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Seven Useful Questions in Density Functional Theory
Steven Crisostomo, Ryan Pederson, John Kozlowski +6
We explore a variety of unsolved problems in density functional theory, where mathematicians might prove useful. We give the background and context of the different problems, and w…
Extending density functional theory with near chemical accuracy beyond pure water
Suhwan Song, Stefan Vuckovic, Youngsam Kim +3
Density functional simulations of condensed phase water are typically inaccurate, due to the inaccuracies of approximate functionals. A recent breakthrough showed that the SCAN app…
Can the Hartree-Fock kinetic energy exceed the exact kinetic energy?
Steven Crisostomo, Mel Levy, Kieron Burke
The Hartree-Fock (HF) approximation has been an important tool for quantum-chemical calculations since its earliest appearance in the late 1920s, and remains the starting point of…
Machine learning and density functional theory
Ryan Pederson, Bhupalee Kalita, Kieron Burke
Over the past decade machine learning has made significant advances in approximating density functionals, but whether this signals the end of human-designed functionals remains to…
Asymptotics of eigenvalue sums when some turning points are complex
Pavel Okun, Kieron Burke
Recent work has shown a deep connection between semilocal approximations in density functional theory and the asymptotics of the sum of the WKB semiclassical expansion for the eige…
Leading correction to the local density approximation for exchange in large- atoms
Nathan Argaman, Jeremy Redd, Antonio C. Cancio +1
The large- asymptotic expansion of atomic energies has been useful in determining exact conditions for corrections to the local density approximation in density functional theor…
Improving results by improving densities: Density-corrected density functional theory
Eunji Sim, Suhwan Song, Stefan Vuckovic +1
DFT calculations have become widespread in both chemistry and materials, because they usually provide useful accuracy at much lower computational cost than wavefunction-based metho…
Conditional probability density functional theory
Ryan Pederson, Jielun Chen, Steven R. White +1
We present conditional probability (CP) density functional theory (DFT) as a formally exact theory. In essence, CP-DFT determines the ground-state energy of a system by finding the…
Lieb's most useful contribution to density functional theory?
Kieron Burke
The importance of the Lieb-Simon proof of the relative exactness of Thomas-Fermi theory in the large-Z limit to modern density functional theory (DFT) is explored. The principle, t…
Correlation energy of the uniform gas determined by ground state conditional probability density functional theory
Dennis Perchak, Ryan J. McCarty, Kieron Burke
Conditional-probability density functional theory (CP-DFT) is a formally exact method for finding correlation energies from Kohn-Sham DFT without evaluating an explicit energy func…