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Finding Density Functionals with Machine Learning
John C. Snyder, Matthias Rupp, Katja Hansen +2
Machine learning is used to approximate density functionals. For the model problem of the kinetic energy of non-interacting fermions in 1d, mean absolute errors below 1 kcal/mol on…
The effect of cusps in time-dependent quantum mechanics
Zeng-hui Yang, Neepa T. Maitra, Kieron Burke
Spatial cusps in initial wavefunctions can lead to non-analytic behavior in time. We suggest a method for calculating the short-time behavior in such situations. For these cases, t…
One-dimensional Continuum Electronic Structure with the Density Matrix Renormalization Group and Its Implications For Density Functional Theory
E. M. Stoudenmire, Lucas O. Wagner, Steven R. White +1
We extend the density matrix renormalization group to compute exact ground states of continuum many-electron systems in one dimension with long-range interactions. We find the exac…
Kondo effect given exactly by density functional theory
Justin P. Bergfield, Zhenfei Liu, Kieron Burke +1
Transport through an Anderson junction (two macroscopic electrodes coupled to an Anderson impurity) is dominated by a Kondo peak in the spectral function at zero temperature. The e…
Avoiding Unbound Anions in Density Functional Calculations
Min-Cheol Kim, Eunji Sim, Kieron Burke
Converged approximate density functional calculations usually do not bind anions, due to large self-interaction error. But Hartree-Fock calculations have no such prob- lem, produci…
The Role of Exact Conditions in TDDFT
Lucas O. Wagner, Kieron Burke
This chapter is devoted to exact conditions in time-dependent density functional theory. Many conditions have been derived for the exact ground-state density functional, and severa…
Electronic structure via potential functional approximations
Attila Cangi, Donghyung Lee, Peter Elliott +2
The universal functional of Hohenberg-Kohn is given as a coupling-constant integral over the density as a functional of the potential. Conditions are derived under which potential-…