 Award ID(s):
 1856165
 NSFPAR ID:
 10220445
 Date Published:
 Journal Name:
 The journal of physical chemistry letters
 Issue:
 0
 ISSN:
 19487185
 Format(s):
 Medium: X
 Sponsoring Org:
 National Science Foundation
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Kohn–Sham (KS) inversion, that is, the finding of the exact KS potential for a given density, is difficult in localized basis sets. We study the precision and reliability of several inversion schemes, finding estimates of densitydriven errors at a useful level of accuracy. In typical cases of substantial densitydriven errors, Hartree–Fock density functional theory (HFDFT) is almost as accurate as DFT evaluated on CCSD(T) densities. A simple approximation in practical HFDFT also makes errors much smaller than the densitydriven errors being calculated. Two paradigm examples, stretched NaCl and the HO·Cl– radical, illustrate just how accurate HFDFT is.more » « less

Most torsional barriers are predicted with high accuracies (about 1 kJ/mol) by standard semilocal functionals, but a small subset was found to have much larger errors. We created a database of almost 300 carbon–carbon torsional barriers, including 12 poorly behaved barriers, that stem from the Y═C—X group, where Y is O or S and X is a halide. Functionals with enhanced exchange mixing (about 50%) worked well for all barriers. We found that poor actors have delocalization errors caused by hyperconjugation. These problematic calculations are densitysensitive (i.e., DFT predictions change noticeably with the density), and using HF densities (HFDFT) fixes these issues. For example, conventional B3LYP performs as accurately as exchangeenhanced functionals if the HF density is used. For longchain conjugated molecules, HFDFT can be much better than exchangeenhanced functionals. We suggest that HFPBE0 has the best overall performance.more » « less

Standard approximations for the exchange–correlation functional in Kohn–Sham density functional theory (KSDFT) typically lead to unacceptably large errors when applied to strongly correlated electronic systems. PartitionDFT (PDFT) is a formally exact reformulation of KSDFT in which the groundstate density and energy of a system are obtained through selfconsistent calculations on isolated fragments, with a partition energy representing interfragment interactions. Here, we show how typical errors of the local density approximation (LDA) in KSDFT can be largely suppressed through a simple approximation, the multifragment overlap approximation (MFOA), for the partition energy in PDFT. Our method is illustrated on simple models of onedimensional strongly correlated linear hydrogen chains. The MFOA, when used in combination with the LDA for the fragments, improves LDA dissociation curves of hydrogen chains and produces results that are comparable to those of spinunrestricted LDA, but without breaking the spin symmetry. MFOA also induces a correction to the LDA electron density that partially captures the correct density dimerization in strongly correlated hydrogen chains. Moreover, with an additional correction to the partition energy that is specific to the onedimensional LDA, the approximation is shown to produce dissociation energies in quantitative agreement with calculations based on the density matrix renormalization group method.

null (Ed.)Accurate computational predictions of band gaps are of practical importance to the modeling and development of semiconductor technologies, such as (opto)electronic devices and photoelectrochemical cells. Among available electronicstructure methods, densityfunctional theory (DFT) with the Hubbard U correction (DFT+U) applied to band edge states is a computationally tractable approach to improve the accuracy of band gap predictions beyond that of DFT calculations based on (semi)local functionals. At variance with DFT approximations, which are not intended to describe optical band gaps and other excitedstate properties, DFT+U can be interpreted as an approximate spectralpotential method when U is determined by imposing the piecewise linearity of the total energy with respect to electronic occupations in the Hubbard manifold (thus removing selfinteraction errors in this subspace), thereby providing a (heuristic) justification for using DFT+U to predict band gaps. However, it is still frequent in the literature to determine the Hubbard U parameters semiempirically by tuning their values to reproduce experimental band gaps, which ultimately alters the description of other totalenergy characteristics. Here, we present an extensive assessment of DFT+U band gaps computed using selfconsistent ab initio U parameters obtained from densityfunctional perturbation theory to impose the aforementioned piecewise linearity of the total energy. The study is carried out on 20 compounds containing transitionmetal or pblock (group IIIIV) elements, including oxides, nitrides, sulfides, oxynitrides, and oxysulfides. By comparing DFT+U results obtained using nonorthogonalized and orthogonalized atomic orbitals as Hubbard projectors, we find that the predicted band gaps are extremely sensitive to the type of projector functions and that the orthogonalized projectors give the most accurate band gaps, in satisfactory agreement with experimental data. This work demonstrates that DFT+U may serve as a useful method for highthroughput workflows that require reliable band gap predictions at moderate computational cost.more » « less

null (Ed.)A major challenge in density functional theory (DFT) is the development of density functional approximations (DFAs) to overcome errors in existing DFAs, leading to more complex functionals. For such functionals, we consider roles of the noninteracting reference systems. The electron density of the Kohn–Sham (KS) reference with a local potential has been traditionally defined as being equal to the electron density of the physical system. This key idea has been applied in two ways: the inverse calculation of such a local KS potential for the reference from a given density and the direct calculation of density and energy based on given DFAs. By construction, the inverse calculation can yield a KS reference with the density equal to the input density of the physical system. In application of DFT, however, it is the direct calculation of density and energy from a DFA that plays a central role. For direct calculations, we find that the selfconsistent density of the KS reference defined by the optimized effective potential (OEP), is not the density of the physical system, when the DFA is dependent on the external potential. This inequality holds also for the density of generalized KS (GKS) or generalized OEP reference, which allows a nonlocal potential, when the DFA is dependent on the external potential. Instead, the density of the physical system, consistent with a given DFA, is given by the linear response of the total energy with respect to the variation of the external potential. This is a paradigm shift in DFT on the use of noninteracting references: the noninteracting KS or GKS references represent the explicit computational variables for energy minimization, but not the density of the physical system for external potentialdependent DFAs. We develop the expressions for the electron density so defined through the linear response for general DFAs, demonstrate the results for orbital functionals and for manybody perturbation theory within the secondorder and the randomphase approximation, and explore the connections to developments in DFT.more » « less