DFT is based, namely, the uniform electron gas (UEG). Several years ago, we showed [2] that traditional DFT functionals which were designed to be exact for an infinite uniform electron gas (IUEG) are, in fact, incorrect when applied to a finite uniform electron gas (FUEG) created by placing n electrons on a sphere [3]. This led us to seek generalizations of the traditional functionals which are exact, by construction, for both infinite and finite UEGs [4]. Long ago, Ceperley and Alder performed landmark Quantum Monte Carlo studies [5] on the correlation energies of IUEGs and their results underpinned the construction of the widely-used Vosko-Wilk-Nusair (VWN) functional [6]. We now need to perform analogous numerical studies on the correlation energies of FUEGs and, subsequently, use those results to construct generalizations of VWN. In this lecture, I will review our progress in calculating accurate correlation energies of n same-spin electrons on spheres of various radii. In particular, I will highlight the usefulness of combining careful basis set extrapolation with Configuration Interaction (CI) calculations using Configuration State Functions to obtain results which are several orders of magnitude more accurate than those of Ceperley and Alder. [1] A. J. Cohen, P. Mori-Sanchez and W. Yang, Science, **321** , 792 (2008). [2] P. M. W. Gill and P. F. Loos, Theor. Chem. Acc., **131** , 1069 (2012). [3] P. F. Loos and P. M. W. Gill, J. Chem. Phys. **135** , 214111 (2011). [4] P. F. Loos, C. J. Ball and P. M. W. Gill, J. Chem. Phys. **140** , 18A524 (2014). [5] D. M. Ceperley and B. J. Alder, Phys. Rev. Lett. **45** , 566 (1980). [6] S. H. Vosko and L. Wilk and M. Nusair, Can. J. Phys. **58** , 1200 (1980). Host: Eduard Matito