We combine a regularized variant of the strongly constrained and appropriately normed semilocal density functional [J. Sun, A. Ruzsinszky, and J. P. Perdew, Phys. Rev. Lett. 115, 036402 (2015)] with the latest generation semi-classical London dispersion correction. The resulting density functional approximation r²SCAN-D4 has the speed of generalized gradient approximations while approaching the accuracy of hybrid functionals for general chemical applications. We demonstrate its numerical robustness in real-life settings and benchmark molecular geometries, general main group and organo-metallic thermochemistry, and non-covalent interactions in supramolecular complexes and molecular crystals. Main group and transition metal bond lengths have errors of just 0.8%, which is competitive with hybrid functionals for main group molecules and outperforms them for transition metal complexes. The weighted mean absolute deviation (WTMAD2) on the large GMTKN55 database of chemical properties is exceptionally small at 7.5 kcal/mol. This also holds for metal organic reactions with an MAD of 3.3 kcal/mol. The versatile applicability to organic and metal–organic systems transfers to condensed systems, where lattice energies of molecular crystals are within the chemical accuracy (errors <1 kcal/mol).

A first-principles density-functional description of the electronic structures of the high-T_c cuprates has remained a long-standing problem since their discovery in 1986, with calculations failing to capture either the insulating (magnetic) state of the pristine compound or the transition from the insulating to metallic state with doping. Here, by taking lanthanum cuprate as an exemplar high-T_c cuprate, we show that the recently developed non-empirical, strongly constrained and appropriately normed density functional accurately describes both the antiferromagnetic insulating ground state of the pristine compound and the metallic state of the doped system. Our study yields new insight into the low-energy spectra of cuprates and opens up a pathway toward wide-ranging first-principles investigations of electronic structures of cuprates and other correlated materials.

$\mathrm{SCAN}+\mathrm{rVV}10$ has been demonstrated to be a versatile van der Waals (vdW) density functional that delivers good predictions of both energetic and structural properties for many types of bonding. Recently, the ${\mathrm{r}}^2\mathrm{SCAN}$ functional was devised as a revised form of SCAN with improved numerical stability. In this work, we refit the rVV10 functional to optimize the ${\mathrm{r}}^2\mathrm{SCAN}+\mathrm{rVV}10$ vdW density functional and test its performance for molecular interactions and layered materials. Our molecular tests demonstrate that ${\mathrm{r}}^2\mathrm{SCAN}+\mathrm{rVV}10$ outperforms its predecessor $\mathrm{SCAN}+\mathrm{rVV}10$ in both efficiency (numerical stability) and accuracy. This good performance is also found in lattice-constant predictions. In comparison with benchmark results from higher-level theories or experiments, ${\mathrm{r}}^2\mathrm{SCAN}+\mathrm{rVV}10$ yields excellent interlayer binding energies and phonon dispersions for layered materials.

Significance: High-temperature superconductivity, first discovered in materials with copper-oxide planes, is still not well understood. Cuprates exhibit complex phase diagrams under temperature and doping and have not been amenable to first-principles description using previous density functionals, but the recent SCAN functional correctly predicts many properties of the undoped and doped YBCO compounds. In the oxygen-doped YBa ₂ Cu ₃ O ₇ , SCAN finds many competing states with charge and spin stripes. Thermal energies will mix these states, creating fluctuations of the spin moments on the copper atoms in the pseudogap phase from which superconductivity emerges. Our study suggests a paradigm in which the physics of the mysterious pseudogap phase in the cuprates is encoded through a landscape of underlying competing phases in the material.