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 0.8 eV. In the cases that we study, the agreement with the reference data is improved by the current density correction.

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. The static electric polarizabilities of hydrogen chains and oligo-acetylene molecules calculated with this meta-GGA are quantitatively close to the ones obtained with exact exchange. The chances and challenges associated with the construction of meta-GGAs that are intended to combine a substantial derivative discontinuity and ultranonlocality with an accurate description of electronic binding are discussed.

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., of turning the range-separation parameter into an explicit semilocal density functional. We impose three simple constraints on the local range-separation parameter that are frequently used in density functional construction: uniform density scaling, the homogeneous electron gas limit, and freedom from one-electron self-interaction. We further discuss different ways of how to model the spin dependence in combination with local range separation. We evaluate our local range-separation energy functionals exactly for closed-shell atoms using the previously suggested hypergeneralized gradient approximation for molecules and assess the quality of this approximation. We find a local range-separated hybrid functional that yields accurate binding energies for a set of small molecules.