First-principles simulation, meaning density-functional theory calculations with plane waves and pseudopotentials, has become a prized technique in condensed-matter theory. Here I look at the basics of the suject, give a brief review of the theory, examining the strengths and weaknesses of its implementation, and illustrating some of the ways simulators approach problems through a small case study. I also discuss why and how modern software design methods have been used in writing a completely new modular version of the CASTEP code.

https://iopscience.iop.org/article/10.1088/0953-8984/14/11/301/pdf

First-principles simulation: ideas, illustrations and the CASTEP code

We present a comprehensive, up-to-date compilation of band parameters for the technologically important III–V zinc blende and wurtzite compound semiconductors: GaAs, GaSb, GaP, GaN, AlAs, AlSb, AlP, AlN, InAs, InSb, InP, and InN, along with their ternary and quaternary alloys. Based on a review of the existing literature, complete and consistent parameter sets are given for all materials. Emphasizing the quantities required for band structure calculations, we tabulate the direct and indirect energy gaps, spin-orbit, and crystal-field splittings, alloy bowing parameters, effective masses for electrons, heavy, light, and split-off holes, Luttinger parameters, interband momentum matrix elements, and deformation potentials, including temperature and alloy-composition dependences where available. Heterostructure band offsets are also given, on an absolute scale that allows any material to be aligned relative to any other.

Band parameters for III–V compound semiconductors and their alloys

We review the dynamical mean-field theory of strongly correlated electron systems which is based on a mapping of lattice models onto quantum impurity models subject to a self-consistency condition. This mapping is exact for models of correlated electrons in the limit of large lattice coordination (or infinite spatial dimensions). It extends the standard mean-field construction from classical statistical mechanics to quantum problems. We discuss the physical ideas underlying this theory and its mathematical derivation. Various analytic and numerical techniques that have been developed recently in order to analyze and solve the dynamical mean-field equations are reviewed and compared to each other. The method can be used for the determination of phase diagrams (by comparing the stability of various types of long-range order), and the calculation of thermodynamic properties, one-particle Green's functions, and response functions. We review in detail the recent progress in understanding the Hubbard model and the Mott metal-insulator transition within this approach, including some comparison to experiments on three-dimensional transition-metal oxides. We present an overview of the rapidly developing field of applications of this method to other systems. The present limitations of the approach, and possible extensions of the formalism are finally discussed. Computer programs for the numerical implementation of this method are also provided with this article.

Dynamical mean-field theory of strongly correlated fermion systems and the limit of infinite dimensions

A set of successively more accurate self-consistent equations for the one-electron Green's function have been derived. They correspond to an expansion in a screened potential rather than the bare Coulomb potential. The first equation is adequate for many purposes. Each equation follows from the demand that a corresponding expression for the total energy be stationary with respect to variations in the Green's function. The main information to be obtained, besides the total energy, is one-particle-like excitation spectra, i.e., spectra characterized by the quantum numbers of a single particle. This includes the low-excitation spectra in metals as well as configurations in atoms, molecules, and solids with one electron outside or one electron missing from a closed-shell structure. In the latter cases we obtain an approximate description by a modified Hartree-Fock equation involving a "Coulomb hole" and a static screened potential in the exchange term. As an example, spectra of some atoms are discussed. To investigate the convergence of successive approximations for the Green's function, extensive calculations have been made for the electron gas at a range of metallic densities. The results are expressed in terms of quasiparticle energies E(k) and quasiparticle interactions f(k, k′). The very first approximation gives a good value for the magnitude of E(k). To estimate the derivative of E(k) we need both the first- and the second-order terms. The derivative, and thus the specific heat, is found to differ from the free-particle value by only a few percent. Our correction to the specific heat keeps the same sign down to the lowest alkali-metal densities, and is smaller than those obtained recently by Silverstein and by Rice. Our results for the paramagnetic susceptibility are unreliable in the alkali-metal-density region owing to poor convergence of the expansion for f. Besides the proof of a modified Luttinger-Ward-Klein variational principle and a related self-consistency idea, there is not much new in principle in this paper. The emphasis is on the development of a numerically manageable approximation scheme. (Less)

/pdf/new-method-for-calculating-the-one-particle-green-s-function-535uroh07d.pdf

New method for calculating the one-particle green's function with application to the electron-gas problem

