Abstract
In the thirty-two years since the birth of the foundational theorems, time-dependent density functional theory has had a tremendous impact on calculations of electronic spectra and dynamics in chemistry, biology, solid-state physics, and materials science. Alongside the wide-ranging applications, there has been much progress in understanding fundamental aspects of the functionals and the theory itself. This Perspective looks back to some of these developments, reports on some recent progress and current challenges for functionals, and speculates on future directions to improve the accuracy of approximations used in this relatively young theory.
Highlights
The wavefunction rose from the early days of quantum mechanics as the central player, the provider of all observable properties of atoms, molecules, and solids
In the thirty-two years since the birth of the foundational theorems, time-dependent density functional theory has had a tremendous impact on calculations of electronic spectra and dynamics in chemistry, biology, solid-state physics, and materials science
In 1984 Erich Runge and Hardy Gross proved that for time-dependent (TD) systems evolving from a given initial wavefunction, all TD properties can be extracted from the time-evolving density
Summary
The wavefunction rose from the early days of quantum mechanics as the central player, the provider of all observable properties of atoms, molecules, and solids. Almost 40 years later, the Hohenberg-Kohn theorem proved that the ground-state density alone provides all observable properties of any static system This is an astonishing result given the simplicity of the density, the probability of finding any one electron at a given point in space, compared with the wavefunction, a function of all electronic coordinates. Given that Hohenberg, Kohn, and Sham had derived such a potential for an electron in a ground-state twenty years earlier, it was natural to wonder whether such a formulation could be extended to the timedependent case, yielding the exact time-dependent potential acting on an electron. This led to the birth of the foundational theorem of TDDFT, the Runge-Gross theorem.. I have brazenly ignored allimportant computational concerns, numerical aspects, details, and algorithms
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