Imagine being able to calculate the exact quantum mechanics of electrons in an atom, molecule, or solid by completely removing the Coulomb repulsion between the electrons and warping the attraction between the electrons and the nuclei. Doesn’t this sound crazy? Yet
Imagine being able to calculate the exact quantum mechanics of electrons in an atom, molecule, or solid by completely removing the Coulomb repulsion between the electrons and warping the attraction between the electrons and the nuclei. Doesn’t this sound crazy? Yet this is exactly the recipe for the remarkably successful, and rigorous, density-functional theory (DFT), which says that one can extract the correct observables of an interacting electronic system by instead treating the electrons as independent particles that interact with a fictitious potential.
Formulated in 1964, DFT has revolutionized electronic structure calculations in materials science and quantum chemistry [1, 2]. The younger, time-dependent extension of DFT, TDDFT, is used to treat electrons that start in nonstationary states or that are subject to external fields [3, 4]. But what is the right way to “warp” the attractive nuclear potential so as to choreograph the noninteracting electrons, whose dance contains all the exact information about the true time-dependent system? Except for a handful of calculations limited to model systems with two electrons, the answer to this question has largely gone unexplored. In Physical Review Letters, James Ramsden and Rex Godby of the University of York, UK, present an algorithm for finding the choreographer—otherwise known as the exact time-dependent Kohn-Sham potential—and apply it to a model semiconductor containing a moving electron. They find that the Kohn-Sham potential for this case has several features that the approximations in today’s TDDFT simulations neglect. Understanding these features leads the way to building better TDDFT approximations for other systems.
TDDFT is an exact reformulation of the quantum dynamics of systems of many identical (nonrelativistic) particles. It states that all observables may be extracted from two quantities: the initial wave function and the time-dependent one-body density,, which is the probability of finding any one particle at point in space at time. The time-dependent correlated many-body wave function, which is exponentially 