Non-empirical Mixing Coefficient for Hybrid XC Functionals from Analysis of the XC Kernel

Abstract

We present an analysis of the static exchange-correlation (XC) kernel computed from hybrid functionals with a single mixing coefficient such as PBE0 and PBE0–1/3. We break down the hybrid XC kernels into the exchange and correlation parts using the Hartree–Fock functional, the exchange-only PBE, and the correlation-only PBE. This decomposition is combined with exact data for the static XC kernel of the uniform electron gas and an Airy gas model within a subsystem functional approach. This gives us a tool for the non-empirical choice of the mixing coefficient under ambient and extreme conditions. Our analysis provides physical insights into the effect of the variation of the mixing coefficient in hybrid functionals, which is of immense practical value. The presented approach is general and can be used for other types of functionals like screened hybrids.

Linear-response time-dependent density functional theory approach to warm dense matter with adiabatic exchange--correlation kernels

“…Therefore, it is clear that XC functional development for the WDM regime requires new innovative approaches. For example, it was recently shown that PBE0 type hybrid level functionals, mixing exact Hartree-Fock exchange with the PBE exchange, can provide a good description of the UEG at WDM parameters if a mixing coefficient is chosen to reproduce the XC kernel of the UEG [51,52]. Now, using the consistent approach presented in this work, this analysis of the PBE0 type hybrid level functionals can be extended to real materials like warm dense hydrogen.…”

“…From a computational point of view, an alternative to the LR-TDDFT is to use a direct perturbation by an external field to measure the density response function connecting the perturbing field with the density change induced by it [48][49][50]. These different formulations and methods for a dynamic density response function have been actively used in the WDM studies [39,[51][52][53][54]. However, in many aspects, the connection between them had not been clearly formulated and understood.…”

“…Additionally, different hybrid XC functionals have been analyzed at WDM conditions using the UEG model in Refs. [51,52]. These prior works used the reference static density response function χ 0 (q) from KS-DFT calculations with zero XC functional.…”

“…We reiterate that the strength of the presented new approach is that it can be used with the static XC kernel of any available XC functional without explicitly computing the second order functional derivative. For example, using the direct perturbation approach, Moldabekov et al [34] presented a static XC kernel for LDA, GGA, and meta-GGA level functionals as well as for various hybrid functionals [51,52]. Moreover, Eq.…”

Physics-enhanced neural networks for equation-of-state calculations

“…While both flavours are in principle exact, they rely on approximations. In KS-DFT, we have to approximate the exchange-correlation (xc) energy functional, for which there exists a wide spectrum of choices [43][44][45], with efforts ongoing to assess the impact of this choice in the WDM regime [26,[46][47][48][49][50][51][52][53]. Meanwhile, OF-DFT relies on approximations for both the kinetic energy density-functional in addition to the xc-energy [54][55][56][57][58].…”