797 publications from this institution
In this paper, the history, present status, and future of density-functional theory (DFT) is informally reviewed and discussed by 70 workers in the field, including molecular scientists, materials scientists, method developers and practitioners.
The classical turning radius Rt of an atom can be defined as the radius where the KS potential is equal to the negative ionisation potential of the atom, i.e. where v_s(R_t)=\epsilon_h. It was recently shown [P.N.A.S. 115, E11578 (2018)] to yield chemically relevant bonding distances, in line with known empirical values. In this work we show that extension of the concept to non-integer electron number yields additional information about atomic systems, and can be used to detect the difficulty of adding or subtracting electrons. Notably, it reflects the ease of bonding in open p-shells, and its greater difficulty in open s-shells. The latter manifests in significant discontinuities in the turning radius as the electron number changes the principal quantum number of the outermost electronic shell (e.g. going from Na to Na^{2+}). We then show that a non-integer picture is required to correctly interpret bonding and dissociation in H_2^+. Results are consistent when properties are calculated exactly, or via an appropriate approximation. They can be interpreted in the context of conceptual density functional theory.
The random-phase approximation (RPA) is exact for the exchange energy of a many-electron ground state, but RPA makes the correlation energy too negative by about 0.5 eV/electron. That large short-range error, which tends to cancel out of isoelectronic energy differences, is largely corrected by an exchange-correlation kernel, or (as in RPA+) by an additive local or semilocal correction. RPA+ is by construction exact for the homogeneous electron gas, and it is also accurate for the jellium surface. RPA+ often gives realistic total energies for atoms or solids in which spin-polarization corrections are absent or small. RPA and RPA+ also yield realistic singlet binding energy curves for ${\mathrm{H}}_{2}$ and ${\mathrm{N}}_{2}$, and thus RPA+ yields correct total energies even for spin-unpolarized atoms with fractional spins and strong correlation, as in stretched ${\mathrm{H}}_{2}$ or ${\mathrm{N}}_{2}$. However, RPA and RPA+ can be very wrong for spin-polarized one-electron systems (especially for stretched ${{\mathrm{H}}_{2}}^{+}$), and also for the spin-polarization energies of atoms. The spin-polarization energy is often a small part of the total energy of an atom, but important for ionization energies, electron affinities, and the atomization energies of molecules. Here we propose a computationally efficient generalized RPA+ (gRPA+) that changes RPA+ only for spin-polarized systems by making gRPA+ exact for all one-electron densities, in the same simple semilocal way that the correlation energy densities of many metageneralized gradient approximations are made self-correlation free. By construction, gRPA+ does not degrade the exact RPA+ description of jellium. gRPA+ is found to greatly improve upon RPA and RPA+ for the ionization energies and electron affinities of light atoms. Many versions of RPA with an approximate exchange-correlation kernel fail to be exact for all one-electron densities, and they can also be self-interaction corrected in this way.
In the exact theory, the ground state energy of an open system varies linearly when the electron number is changed between two adjacent integers. This linear dependence is not reproduced by common approximate density functionals. Deviation from linearity in this dependence has been suggested as a basis for the concept of many-electron self-interaction error (SIE). In this paper, we quantify many-electron SIE of a number of approximations by performing calculations on fractionally charged atoms. We demonstrate the direct relevance of these studies to such problems of common approximate functionals as instabilities of anions, spurious fractional charges on dissociated atoms, and poor description of charge transfer. Semilocal approximations have the largest many-electron SIE, which is only slightly reduced in typical global hybrids. In these approximations the energy versus fractional electron number curves upward, while in Hartree-Fock theory the energy curves downward. Perdew-Zunger self-interaction correction [Phys. Rev. B 23, 5048 (1981)] significantly reduces the many-electron SIE of semilocal functionals but impairs their accuracy for equilibrium properties. In contrast, a long-range corrected hybrid functional can be nearly many-electron SIE-free in many cases (for reasons we discuss) and at the same time performs remarkably well for many molecular properties.
A Reply to the Comment by Ann E. Mattsson, Rickard Armiento, and Thomas R. Mattsson.Received 23 September 2008DOI:https://doi.org/10.1103/PhysRevLett.101.239702©2008 American Physical Society
The electron density, its gradient, and the Kohn-Sham orbital kinetic energy density are the local ingredients of a meta-generalized gradient approximation (meta-GGA). We construct a meta-GGA density functional for the exchange-correlation energy that satisfies exact constraints without empirical parameters. The exchange and correlation terms respect two paradigms: one- or two-electron densities and slowly varying densities, and so describe both molecules and solids with high accuracy, as shown by extensive numerical tests. This functional completes the third rung of "Jacob's ladder" of approximations, above the local spin density and GGA rungs.
© 2016 Author(s). The uniform electron gas and the hydrogen atom play fundamental roles in condensed matter physics and quantum chemistry. The former has an infinite number of electrons uniformly distributed over the neutralizing positively charged background, and the latter only one electron bound to the proton. The uniform electron gas was used to derive the local spin density approximation to the exchange-correlation functional that undergirds the development of the Kohn-Sham density functional theory. We show here that the ground-state exchange-correlation energies of the hydrogen atom and many other 1- and 2-electron systems are modeled surprisingly well by a different local spin density approximation (LSDA0). LSDA0 is constructed to satisfy exact constraints but agrees surprisingly well with the exact results for a uniform two-electron density in a finite, curved three-dimensional space. We also apply LSDA0 to excited or noded 1-electron densities, where it works less well. Furthermore, we show that the localization of the exact exchange hole for a 1- or 2-electron ground state can be measured by the ratio of the exact exchange energy to its optimal lower bound.
