Recent Quantum Monte Carlo data for the exchange‐correlation energy density of pseudopotential systems strongly suggest the value of using the Laplacian of the density as a variable for constructing first‐order corrections to the local density approximation of density functional theory. We report on an exchange functional built on these observations and extended to the all‐electron case. The model keeps the typical properties of constraint‐based generalized gradient approximations (GGAs) and also has a finite‐valued potential at the nucleus, unlike the GGA. Problems with oscillatory behavior in the potential due to higher order derivatives are controlled by a curvature minimization constraint. The results are tested against exact potentials for the He and Ne atom. A combination of gradient and Laplacian as suggested by a gradient expansion of the exchange hole gives the best overall results. © 2012 Wiley Periodicals, Inc.

The Mossbauer effect of the 26.5-keV -y-ray transition of Dy 161 has been employed to study relaxation effects in dysprosium ethyl sulfate. The relaxation times determined from the Mossbauer spectra, while showing a typical exponential temperature dependence, were found to be faster than the corresponding rates extrapolated from the results obtained with "standard" relaxation-time measurements. Measurements employing oriented single crystals demonstrate "spin memory" of nuclear orientation during the relaxation processes: The selection rules Araj=0 are verified for the Orbach relaxation processes. ^° 10 .a" MOSSBAUER J L iiiit LINEWIDTH 0.8 0,7 0.6 0.5 0.4 0.3 0.2 0.1 0.0 J I L_ l/T ( 0 K" , > FIG. 4. Summary of relaxation times in DyES. The Hartshorne bridge measurements are from Refs. 9-12, the Faraday rotation measurement from Ref. 13, and the linewidth measurement from Ref. 14.

It is well known that in the gradient expansion approximation to density functional theory (DFT) the gradient and Laplacian of the density make interchangeable contributions to the exchange correlation (XC) energy. This is an arbitrary "gauge" freedom for building DFT models, normally used to eliminate the Laplacian from the generalized gradient approximation (GGA) level of DFT development. We explore the implications of keeping the Laplacian at this level of DFT, to develop a model that fits the known behavior of the XC hole, which can only be described as a system average in conventional GGA. We generate a family of exchange models that obey the same constraints as conventional GGA's, but which in addition have a finite-valued potential at the atomic nucleus unlike GGA's. These are tested against exact densities and exchange potentials for small atoms, and for constraints chosen to reproduce the SOGGA and the APBE variants of the GGA. The model reliably reproduces exchange energies of closed shell atoms, once constraints such the local Lieb-Oxford bound, whose effects depend upon choice of energy-density gauge, are recast in invariant form.