4,851 research outputs found

### All-electron GW calculation for molecules: Ionization energy and electron affinity of conjugated molecules

An efficient all-electron G$^0$W$^0$ method and a quasiparticle
selfconsistent GW (QSGW) method for molecules are proposed in the molecular
orbital space with the full random phase approximation. The convergence with
basis set is examined. As an application, the ionization energy ($I$) and
electron affinity ($A$) of a series of conjugated molecules (up to 32 atoms)
are calculated and compared to experiment. The QSGW result improves the
G$^0$W$^0$ result and both of them are in significantly better agreement with
experimental data than those from Hartree-Fock (HF) and hybrid density
functional calculations, especially for $A$. The nearly correct energy gap and
suppressed self-interaction error by the HF exchange make our method a good
candidate for investigating electronic and transport properties of molecular
systems.Comment: 4 pages, 2 figures, 1 tabl

### An exactly size consistent geminal power via Jastrow factor networks in a local one particle basis

The accurate but expensive product of geminals ansatz may be approximated by
a geminal power, but this approach sacrifices size consistency. Here we show
both analytically and numerically that a size consistent form very similar to
the product of geminals can be recovered using a network of location specific
Jastrow factors. Upon variational energy minimization, the network creates
particle number projections that remove the charge fluctuations responsible for
size inconsistency. This polynomial cost approach captures strong many-electron
correlations, giving a maximum error of just 1.8 kcal/mol during the
double-bond dissociation of H2O in an STO-3G atomic orbital basis.Comment: Updated the original arXiv submission to include improvements
resulting from journal peer review. 5 pages, 4 figures, 1 tabl

### Comment on "Modifying the variational principle in the action integral functional derivation of time-dependent density functional theory" by Jochen Schirmer [arXiv:1010.4223]

In a paper recently published in Phys. Rev. A [arXiv:1010.4223], Schirmer has
criticized an earlier work of mine [arXiv:0803.2727], as well as the
foundations of time-dependent density functional theory. In Ref.[2], I showed
that the so-called "causality paradox" - i.e., the failure of the
exchange-correlation potential derived from the Runge-Gross time-dependent
variational principle to satisfy causality requirements - can be solved by a
careful reformulation of that variational principle. Fortunately, the criticism
presented in Ref.[1] is based on elementary misunderstandings of the nature of
functionals, gauge transformations, and the time-dependent variational
principle. In this Comment I wish to point out and clear these
misunderstandings.Comment: 4 pages. Accepted for publication in Phys. Rev.

### Treatments of the exchange energy in density-functional theory

Following a recent work [Gal, Phys. Rev. A 64, 062503 (2001)], a simple
derivation of the density-functional correction of the Hartree-Fock equations,
the Hartree-Fock-Kohn-Sham equations, is presented, completing an integrated
view of quantum mechanical theories, in which the Kohn-Sham equations, the
Hartree-Fock-Kohn-Sham equations and the ground-state Schrodinger equation
formally stem from a common ground: density-functional theory, through its
Euler equation for the ground-state density. Along similar lines, the Kohn-Sham
formulation of the Hartree-Fock approach is also considered. Further, it is
pointed out that the exchange energy of density-functional theory built from
the Kohn-Sham orbitals can be given by degree-two homogeneous N-particle
density functionals (N=1,2,...), forming a sequence of degree-two homogeneous
exchange-energy density functionals, the first element of which is minus the
classical Coulomb-repulsion energy functional.Comment: 19 pages; original manuscript from 2001 (v1) revised for publication,
with presentation substantially improved, some errors corrected, plus an
additional summarizing figure (Appendix B) include

### First principles investigation of finite-temperature behavior in small sodium clusters

A systematic and detailed investigation of the finite-temperature behavior of
small sodium clusters, Na_n, in the size range of n= 8 to 50 are carried out.
The simulations are performed using density-functional molecular-dynamics with
ultrasoft pseudopotentials. A number of thermodynamic indicators such as
specific heat, caloric curve, root-mean-square bond length fluctuation,
deviation energy, etc. are calculated for each of the clusters. Size dependence
of these indicators reveals several interesting features. The smallest clusters
with n= 8 and 10, do not show any signature of melting transition. With the
increase in size, broad peak in the specific heat is developed, which
alternately for larger clusters evolves into a sharper one, indicating a
solidlike to liquidlike transition. The melting temperatures show irregular
pattern similar to experimentally observed one for larger clusters [ M. Schmidt
et al., Nature (London) 393, 238 (1998) ]. The present calculations also reveal
a remarkable size-sensitive effect in the size range of n= 40 to 55. While
Na_40 and Na_55 show well developed peaks in the specific heat curve, Na_50
cluster exhibits a rather broad peak, indicating a poorly-defined melting
transition. Such a feature has been experimentally observed for gallium and
aluminum clusters [ G. A. Breaux et al., J. Am. Chem. Soc. 126, 8628 (2004); G.
A.Breaux et al., Phys. Rev. Lett. 94, 173401 (2005) ].Comment: 8 pages, 11 figure

