Balancing the Contributions to the Gradient Expansion: Accurate Binding and Band Gaps with a Nonempirical Meta-GGA.

The gradient expansion has been a long-standing guide rail in density-functional theory. We here demonstrate that for exchange-correlation approximations that depend on the gradient of the density and the kinetic energy density, i.e.

Meta-generalized gradient approximations in time dependent generalized Kohn-Sham theory: Importance of the current density correction.

We revisit the use of Meta-Generalized Gradient Approximations (mGGAs) in time-dependent density functional theory, reviewing conceptual questions and solving the generalized Kohn-Sham equations by real-time propagation. After discussing the technical aspects of using mGGAs in combination with pseudopotentials and comparing real-space and basis set results, we focus on investigating the importance of the current-density based gauge invariance correction. For the two modern mGGAs that we investigate in this work, TASK and r2SCAN, we observe that for some systems, the current density correction leads to negligible changes, but for others, it changes excitation energies by up to 40% and more than 0.

Exact exchange-like electric response from a meta-generalized gradient approximation: A semilocal realization of ultranonlocality.

We review the concept of ultranonlocality in density functional theory and the relation between ultranonlocality, the derivative discontinuity of the exchange energy, and the static electric response in extended molecular systems. We present the construction of a new meta-generalized gradient approximation for exchange that captures the ultranonlocal response to a static electric field in very close correspondence to exact exchange, yet at a fraction of its computational cost. This functional, in particular, also captures the dependence of the response on the system size.

Exploring local range separation: The role of spin scaling and one-electron self-interaction.

Range-separated hybrid functionals with a fitted or tuned global range-separation parameter are frequently used in density functional theory. We here explore the concept of local range separation, i.e.