The coupling constant averaged exchange–correlation energy density

ABSTRACT

The exchange–correlation energy, central to density-functional theory, may be represented in terms of the coupling constant averaged (CCA) exchange–correlation energy density. We present an approach to calculate the CCA energy density using accurate ab initio methods and its application to simple atomic systems. This function provides a link between intrinsically non-local, many-body electronic structure methods and simple local and semi-local density-functional approximations (DFAs). The CCA energy density is resolved into separate exchange and correlation terms and the features of each compared with those of quantities commonly used to construct DFAs. In particular, the more complex structure of the correlation energy density is found to exhibit features that align well with those present in the Laplacian of the density, suggesting its role as a key variable to be used in the construction of improved semi-local correlation functionals. The accurate results presented in this work are also compared with those provided by the Laplacian-dependent Becke–Roussel model for the exchange energy.     

Simulation of all-order density-functional perturbation theory, using the second order and the strong-correlation limit

To boost the accuracy of electronic structure calculations, the exchange-correlation energy may be constructed from the Kohn-Sham orbitals. A formally exact construction is the density-functional perturbation series, which appears to diverge for many real systems. We predict the radius of convergence and resum this series, using only exact exchange and second-order correlation plus explicit density functionals for the strong-interaction limit. Our new correlation functional, along with exact exchange, predicts atomization energies with competitive accuracy and without the usual error cancellation.     

Van der Waals interactions in ionic and semiconductor solids

van der Waals (vdW) energy corrected density-functional theory [Phys. Rev. Lett. 102, 073005 (2009)] is applied to study the cohesive properties of ionic and semiconductor solids (C, Si, Ge, GaAs, NaCl, and MgO). The required polarizability and dispersion coefficients are calculated using the dielectric function obtained from time-dependent density-functional theory. Coefficients for "atoms in the solid" are then calculated from the Hirshfeld partitioning of the electron density. It is shown that the Clausius-Mossotti equation that relates the polarizability and the dielectric function is accurate even for covalently-bonded semiconductors. We find an overall improvement in the cohesive properties of Si, Ge, GaAs, NaCl, and MgO, when vdW interactions are included on top of the Perdew-Burke-Ernzerhof or Heyd-Scuseria-Ernzerhof functionals. The relevance of our findings for other solids is discussed.     

Exact ground state density-functional theory for impurity models coupled to external reservoirs and transport calculations

A method is presented employing the density matrix renormalization group to construct exact ground state (GS) exchange correlation functionals for models of correlated electrons coupled to leads. We apply it to show that conductance calculations with Kohn-Sham GS density-functional theory can yield quantitative results in the Coulomb blockade regime. Our study is relevant for "molecular electronics" since it strongly suggests that the well documented discrepancies between theoretical and experimental transport coefficients originate (mainly) from approximations in GS functionals.     

A self-consistent density-functional approach to the structure of electric double layer: charge-asymmetric electrolytes

A self-consistent density-functional approach has been employed to study the structure of an electric double layer formed from a charge-asymmetric (2:l) electrolyte within the restricted primitive model which corresponds to charged hard sphere ions and a continuum solvent. The particle correlation due to hard-core exclusions is evaluated by making use of the universality of the density functionals and the correlation function of the uniform hard sphere fluid obtained through the integral equation theory with an accurate closure relation whereas mean spherical approximation is employed for the electrical contribution. Numerical results on the diffuse layer potential drop, ionic density profile, and the mean electrostatic potential near the electrode surface at several surface charge densities are found to be in quantitative agreement with the available simulation data.     