### Non-empirical hyper-generalized-gradient functionals constructed from the Lieb-Oxford bound

A simple and completely general representation of the exact
exchange-correlation functional of density-functional theory is derived from
the universal Lieb-Oxford bound, which holds for any Coulomb-interacting
system. This representation leads to an alternative point of view on popular
hybrid functionals, providing a rationale for why they work and how they can be
constructed. A similar representation of the exact correlation functional
allows to construct fully non-empirical hyper-generalized-gradient
approximations (HGGAs), radically departing from established paradigms of
functional construction. Numerical tests of these HGGAs for atomic and
molecular correlation energies and molecular atomization energies show that
even simple HGGAs match or outperform state-of-the-art correlation functionals
currently used in solid-state physics and quantum chemistry.Comment: v2: Major revison. Added information on relation to the gradient
expansion and to local hybrids, improved discussion of size consistency and
of performance relative to other functional

### Spin-independent v-representability of Wigner crystal oscillations in one-dimensional Hubbard chains: The role of spin-charge separation

Electrons in one-dimension display the unusual property of separating their
spin and charge into two independent entities: The first, which derive from
uncharged spin-1/2 electrons, can travel at different velocities when compared
with the second, built from charged spinless electrons. Predicted theoretically
in the early sixties, the spin-charge separation has attracted renewed
attention since the first evidences of experimental observation, with usual
mentions as a possible explanation for high-temperature superconductivity. In
one-dimensional (1D) model systems, the spin-charge separation leads the
frequencies of Friedel oscillations to suffer a 2k_F -- 4k_F crossover, mainly
when dealing with strong correlations, where they are referred to as Wigner
crystal oscillations. In non-magnetized systems, the current density
functionals which are applied to the 1D Hubbard model are not seen to reproduce
this crossover, referring to a more fundamental question: Are the Wigner
crystal oscillations in 1D systems non-interacting v-representable? Or, is
there a spin-independent Kohn-Sham potential which is able to yield spin-charge
separation? Finding an appropriate answer to both questions is our main task
here. By means of exact and DMRG solutions, as well as, a new approach of
exchange-correlation potential, we show the answer to be positive.
Specifically, the v-representable 4k_F oscillations emerge from attractive
interactions mediated by positively charged spinless holes -- the holons -- as
an additional contribution to the repulsive on-site Hubbard interaction

### Density-density functionals and effective potentials in many-body electronic structure calculations

We demonstrate the existence of different density-density functionals
designed to retain selected properties of the many-body ground state in a
non-interacting solution starting from the standard density functional theory
ground state. We focus on diffusion quantum Monte Carlo applications that
require trial wave functions with optimal Fermion nodes. The theory is
extensible and can be used to understand current practices in several
electronic structure methods within a generalized density functional framework.
The theory justifies and stimulates the search of optimal empirical density
functionals and effective potentials for accurate calculations of the
properties of real materials, but also cautions on the limits of their
applicability. The concepts are tested and validated with a near-analytic
model.Comment: five figure

### Random-phase-approximation-based correlation energy functionals: Benchmark results for atoms

The random phase approximation (RPA) for the correlation energy functional of
density functional theory has recently attracted renewed interest. Formulated
in terms of the Kohn-Sham (KS) orbitals and eigenvalues, it promises to resolve
some of the fundamental limitations of the local density and generalized
gradient approximations, as for instance their inability to account for
dispersion forces. First results for atoms, however, indicate that the RPA
overestimates correlation effects as much as the orbital-dependent functional
obtained by a second order perturbation expansion on the basis of the KS
Hamiltonian. In this contribution, three simple extensions of the RPA are
examined, (a) its augmentation by an LDA for short-range correlation, (b) its
combination with the second order exchange term, and (c) its combination with a
partial resummation of the perturbation series including the second order
exchange. It is found that the ground state and correlation energies as well as
the ionization potentials resulting from the extensions (a) and (c) for closed
sub-shell atoms are clearly superior to those obtained with the unmodified RPA.
Quite some effort is made to ensure highly converged RPA data, so that the
results may serve as benchmark data. The numerical techniques developed in this
context, in particular for the inherent frequency integration, should also be
useful for applications of RPA-type functionals to more complex systems.Comment: 11 pages, 7 figure

### How tight is the Lieb-Oxford bound?

Density-functional theory requires ever better exchange-correlation (xc)
functionals for the ever more precise description of many-body effects on
electronic structure. Universal constraints on the xc energy are important
ingredients in the construction of improved functionals. Here we investigate
one such universal property of xc functionals: the Lieb-Oxford lower bound on
the exchange-correlation energy, $E_{xc}[n] \ge -C \int d^3r n^{4/3}$, where
$C\leq C_{LO}=1.68$. To this end, we perform a survey of available exact or
near-exact data on xc energies of atoms, ions, molecules, solids, and some
model Hamiltonians (the electron liquid, Hooke's atom and the Hubbard model).
All physically realistic density distributions investigated are consistent with
the tighter limit $C \leq 1$. For large classes of systems one can obtain
class-specific (but not fully universal) similar bounds. The Lieb-Oxford bound
with $C_{LO}=1.68$ is a key ingredient in the construction of modern xc
functionals, and a substantial change in the prefactor $C$ will have
consequences for the performance of these functionals.Comment: 10 pages, 3 figure

- …