S. B. Trickey

Full-potential, linearized augmented plane wave programs for crystalline systems

In solids, linearized augmented plane waves (LAPWs) have proven to be an effective basis for the solution of the Kohn-Sham equations, the main calculational task in the local spin density approximation (LSDA) to density functional theory. The WIEN package uses LAPWs to calculate the LSDA total energy, spin densities, Kohn-Sham eigenvalues, and the electric field gradients at nuclear sites for a broad variety of space groups. Options include retention or omission of non-muffin-tin contributions (hence WIEN is a full-potential or F-LAPW code) and relativistic corrections (full treatment for core states, Scalar-relativistic for valence states).

Quantum fluids and solids

Information on the physics of superfluids and quantum solids is covered in the proceedings. Areas covered include: neutron scattering, ion motion and zero sound in liquid /sup 3/He; unusual quantum systems like spin-aligned hydrogen, /sup 6/He, superfluid solids, and liquid crystals; solid helium; quantum fluids and solids at low dimensionality; and properties of /sup 3/He-/sup 4/He mixtures. (GHT)

Comment on “Concerning the applicability of density functional methods to atomic and molecular negative ions” [J. Chem. Phys. 105, 862 (1996)]

We systematize and clarify the significance and relationship of recently published numerical findings regarding atomic and molecular anions to both density functional theory fundamentals and approximations. Calculations for F− with all-numerical codes are included as brief examples.

Variational fitting methods for electronic structure calculations

We review the basics and the evolution of a powerful and widely applicable general approach to the systematic reduction of computational burden in many-electron calculations. Variational fitting of electron densities (either total or partial) has the great advantage, for quantum mechanical calculations, that it respects the stationarity property, which is at the heart of the success of the basis set expansion methods ubiquitous in computational chemistry and materials physics. The key point is easy. In a finite system, independent of whether the fitted charge distribution is constrained to contain the proper amount of charge, variational fitting guarantees that the quantum mechanical total energy retains the stationarity property. Thus, many-electron quantum mechanics with variational fitting of an electronic density in an incomplete density-fitting basis set behaves similarly as the exact quantum mechanical energy does when evaluated with an incomplete basis set to fit wavefunctions or spin-orbitals. Periodically bounded systems are a bit more subtle but the essential stationarity is preserved. This preservation of an exact property is quite distinct from truncation of the resolution of the identity in a basis. Variational fitting has proven to have benefits far beyond the original objective of making a Gaussian-orbital basis calculation of an early density functional computationally feasible. We survey many of those developments briefly, with guidance to the pertinent literature and a few remarks about the connections with Quantum Theory Project.

Issues and challenges in orbital-free density functional calculations

a b s t r a c t Solving the Euler equation which corresponds to the energy minimum of a density functional expressed in orbital-free form involves related but distinct computational challenges. One is the choice between allelectron and pseudopotential calculations and, if the latter, construction of the pseudopotential. Another is the stability, speed, and accuracy of solution algorithms. Underlying both is the fundamental issue of satisfactory quality of the approximate functionals (kinetic energy and exchange–correlation). We address both computational issues and illustrate them by some comparative performance testing of our recently developed modified-conjoint generalized gradient approximation kinetic energy functionals. Comparisons are given for atoms, diatomic molecules, and some simple solids.

Electronic structure of solids with WIEN2k

Aspects of the progress over the last 40–50 years in calculating the electronic structure of solids and surfaces are sketched in the context of collaboration on the code now called WIEN2k. Different facets that are relevant for material sciences are discussed, ranging from quantum mechanics to the augmented plane wave (APW) method, as well as improvements in computer hardware and algorithms and related numerical accuracy. In this long period, the complexity and realism of applications to condensed matter systems has significantly increased and many properties which are closely related to experiments can now be calculated. This progress is illustrated by the fact that WIEN2k now is used worldwide by more than 1600 groups. The major steps in this development are illustrated for a few selected examples.