On the exact formulation of multi-configuration density-functional theory: electron density versus orbitals occupation

The exact formulation of multi-configuration density-functional theory is discussed in this work. As an alternative to range-separated methods, where electron correlation effects are split in the coordinate space, the combination of configuration interaction methods with orbital occupation functionals is explored at the formal level through the separation of correlation effects in the orbital space. When applied to model Hamiltonians, this approach leads to an exact site-occupation embedding theory (SOET). An adiabatic connection expression is derived for the complementary bath functional and a comparison with density matrix embedding theory is made. Illustrative results are given for the simple two-site Hubbard model. SOET is then applied to a quantum chemical Hamiltonian, thus leading to an exact complete active space site-occupation functional theory (CASSOFT) where active electrons are correlated explicitly within the CAS and the remaining contributions to the correlation energy are described with an orbital occupation functional. The computational implementation of SOET and CASSOFT as well as the development of approximate functionals are left for future work.     

Multicomponent density-functional theory for electrons and nuclei

A multicomponent density-functional theory is developed for the combined system of electrons and nuclei. We construct approximate functionals for the electron-nuclear correlation energy and illustrate the theory by explicit calculations for the H+2 molecular ion.     

Random-phase approximation correlation methods for molecules and solids

Random-phase approximation (RPA) correlation methods based on Kohn–Sham density-functional theory and Hartree–Fock are derived using the adiabatic-connection fluctuation dissipation theorem. It is shown that the correlation energy within the adiabatic-connection fluctuation-dissipation theorem is exact in a Kohn–Sham framework while for Hartree–Fock reference states this is not the case. This shows that Kohn–Sham reference states are probably better suited to describe electron correlation for use in RPA methods than Hartree–Fock reference states. Both, Kohn–Sham and Hartree–Fock RPA methods are related to each other both by comparing the underlying correlation functionals and numerically through the comparison of total energies and reaction energies for a set of small organic molecules.     

Decay of correlations under Dobrushin's uniqueness condition and its applications

An estimate on the correlation of functionals of Gibbs fields satisfying Dobrushin's uniqueness condition is given. As a consequence a result of Gross saying that the truncated pair correlation function decays in the same weighted summability sense as the potential can be extended to the whole Dobrushin uniqueness region. Applications to the central limit theorem and the second derivative of the pressure are also given.     

High-level correlated approach to the jellium surface energy, without uniform-gas input

We resolve the long-standing controversy over the metal surface energy: Density-functional methods that require uniform-electron-gas input agree with each other, but not with high-level correlated calculations such as Fermi hypernetted chain and diffusion Monte Carlo calculations that predict the uniform-gas correlation energy. Here we apply the inhomogeneous Singwi-Tosi-Land-Sj?lander method, and find that the density functionals are indeed reliable (because the surface energy is bulklike). Our work also vindicates the use of uniform-gas-based nonlocal kernels in time-dependent density-functional theory.     

Hybrid functionals and GW approximation in the FLAPW method

We present recent advances in numerical implementations of hybrid functionals and the GW approximation within the full-potential linearized augmented-plane-wave (FLAPW) method. The former is an approximation for the exchange–correlation contribution to the total energy functional in density-functional theory, and the latter is an approximation for the electronic self-energy in the framework of many-body perturbation theory. All implementations employ the mixed product basis, which has evolved into a versatile basis for the products of wave functions, describing the incoming and outgoing states of an electron that is scattered by interacting with another electron. It can thus be used for representing the nonlocal potential in hybrid functionals as well as the screened interaction and related quantities in GW calculations. In particular, the six-dimensional space integrals of the Hamiltonian exchange matrix elements (and exchange self-energy) decompose into sums over vector–matrix–vector products, which can be evaluated easily. The correlation part of the GW self-energy, which contains a time or frequency dependence, is calculated on the imaginary frequency axis with a subsequent analytic continuation to the real axis or, alternatively, by a direct frequency convolution of the Green function G and the dynamically screened Coulomb interaction W along a contour integration path that avoids the poles of the Green function. Hybrid-functional and GW calculations are notoriously computationally expensive. We present a number of tricks that reduce the computational cost considerably, including the use of spatial and time-reversal symmetries, modifications of the mixed product basis with the aim to optimize it for the correlation self-energy and another modification that makes the Coulomb matrix sparse, analytic expansions of the interaction potentials around the point of divergence at k = 0, and a nested density and density-matrix convergence scheme for hybrid-functional calculations. We show CPU timings for prototype semiconductors and illustrative results for GdN and ZnO.     

