35,916 research outputs found
Energy surface, chemical potentials, Kohn-Sham energies in spin-polarized density functional theory
On the basis of the zero-temperature grand canonical ensemble generalization
of the energy E[N,N_s,v,B] for fractional particle N and spin N_s numbers, the
energy surface over the (N,N_s) plane is displayed and analyzed in the case of
homogeneous external magnetic fields B(r). The (negative of the)
left/right-side derivatives of the energy with respect to N, N_up, and N_down
give the fixed-N_s, spin-up, and spin-down ionization potentials/electron
affinities, respectively, while the derivative of E[N,N_s,v,B] with respect to
N_s gives the (signed) half excitation energy to a state with N_s increased (or
decreased) by 2. The highest occupied and lowest unoccupied Kohn-Sham
spin-orbital energies are identified as the corresponding spin-up and spin-down
ionization potentials and electron affinities. The excitation energies to the
states with N_s+2, N_s-2, can be obtained as the differences between the lowest
unoccupied and the opposite-spin highest occupied spin-orbital energies, if the
(N,N_s) representation of the Kohn-Sham spin-potentials is used. The cases
where the convexity condition on the energy does not hold are also discussed.
Finally, the discontinuities of the energy derivatives and the Kohn-Sham
potential are analyzed and related.Comment: 35 pages, to appear in JCP; text made more precise, Aufbau discussed,
T_s derivative discontinuities given too, two Appendices adde
Empirical analysis of the Lieb-Oxford bound in ions and molecules
Universal properties of the Coulomb interaction energy apply to all
many-electron systems. Bounds on the exchange-correlation energy, inparticular,
are important for the construction of improved density functionals. Here we
investigate one such universal property -- the Lieb-Oxford lower bound -- for
ionic and molecular systems. In recent work [J. Chem. Phys. 127, 054106
(2007)], we observed that for atoms and electron liquids this bound may be
substantially tightened. Calculations for a few ions and molecules suggested
the same tendency, but were not conclusive due to the small number of systems
considered. Here we extend that analysis to many different families of ions and
molecules, and find that for these, too, the bound can be empirically tightened
by a similar margin as for atoms and electron liquids. Tightening the
Lieb-Oxford bound will have consequences for the performance of various
approximate exchange-correlation functionals.Comment: 8 pages, 3 color figure
Correlation energy, pair-distribution functions and static structure factors of jellium
We discuss and clarify a simple and accurate interpolation scheme for the
spin-resolved electron static structure factor (and corresponding pair
correlation function) of the 3D unpolarized homogeneous electron gas which,
along with some analytic properties of the spin-resolved pair-correlation
functions, we have just published. We compare our results with the very recent
spin-resolved scheme by Schmidt et al., and focus our attention on the
spin-resolved correlation energies and the high-density limit of the
correlation functions.Comment: 8 pages, 3 figures. Proceedings of the conference on Statistical
Mechanics and Strongly Correlated Systems (Bachelet, Parisi & Vulpiani Eds.)