Accurate Homogeneous Electron Gas Exchange-Correlation Free Energy for Local Spin-Density Calculations

An accurate analytical parametrization for the exchange-correlation free energy of the homogeneous electron gas, including interpolation for partial spin-polarization, is derived via thermodynamic analysis of recent restricted path integral Monte-Carlo (RPIMC) data. This parametrization constitutes the local spin density approximation (LSDA) for the exchange-correlation functional in density functional theory. The new finite-temperature LSDA reproduces the RPIMC data well, satisfies the correct high-density and lowand high-T asymptotic limits, and is well-behaved beyond the range of the RPIMC data, suggestive of broad utility.

Non-empirical improvement of PBE and its hybrid PBE0 for general description of molecular properties

Imposition of the constraint that, for the hydrogen atom, the exchange energy cancels the Coulomb repulsion energy yields a non-empirical re-parameterization of the Perdew-Burke-Ernzerhof (PBE) generalized gradient approximation (GGA) exchange-correlation energy functional, and of the related PBE hybrid (PBE0). The re-parameterization, which leads to an increase of the gradient contribution to the exchange energy with respect to the original PBE functional, is tested through the calculation of heats of formation, ionization potentials, electron affinities, proton affinities, binding energies of weakly interacting systems, barrier heights for hydrogen and non-hydrogen transfer reactions, bond distances, and harmonic frequencies, for some well known test sets designed to validate energy functionals. The results for the re-parameterized PBE GGA, called PBEmol, give substantial improvement over the original PBE in the prediction of the heats of formation, while retaining the quality of the original PBE functional for description of all the other properties considered. The results for the hybrids indicate that, although the PBE0 functional provides a rather good description of these properties, the predictions of the re-parameterized functional, called PBEmolβ0, are, except in the case of the ionization potentials, modestly better. Also, the results for PBEmolβ0 are comparable to those of B3LYP. In particular, the mean absolute error for the bond distance test set is 17% lower than the corresponding error for B3LYP. The re-parameterization for the pure GGA (PBEmol) differs from that for the hybrid (PBEmolβ0), illustrating that improvement at the GGA level of complexity does not necessarily provide the best GGA for use in a hybrid.

Calculation of the magnetization and total energy of vanadium as a function of lattice parameter

Abstract Self-consistent spin-polarized APW calculations have been performed to determine the energy band structure of metallic vanadium in an assumed ferromagnetic b.c.c. structure as a function of lattice parameter. The statistical exchange (‘Xα’) and muffin-tin approximations were used. At each lattice parameter for which a calculation was performed, the Xα cohesive energy, the pressure, and the magnetization were calculated. The calculated cohesive energy and pressure agree fairly well with experiment. The calculations also correctly predict the absence of a magnetic moment for vanadium at its equilibrium lattice constant. However, a nonmagnetic-to-magnetic transition is found to occur abruptly at a lattice constant which is about a factor of 1·25 larger than the equilibrium value, and which is in good qualitative agreement with the appearance of a local magnetic moment in certain vanadium alloys.

Properties of constraint-based single-point approximate kinetic energy functionals

We present an analysis and extension of our constraint-based approach to orbital-free OF kinetic-energy KE density functionals intended for the calculation of quantum-mechanical forces in multiscale moleculardynamics simulations. Suitability for realistic system simulations requires that the OF-KE functional yield accurate forces on the nuclei yet be computationally simple. We therefore require that the functionals be based on density-functional theory constraints, be local, be dependent at most upon a small number of parameters fitted to a training set of limited size, and be applicable beyond the scope of the training set. Our previous “modified-conjoint” generalized-gradient-type functionals were constrained to producing a positive-definite Pauli potential. Though distinctly better than several published generalized-gradient-approximation-type functionals in that they gave semiquantitative agreement with Born-Oppenheimer forces from full Kohn-Sham results, those modified-conjoint functionals suffer from unphysical singularities at the nuclei. Here we show how to remove such singularities by introducing higher-order density derivatives and analyze the consequences. We give a simple illustration of such a functional and a few tests of it.