John P. Perdew’s research while affiliated with Temple University and other places

To accurately describe the energetics of transition metal systems, density functional approximations (DFAs) must provide a balanced description of s- and d- electrons. One measure of this is the sd transfer error, which has previously been defined as $E(\mathrm{3d}^{n-1} \mathrm{4s}^1) -E(\mathrm{3d}^{n-2} \mathrm{4s}^2)$. Theoretical concerns have been raised on the validity of these results owing to the evaluation of excited-state energies using ground-state DFAs. A more serious concern appears to be strong correlations in the $\mathrm{4s}^2$ configuration. Here we define a ground-state measure of the sd transfer error, based on the errors of s- and d-electron second ionization energies of the atoms, that effectively circumvents the aforementioned problems. We find an improved performance as we move from LSDA to PBE to r$^2$SCAN for first-row transition metal atoms. However, we found large (~ 2 eV) ground-state sd transfer errors when applying a Perdew-Zunger self-interaction correction. This is attributed to an "energy penalty" associated with the noded 3d orbitals. A local scaling of the self-interaction correction to LSDA results in a cancellation of s- and d-errors.

Monolayer $\mathrm{MoS_2}$ under strain has many interesting properties and possible applications in technology. A recent experimental study examined the effect of strain on the bandgap of monolayer $\mathrm{MoS_2}$ on a mildly curved graphite surface, reporting that under biaxial strain with a Poisson's ratio of 0.44, the bandgap decreases at a rate of 400 meV/% strain. In this work, we performed density functional theory (DFT) calculations for a free-standing $\mathrm{MoS_2}$ monolayer, using the generalized gradient approximation (GGA) PBE, the hybrid functional HSE06, and many-body perturbation theory with the GW approximation using PBE wavefunctions (G0W0@PBE). We found that under biaxial strain with the experimental Poisson's ratio, the bandgap decreases at rates of 63 meV/% strain (PBE), 73 meV/% strain (HSE06), and 43 meV/% strain (G0W0@PBE), which are significantly smaller than the experimental rate. We also found that PBE predicts a similarly smaller rate (90 meV/% strain) for a different Poisson's ratio of 0.25. Spin-orbit correction (SOC) has little effect on the gap or its strain dependence. Additionally, we observed a semiconductor-to-metal transition under an equal tensile biaxial strain of 10% and a transition from a direct to an indirect bandgap, consistent with previous theoretical work.

Are the vertical ionization energies from a bound electronic system, initially in its ground state, equal to minus the corresponding exact Kohn-Sham orbital energies of density functional theory (DFT)? This is known to be true for the first or lowest vertical ionization energy. We show that the correction from time-dependent DFT arises from the continuum and need not vanish. Recent work compared the experimental photoemission thresholds of the molecules Cu2O−, CuO−, CuO− 2 , and CuO3− with minus the corresponding orbital energies from a generalized gradient approximation (GGA) and its global and range-separated hybrids with exact exchange, finding striking differences which were attributed to self-interaction error, strong correlation, or both. Here we extend that work to include the local spin density approximation (LSDA), its Perdew-Zunger self-interaction correction with Fermi-L¨owdin localized orbitals (LSDASIC), a quasi-self-consistent locally scaled-down version of LSDA-SIC (QLSIC), and the Quantum Theory Project QTP02 range-separated hybrid functional, all but LSDA implemented in a generalized Kohn-Sham approach. QTP02 impressively yields a near equality for many sp-bonded molecules. But, for the copper oxide anions studied here, none of the tested methods reproduces the experimental photoemission thresholds.

Bolstered by recent calculations of exact functional-driven errors (FEs) and density-driven errors (DEs) of semi-local density functionals in the water dimer binding energy [Kanungo et al., J. Phys. Chem. Lett. 2023, 15, 323], we investigate approximate FEs and DEs in neutral water clusters containing up to 20 monomers, charged water clusters, and alkali- and halide-water clusters. Our proxy for the exact density is r2SCAN50, a 50% global hybrid of exact exchange with r2SCAN, which may be less correct than r2SCAN for the compact water monomer but importantly more correct for long-range electron transfers in the non-compact water clusters. We show that SCAN makes substantially larger FEs for neutral water clusters than r2SCAN, while both make essentially the same DEs. Unlike the case for barrier heights, these FEs are small in a relative sense, and become large in an absolute sense only due to an increase in cluster size. SCAN@HF produces a cancellation of errors that makes it chemically accurate for predicting the absolute binding energies of water clusters. Likewise, adding a long-range dispersion correction to r2SCAN@HF, as in the composite method HF-r2SCAN-DC4, makes its FE more negative than in r2SCAN@HF, permitting a near-perfect cancellation of FE and DE. r2SCAN by itself (and even more so, r2SCAN evaluated on the r2SCAN50 density), is almost perfect for the energy differences between water hexamers, and thus probably also for liquid water away from the boiling point. Thus the accuracy of composite methods like SCAN@HF and HF-r2SCAN-DC4 is not due to the HF density being closer to the exact density, but to a compensation of errors from its greater degree of localization. We also give an argument for the approximate reliability of this unconventional error cancellation for diverse molecular properties. Finally, we confirm this unconventional error cancellation for the SCAN description of the water trimer via Kohn-Sham inversion of the CCSD(T) density.

Density functional approximations to the exchange–correlation energy can often identify strongly correlated systems and estimate their energetics through energy-minimizing symmetry-breaking. In particular, the binding energy curve of the strongly correlated chromium dimer is described qualitatively by the local spin density approximation (LSDA) and almost quantitatively by the Perdew–Burke–Ernzerhof generalized gradient approximation (PBE-GGA), where the symmetry breaking is antiferromagnetic for both. Here, we show that a full Perdew–Zunger self-interaction-correction (SIC) to LSDA seems to go too far by creating an unphysical symmetry-broken state, with effectively zero magnetic moment but non-zero spin density on each atom, which lies ∼4 eV below the antiferromagnetic solution. A similar symmetry-breaking, observed in the atom, better corresponds to the 3d↑↑4s↑3d↓↓4s↓ configuration than to the standard 3d↑↑↑↑↑4s↑. For this new solution, the total energy of the dimer at its observed bond length is higher than that of the separated atoms. These results can be regarded as qualitative evidence that the SIC needs to be scaled down in many-electron regions.

VO2 is renowned for its electric transition from an insulating monoclinic (M1) phase, characterized by V–V dimerized structures, to a metallic rutile (R) phase above 340 K. This transition is accompanied by a magnetic change: the M1 phase exhibits a non-magnetic spin-singlet state, while the R phase exhibits a state with local magnetic moments. Simultaneous simulation of the structural, electric, and magnetic properties of this compound is of fundamental importance, but the M1 phase alone has posed a significant challenge to the density functional theory (DFT). In this study, we show none of the commonly used DFT functionals, including those combined with on-site Hubbard U to treat 3d electrons better, can accurately predict the V–V dimer length. The spin-restricted method tends to overestimate the strength of the V–V bonds, resulting in a small V–V bond length. Conversely, the spin-symmetry-breaking method exhibits the opposite trends. Each of these two bond-calculation methods underscores one of the two contentious mechanisms, i.e., Peierls lattice distortion or Mott localization due to electron–electron repulsion, involved in the metal–insulator transition in VO2. To elucidate the challenges encountered in DFT, we also employ an effective Hamiltonian that integrates one-dimensional magnetic sites, thereby revealing the inherent difficulties linked with the DFT computations.