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

Nonlinear instability of density-independent orbital-free kinetic energy functionals

We study in this article the mathematical properties of a class of orbital-free kinetic energy functionals. We prove that these models are linearly stable but nonlinearly unstable, in the sense that the corresponding kinetic energy functionals are not bounded from below. As a matter of illustration, we provide an example of an electronic density of simple shape the kinetic energy of which is negative.Comment: 14 pages, 1 figur