Electronic levels and electrical response of periodic molecular structures from plane-wave orbital-dependent calculations

Plane-wave electronic-structure predictions based upon orbital-dependent density-functional theory (OD-DFT) approximations, such as hybrid density-functional methods and self-interaction density-functional corrections, are severely affected by computational inaccuracies in evaluating electron interactions in the plane-wave representation. These errors arise from divergence singularities in the plane-wave summation of electrostatic and exchange interaction contributions. Auxiliary-function corrections are reciprocal-space countercharge corrections that cancel plane-wave singularities through the addition of an auxiliary function to the point-charge electrostatic kernel that enters into the expression of interaction terms. At variance with real-space countercharge corrections that are employed in the context of density-functional theory (DFT), reciprocal-space corrections are computationally inexpensive, making them suited to more demanding OD-DFT calculations. Nevertheless, there exists much freedom in the choice of auxiliary functions and various definitions result in different levels of performance in eliminating plane-wave inaccuracies. In this work, we derive exact point-charge auxiliary functions for the description of molecular structures of arbitrary translational symmetry, including the yet unaddressed one-dimensional case. In addition, we provide a critical assessment of different reciprocal-space countercharge corrections and demonstrate the improved accuracy of point-charge auxiliary functions in predicting the electronic levels and electrical response of conjugated polymers from plane-wave OD-DFT calculations.Comment: 11 pages, 7 figure

Assessment of regional trade and virtual water flows in China

The success of China's economic development has left deep marks on resource availability and quality. Some regions in China are relatively poor with regards to water resources. This problem is exacerbated by economic growth. Flourishing trade activities on both domestic and international levels have resulted in significant amounts of water withdrawal and water pollution. Hence the goal of this paper is to evaluate the current inter-regional trade structure and its effects on water consumption and pollution via ‘virtual water flows’. Virtual water is the water embedded in products and used in the whole production chain, and that is traded between regions or exported to other countries. For this assessment of trade flows and effects on water resources, we have developed an extended regional input–output model for eight hydro-economic regions in China to account for virtual water flows between North and South China. The findings show that the current trade structure in China is not very favorable with regards to water resource allocation and efficiency. North China as a water scarce region virtually exports about 5% of its total available freshwater resources while accepting large amounts of wastewater for other regions' consumption. By contrast, South China a region with abundant water resources is virtually importing water from other regions while their imports are creating waste water polluting other regions' hydro-ecosystems

Robust quantile estimation and prediction for spatial processes

In this paper, we present a statistical framework for modeling conditional quantiles of spatial processes assumed to be strongly mixing in space. We establish the $L_1$ consistency and the asymptotic normality of the kernel conditional quantile estimator in the case of random fields. We also define a nonparametric spatial predictor and illustrate the methodology used with some simulations.Comment: 13 page

Revised self-consistent continuum solvation in electronic-structure calculations

The solvation model proposed by Fattebert and Gygi [Journal of Computational Chemistry 23, 662 (2002)] and Scherlis et al. [Journal of Chemical Physics 124, 074103 (2006)] is reformulated, overcoming some of the numerical limitations encountered and extending its range of applicability. We first recast the problem in terms of induced polarization charges that act as a direct mapping of the self-consistent continuum dielectric; this allows to define a functional form for the dielectric that is well behaved both in the high-density region of the nuclear charges and in the low-density region where the electronic wavefunctions decay into the solvent. Second, we outline an iterative procedure to solve the Poisson equation for the quantum fragment embedded in the solvent that does not require multi-grid algorithms, is trivially parallel, and can be applied to any Bravais crystallographic system. Last, we capture some of the non-electrostatic or cavitation terms via a combined use of the quantum volume and quantum surface [Physical Review Letters 94, 145501 (2005)] of the solute. The resulting self-consistent continuum solvation (SCCS) model provides a very effective and compact fit of computational and experimental data, whereby the static dielectric constant of the solvent and one parameter allow to fit the electrostatic energy provided by the PCM model with a mean absolute error of 0.3 kcal/mol on a set of 240 neutral solutes. Two parameters allow to fit experimental solvation energies on the same set with a mean absolute error of 1.3 kcal/mol. A detailed analysis of these results, broken down along different classes of chemical compounds, shows that several classes of organic compounds display very high accuracy, with solvation energies in error of 0.3-0.4 kcal/mol, whereby larger discrepancies are mostly limited to self-dissociating species and strong hydrogen-bond forming compounds.Comment: The following article has been accepted by The Journal of Chemical Physics. After it is published, it will be found at http://link.aip.org/link/?jcp