Reproducibility of density functional approximations: how new functionals should be reported

Density functional theory is the workhorse of chemistry and materials science, and novel density functional approximations (DFAs) are published every year. To become available in program packages, the novel DFAs need to be (re)implemented. However, according to our experience as developers of Libxc [Lehtola et al, SoftwareX 7, 1 (2018)], a constant problem in this task is verification, due to the lack of reliable reference data. As we discuss in this work, this lack has lead to several non-equivalent implementations of functionals such as BP86, PW91, PBE, and B3LYP across various program packages, yielding different total energies. Through careful verification, we have also found many issues with incorrect functional forms in recent DFAs. The goal of this work is to ensure the reproducibility of DFAs: DFAs must be verifiable in order to prevent reappearances of the abovementioned errors and incompatibilities. A common framework for verification and testing is therefore needed. We suggest several ways in which reference energies can be produced with free and open source software, either with non-self-consistent calculations with tabulated atomic densities or via self-consistent calculations with various program packages. The employed numerical parameters -- especially, the quadrature grid -- need to be converged to guarantee the $\lesssim0.1\mu E_{h}$ precision for fully numerical calculations which routinely afford such precision in the total energy. Such sub-$\mu E_{h}$ level of agreement can only be achieved when fully equivalent implementations of the DFA are used. Therefore, also the source code of the reference implementation should be made available in any publication describing a new DFA.Comment: 15 pages, 1 figur

Many recent density functionals are numerically ill-behaved

Most computational studies in chemistry and materials science are based on the use of density functional theory. Although the exact density functional is unknown, several density functional approximations (DFAs) offer a good balance of affordable computational cost and semi-quantitative accuracy for applications. The development of DFAs still continues on many fronts, and several new DFAs aiming for improved accuracy are published every year. However, the numerical behavior of these DFAs is an often overlooked problem. In this work, we look at all 592 DFAs for three-dimensional systems available in Libxc 5.2.2 and examine the convergence of the density functional total energy based on tabulated atomic Hartree-Fock wave functions. We show that several recent DFAs, including the celebrated SCAN family of functionals, show impractically slow convergence with typically used numerical quadrature schemes, making these functionals unsuitable both for routine applications or high-precision studies, as thousands of radial quadrature points may be required to achieve sub-$\mu E_{h}$ accurate total energies for these unctionals, while standard quadrature grids like the SG-3 grid only contain $\mathcal{O}(100)$ radial quadrature points. These results are both a warning to users to lways check the sufficiency of the quadrature grid when adopting novel functionals, as well as a guideline to the theory community to develop better behaved density functionals.Comment: 16 pages, 6 figure

Meta-Local Density Functionals : A New Rung on Jacob's Ladder

The homogeneous electron gas (HEG) is a key ingredient in the construction of most exchange-correlation functionals of density-functional theory. Often, the energy of the HEG is parameterized as a function of its spin density n(sigma), leading to the local density approximation (LDA) for inhomogeneous systems. However, the connection between the electron density and kinetic energy density of the HEG can be used to generalize the LDA by evaluating it on a geometric average n(sigma)(avg)(r) = n(sigma)(1-x)(r) n(sigma)(x) (r) of the local spin density n(sigma)(r) and the spin density n(sigma)(r) of a HEG that has the local kinetic energy density ts(r) of the inhomogeneous system. This leads to a new family of functionals that we term meta-local density approximations (meta-LDAs), which are still exact for the HEG, which are derived only from properties of the HEG and which form a new rung of Jacob's ladder of density functionals [AIP Conf. Proc. 2001, 577, 1]. The first functional of this ladder, the local tau approximation (LTA) of Ernzerhof and Scuseria [J. Chem. Phys. 1999, 111, 911] that corresponds to x = 1 is unfortunately not stable enough to be used in self-consistent field calculations because it leads to divergent potentials, as we show in this work. However, a geometric averaging of the LDA and LTA densities with smaller values of x not only leads to numerical stability of the resulting functional but also yields more accurate exchange energies in atomic calculations than the LDA, the LTA, or the tLDA functional (x = 1/4) of Eich and Hellgren [J. Chem. Phys. 2014, 141, 224107]. We choose x = 0.50, as it gives the best total energy in self-consistent exchange-only calculations for the argon atom. Atomization energy benchmarks confirm that the choice x = 0.50 also yields improved energetics in combination with correlation functionals in molecules, almost eliminating the well-known overbinding of the LDA and reducing its error by two thirds.Peer reviewe