to appear as a special issue of Physica A (Elsevier, Amsterdam 2000
Two Avenues to Self-Interaction Correction within Kohn-Sham Theory: Unitary Invariance is the Shortcut
The most widely-used density functionals for the exchange-correlation energy
are inexact for one-electron systems. Their self-interaction errors can be
severe in some applications. The problem is not only to correct the
self-interaction error, but to do so in a way that will not violate
size-consistency and will not go outside the standard Kohn-Sham density
functional theory. The solution via the optimized effective potential (OEP)
method will be discussed, first for the Perdew-Zunger self-interaction
correction (whose performance for molecules is briefly summarized) and then for
the more modern self-interaction corrections based upon unitarily-invariant
indicators of iso-orbital regions. For the latter approaches, the OEP
construction is greatly simplified. The kinetic-energy-based iso-orbital
indicator \tau^W_\sigma(\re)/\tau_\sigma(\re) will be discussed and plotted,
along with an alternative exchange-based indicator
Nonempirical Density Functionals Investigated for Jellium: Spin-Polarized Surfaces, Spherical Clusters, and Bulk Linear Response
Earlier tests show that the Tao-Perdew-Staroverov-Scuseria (TPSS)
nonempirical meta-generalized gradient approximation (meta-GGA) for the
exchange-correlation energy yields more accurate surface energies than the
local spin density (LSD) approximation for spin-unpolarized jellium. In this
study, work functions and surface energies of a jellium metal in the presence
of ``internal'' and external magnetic fields are calculated with LSD,
Perdew-Burke-Ernzerhof (PBE) GGA, and TPSS meta-GGA and its predecessor, the
nearly nonempirical Perdew-Kurth-Zupan-Blaha (PKZB) meta-GGA, using
self-consistent LSD orbitals and densities. The results show that: (i) For
normal bulk densities, the surface correlation energy is the same in TPSS as in
PBE, as it should be since TPSS strives to represent a self-correlation
correction to PBE; (ii) Normal surface density profiles can be scaled uniformly
to the low-density or strong-interaction limit, and TPSS provides an estimate
for that limit that is consistent with (but probably more accurate than) other
estimates; (iii) For both normal and low densities, TPSS provides the same
description of surface magnetism as PBE, suggesting that these approximations
may be generally equivalent for magnetism. The energies of jellium spheres with
up to 106 electrons are calculated using density functionals and compared to
those obtained with Diffusion Quantum Monte Carlo data, including our estimate
for the fixed-node correction. Finally we calculate the linear response of bulk
jellium using these density functionals, and find that not only LSD but also
PBE GGA and TPSS meta-GGA yield a linear-response in good agreement with that
of the Quantum Monte Carlo method, for wavevectors of the perturbing external
potential up to twice the Fermi wavevector.Comment: 14 pages, 9 figure
Localization and delocalization errors in density functional theory and implications for band-gap prediction
The band-gap problem and other systematic failures of approximate functionals
are explained from an analysis of total energy for fractional charges. The
deviation from the correct intrinsic linear behavior in finite systems leads to
delocalization and localization errors in large or bulk systems. Functionals
whose energy is convex for fractional charges such as LDA display an incorrect
apparent linearity in the bulk limit, due to the delocalization error. Concave
functionals also have an incorrect apparent linearity in the bulk calculation,
due to the localization error and imposed symmetry. This resolves an important
paradox and opens the possibility to obtain accurate band-gaps from DFT.Comment: 4 pages 4 figure
Ab initio pseudopotentials for electronic structure calculations of poly-atomic systems using density-functional theory
The package fhi98PP allows one to generate norm-conserving pseudopotentials
adapted to density-functional theory total-energy calculations for a multitude
of elements throughout the periodic table, including first-row and transition
metal elements. The package also facilitates a first assessment of the
pseudopotentials' transferability, either in semilocal or fully separable form,
by means of simple tests carried out for the free atom. Various
parameterizations of the local-density approximation and the generalized
gradient approximation for exchange and correlation are implemented.Comment: 44 pages, 5 Postscript figures, epsfig, elsart, psfrag, submitted to
Comput. Phys. Commun. Other related publications can be found at
http://www.rz-berlin.mpg.de/th/paper.htm
Density-Functional-Based Determination of the CH3-CH4 Hydrogen Exchange Reaction Barrier
Due to the overbinding that is inherent in existing {\em local}
approximations to the density-functional formalism, certain reaction energies
have not been accessible. Since the generalized gradient approximation
significantly decreases the overbinding, prospects for density-functional-based
reaction dynamics are promising. Results on the generalized-gradient based
determination of the CH3-CH4 hydrogen exchange reaction are presented.
Including all Born-Oppenheimer effects an energy barrier of 9.5 kcal/Mole is
found which is a very significant improvement over the local-density
approximation.Comment: 5 twocolumn pages (needs twocolumn.sty), revtex, 3 figures, To appear
in Chem.Phys.Let
Exchange and Correlation in Open Systems of Fluctuating Electron Number
While the exact total energy of a separated open system varies linearly as a
function of average electron number between adjacent integers, the energy
predicted by semi-local density functional approximations curves upward and the
exact-exchange-only or Hartree-Fock energy downward. As a result, semi-local
density functionals fail for separated open systems of fluctuating electron
number, as in stretched molecular ions A and in solid transition metal
oxides. We develop an exact-exchange theory and an exchange-hole sum rule that
explain these failures and we propose a way to correct them via a local hybrid
functional.Comment: 4 pages, 2 figure
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