The challenges of developing computational physics : the case of South Africa

Most modern scientific research problems are complex and interdisciplinary in nature. It is impossible to study such problems in detail without the use of computation in addition to theory and experiment. Although it is widely agreed that students should be introduced to computational methods at the undergraduate level, it remains a challenge to do this in a full traditional undergraduate curriculum. In this paper, we report on a survey that we conducted of undergraduate physics curricula in South Africa to determine the content and the approach taken in the teaching of computational physics. We also considered the pedagogy of computational physics at the postgraduate and research levels at various South African universities, research facilities and institutions. We conclude that the state of computational physics training in South Africa, especially at the undergraduate teaching level, is generally weak and needs to be given more attention at all universities. Failure to do so will impact negatively on the country's capacity to grow its endeavours generally in the field of computational sciences, with negative impacts on research, and in commerce and industry.The NRF and the department of Physics at the UPhttp://iopscience.iop.org/1742-6596ai201

Enhancing the understanding of entropy through computation

We devise a hierarchy of computational algorithms to enumerate the microstates of a system comprising N independent, distinguishable particles. An important challenge is to cope with integers that increase exponentially with system size, and which very quickly become too large to be addressed by the computer. A related problem is that the computational time for the most obvious brute-force method scales exponentially with the system size which makes it difficult to study the system in the large N limit. Our methods address these issues in a systematic and hierarchical manner. Our methods are very general and applicable to a wide class of problems such as harmonic oscillators, free particles, spin J particles, etc. and a range of other models for which there are no analytical solutions, for example, a system with single particle energy spectrum given by ε(p, q) = ε0(p2 +q4), where p and q are non-negative integers and so on. Working within the microcanonical ensemble, our methods enable one to directly monitor the approach to the thermodynamic limit (N ! 1), and in so doing, the equivalence with the canonical ensemble is made more manifest. Various thermodynamic quantities as a function of N may be computed using our methods; in this paper, we focus on the entropy, the chemical potential and the temperature.http://ajp.aapt.org/nf201

Probing the extensive nature of entropy

We have devised a general numerical scheme applied to a system of independent, distinguishable, non-interacting particles, to demonstrate in a direct manner the extensive nature of statistical entropy. Working within the microcanonical ensemble, our methods enable one to directly monitor the approach to the thermodynamic limit (N ! 1) in a manner that has not been known before. We show that (sN − s∞) ! N− where sN is the entropy per particle for N particles and s∞ is the entropy per particle in the thermodynamic limit. We demonstrate universal behaviour by considering a number of different systems each defined by its unique single-particle spectrum. Various thermodynamic quantities as a function of N may be computed using our methods; in this paper, we focus on the entropy, the chemical potential and the temperature. Our results are applicable to systems of finite size, e.g. nano-particle systems. Furthermore, we demonstrate a new phenomenon, referred to as entropic interference, which manifests as a cancellation of terms in the thermodynamic limit and which results in the additive nature of entropy.NC thanks the University of Pretoria and the National Institute for Theoretical Physics for support. TS is supported by a National Research Foundation postdoctoral fellowship.http://iopscience.iop.org/1742-6596am2014ai201

First principles molecular dynamics study of nitrogen vacancy complexes in boronitrene

We present the results of first principles molecular-dynamics simulations of nitrogen vacancy complexes in monolayer hexagonal boron nitride. The threshold for local structure reconstruction is found to be sensitive to the presence of a substitutional carbon impurity. We show that an activated nitrogen dynamics triggers the annihilation of defects in the layer through formation of Stone-Wales-type structures. The lowest energy state of nitrogen vacancy complexes is negatively-charged and spin-polarised. Using the divacancy complex, we show that their formation induces spontaneous magnetic moments, which is tuneable by electron or hole injection. The Fermi level s-resonant defect state is identified as a unique signature of the ground state of the divacancy complex. Due to their ability to enhance the structural cohesion, only the di-vacancy and the nitrogen vacancy carbon-antisite complexes are able to suppress the Fermi level resonant defect state to open a gap between the conduction and valence bands.The University of Pretoria under E2020 Project No. 5 and the National Institute of Theoretical Physicshttp://iopscience.iop.org/0953-8984nf201

Half-metallic ferromagnetism in substitutionally doped boronitrene

We perform first principles molecular dynamics simulations to investigate the magnetoelectronic response of substitutionally-doped boronitrene to thermal excitation. We show that the local geometry, size and edge-termination of the substitutional complexes of boron, carbon or nitrogen determine the thermodynamic stability of the monolayer. We find that hexagonal boron or triangular carbon clusters induce finite magnetic moments with 100% spinpolarized Fermi-level electrons in boronitrene. In such carbon substitutions, the spontaneous magnetic moment increases with the size of the embedded carbon cluster, and results in halfmetallic ferromagnetism above 750 K with a corresponding Curie point of 1250 K, above which the magnetization density vanishes. We predict an ultra-high temperature half-metallic ferromagnetic phase in impurity-free boronitrene, when any three nearest neighbour nitrogen atoms are substituted with boron, with unquenched magnetic moment up to its melting point.University of Pretoria (UP). Grant E2020(5).http://prb.aps.org/hb2013ai201