Quantum ESPRESSO is an integrated suite of open-source computer codes for quantum simulations of materials using state-of-the-art electronic-structure techniques, based on density-functional theory, density-functional perturbation theory, and many-body perturbation theory, within the plane-wave pseudopotential and projector-augmented-wave approaches Quantum ESPRESSO owes its popularity to the wide variety of properties and processes it allows to simulate, to its performance on an increasingly broad array of hardware architectures, and to a community of researchers that rely on its capabilities as a core open-source development platform to implement their ideas In this paper we describe recent extensions and improvements, covering new methodologies and property calculators, improved parallelization, code modularization, and extended interoperability both within the distribution and with external software

/pdf/advanced-capabilities-for-materials-modelling-with-quantum-40poaosrve.pdf

Advanced capabilities for materials modelling with Quantum ESPRESSO.

Ab initio total energy calculations based on a new optimized oxygen psuedopotential have been used to study the structures and relative energies of α-quartz, a partly (OH)4 substituted version of the α-quartz structure, and interstitial water molecules in α-quartz. Hydrogen bonds formed from two hydroxyl groups of the (OH)4 defects in the substituted α-quartz structure promote a stable structure for the defect α-quartz at low temperature. Comparable ab initio calculation of the energy of the interstitial water molecule in the quartz structure indicates that, energetically, the (OH)4 defect is likely to be strongly favoured as a mode for the incorporation of water. Ab initio stress calculations confirm that the (OH)4 defect in quartz has a large associated stress field which is likely to lead to segregation of these defects on supersaturation in wet quartz. The calculations indicate that segregation should occur in the plane (10\(\bar 1\)0) of the α-quartz structure.

Ab initio calculations on (OH)4 defects in α-quartz

Analysis of the electronic pressure in transition and noble metals.

The results of a lengthy computational study into the origin of SiC polytypes are summarized. The 6H structure is found to be the stable phase at high temperature in agreement with experiment. The 4H is almost certainly the equilibrium phase at lower temperature, with 15R being stable over a surprisingly wide range in between. Other higher order polytypes are likely to be equilibrium phases around the phase boundaries of 15R with 6H and 4H respectively. The cubic structure is not stable at any temperature but its formation can be easily understood as a result of a local constrained equilibrium during crystal growth. The effects of donor and acceptor impurities are mentioned and two experiments are suggested to clarify the subject further.

A computational study into the origin of SiC polytypes

The stability of SiC polytypes has been discussed elsewhere in terms of successive, pairwise, interplanar interactions Jn between Ising-like pseudo-spins. Here the model is first critically re-examined to resolve some doubts about the generality of the energy expression and the meaning of the Jn. The original expression is validated as the correct most general form, with the four-spin coupling term K re-interpreted as a modification of the third-neighbour interaction depending on the local geometry. Secondly the authors note the moderately long range of the interaction to third-neighbour atomic double layers found in density functional calculations on Si and SiC. They argue that this can be interpreted as the remnant in the semiconductor of what would be Friedel oscillations in a metal.

The nature of interplanar interactions in SiC polytypes

The negative thermal expansion recently observed over a wide range of temperatures in the ambient pressure phase was attributed to the existence of low-frequency phonon modes which propagate with minimal distortion of the tetrahedra and octahedra, the so-called `rigid unit modes'. The flexibility afforded this structure by these modes raises questions about the structure's behaviour with pressure. Further experiments found a high-pressure phase which also exhibited negative thermal expansion. Calculations using the rigid unit mode model have shown that the mechanism described earlier in the context of is consistent with the negative thermal expansion in . Atomistic simulations have been used to calculate further properties of these two phases (e.g. transition pressure, compressibilities) using interatomic potentials derived for the earlier work on . The reproduction of the cell parameters and bond lengths measured for does not imply a substantial change in the bonding character of the W-O interactions.

https://iopscience.iop.org/article/10.1088/0953-8984/10/38/004/pdf

Volker Heine

Papers

Ab initio calculations on (OH)4 defects in α-quartz

Analysis of the electronic pressure in transition and noble metals.

A computational study into the origin of SiC polytypes

The nature of interplanar interactions in SiC polytypes

Simulation studies of at high pressure