Strong correlations within a symmetry-unbroken ground-state wavefunction can show up in approximate density functional theory as symmetry-broken spin densities or total densities, which are sometimes observable. They can arise from soft modes of fluctuations (sometimes collective excitations) such as spin-density or charge-density waves at nonzero wavevector. In this sense, an approximate density functional for exchange and correlation that breaks symmetry can be more revealing (albeit less accurate) than an exact functional that does not. The examples discussed here include the stretched H2 molecule, antiferromagnetic solids, and the static charge-density wave/Wigner crystal phase of a low-density jellium. Time-dependent density functional theory is used to show quantitatively that the static charge-density wave is a soft plasmon. More precisely, the frequency of a related density fluctuation drops to zero, as found from the frequency moments of the spectral function, calculated from a recent constraint-based wavevector- and frequency-dependent jellium exchange-correlation kernel.

Semi-local approximations to the density functional for the exchangecorrelation energy of a many-electron system necessarily fail for lobed one-electron densities, including not only the familiar stretched densities but also the less familiar but closely-related noded ones. The Perdew-Zunger (PZ) self-interaction correction (SIC) to a semi-local approximation makes that approximation exact for all oneelectron ground-or excited-state densities and accurate for stretched bonds. When the minimization of the PZ total energy is made over real localized orbitals, the orbital densities can be noded, leading to energy errors in many-electron systems. Minimization over complex localized orbitals yields nodeless orbital densities, which reduce but typically do not eliminate the SIC errors of atomization energies. Other errors of PZ SIC remain, attributable to the loss of the exact constraints and appropriate norms that the semi-local approximations satisfy, and suggesting the need for a generalized SIC. These conclusions are supported by calculations for oneelectron densities, and for many-electron molecules. While PZ SIC raises and improves the energy barriers of standard generalized gradient approximations (GGA's) and meta-GGA's, it reduces and often worsens the atomization energies of molecules. Thus PZ SIC raises the energy more as the nodality of the valence localized orbitals increases from atoms to molecules to transition states. PZ SIC is applied here in particular to the SCAN meta-GGA, for which the correlation part is already self-interaction-free. That property makes SCAN a natural first candidate for a generalized SIC.

According to time-dependent density functional theory, the exact exchange-correlation kernel f xc (n, q, ω) for wave vector q and frequency ω determines not only the ground-state energy but also the excited-state energies/lifetimes and time-dependent linear density response of an electron gas of uniform density n = 3/(4π r 3 s ). Here we propose a parametrization of this function based upon the satisfaction of exact constraints. For the static (ω = 0) limit, we modify the model of Constantin and Pitarke to recover at small q the known second-order gradient expansion, and to correct its approach to the large q limit. For all ω at q = 0, we use the model of Gross, Kohn, and Iwamoto. A Cauchy integral extends this model to complex ω. Scaling relations are identified. We then combine these ingredients, damping out the ω dependence at large q. Away from q = 0 and ω = 0, the correlation contribution to the kernel becomes dominant over exchange, even at r s = 4. The resulting correlation energies for 1 r s 10 from integration over imaginary ω are essentially exact. The plasmon pole of the density response function is found by analytic continuation of f xc to ω just below the real axis, and the resulting plasmon lifetime at r s = 4 is found for q < k F . A static charge-density wave is found for r s > 69, and shown to be associated with softening of the plasmon mode.

The mechanical and electronic properties of transition metal dichalcogenide (TMD) monolayers corresponding to transition groups IV, VI, and X are explored under mechanical bending from first principles calculations using the strongly constrained and appropriately normed (SCAN) meta-GGA (MGGA). SCAN provides an accurate description of the phase stability of the TMD monolayers. Our calculated lattice parameters and other structure parameters agree well with experiment. We find that bending stiffness (or flexural rigidity) increases as the transition metal group goes from IV to X to VI, with the exception of PdTe 2 . Variation in mechanical properties (local strain, physical thickness) and electronic properties (local charge density, band structure) with bending curvature is discussed. The local strain profile of these TMD monolayers under mechanical bending is highly non-uniform. The mechanical bending tunes not only the thickness of the TMD monolayers, but also the local charge distribution as well as the band structures, adding more functionalization options to these materials.1 arXiv:1904.05445v3 [cond-mat.mtrl-sci]

No abstract