A theoretical study of thorium titanium-based alloys

Using theoretical quantum chemical methods, we investigate the dearth of ordered alloys involving thorium and titanium. Whereas both these elements are known to alloy very readily with various other elements, for example with oxygen, current experimental data suggests that Th and Ti do not alloy very readily with each other. In this work, we consider a variety of ordered alloys at varying stoichiometries involving these elements within the framework of density functional theory using the generalized gradient approximation for the exchange and correlation functional. By probing the energetics, electronic, phonon and elastic properties of these systems, we confirm the scarcity of ordered alloys involving Th and Ti, since for a variety of reasons many of the systems that we considered were found to be unfavorable. However, our investigations resulted in one plausible ordered structure: We propose ThTi3 in the Cr3Si structure as a metastable ordered alloy.University of Pretoriahttp://www.elsevier.com/locate/jnucmathb2014ai201

Density functional studies of the defect-induced electronic structure modifications in bilayer boronitrene

The van der Waals interaction-corrected density functional theory is used in this study to investigate the formation, energetic stability, and inter-layer cohesion in bilayer hexagonal boronitrene. The effect of inter-layer separation on the electronic structure is systematically investigated. The formation and energetic stability of intrinsic defects are also investigated at the equilibrium inter-layer separation. It is found that nonstoichiometric defects, and their complexes, that induce excess nitrogen or excess boron, in each case, are relatively more stable in the atmosphere that corresponds to the excess atomic species. The modifications of the electronic structure due to formation of complexes are also investigated. It is shown that van der Waals density functional theory gives an improved description of the cohesive properties but not the electronic structure in bilayer boronitrene compared to other functionals. We identify energetically favourable topological defects that retain the energy gap in the electronic structure, and discuss their implications for band gap engineering in low-n layer boronitrene insulators. The relative strengths and weaknesses of the functionals in predicting the properties of bilayer boronitrene are also discussed.The University of Pretoria under E2020 Project No. 5.http://iopscience.iop.org/1742-6596nf201

GGA + U studies of the early actinide mononitrides and dinitrides

We present a detailed comparative study of the electronic and mechanical properties of the early actinide mononitrides and dinitrides within the framework of the Perdew–Burke–Ernzerhof generalized gradient approximation (GGA [PBE]) and GGA + U implementations of density functional theory with the inclusion of spin–orbit coupling. The dependence of selected observables of these materials on the effective U parameter is investigated in detail. The properties include the lattice constant, bulk modulus, charge density distribution, hybridization of the atomic orbitals, energy of formation and the lattice dynamics. The inclusion of the Hubbard U parameter results in a proper description of the 5f electrons, and is subsequently used in the determination of the structural and electronic properties of these compounds. The mononitrides and dinitrides of the early actinides are metallic except for UN2, which is a semiconductor. These actinide nitrides are non-magnetic with the exception of UN, NpN, PuN, NpN2 and PuN2 that are magnetic systems with orbital-dependent magnetic moments oriented in the z-axis. We observed that ThN2 is elastically unstable to isotropic pressure. We discovered that UN2 is thermodynamically unstable, but may be stabilized by N vacancy formation.University of Pretoriahttp://www.elsevier.com/locate/jnucmathb2014ai201

First principles LDA+U and GGA+U study of protactinium and protactinium oxides : dependence on the effective U parameter

The electronic structure and properties of protactinium and its oxides (PaO and PaO2) have been studied within the framework of the local density approximation (LDA), the Perdew–Burke–Ernzerhof generalized gradient approximation [GGA(PBE)], LDA C U and GGA(PBE) C U implementations of density functional theory. The dependence of selected observables of these materials on the effective U parameter has been investigated in detail. The examined properties include lattice constants, bulk moduli, the effect of charge density distributions, the hybridization of the 5f orbital and the energy of formation for PaO and PaO2. The LDA gives better agreement with experiment for the bulk modulus than the GGA for Pa but the GGA gives better structural properties. We found that PaO is metallic and PaO2 is a Mott–Hubbard insulator. This is consistent with observations for the other actinide oxides. We discover that GGA and LDA incorrectly give metallic behavior for PaO2. The GGA(PBE) + U calculated indirect band gap of 3.48 eV reported for PaO2 is a prediction and should stimulate further studies of this material.http://iopscience.iop.org/0953-8984hb201

Simplified pseudopotential problems for the classroom

Ab initio methods have been used for many decades to accurately predict properties of solids such as the physical, electronic, optical, magnetic, and elastic properties. A generation ago, many research groups developed their own in-house codes to perform ab initio calculations. In doing so, research students were intimately involved in many aspects of the coding, such as developing the theoretical framework, and algorithmic and programming details. Over time however, collaborations between various research groups within academia and in industry have resulted in the creation of more than 50 large opensource and commercial electronic structure packages. These software packages are widely used today for condensed matter research by students who, unfortunately, often have very little understanding of the fundamental aspects of these codes. To address this shortcoming, we have embarked on a program at the University of Pretoria to devise a range of simplified, easily programmable computational problems appropriate for the classroom, which can be used to teach advanced undergraduate students about particular theoretical and computational aspects of the electronic structure method. In this paper, we focus on the pseudopotential, which is a centrally important concept in many modern ab initio methods. Whereas the full implementation of the pseudopotential construct in a real electronic structure code requires complex numerical methods, e.g. accelerated convergence to self-consistency including the interactions between all the electrons in the system, we show that the essential principles of the pseudopotential can, nevertheless, be presented in a simpler class of problems, which can readily be coded by students.National Research Foundation and the University of Pretoria.http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=5992hb201