Abstract
In contrast to nonrelativistic density functional theory, the ratio between the von Weizsäcker and the Kohn-Sham kinetic energy density, commonly used as iso-orbital indicator t within exchange-correlation functionals beyond the generalized-gradient level, violates the exact iso-orbital limit and the appropriate parameter range, 0 ≤ t ≤ 1, in relativistic density functional theory. Based on the exact decoupling procedure within the infinite-order two-component method and the Cauchy-Schwarz inequality, we present corrections to the relativistic and the picture-change-transformed nonrelativistic kinetic energy density that restores these exact constraints. We discuss the origin of the new correction terms and illustrate the effectiveness of the current approach for several representative cases. The proposed generalized iso-orbital indicator tλ is expected to be a useful ingredient for the development of relativistic exchange-correlation functionals.
Highlights
Owing to its excellent accuracy-to-cost ratio, especially for calculations on larger molecular systems, the Kohn–Sham (KS) density functional theory (DFT)1–3 has evolved into one of the main pillars of modern quantum chemistry and related fields
In analogy to t0, the nonrelativistic limit of t1 could be used within current-meta-generalized gradient approximation (GGA) in current-density functional theory (CDFT), i.e., the correction term is applied to the nonrelativistic von Weizsäcker kinetic energy density and not to the nonrelativistic KS kinetic energy density
We proposed a novel scheme to correct errors in the conventional definition of the common iso-orbital indicator t, when employed within relativistic DFT
Summary
Owing to its excellent accuracy-to-cost ratio, especially for calculations on larger molecular systems, the Kohn–Sham (KS) density functional theory (DFT) has evolved into one of the main pillars of modern quantum chemistry and related fields. While DFT as described so far has been developed based on the nonrelativistic Schrödinger equation, relativistic quantum chemistry employs the Dirac Hamiltonian. Regarding the relativistic XC functional, only approximations up to the GGA level have been developed far.76 As differences to their nonrelativistic analogs have been shown to be negligible for some noncore spectroscopic properties, mostly nonrelativistic XC functionals are employed within relativistic DFT calculations. As will be shown later, the straightforward definition of the relativistic kinetic energy density does not satisfy these requirements when used within nonrelativistic XC functionals. We work within a two-component relativistic framework employing the PCT density matrix scheme, recently introduced by the authors to enable an efficient calculation of relativistic exact exchange, along with the infinite-order two-component (IOTC) method..
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