Energetics of the AK13 Semi-Local Kohn-Sham Exchange Energy Functional

The recent non-empirical semi-local exchange functional of Armiento and K\"ummel, the AK13 [PRL 111, 036402 (2013)] incorporates a number of features reproduced by higher-order theory. The AK13 potential behaves analogously with the discontinuous jump associated with the derivative discontinuity at integer particle numbers. Recent works have established that AK13 gives a qualitatively improved orbital description compared to other semi-local methods, and reproduces a band structure closer to higher-order theory. However, its energies and energetics are inaccurate. The present work further investigates the deficiency in energetics. In addition to AK13 results, we find that applying the local-density approximation (LDA) non-self-consistently on the converged AK13 density gives very reasonable energetics with equilibrium lattice constants and bulk moduli well described across 14 systems. We also confirm that the attractive orbital features of AK13 are retained even after full structural relaxation. Hence, the deficient energetics cannot be a result of the AK13 orbitals having adversely affected the quality of the electron density compared to that of usual semi-local functionals; an improved orbital description and good energetics are not in opposition. We also prove that the non-self-consistent scheme is equivalent to using a single external-potential dependent functional in an otherwise consistent KS-DFT scheme. Furthermore, our results also demonstrate that, while an internally consistent KS functional is presently missing, non-self-consistent LDA on AK13 orbitals works as a practical non-empirical computational scheme to predict geometries, bulk moduli, while retaining the band structure features of AK13 at the computational cost of semi-local DFT.Comment: 7 pages, 4 figure

Quantum oscillations in the kinetic energy density: Gradient corrections from the Airy gas

We derive a closed form expression for the quantum corrections to the kinetic energy density (KED) in the Thomas-Fermi (TF) limit of a linear potential model system in three dimensions (the Airy gas). The universality of the expression is tested numerically in a number of three dimensional model systems: (i) jellium surfaces, (ii) hydrogen-like potentials, (iii) systems confined by an harmonic potential in one and (iv) all three dimensions, and (v) a system with a cosine potential (the Mathieu gas). Our results confirm that the usual gradient expansion of extended Thomas-Fermi theory (ETF) does not describe the quantum oscillations for systems that incorporate surface regions where the electron density drops off to zero. We find that the correction derived from the Airy gas is universally applicable to relevant spatial regions of systems of type (i), (ii), and (iv), but somewhat surprisingly not (iii). We discuss possible implications of our findings to the development of functionals for the kinetic energy density.Comment: 15 pages, 9 figure

On the challenge to improve the density response with unusual gradient approximations

Certain excitations, especially ones of long-range charge transfer character, are poorly described by time-dependent density functional theory (TDDFT) when typical (semi-)local functionals are used. A proper description of these excitations would require an exchange-correlation response differing substantially from the usual (semi-)local one. It has recently been shown that functionals of the generalized gradient approximation (GGA) type can yield unusual potentials, mimicking features of the exact exchange derivative discontinuity and showing divergences on orbital nodal surfaces. We here investigate whether these unusual potential properties translate into beneficial response properties. Using the Sternheimer formalism we closely investigate the response obtained with the 2013 exchange approximation by Armiento and K\"ummel (AK13) and the 1988 exchange approximation by Becke (B88), both of which show divergences on orbital nodal planes. Numerical calculations for Na2 as well as analytical and numerical calculations for the hydrogen atom show that the response of AK13 behaves qualitatively different from usual semi local functionals. However, the AK13 functional leads to fundamental instabilities in the asymptotic region that prevent its practical application in TDDFT. Our findings may help the development of future improved functionals, and corroborate that the frequency-dependent Sternheimer formalism is excellently suited for running and analyzing TDDFT calculations

Global hybrids from the semiclassical atom theory satisfying the local density linear response

We propose global hybrid approximations of the exchange-correlation (XC) energy functional which reproduce well the modified fourth-order gradient expansion of the exchange energy in the semiclassical limit of many-electron neutral atoms and recover the full local density approximation (LDA) linear response. These XC functionals represent the hybrid versions of the APBE functional [Phys. Rev. Lett. 106, 186406, (2011)] yet employing an additional correlation functional which uses the localization concept of the correlation energy density to improve the compatibility with the Hartree-Fock exchange as well as the coupling-constant-resolved XC potential energy. Broad energetical and structural testings, including thermochemistry and geometry, transition metal complexes, non-covalent interactions, gold clusters and small gold-molecule interfaces, as well as an analysis of the hybrid parameters, show that our construction is quite robust. In particular, our testing shows that the resulting hybrid, including 20\% of Hartree-Fock exchange and named hAPBE, performs remarkably well for a broad palette of systems and properties, being generally better than popular hybrids (PBE0 and B3LYP). Semi-empirical dispersion corrections are also provided.Comment: 12 pages, 4 figure

