The education of Walter Kohn and the creation of density functional theory

Zangwill, Andrew

doi:10.1007/s00407-014-0140-x

Cited by 15 publications

(6 citation statements)

References 207 publications

(203 reference statements)

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“…Of course, later that year, they also published the rather more famous Kohn-Sham equations [28], pointing out their exactness in a legendary note added in proof, and simultaneously inventing the modern LDA approximation. Their scheme proved successful beyond their wildest dreams [29], and Walter Kohn shared the Nobel prize in chemistry some 30 years later.…”

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confidence: 99%

Semiclassics: The hidden theory behind the success of DFT

Okun¹,

Burke²

2021

Preprint

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It is argued that the success of DFT can be understood in terms of a semiclassical expansion around a very specific limit. This limit was identified long ago by Lieb and Simon for the total electronic energy of a system. This is a universal limit of all (non-relativistic) electronic structure: atoms, molecules, and solids. In the simple case of neutral atoms, this limit corresponds to an expansion of the total energy in powers of Z −1/3 . For the total energy, Thomas-Fermi theory becomes relatively exact in the limit. The limit can also be studied for much simpler model systems, including non-interacting fermions in a onedimensional well, where the WKB approximation applies for individual eigenvalues and eigenfunctions. Summation techniques lead to energies and densities that are functionals of the potential. We consider several examples in one dimension (fermions in a box, in a harmonic well, in a linear half-well, and in the Pöschl-Teller well. The effects of higher dimension are also illustrated with the three-dimensional harmonic well and the Bohr atom, non-interacting fermions in a Coulomb well. Modern density functional calculations use the Kohn-Sham scheme almost exclusively. The same semiclassical limit can be studied for the Kohn-Sham kinetic energy, for the exchange energy, and for the correlation energy. For all three, the local density approximation appears to become relatively exact in this limit. Recent work, both analytic and numerical, explores how this limit is approached, in an effort to deduce the leading corrections to the local approximation. A simple scheme, using the Euler-Maclaurin summation formula, is the result of many different attempts at this problem. In very simple cases, the correction formulas are much more accurate than standard density functionals. Several functionals are already in widespread use in both chemistry and materials that incorporate these limits, and prospects for the future are discussed.

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confidence: 99%

Semiclassics: The hidden theory behind the success of DFT

Okun¹,

Burke²

2021

Preprint

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“…A recent issue of the Journal of Chemical Physics celebrated 50 years of modern density functional theory, and the articles range across many topics of current interest (Yang, 2014). A review of solid state applications of DF theory is provided by Hasnip et al (2014), and Zangwill (2014) discussed the life and work of Walter Kohn, particularly in this context. I use numerous citations of participants in (and observers of) this story to illustrate how perspectives on the approach have changed.…”

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Density functional theory: Its origins, rise to prominence, and future

2015

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In little more than 20 years, the number of applications of the density functional (DF) formalism in chemistry and materials science has grown in an astonishing fashion. The number of publications alone shows that DF calculations make up a huge success story, and many younger colleagues are surprised to learn that the widespread application of density functional methods, particularly in chemistry, began only after 1990. This is indeed unexpected, because the origins are usually traced to the papers of Hohenberg, Kohn, and Sham more than a quarter of a century earlier. The DF formalism, its applications, and prospects were reviewed for this journal in 1989. About the same time, the combination of DF calculations with molecular dynamics promised to provide an efficient way to study structures and reactions in molecules and extended systems. This paper reviews the development of density-related methods back to the early years of quantum mechanics and follows the breakthrough in their application after 1990. The two examples from biochemistry and materials science are among the many current applications that were simply far beyond expectations in 1990. The reasons why-50 years after its modern formulation and after two decades of rapid expansionsome of the most cited practitioners in the field are concerned about its future are discussed.

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“…To emphasize this personal flavour we have included several first-person accounts and quoted Kohn's own words at times (mostly from his Nobel auto-biography) (11). For an in-depth discussion of the development of Walter's scientific ideas we strongly recommend the perceptive paper by Andrew Zangwill (Zangwill 2014).…”

Section: Acknowledgementsmentioning

confidence: 99%

Walter Kohn. 9 March 1923—19 April 2016

Hohenberg

Langer

2018

Biogr. Mems Fell. R. Soc.

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Walter Kohn, a giant of theoretical physics, died at his home in Santa Barbara, California, on 19 April 2016, at the age of 93. Walter's life epitomized both the hardships and the wondrous achievements of physicists in the twentieth century. He escaped from Nazi-occupied Austria on one of the last children's rescue trains (the Kindertransport ) and during World War II spent 18 months confined in internment camps in England and Canada. He learned only after the War that both of his parents had perished in Auschwitz. After earning physics degrees at the University of Toronto and at Harvard University, he rapidly emerged as a leader in bringing quantum theory to bear on problems in the electron theory of solids. Walter's devotion to basic scientific principles led to the density functional theory of electrons in solids and in chemical molecules in the 1960s. Thirty years later, once the vast importance of this theory had become clear, he was awarded a Nobel Prize in Chemistry for this discovery. In his later years Walter turned much of his attention to institution building and public affairs. He was the founding director of the Institute for Theoretical Physics at the University of California, Santa Barbara. He was deeply committed to the control of nuclear weapons, the development of renewable clean energy and the free exchange of knowledge among scientists throughout the world.

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The education of Walter Kohn and the creation of density functional theory

Cited by 15 publications

References 207 publications

Semiclassics: The hidden theory behind the success of DFT

Semiclassics: The hidden theory behind the success of DFT

Density functional theory: Its origins, rise to prominence, and future

Walter Kohn. 9 March 1923—19 April 2016

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