Static Exchange-Correlation Kernel Across Jacob’s Ladder and Temperature Regimes for Linear Response TDDFT of warm dense matter

The exchange correlation kernel (XC) naturally arises within the framework of linear response theory as a key quantity for describing correlated systems of many particles. Particularly, the XC kernel is needed in linear response TDDFT (LR-TDDFT), which is a powerful ab initio method that
allows one to describe dynamical and transport properties of equilibrium quantum-many body systems. A standard approach of the calculation of the XC kernel in LR-TDDFT is based on the computation of the second order functional derivative of a XC functional with respect to density. For extended systems, this approach is limited to simple static (adiabatic) LDA and GGA (such as PBE ) level XC functionals due to mathematical and computational challenges of computing functional derivatives of meta-GGA and hybrid level functionals. In fact, only adiabatic LDA (ALDA) is available in commonly used open source DFT codes. We have overcome these limitations by developing a new method of the calculation of the XC kernel [1], which utilizes the method of a direct harmonic perturbation. The essence of the developed approach is to compute a static density response function of a system by measuring the density perturbation induced by an external static harmonic field; with density being extracted from an equilibrium KS-DFT simulation. An alternative and equivalent definition of the XC kernel as a difference between the inverse values of the density response functions of systems with non-zero and zero XC functionals allows us to access the XC kernel without explicitly computing functional derivatives. This allows one to compute the XC kernel using available XC functionals through the ranks of Jacob's ladder and for any temperature. We demonstrated the utility of this method by analyzing the XC kernel beyond GGA level including meta-GGA and hybrid XC functionals [1-3]. In addition, we have presented a workflow for using the static XC kernel from the direct perturbation approach in the
LR-TDDFT of warm dense matter [4].

[1] Zhandos Moldabekov, Maximilian Böhme, Jan Vorberger, David Blaschke, and Tobias
Dornheim, Ab Initio Static Exchange–Correlation Kernel across Jacob’s Ladder without Functional
Derivatives, Journal of Chemical Theory and Computation 19 (4), 1286-1299 (2023 )
[2] Zhandos A. Moldabekov, Mani Lokamani, Jan Vorberger, Attila Cangi, Tobias Dornheim,
Assessing the accuracy of hybrid exchange-correlation functionals for the density response of warm
dense electrons. J. Chem. Phys. 158 (9), 094105 (2023).
[3] Zhandos A. Moldabekov, Mani Lokamani, Jan Vorberger, Attila Cangi, and Tobias Dornheim,
Non-empirical Mixing Coefficient for Hybrid XC Functionals from Analysis of the XC Kernel, The
Journal of Physical Chemistry Letters 14 (5), 1326-1333 (2023)
[4] Zhandos A. Moldabekov, Michele Pavanello, Maximilian P. Böhme, Jan Vorberger, and Tobias
Dornheim, Linear-response time-dependent density functional theory approach to warm dense
matter with adiabatic exchange-correlation kernels, Phys. Rev. Research 5, 023089 (2023)