Abstract:
We extend the recently proposed thermally-assisted-occupation density functional theory (TAO-DFT) [J.-D. Chai, J. Chem. Phys. 136, 154104 (2012)] to generalized-gradient approximation (GGA) exchange-correlation density functionals. Relative to our previous TAO-LDA (i.e., the local density approximation to TAO-DFT), the resulting TAO-GGAs are significantly superior for a wide range of applications, such as thermochemistry, kinetics, and reaction energies. For noncovalent interactions, TAO-GGAs with empirical dispersion corrections are shown to yield excellent performance. Due to their computational efficiency for systems with strong static correlation effects, TAO-LDA and TAO-GGAs are applied to study the electronic properties (e.g., the singlet-triplet energy gaps, vertical ionization potentials, vertical electron affinities, fundamental gaps, and symmetrized von Neumann entropy) of acenes with different number of linearly fused benzene rings (up to 100), which is very challenging for conventional electronic structure methods. The ground states of acenes are shown to be singlets for all the chain lengths studied here. With the increase of acene length, the singlet-triplet energy gaps, vertical ionization potentials, and fundamental gaps decrease monotonically, while the vertical electron affinities and symmetrized von Neumann entropy (i.e., a measure of polyradical character) increase monotonically.

Abstract:
In contrast to the original Kohn-Sham (KS) formalism, we propose a density functional theory (DFT) with fractional orbital occupations for the study of ground states of many-electron systems, wherein strong static correlation is shown to be described. Even at the simplest level represented by the local density approximation (LDA), our resulting DFT-LDA is shown to improve upon KS-LDA for multi-reference systems, such as dissociation of H2 and N2, and twisted ethylene, while performing similarly to KS-LDA for single-reference systems, such as reaction energies and equilibrium geometries. Because of its computational efficiency (similar to KS-LDA), this DFT-LDA is applied to the study of the singlet-triplet energy gaps (ST gaps) of acenes, which are "challenging problems" for conventional electronic structure methods due to the presence of strong static correlation effects. Our calculated ST gaps are in good agreement with the existing experimental and high-level ab initio data. The ST gaps are shown to decrease monotonically with the increase of chain length, and become vanishingly small (within 0.1 kcal/mol) in the limit of an infinitely large polyacene. In addition, based on our calculated active orbital occupation numbers, the ground states for large acenes are shown to be polyradical singlets.

Abstract:
We try to improve the Thomas-Fermi model for the total energy and electron density of atoms and molecules by directly modifying the Euler equation for the electron density, which we argue is less affected by nonlocal corrections. Here we consider the simplest such modification by adding a linear gradient term to the Euler equation. For atoms, the coefficient of the gradient term can be chosen so that the correct exponential decay constant far from the nucleus is obtained. This model then gives a much improved description of the electron density at smaller distances, yielding in particular a finite density at the nucleus that is in good qualitative agreement with exact results. The cusp condition differs from the exact value by a factor of two. Values for the total energy of atomic systems, obtained by coupling parameter integration of the densities given by the Euler equation, are about as accurate as those given by very best Thomas-Fermi-Weizsacker models, and the density is much more accurate. Possible connections to orbital-free methods for the kinetic-energy functional in density functional theory are discussed.

Abstract:
In the density functional (DF) theory of Kohn and Sham, the kinetic energy of the ground state of a system of noninteracting electrons in a general external field is calculated using a set of orbitals. Orbital free methods attempt to calculate this directly from the electron density by approximating the universal but unknown kinetic energy density functional. However simple local approximations are inaccurate and it has proved very difficult to devise generally accurate nonlocal approximations. We focus instead on the kinetic potential, the functional derivative of the kinetic energy DF, which appears in the Euler equation for the electron density. We argue that the kinetic potential is more local and more amenable to simple physically motivated approximations in many relevant cases, and describe two pathways by which the value of the kinetic energy can be efficiently calculated. We propose two nonlocal orbital free kinetic potentials that reduce to known exact forms for both slowly varying and rapidly varying perturbations and also reproduce exact results for the linear response of the density of the homogeneous system to small perturbations. A simple and systematic approach for generating accurate and weak ab-initio local pseudopotentials which produce a smooth slowly varying valence component of the electron density is proposed for use in orbital free DF calculations of molecules and solids. The use of these local pseudopotentials further minimizes the possible errors from the kinetic potentials. Our theory yields results for the total energies and ionization energies of atoms, and for the shell structure in the atomic radial density profiles that are in very good agreement with calculations using the full Kohn-Sham theory.