First-principles calculations of the Urbach tail in the optical absorption spectra of silica glass

We present density-functional theory calculations of the optical absorption spectra of silica glass for temperatures up to 2400?K. The calculated spectra exhibit exponential tails near the fundamental absorption edge that follow the Urbach rule in good agreement with experiments. We discuss the accuracy of our results by comparing to hybrid exchange correlation functionals. We show that the Urbach rule holds in a frequency interval where optical absorption is Poisson distributed with very large statistical fluctuations. In this regime, a direct relation between the optical absorption coefficient and electronic density of states is derived, which provides a link between photoemission and absorption spectra and is used to determine the lower bound to the Urbach frequency regime.     

Nonlinear transport in the Boltzmann limit

Formal expressions for the irreversible fluxes of a simple fluid are obtained as functionals of the thermodynamic forces and local equilibrium time correlation functions. The Boltzmann limit of the correlation functions is shown to yield expressions for the irreversible fluxes equivalent to those obtained from the nonlinear Boltzmann kinetic equation. Specifically, for states near equilibrium, the fluxes may be formally expanded in powers of the thermodynamic gradients and the associated transport coefficients identified as integrals of time correlation functions. It is proved explicitly through nonlinear Burnett order that the time correlation function expressions for these transport coefficients agree with those of the Chapman-Enskog expansion of the nonlinear Boltzmann equation. For states far from equilibrium the local equilibrium time correlation functions are determined in the Boltzmann limit and a similar equivalence to the Boltzmann equation solution is established. Other formal representations of the fluxes are indicated; in particular, a projection operator form and its Boltzmann limit are discussed. As an example, the nonequilibrium correlation functions for steady shear flow are calculated exactly in the Boltzmann limit for Maxwell molecules.Research supported in part by NSF grant PHY 76-21453.     

Hydrogen bonds and van der waals forces in ice at ambient and high pressures

The first principles methods, density-functional theory and quantum Monte Carlo, have been used to examine the balance between van der Waals (vdW) forces and hydrogen bonding in ambient and high-pressure phases of ice. At higher pressure, the contribution to the lattice energy from vdW increases and that from hydrogen bonding decreases, leading vdW to have a substantial effect on the transition pressures between the crystalline ice phases. An important consequence, likely to be of relevance to molecular crystals in general, is that transition pressures obtained from density-functional theory exchange-correlation functionals which neglect vdW forces are greatly overestimated.     

A metric space of interactions and the thermodynamic limit

A metric space of interactions is formed for classical continuous systems and for quantum and classical lattice systems. It is shown that the thermodynamic limit of the grand canonical pressure exists on an extended class of potentials. In each neighborhood of each superstable lower regular, weakly tempered pair interaction and for each of a countable number of test functions there is an interaction for which the Fisher thermodynamic limit of the correlation functionals applied to the test function exists.     

Positron annihilation in small metal voids

The electron density profile around small voids of varying radii in Al is calculated in a fully self-consistent manner using the density-functional formalism of Hohenberg-Kohn-Sham. The results are then used to calculate positron lifetimes and angular correlation between annihilation photons as a function of the size of the void.     

Optical saturation driven by exciton confinement in molecular chains: a time-dependent density-functional theory approach

We identify excitonic confinement in one-dimensional molecular chains (i.e., polyacetylene and H2) as the main driving force for the saturation of the chain polarizability as a function of the number of molecular units. This conclusion is based on first principles time-dependent density-functional theory calculations using a recently developed exchange-correlation kernel that accounts for excitonic effects. The failure of simple local and semilocal functionals is shown to be linked to the lack of memory effects, spatial ultranonlocality, and self-interaction corrections. These effects get smaller as the gap reduces, in which case such simple approximations do perform better.