Semiclassical origins of DFT

Contrary to current belief, there is a systematic expansion that lies behind the successes of modern DFT calculations. This is a formal expansion in powers of $\hbar$ and was first identified four decades ago by Lieb and Simon in the case of Thomas-Fermi (TF) theory. In this semiclassical limit, the exact Hohenberg- Kohn functional $F [n]$, where $n(r)$ is the one-particle density, tends to its TF counterpart (local approximation for the kinetic energy and Hartree approximation for Coulomb repul- sion). In the same limit, the exchange-correlation energy,$E_{\xc} [n]$, used in the Kohn-Sham (KS) method tends to its local density approximation (LDA),

The focus of this project is to find the leading corrections to the local approximation in this expansion (as has been tried in nuclear physics, in terms of path integrals and density matrices, and more recently for quantum dots). For slowly-varying densities, these are the well-known gradient corrections which form the starting point of Perdew’s generalized gradient approximations (GGAs). But for all other cases, including all atoms, molecules, and most solids, the dominant correction is an oscillation generated by the classical caustic structure of the KS potential, $v_s(r)$. These corrections have been derived in several specific situations. They are universal functionals of the potential, rather than of the density, and so have remained elusive in DFT.

Publications
[159] Corrections to Thomas-Fermi Densities at Turning Points and Beyond Raphael F. Ribeiro, Donghyung Lee, Attila Cangi, Peter Elliott, Kieron Burke, Phys. Rev. Lett. 114, 050401 (2015). [bibtex] [pdf] [doi]
[158] Atomic correlation energies and the generalized gradient approximation Kieron Burke, Antonio Cancio, Tim Gould, Stefano Pittalis, submitted and ArXiv:1409.4834 (2014). [bibtex] [pdf]
[157] Almost exact exchange at almost no computational cost in electronic structure Peter Elliott, Attila Cangi, Stefano Pittalis, E. K. U. Gross, Kieron Burke, Phys. Rev. A 92, 022513 (2015). [bibtex] [pdf] [doi]
[146] Potential functionals versus density functionals Attila Cangi, E. K. U. Gross, Kieron Burke, Phys. Rev. A 88, 062505 (2013). [bibtex] [pdf] [doi]
[130] Electronic Structure via Potential Functional Approximations Attila Cangi, Donghyung Lee, Peter Elliott, Kieron Burke, E. K. U. Gross, Phys. Rev. Lett. 106, 236404 (2011). [bibtex] [pdf] [doi]
[128] Communication: Ionization potentials in the limit of large atomic number Lucian A. Constantin, John C. Snyder, John P. Perdew, Kieron Burke, The Journal of Chemical Physics 133, 241103 (2010). [bibtex] [pdf] [doi]
[125] Leading corrections to local approximations Attila Cangi, Donghyung Lee, Peter Elliott, Kieron Burke, Phys. Rev. B 81, 235128 (2010). [bibtex] [pdf] [doi]
[122] Potential scaling in density functional theory Peter Elliott, Kieron Burke, (2009). [bibtex] [pdf]
[118] Non-empirical derivation of the parameter in the B88 exchange functional Peter Elliott, Kieron Burke, Canadian Journal of Chemistry 87, 1485-1491 (2009). [bibtex] [pdf] [doi]
[114] Perdew et al. Reply John P. Perdew, Adrienn Ruzsinszky, Gábor I. Csonka, Oleg A. Vydrov, Gustavo E. Scuseria, Lucian A. Constantin, Xiaolan Zhou, Kieron Burke, Phys. Rev. Lett. 101, 239702 (2008). (Mattsson's comment (Phys. Rev. Lett. 101, 239701 (2008))) [bibtex] [pdf] [doi]
[112] Charge Transfer in Partition Theory\textdagger Morrel H. Cohen, Adam Wasserman, Roberto Car, Kieron Burke, The Journal of Physical Chemistry A 113, 2183-2192 (2009). (PMID: 19215125) [bibtex] [pdf] [doi]
[111] Semiclassical Origins of Density Functionals Peter Elliott, Donghyung Lee, Attila Cangi, Kieron Burke, Phys. Rev. Lett. 100, 256406 (2008). [bibtex] [pdf] [doi]
[99] Relevance of the Slowly Varying Electron Gas to Atoms, Molecules, and Solids John P. Perdew, Lucian A. Constantin, Espen Sagvolden, Kieron Burke, Phys. Rev. Lett. 97, 223002 (2006). [bibtex] [pdf] [doi]

Funding
We graciously acknowledge support from the NSF Grant No. CHE-1464795

Current Student

Raphael Ribeiro

Alumni

Donghyung Lee

Attila Cangi

Peter Elliott

Stefano Pittalis

Senior Collaborator

E. K. U. Gross