Optimally tuned range-separated hybrid van der Waals density functional for molecular binding and quasiparticle characterizations

We introduce and illustrate use of two closely related range-separated hybrid (RSH) van der Waals density functionals (vdW-DFs), denoted AHBR-mRSH and AHBR-mRSH*, for total-energy and quasiparticle characterizations of molecules using generalized Kohn-Sham (gKS) density functional theory (DFT). For comparison, we also introduce and document a traditional design for a long-range corrected (LRC) vdW-DF, denoted 'B86R-LRC'. All three new vdW-DFs set the exchange potential as free of asymptotic screening in the coupling between the electron and its associated exchange hole. Our two AHBR-mRSHs are key members of a broader class 'AHBR-mRSH(<i>γ</i>)' defined by an inverse length scale<i>γ</i>for a crossover in weighting short- and long-ranged exchange contributions; we obtain a highly accurate predictor of general molecular-energy differences by keeping<i>γ</i> = 0.106 (inverse Bohr) deliberately fixed in AHBR-mRSH. We obtain an optimally tuned (OT) form AHBR-mRSH* = AHBR-mRSH(γ∗) by computing a plausible value ofγ∗for specific types of systems. This AHBR-mRSH* permits characterizations of molecular quasiparticles and generalizes (1) the existing 'OT-RSH' (Stein<i>et al</i>2010<i>Phys. Rev. Lett.</i><b>105</b>266802; Rafaely-Abramson<i>et al</i>2012<i>Phys. Rev. Lett.</i><b>109</b>226405) approach by a systematic inclusion of truly nonlocal correlations, and (2) more traditional LRC forms (e.g. B86R-LRC) by setting the short-range exchange description as in vdW-DF2-ahbr (Shukla<i>et al</i>2022<i>Phys. Rev. X</i><b>12</b>041003).<i>Importantly,</i>we may view AHBR-mRSH and AHBR-mRSH* as internally consistent functionals for gKS-DFT, being simultaneously accurate on molecular energies and quasiparticles. This is possible because the 'AHBR-mRSH(<i>γ</i>)' class has enough transferability to almost always limit adverse impacts of tuning<i>γ</i>, as tested here on the GMTKN55 benchmark suite (Goerigk<i>et al</i>2017<i>Phys. Chem. Chem. Phys.</i><b>19</b>32184). We find that AHBR-mRSH generally outperforms B86R-LRC on molecular problems. To illustrate usage, we complete the OT design of an AHBR-mRSH* for nucleobases and show that it provides quasiparticle predictions that are in good agreement with both literature theory and experimental values for adenine, thymine, cytosine, and guanine.