A reformulation of time-dependent Kohn-Sham theory in terms of the second time derivative of the density

Abstract

The Kohn-Sham approach to time-dependent density-functional theory (TDDFT) can be formulated, in principle exactly, by invoking the force-balance equation for the density, which leads to an explicit expression for the exchange-correlation potential as an implicit density functional. It is shown that this suggests a reformulation of TDDFT in terms of the second time derivative of the density, rather than the density itself. The result is a time-local Kohn-Sham scheme of second order in time whose causal structure is more transparent than that of the usual Kohn-Sham formalism. The scheme can be used to construct new approximations at the exchange-only level and beyond, and it offers a straightforward definition of the exact adiabatic approximation.

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• Why neural functionals suit statistical mechanics
• Force balance in thermal quantum many-body systems from Noether's theorem
• Comparative study of force-based classical density functional theory
• A Snapshot of Time-Dependent Density-Functional Theory
• The Exact Exchange-Correlation Potential in Time-Dependent Density Functional Theory: Choreographing Electrons with Steps and Peaks
• Exchange energies with forces in density-functional theory