Abstract:
We review our previous work on the dynamic structure factor S(k,omega) of liquid Ge (l-Ge) at temperature T = 1250 K, and of amorphous Ge (a-Ge) at T = 300 K, using ab initio molecular dynamics [Phys. Rev. B67, 104205 (2003)]. The electronic energy is computed using density-functional theory, primarily in the generalized gradient approximation, together with a plane wave representation of the wave functions and ultra-soft pseudopotentials. We use a 64-atom cell with periodic boundary conditions, and calculate averages over runs of up to 16 ps. The calculated liquid S(k,omega) agrees qualitatively with that obtained by Hosokawa et al, using inelastic X-ray scattering. In a-Ge, we find that the calculated S(k,omega) is in qualitative agreement with that obtained experimentally by Maley et al. Our results suggest that the ab initio approach is sufficient to allow approximate calculations of S(k,omega) in both liquid and amorphous materials.

Abstract:
By incorporating the nonempirical SCAN semilocal density functional [Sun, Ruzsinszky, and Perdew, Phys. Rev. Lett. 115, 036402 (2015)] in the underlying expression of four existing parameter-free hybrid and double-hybrid models, we propose one hybrid (SCAN0) and three double-hybrid (SCAN0-DH, SCAN-QIDH, and SCAN0-2) density functionals, which are free of any empirical parameter. The SCAN-based hybrid and double-hybrid functionals consistently outperform their parent SCAN semilocal functional for a diverse range of applications. The SCAN-based semilocal, hybrid, and double-hybrid functionals generally perform better than the corresponding PBE-based functionals. In addition, the SCAN0-2 and SCAN-QIDH double-hybrid functionals significantly reduce the self-interaction error and noncovalent interaction error associated with their parent SCAN semilocal functional, extending the applicability of SCAN-based functionals to a very wide variety of systems.

Abstract:
We calculate the dynamic structure factor S(k,omega) of liquid Ge (l-Ge) at temperature T = 1250 K, and of amorphous Ge (a-Ge) at T = 300 K, using ab initio molecular dynamics. The electronic energy is computed using density-functional theory, primarily in the generalized gradient approximation, together with a plane wave representation of the wave functions and ultra-soft pseudopotentials. We use a 64-atom cell with periodic boundary conditions, and calculate averages over runs of up to 16 ps. The calculated liquid S(k,omega) agrees qualitatively with that obtained by Hosokawa et al, using inelastic X-ray scattering. In a-Ge, we find that the calculated S(k,omega) is in qualitative agreement with that obtained experimentally by Maley et al. Our results suggest that the ab initio approach is sufficient to allow approximate calculations of S(k,omega) in both liquid and amorphous materials.

Abstract:
We describe a simple model for calculating the zero-temperature superfluid density of Zn-doped YBa_2Cu_3O_{7-\delta} as a function of the fraction x of in-plane Cu atoms which are replaced by Zn. The basis of the calculation is a ``Swiss cheese'' picture of a single CuO_2 layer, in which a substitutional Zn impurity creates a normal region of area $\pi\xi_{ab}^2$ around it as originally suggested by Nachumi et al. Here $\xi_{ab}$ is the zero-temperature in-plane coherence length at x = 0. We use this picture to calculate the variation of the in-plane superfluid density with x at temperature T = 0, using both a numerical approach and an analytical approximation. For $\delta = 0.37$, if we use the value $\xi_{ab}$ = 18.3 angstrom, we find that the in-plane superfluid decreases with increasing x and vanishes near $x_c = 0.01$ in the analytical approximation, and near $x_c = 0.014$ in the numerical approach. $x_c$ is quite sensitive to $\xi_{ab}$, whose value is not widely agreed upon. The model also predicts a peak in the real part of the conductivity, Re$\sigma_e(\omega, x)$, at concentrations $x \sim x_c$, and low frequencies, and a variation of critical current density with x of the form $J_c(x) \propto n_{S,e}(x)^{7/4}$ near percolation, where $n_{S,e}(x)$ is the in-plane superfluid density.

Abstract:
Without the use of any empirical fitting to experimental or high-level ab initio data, we present a double-hybrid density functional approximation for the exchange-correlation energy, combining the exact Hartree-Fock exchange and second-order Moller-Plesset (MP2) correlation with the Perdew-Burke-Ernzerhof (PBE) functional. This functional, denoted as PBE0-2, is shown to be accurate for a wide range of applications, when compared with other functionals and the ab initio MP2 method. The qualitative failures of conventional density functional approximations, such as self-interaction error and noncovalent interaction error, are significantly reduced by PBE0-2.

Abstract:
From the perspective of perturbation theory, we propose a systematic procedure for the evaluation of the derivative discontinuity (DD) of the exchange-correlation energy functional in Kohn-Sham density functional theory (KS-DFT), wherein the exact DD can in principle be obtained by summing up all the perturbation corrections to infinite order. Truncation of the perturbation series at low order yields an efficient scheme for obtaining the approximate DD. While the zeroth-order theory yields a vanishing DD, the first-order correction to the DD can be expressed as an explicit universal functional of the ground-state density and the KS lowest unoccupied molecular orbital density, allowing the direct evaluation of the DD in the standard KS method without extra computational cost. The fundamental gap can be predicted by adding the estimated DD to the KS gap. This scheme is shown to be accurate in the prediction of the fundamental gaps for a wide variety of atoms and molecules.