Abstract
We present a physically motivated correlation functional belonging to the meta-generalized gradient approximation (meta-GGA) rung, which can be supplemented with long-range dispersion corrections without introducing double-counting of correlation contributions. The functional is derived by the method of constraint satisfaction, starting from an analytical expression for a real-space spin-resolved correlation hole. The model contains a position-dependent function that controls the range of the interelectronic correlations described by the semilocal functional. With minimal empiricism, this function may be adjusted so that the correlation model blends with a specific dispersion correction describing long-range contributions. For a preliminary assessment, our functional has been combined with an atom-pairwise dispersion correction and full Hartree-Fock (HF)-like exchange. Despite the HF-exchange approximation, its predictions compare favorably with reference interaction energies in an extensive set of non-covalently bound dimers.
Highlights
Inclusion of the dispersion interactions into the set of phenomena accounted for by DFT models is recognized as one of the challenges in the development of new density functional approximations (DFAs).[1,2,3,4] Several ways have been proposed to correct the currently available semilocal (SL) DFAs for the lacking nonlocal (NL) correlation contribution responsible for the dispersion interactions.[1,3] Hereafter, global hybrid and range-separated hybrid functionals will be called SL DFAs
Our model reflects the following physical properties: 1. Short-range electronic correlation is modeled by an expression borrowed from the homogeneous electron gas, which is appropriate for real systems.[51,77–79] (See Eqs 25, 26, and 31.) To the best of our knowledge, we present the first beyond-local-density approximation (LDA) functional which incorporates analytic representation of the short-range correlation function of the HEG developed by Gori-Giorgi and Perdew 58
Eint denotes interaction energy calculated using the correlation functional described in this work combined with 100% HF-like exchange and DFT-D3 correction
Summary
Inclusion of the dispersion interactions into the set of phenomena accounted for by DFT models is recognized as one of the challenges in the development of new density functional approximations (DFAs).[1,2,3,4] Several ways have been proposed to correct the currently available semilocal (SL) DFAs for the lacking nonlocal (NL) correlation contribution responsible for the dispersion interactions.[1,3] Hereafter, global hybrid and range-separated hybrid functionals will be called SL DFAs. The examples of such dispersion-corrected methods are: (i) the exchange-hole dipole method (XDM),[5–9] (ii) the atom pairwise additive schemes of Goerigk and Grimme, DFT-D3,10 and Tkatchenko-Scheffler approach,[11] (iii) seamless van der Waals density functionals.[4,12–17] It is clear that the accuracy of these methods depends on a faithful representation of long-range electronic correlations, and on a consistent matching of a dispersion correction and the chosen SL complement
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