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.

The authors extend the model of phase III biphenyl (introduced by Heine and Price in 1985), based on enmeshed rotation of phenyl rings of neighbouring molecules, by including an intramolecular potential in the form of a double well: Vintra=1/2AQ2+1/4BQ4 where Q is the twist of one ring. Within this model, they study both the transition to the incommensurate phase and the possibility that this may be biphenyl's ground state as some experiments have indicated. They build up a coherent picture of biphenyl which includes the following physical properties: (i) the possibility of lack of lock-in as T to O; (ii) squaring up of the modulation as T drops below Tc; (iii) an optimal twist angle for the molecule in the solid (5.1 degrees ) that is lower than that in the vapour phase (21 degrees ); and (iv) the temperature of a notional I-III transition (which should be very close to the temperature of the actual I-II transition). This picture agrees both qualitatively and quantitatively with experimental results.

http://iopscience.iop.org/article/10.1088/0022-3719/20/22/007/pdf

The incommensurate phase transition of biphenyl

We apply the Rigid Unit Mode model, which was initially developed for crystalline silicates, to the study of the flexibility of silica glass. Using a density-of-states approach we show that silica glass has the same flexibility against infinitesimal displacements of crystalline phases. Molecular dynamics simulations also show that parts of the silica structure are able to undergo large spontaneous changes through reorientations of the SiO4 tetrahedra with no energy cost.

Amorphous silica from the Rigid Unit Mode approach

Gallium as an impurity in aluminium is an extreme example of a grain boundary embrittler. The energetics of substituting Ga in various sites, individually and together, has been calculated by ab initio techniques in a Sigma = 11 (1 1 3) symmetric tilt boundary. This boundary has one relatively short nearest-neighbour distance across the boundary, which is relaxed on substitution by Ga. A picture is developed of the attraction of Ga towards the tight sites in the Al grain boundaries, and of its role as a substitutional embrittling impurity.

Ab initio computational study of Ga in an Al grain boundary

The formation of kinetic, transient microstructures in structural phase transitions is analysed within the framework of time-dependent Landau-Ginzburg theories. The mesoscopic rate equation is delta phi / delta t= phi - phi 3+ delta 2 phi / delta x2- gamma delta 2 phi / delta x4+ delta delta 6 phi / delta x6. A front of a stable state phi =1 can grow into an unstable region with phi =0 in an oscillatory manner. It will then leave behind a transient domain structure with quasi-periodic walls. Such domain structures occur for positive and negative values of gamma with sufficiently large values of mod gamma mod . The phase diagram in ( gamma , delta ) space is explored using computer simulation. The repetition length does not diverge at the bifurcation between an oscillatory and solitonic regime except at the point gamma =1/12. delta =0 studied previously. It is shown that recent computer simulation studies of realistic microstructures used implicit values of gamma and delta close to the bifurcation condition.

Pattern formation during phase transitions: kinetics of partially conserved order parameters and the role of gradient energies

For f.c.c. and h.c.p. crystals structural phase transitions involving soft acoustic modes are discussed. A simple nearest neighbour force model is used. Two extreme types of transition are distinguished; one of these entails a softening of all modes whereas in the second type there is only appreciable softening of a single mode.

Volker Heine

Papers

The incommensurate phase transition of biphenyl

Amorphous silica from the Rigid Unit Mode approach

Ab initio computational study of Ga in an Al grain boundary

Pattern formation during phase transitions: kinetics of partially conserved order parameters and the role of gradient energies

A simple theory of some phase transitions