Hellman-Feynman operator sampling in Diffusion Monte Carlo calculations

Diffusion Monte Carlo (DMC) calculations typically yield highly accurate results in solid-state and quantum-chemical calculations. However, operators that do not commute with the Hamiltonian are at best sampled correctly up to second order in the error of the underlying trial wavefunction, once simple corrections have been applied. This error is of the same order as that for the energy in variational calculations. Operators that suffer from these problems include potential energies and the density. This paper presents a new method, based on the Hellman-Feynman theorem, for the correct DMC sampling of all operators diagonal in real space. Our method is easy to implement in any standard DMC code

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

Interaction-Induced Spin Polarization in Quantum Dots

The electronic states of lateral many electron quantum dots in high magnetic fields are analyzed in terms of energy and spin. In a regime with two Landau levels in the dot, several Coulomb blockade peaks are measured. A zig-zag pattern is found as it is known from the Fock-Darwin spectrum. However, only data from Landau level 0 show the typical spin-induced bimodality, whereas features from Landau level 1 cannot be explained with the Fock-Darwin picture. Instead, by including the interaction effects within spin-density-functional theory a good agreement between experiment and theory is obtained. The absence of bimodality on Landau level 1 is found to be due to strong spin polarization.Comment: 4 pages, 5 figure

Quantum Monte Carlo modelling of the spherically averaged structure factor of a many-electron system

The interaction and exchange-correlation contributions to the ground-state energy of an arbitrary many-electron system can be obtained from a spherical average of the wavevector-dependent diagonal structure factor (SF). We model the continuous-k spherically averaged SF using quantum Monte Carlo calculations in finite simulation cells. We thus derive a method that allows to substantially reduce the troublesome Coulomb finite-size errors that are usually present in ground-state energy calculations. To demonstrate this, we perform variational Monte Carlo calculations of the interaction energy of the homogeneous electron gas. The method is, however, equally applicable to arbitrary inhomogeneous systems.Comment: 4 pages, 5 figure

Dimensional-scaling estimate of the energy of a large system from that of its building blocks: Hubbard model and Fermi liquid

A simple, physically motivated, scaling hypothesis, which becomes exact in important limits, yields estimates for the ground-state energy of large, composed, systems in terms of the ground-state energy of its building blocks. The concept is illustrated for the electron liquid, and the Hubbard model. By means of this scaling argument the energy of the one-dimensional half-filled Hubbard model is estimated from that of a 2-site Hubbard dimer, obtaining quantitative agreement with the exact one-dimensional Bethe-Ansatz solution, and the energies of the two- and three-dimensional half-filled Hubbard models are estimated from the one-dimensional energy, recovering exact results for $U\to 0$ and $U\to \infty$ and coming close to Quantum Monte Carlo data for intermediate $U$.Comment: 3 figure

Relativistic model for nuclear matter and atomic nuclei with momentum-dependent self-energies

The Lagrangian density of standard relativistic mean-field (RMF) models with density-dependent meson-nucleon coupling vertices is modified by introducing couplings of the meson fields to derivative nucleon densities. As a consequence, the nucleon self energies, that describe the effective in-medium interaction, become momentum dependent. In this approach it is possible to increase the effective (Landau) mass of the nucleons, that is related to the density of states at the Fermi energy, as compared to conventional relativistic models. At the same time the relativistic effective (Dirac) mass is kept small in order to obtain a realistic strength of the spin-orbit interaction. Additionally, the empirical Schroedinger-equivalent central optical potential from Dirac phenomenology is reasonably well described. A parametrization of the model is obtained by a fit to properties of doubly magic atomic nuclei. Results for symmetric nuclear matter, neutron matter and finite nuclei are discussed.Comment: 14 pages, 7 figures, 5 tables, extended introduction and conclusions, additional references, minor corrections, accepted for publication in Phys. Rev.

Extracting convergent surface energies from slab calculations

The formation energy of a solid surface can be extracted from slab calculations if the bulk energy per atom is known. It has been pointed out previously that the resulting surface energy will diverge with slab thickness if the bulk energy is in error, in the context of calculations which used different methods to study the bulk and slab systems. We show here that this result is equally relevant for state-of-the-art computational methods which carefully treat bulk and slab systems in the same way. Here we compare different approaches, and present a solution to the problem that eliminates the divergence and leads to rapidly convergent and accurate surface energies.Comment: 3 revtex pages, 1 figure, in print on J. Phys. Cond. Mat

Van der Waals Coefficients of Atoms and Molecules from a Simple Approximation for the Polarizability

A simple and computationally efficient scheme to calculate approximate imaginary-frequency dependent polarizability, hence asymptotic van der Waals coefficient, within density functional theory is proposed. The dynamical dipolar polarizabilities of atoms and molecules are calculated starting from the Thomas-Fermi-von Weizs\"acker (TFvW) approximation for the independent-electron kinetic energy functional. The van der Waals coefficients for a number of closed-shell ions and a few molecules are hence calculated and compared with available values obtained by fully first-principles calculations. The success in these test cases shows the potential of the proposed TFvW approximate response function in capturing the essence of long range correlations and may give useful information for constructing a functional which naturally includes van der Waals interactions.Comment: 6 pages, 4 figures. To appear in Phys. Rev.

Momentum distributions in time-dependent density functional theory: Product phase approximation for non-sequential double ionization in strong laser fields

We investigate the possibility to deduce momentum space properties from time-dependent density functional calculations. Electron and ion momentum distributions after double ionization of a model Helium atom in a strong few-cycle laser pulse are studied. We show that, in this case, the choice of suitable functionals for the observables is considerably more important than the choice of the correlation potential in the time-dependent Kohn-Sham equations. By comparison with the solution of the time-dependent Schroedinger equation, the insufficiency of functionals neglecting electron correlation is demonstrated. We construct a functional of the Kohn-Sham orbitals, which in principle yields the exact momentum distributions of the electrons and the ion. The product-phase approximation is introduced, which reduces the problem of approximating this functional significantly.Comment: 8 pages, 5 figures, RevTeX