arXiv subjects
Publications and source records attributed to Peter Elliott.
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-functional approximations are variational. Construction via this method and imposition of these conditions are shown to greatly improve the accuracy of the non-interacting kinetic energy needed for orbital-free Kohn-Sham calculations.
The adiabatic approximation in time-dependent density functional theory (TDDFT) yields reliable excitation spectra with great efficiency in many cases, but fundamentally fails for states of double excitation character. We discuss how double-excitations are at the root of some of the most challenging problems for TDDFT today. We then present new results for (i) the calculation of autoionizing resonances in the helium atom, (ii) understanding the nature of the double excitations appearing in the quadratic response function, and (iii) retrieving double-excitations through a real-time semiclassical approach to correlation in a model quantum dot.
For the kinetic energy of 1d model finite systems the leading corrections to local approximations as a functional of the potential are derived using semiclassical methods. The corrections are simple, non-local functionals of the potential. Turning points produce quantum oscillations leading to energy corrections, which are completely different from the gradient corrections that occur in bulk systems with slowly-varying densities. Approximations that include quantum corrections are typically much more accurate than their local analogs. The consequences for density functional theory are discussed.
Partition density functional theory is a formally exact procedure for calculating molecular properties from Kohn-Sham calculations on isolated fragments, interacting via a global partition potential that is a functional of the fragment densities. An example is given and consequences discussed.
Density scaling has a rich history in density functional theory, providing exact conditions for use in the construction of ever more accurate approximations to the unknown exchange-correlation functional. We define a conjugate potential scaling for each density scaling. This provides exact relations on various important density functionals, in particular, relating functionals evaluated on exact densities of different potentials. We illustrate these conditions on the two- and four-electron ion series.
The B88 exchange energy density functional (created by Becke in 1988) is a crucial part of the most popular density functional in use today, B3LYP. B88 contains one empirical parameter which was fitted to Hartree-Fock exchange energies for the noble gas atoms. We show how local approximations to exchange become relatively exact under a very specific approach to the limit of large numbers, but that the usual gradient expansion does not. The leading corrections can be captured by generalized gradient approximations, producing a non-empirical derivation of the parameter in B88.
Time-dependent density functional theory (TDDFT) is presently enjoying enormous popularity in quantum chemistry, as a useful tool for extracting electronic excited state energies. This article explains what TDDFT is, and how it differs from ground-state DFT. We show the basic formalism, and illustrate with simple examples. We discuss its implementation and possible sources of error. We discuss many of the major successes and challenges of the theory, including weak fields, strong fields, continuum states, double excitations, charge transfer, high harmonic generation, multiphoton ionization, electronic quantum control, van der Waals interactions, transport through single molecules, currents, quantum defects, and, elastic electron-atom scattering.