# Obituary for Walter Kohn (1923–2016)

^{1}

^{2}

^{3}

^{4}

^{5}

^{*}

**r**). There are two classes of electronic structure methods: wave-function-based and density-based schemes, both of which have their advantages and disadvantages.

_{ext}(

**r**), the ground-state density is uniquely determined. In this formulation of DFT, they demonstrated a unique one-to-one mapping between the external potential V

_{ext}(r) (from the nuclei) applied to a nondegenerate electronic system and its ground state density ρ(

**r**), which depends on the position

**r**(i.e., only three coordinates). This mapping implies that the ground state energy E of the system is a functional of its ground states density ρ(

**r**). The Thomas–Fermi model of 1927 already had a similar goal, but was a severe approximation insufficient for chemical accuracy. The fundamental work by Hohenberg and Kohn showed that a universal functional for the energy E[ρ(

**r**)] can be defined in terms of the density. The exact ground state is the global minimum value of this functional. In principle, this formulation is exact; however, since the explicit mathematical form is unknown, one does not fully know how to express the interaction between individual electrons, making approximations necessary.

^{3}), nowadays called “order-N method”. In terms of applications, this means that larger systems (which are a more realistic representation of a real material) can be studied. In this talk, he made the bridge from chemistry to applications. Not only was his talk in Athens impressive, but so too was the fact that he joined the participants to visit the Acropolis in the age of 88 years (Figure 2).

## Acknowledgments

## Conflicts of Interest

## References

- Hohenberg, P.; Kohn, W. Inhomogeneous Electron Gas. Phys. Rev.
**1964**, 136, B864. [Google Scholar] [CrossRef] - Kohn, W.; Sham, L.J. Self-Consistent Equations Including Exchange and Correlation Effects. Phys. Rev.
**1965**, 140, A1133. [Google Scholar] [CrossRef] - Lejaeghere, K.; Bihlmayer, G.; Björkman, T.; Blaha, P.; Blügel, S.; Blum, V.; Caliste, D.; Castelli, I.E.; Clark, S.J.; Dal Corso, A.; et al. Reproducibility in density-functional theory calculations of solids. Science
**2016**, 351. [Google Scholar] [CrossRef] [PubMed] [Green Version]

**Figure 1.**Walter Kohn was presented receiving an honorary Doctor of Science degree by the Harvard University (AP Photo/Steven Senne).

**Figure 2.**Walter Kohn at the excursion to Acropolis during the density functional theory (DFT) conference held in Athens in 2011.

© 2016 by the authors; licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC-BY) license (http://creativecommons.org/licenses/by/4.0/).

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**MDPI and ACS Style**

Schwarz, K.; Sham, L.J.; Mattsson, A.E.; Scheffler, M.
Obituary for Walter Kohn (1923–2016). *Computation* **2016**, *4*, 40.
https://doi.org/10.3390/computation4040040

**AMA Style**

Schwarz K, Sham LJ, Mattsson AE, Scheffler M.
Obituary for Walter Kohn (1923–2016). *Computation*. 2016; 4(4):40.
https://doi.org/10.3390/computation4040040

**Chicago/Turabian Style**

Schwarz, Karlheinz, Lu J. Sham, Ann E. Mattsson, and Matthias Scheffler.
2016. "Obituary for Walter Kohn (1923–2016)" *Computation* 4, no. 4: 40.
https://doi.org/10.3390/computation4040040