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 (HF-DFT) is almost as accurate as DFT evaluated on CCSD(T) densities. A simple approximation in practical HF-DFT also makes errors much smaller than the density-driven errors being calculated. Two paradigm examples, stretched NaCl and the HO•Cl − radical, illustrate just how accurate HF-DFT is.

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 density-sensitive (i.e., DFT predictions change noticeably with the density), and using HF densities (HF-DFT) fixes these issues. For example, conventional B3LYP performs as accurately as exchange-enhanced functionals if the HF density is used. For long-chain conjugated molecules, HF-DFT can be much better than exchange-enhanced functionals. We suggest that HF-PBE0 has the best overall performance.

A Kohn-Sham (KS) inversion determines a KS potential and orbitals corresponding to a given electron density, a procedure which has applications in developing and evaluating functionals used in density functional theory. Despite the utility of KS inversions, the application of these methods among the research community is disproportional small. We implement the KS inversion methods of Zhao-Morrison-Parr and Wu-Yang in a framework which simplifies analysis and conversion of the resulting potential in real-space. Fully documented python scripts integrate with PySCF, a popular electronic structure prediction software, and alternative Fortran code is provided for computational hot spots.

We have investigated conformational structures of meso- meso linked porphyrin arrays (Z n) by single molecule fluorescence spectroscopy. Modulation depths ( M values) were measured by excitation polarization fluorescence spectroscopy. The M value decreases from 0.85 to 0.46 as the number of porphyrin units increases from 3 to 128, indicating that longer arrays exhibit coiled structures. Such conformational changes depending on the length have been confirmed by coarse-grained simulation. The histograms of M values and traces of centroid position of emitting sites by localization microscopy showed that the structures of longer arrays changed to more stretched after solvent vapor annealing with tetrahydrofuran.

Most torsional barriers are predicted to high accuracy (about 1 kJ/mol) by standard semilocal functionals, but a small subset has been found to have much larger errors. We create a database of almost 300 carbon-carbon torsional barriers, including 12 poorly behaved barriers, all stemming from Y=C-X group, where X is O or S, and Y is a halide. Functionals with enhanced exchange mixing (about 50%) work well for all barriers. We find that poor actors have delocalization errors caused by hyperconjugation. These problematic calculations are density sensitive (i.e., DFT predictions change noticeably with the density), and using HF densities (HF-DFT) fixes these issues. For example, conventional B3LYP performs as accurately as exchange-enhanced functionals if the HF density is used. For long-chain conjugated molecules, HF-DFT can be much better than exchange-enhanced functionals. We suggest that HF-PBE0 has the best overall performance.