Stress distribution in GaN nanopillars using confocal Raman mapping technique

In this Letter, high-resolution confocal Raman mapping of stress distribution in etched and re-grown GaN nanopillar structures is investigated. Results of the E2(high) phonon line mapping of the top surfaces of individual nanopillars reveal differences in stress between both the center and edge of the nanopillar top surfaces and between the etched and re-grown GaN nanopillar structures. In-plane biaxial compressive stress with the values of 0.36–0.42 GPa and 0.49–0.54 GPa is observed at the center of etched and re-grown GaN nanopillars, respectively. The in-plane biaxial compressive stress decreases from center to edge in re-grown GaN nanopillar due to the tilted facets. Also, the A1(LO) phonon frequency increases from center to edges, or tilted facets, due to the tilt of the c-axis of re-grown GaN nanopillar.Peer reviewe

Business process modelling and visualisation to support e-government decision making: Business/IS alignment

© 2017 Springer-Verlag. The final publication is available at Springer via https://doi.org/10.1007/978-3-319-57487-5_4.Alignment between business and information systems plays a vital role in the formation of dependent relationships between different departments in a government organization and the process of alignment can be improved by developing an information system (IS) according to the stakeholders’ expectations. However, establishing strong alignment in the context of the eGovernment environment can be difficult. It is widely accepted that business processes in the government environment plays a pivotal role in capturing the details of IS requirements. This paper presents a method of business process modelling through UML which can help to visualise and capture the IS requirements for the system development. A series of UML models have been developed and discussed. A case study on patient visits to a healthcare clinic in the context of eGovernment has been used to validate the models

Dynamics of forced biopolymer translocation

We present results from our simulations of biopolymer translocation in a solvent which explain the main experimental findings. The forced translocation can be described by simple force balance arguments for the relevant range of pore potentials in experiments and biological systems. Scaling of translocation time with polymer length varies with pore force and friction. Hydrodynamics affects this scaling and significantly reduces translocation times.Comment: Published in: http://www.iop.org/EJ/article/0295-5075/85/5/58006/epl_85_5_58006.htm

NEEDLE IN A HAYSTACK: FEASIBILITY OF IDENTIFYING SMALL SAFETY ASSETS FROM POINT CLOUDS USING DEEP LEARNING

Asset management systems are beneficial for maintaining building infrastructure and can be used to keep up-to-date records of relevant safety assets, such as smoke detectors, exit signs, and fire extinguishers. Existing methods for locating and identifying these assets in buildings primarily rely on surveys and images, which only provide 2D locations and can be tedious for large-scale structures. Indoor point clouds, which can be captured quickly for buildings using mobile scanning techniques, can provide us with 3D asset locations. In this paper, we study the feasibility of using 3D point clouds of buildings combined with deep learning techniques to identify safety-related assets, particularly small-sized assets like fire switches and exit signs. We adopt the state-of-the-art Deep Learning network, Kernel Point-Fully Convolutional Network (KP-FCNN), to identify these assets through semantic segmentation. Using the obtained results, we create a 3D-geometry model of the building with assets pinpointed, providing scene semantics and delivering more value. Our method is tested using three different point cloud datasets obtained from a depth camera, a mobile laser scanner, and an iPhone lidar sensor

Associations of age and sex with brain volumes and asymmetry in 2–5-week-old infants

Information on normal brain structure and development facilitates the recognition of abnormal developmental trajectories and thus needs to be studied in more detail. We imaged 68 healthy infants aged 2–5 weeks with high-resolution structural MRI (magnetic resonance imaging) and investigated hemispheric asymmetry as well as the associations of various total and lobar brain volumes with infant age and sex. We found similar hemispheric asymmetry in both sexes, seen as larger volumes of the right temporal lobe, and of the left parietal and occipital lobes. The degree of asymmetry did not vary with age. Regardless of controlling for gestational age, gray and white matter had different age-related growth patterns. This is a reflection of gray matter growth being greater in the first years, while white matter growth extends into early adulthood. Sex-dependent differences were seen in gray matter as larger regional absolute volumes in males and as larger regional relative volumes in females. Our results are in line with previous studies and expand our understanding of infant brain development.</p

Resting-state networks of the neonate brain identified using independent component analysis

Resting-state functional magnetic resonance imaging (rs-fMRI) has been successfully used to probe the intrinsic functional organization of the brain and to study brain development. Here, we implemented a combination of individual and group independent component analysis (ICA) of FSL on a 6-min resting-state data set acquired from 21 naturally sleeping term-born (age 26 +/- 6.7 d), healthy neonates to investigate the emerging functional resting-state networks (RSNs). In line with the previous literature, we found evidence of sensorimotor, auditory/language, visual, cerebellar, thalmic, parietal, prefrontal, anterior cingulate as well as dorsal and ventral aspects of the default-mode-network. Additionally, we identified RSNs in frontal, parietal, and temporal regions that have not been previously described in this age group and correspond to the canonical RSNs established in adults. Importantly, we found that careful ICA-based denoising of fMRI data increased the number of networks identified with group-ICA, whereas the degree of spatial smoothing did not change the number of identified networks. Our results show that the infant brain has an established set of RSNs soon after birth