How to tell when a model Kohn–Sham potential is not a functional derivative

Gaiduk, Alex P.; Staroverov, Viktor N.

doi:10.1063/1.3176515

Cited by 75 publications

(75 citation statements)

References 60 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Accordingly, our findings are also in support of the key feature of the LC hybrid functionals for systems with Coulomb interactions, which have recently been found to provide supreme performance for a very wide range of applications [57,58], especially for problems related to the asymptote of the XC potential [59][60][61][62][63][64][65][66], self-interaction errors [67,68], fundamental gaps [69][70][71][72][73][74][75][76][77][78][79][80][81][82], and charge-transfer excitations [83][84][85][86][87][88][89]. Besides, empirical atom-atom dispersion potentials [51,55,56,[90][91][92] or MP2 correlation energy [43,53,[93][94][95] can be added to the KS-DFT energy in order to improve the description of noncovalent interactions (e.g., vdW interactions).…”

Section: Resultssupporting

confidence: 83%

The van der Waals interactions in rare-gas dimers: the role of interparticle interactions

Chen

Hui

Chai

2016

Phys. Chem. Chem. Phys.

View full text Add to dashboard Cite

We investigate the potential energy curves of rare-gas dimers with various ranges and strengths of interparticle interactions (nuclear-electron, electron-electron, and nuclear-nuclear interactions).Our investigation is based on the highly accurate coupled-cluster theory associated with those interparticle interactions. For comparison, the performance of the corresponding Hartree-Fock theory, second-order Møller-Plesset perturbation theory, and density functional theory is also investigated.Our results reveal that when the interparticle interactions retain the long-range Coulomb tails, the nature of van der Waals interactions in the rare-gas dimers remains similar. By contrast, when the interparticle interactions are sufficiently short-range, the conventional van der Waals interactions in the rare-gas dimers completely disappear, yielding purely repulsive potential energy curves.

show abstract

Section: Resultssupporting

confidence: 83%

The van der Waals interactions in rare-gas dimers: the role of interparticle interactions

Chen

Hui

Chai

2016

Phys. Chem. Chem. Phys.

View full text Add to dashboard Cite

show abstract

“…The BJ model potential is a construct that directly models the KS potential. It is an ingenious potential construction, but as such, its corresponding energy functional is not merely unknown, it does not exist [76,77], and this deficiency cannot easily be corrected [78]. Since the KS equations are derived from variational calculus of an energy equation that involves the energy xc functional, the use of BJ-type potentials has a very weak formal theoretical basis.…”

Section: B Discussionmentioning

confidence: 99%

Improved ground-state electronic structure and optical dielectric constants with a semilocal exchange functional

et al. 2015

View full text Add to dashboard Cite

A recently published generalized gradient approximation functional within density functional theory (DFT) has shown, in a few paradigm tests, an improved KS orbital description over standard (semi)local approximations. The characteristic feature of this functional is an enhancement factor that diverges like s ln(s) for large reduced density gradients s which leads to unusual properties. We explore the improved orbital description of this functional more thoroughly by computing the electronic band structure, band gaps, and the optical dielectric constants in semiconductors, Mott insulators, and ionic crystals. Compared to standard semilocal functionals, we observe improvement in both the band gaps and the optical dielectric constants. In particular, the results are similar to those obtained with orbital functionals or by perturbation theory methods in that it opens band gaps in systems described as metallic by standard (semi)local density functionals, e.g., Ge, α-Sn, and CdO.

show abstract

“…As it is a potential functional, it has the major drawback that no corresponding exchange functional exists [24,[61][62][63]. For a regular decaying density in the sense of Eq.…”

Section: A the Bj Potential Functional In The Vicinity Of Nodal Surfmentioning

confidence: 99%

Orbital nodal surfaces: Topological challenges for density functionals

2017

View full text Add to dashboard Cite

Nodal surfaces of orbitals, in particular of the highest occupied one, play a special role in Kohn-Sham density-functional theory. The exact Kohn-Sham exchange potential, for example, shows a protruding ridge along such nodal surfaces, leading to the counterintuitive feature of a potential that goes to different asymptotic limits in different directions. We show here that nodal surfaces can heavily affect the potential of semilocal densityfunctional approximations. For the functional derivatives of the Armiento-Kümmel (AK13) 2421 (1994)] model potentials, we explicitly demonstrate exponential divergences in the vicinity of nodal surfaces. We further point out that many other semilocal potentials have similar features. Such divergences pose a challenge for the convergence of numerical solutions of the Kohn-Sham equations. We prove that for exchange functionals of the generalized gradient approximation (GGA) form, enforcing correct asymptotic behavior of the potential or energy density necessarily leads to irregular behavior on or near orbital nodal surfaces. We formulate constraints on the GGA exchange enhancement factor for avoiding such divergences.

show abstract

How to tell when a model Kohn–Sham potential is not a functional derivative

Cited by 75 publications

References 60 publications

The van der Waals interactions in rare-gas dimers: the role of interparticle interactions

The van der Waals interactions in rare-gas dimers: the role of interparticle interactions

Improved ground-state electronic structure and optical dielectric constants with a semilocal exchange functional

Orbital nodal surfaces: Topological challenges for density functionals

Contact Info

Product

Resources

About