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Commentary on "The Most-Cited Physicists of the Past 30 Years" and "The Most-Cited Physics Papers of the Past 30 Years": Leadership Role of Density Functional Theory Introduction Journal articles in science typically cite or reference other articles on which they are partly based. The analysis of citation patterns (as championed by Eugene Garfield [1] and the Institute for Scientific Information) can thus show something about how science has developed. The Web of Science was constructed as a way of tracking articles, authors, topics, and citations in science. Citation counts are sometimes used to measure an author's scientific achievements, as in the Hirsch index [2] or the Science Author Rank Algorithm [3]. Except in an overall statistical sense, this measurement is rough, and is not a substitute for the informed judgment of an expert. The more reliable use of citations is to show how science has developed, not to measure individual achievement. Definitions and Methodology The 327 most-cited physicists for cited and citing papers published 1981-2008 are listed by name at www.isihighlycited.com (although it appears that some who should have been included were not). This list and its starting date were chosen for reasons of practicality and consistency. A "physicist" is anyone who publishes in physics journals, while a "paper" and a "citation" are from any science journal. Each co-author of a paper is credited with all its citations. Each of the 327 most-cited physicists has a "distinct author set" on the Web of Science. These sets attempt to distinguish among authors who have the same abbreviated author name. Each of the 327 most-cited physicists can be recognized by the words "View author biography" attached to his or her distinct author set. The "citation report" for each was run to show total citations to papers published 1981 or later, and a list of those papers ranked by their citation numbers. Note that there are many well-cited papers published before 1981 that are not included here, because they were not used to establish the short list of 327 physicists. These lists have been compiled from the Web of Science at Tulane University by Alan Liu, in a careful but not infallible way. Some of the distinct author sets provided by the Web of Science are incorrect, either con-mingling papers by more than one author in the same set or distributing papers by the same author over several sets. These errors are less frequent for the more highly-cited authors. An attempt was made to correct these errors, but further correction is welcome. Results and Perspectives These lists show that the density functional theory of electronic structure has been the citation leader in physics (and perhaps also in chemistry) for the past 30 years: (1) Of the five most-cited "physicists" (for whom there is no "distinct author set" problem),

two (Smalley, Heeger) are Nobelists in Chemistry, one (Witten) is regarded as a candidate for the Nobel in Physics, and two (Perdew, Becke) are density functional theorists. Among the remaining 31 "physicists" with 30,000 or more citations are 7 other density functional developers or users (Parr, Kresse, Yang, Zunger, Cohen, Lee, and Parrinello). Other DFT-related authors on the full list are Joannopoulos, Louie, Freeman, Hafner, Vanderbilt, Scheffler, Car, Sawatzky, Hamann, Gunnarsson, Schlueter, etc. (Note that, if www.isihighlycited.com had been updated since 2008, more authors would have been added to the full list, including the density functional theorists Burke and Ernzerhof.) (2) Of the 18 "physics papers" cited 5,000 times or more over this period, 10 are density functional papers. Density functional theory was created by Pierre Hohenberg and Walter Kohn 1964 [4] and by Walter Kohn and Lu Sham 1965 [5], following earlier and less rigorous work by Thomas, Fermi, Slater, and others. It became popular in condensed matter physics after 1970, and (with the development of improved approximate functionals pioneered by David Langreth [6]) in quantum chemistry after 1980. Important formal work was also done by theoretical chemist Mel Levy [7] at Tulane, and by von Barth, Gunnarsson, Lundqvist, Jones, Vosko, and others. This theory is widely used for the accurate but efficient prediction of what atoms, molecules, and solids can exist, and with what properties. Walter Kohn received the Nobel Prize in Chemistry 1998 for it (and an honorary doctorate from Tulane in 2004). The 1998 Prize was shared by physicist Kohn and theoretical chemist John Pople, who developed powerful computational methods and computer codes for both wavefunction and density functional theories. One of the founding papers of density functional theory is Kohn and Sham 1965 [5]. It does not show up in this study, because it was published before 1981, but it is one of the most-cited physics papers in history, with over 17,000 citations. It should also be credited with the huge number of "implied citations" it receives from nearly every density functional paper published since 1965. More generally, the citations to density functional papers published in 1981 and later belong to the subfield of density functional theory and to its pioneers, and not just to the cited authors. As a paper becomes more well-known, its citation rate can for that very reason slow down. For example, the foundational papers of quantum mechanics remain almost universally influential, but are seldom cited anymore. An article's potential for citedness depends strongly on the population of researchers in its field and sub-field. Even within a sub-field, the most-cited papers are not always the best ones. For example, my favorite co-authored paper [8] has been cited less than a thousand times, and does not come close to being on the list of most-cited papers. My co-authored papers that appear on this list do so because they provide widely-used approximate functionals for electronic structure calculations. Those papers still count among my best. The most-cited papers are not necessarily even the most-read ones. For example, one of my co-authored papers [9] received thousands of citations because it was

mistakenly listed as the source of the Perdew-Wang 1991 generalized gradient approximation in the bibliographies of some popular computer codes for electronic structure calculations. In summary, density functional theory appears to be the clear citation leader of physics over the past 30 years, because it is useful to a large cadre of active researchers in physics, chemistry and other sciences, and because it is not so universally known as to require no citation. Even when the study is restricted to citations to and from the Physical Review family of journals [10], density functional theory continues to stand out.

John P. Perdew Professor of Physics Tulane University New Orleans September 9, 2010

Partial List of References [1] Eugene Garfield, Essays of an Information Scientist, Vols. 1-15 (1962-1993) (www.garfieldlibrary.upenn.edu). [2] J.E. Hirsch, An index to quantify an individual's scientific research output, Proceedings of the National Academy of Sciences 102, 16569 (2005). [3] F. Radicchi, S. Fortunato, B. Markines, and A. Vespignani, Diffusion of scientific credits and the ranking of scientists, Physical Review E 80, 056103 (2009). [4] P. Hohenberg and W. Kohn, Inhomogeneous electron gas, Physical Review 136, B864 (1964). [5] W. Kohn and L.J. Sham, Self-consistent equations including exchange and correlation effects, Physical Review 140, A1133 (1965). [6] D.C. Langreth and J.P. Perdew, Theory of nonuniform electronic systems. I. Analysis of the gradient approximation and a generalization that works, Physical Review B 21, 5469 (1980). [7] M. Levy and J.P. Perdew, Hellmann-Feynman, virial, and scaling requisites for the exact universal density functionals; Shape of the correlation potential and diamagnetic susceptibility for atoms, Physical Review A 32, 2010 (1985).

[8] J.P. Perdew, R.G. Parr, M. Levy, and J.L. Balduz, Density functional theory for fractional particle number: Derivative discontinuities of the energy, Physical Review Letters 49, 1691 (1982). [9] J.P. Perdew and Y. Wang, Accurate and simple analytic representation of the electron gas correlation energy, Physical Review B 45, 13244 (1992). [10] S. Redner, Citation Statistics from 110 Years of Physical Review, Physics Today 58, 49 (2005).

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