The Way Forward

As understanding of the interdependence between a healthy planet and healthy people becomes more developed, complex issues that thread through systems and societies gain new importance. Beyond the traditional Global Environment Outlook (GEO) themes addressing air, biodiversity, oceans, land and fresh water, this GEO-6 assessment addresses cross-cutting issues worthy of further examination. Using a systems approach, these cross-cutting issues offer entry points allowing another dimension for analysing GEO-6 themes as well as understanding the network of interconnections throughout earth and human systems. These cross-cutting issues are grouped according to shared characteristics: health, environmental disasters, gender, education and urbanization are grouped as ‘people and livelihoods’; climate change, polar and mountain regions, chemicals and waste and wastewater are grouped as ‘changing environments’; and resource use, energy and food systems are considered as ‘resources and materials’. While each issue provides useful entry points into GEO-6 themes, it is important to discuss the state of the environment and policy context for each one

Analytic philosophy for biomedical research: the imperative of applying yesterday's timeless messages to today's impasses

The mantra that "the best way to predict the future is to invent it" (attributed to the computer scientist Alan Kay) exemplifies some of the expectations from the technical and innovative sides of biomedical research at present. However, for technical advancements to make real impacts both on patient health and genuine scientific understanding, quite a number of lingering challenges facing the entire spectrum from protein biology all the way to randomized controlled trials should start to be overcome. The proposal in this chapter is that philosophy is essential in this process. By reviewing select examples from the history of science and philosophy, disciplines which were indistinguishable until the mid-nineteenth century, I argue that progress toward the many impasses in biomedicine can be achieved by emphasizing theoretical work (in the true sense of the word 'theory') as a vital foundation for experimental biology. Furthermore, a philosophical biology program that could provide a framework for theoretical investigations is outlined

A Stimuli-Responsive Nanocomposite for 3D Anisotropic Cell-Guidance and Magnetic Soft Robotics

Stimuli-responsive materials have the potential to enable the generation of new bioinspired devices with unique physicochemical properties and cell-instructive ability. Enhancing biocompatibility while simplifying the production methodologies, as well as enabling the creation of complex constructs, i.e., via 3D (bio)printing technologies, remains key challenge in the field. Here, a novel method is presented to biofabricate cellularized anisotropic hybrid hydrogel through a mild and biocompatible process driven by multiple external stimuli: magnetic field, temperature, and light. A low-intensity magnetic field is used to align mosaic iron oxide nanoparticles (IOPs) into filaments with tunable size within a gelatin methacryloyl matrix. Cells seeded on top or embedded within the hydrogel align to the same axes of the IOPs filaments. Furthermore, in 3D, C2C12 skeletal myoblasts differentiate toward myotubes even in the absence of differentiation media. 3D printing of the nanocomposite hydrogel is achieved and creation of complex heterogeneous structures that respond to magnetic field is demonstrated. By combining the advanced, stimuli-responsive hydrogel with the architectural control provided by bioprinting technologies, 3D constructs can also be created that, although inspired by nature, express functionalities beyond those of native tissue, which have important application in soft robotics, bioactuators, and bionic devices

Optimization of loading protocols for tissue engineering experiments

Tissue engineering (TE) combines cells and biomaterials to treat orthopedic pathologies. Maturation of de novo tissue is highly dependent on local mechanical environments. Mechanical stimulation influences stem cell differentiation, however, the role of various mechanical loads remains unclear. While bioreactors simplify the complexity of the human body, the potential combination of mechanical loads that can be applied make it difficult to assess how different factors interact. Human bone marrow-derived mesenchymal stromal cells were seeded within a fibrin-polyurethane scaffold and exposed to joint-mimicking motion. We applied a full factorial design of experiment to investigate the effect that the interaction between different mechanical loading parameters has on biological markers. Additionally, we employed planned contrasts to analyze differences between loading protocols and a linear mixed model with donor as random effect. Our approach enables screening of multiple mechanical loading combinations and identification of significant interactions that could not have been studied using classical mechanobiology studies. This is useful to screen the effect of various loading protocols and could also be used for TE experiments with small sample sizes and further combinatorial medication studies

Random-phase approximation and its applications in computational chemistry and materials science

The random-phase approximation (RPA) as an approach for computing the electronic correlation energy is reviewed. After a brief account of its basic concept and historical development, the paper is devoted to the theoretical formulations of RPA, and its applications to realistic systems. With several illustrating applications, we discuss the implications of RPA for computational chemistry and materials science. The computational cost of RPA is also addressed which is critical for its widespread use in future applications. In addition, current correction schemes going beyond RPA and directions of further development will be discussed.Comment: 25 pages, 11 figures, published online in J. Mater. Sci. (2012