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 properties of metal-to-semiconductor junctions and of free semiconductor surfaces are usually explained on the basis of surface states. The theory of the metal contacts is discussed critically, because strictly speaking localized surface states cannot exist in such junctions. However, it is shown that virtual or resonance surface states can exist which behave for practical purposes in the same way. They are really the tails of the metal wave functions rather than separate states. In the past, the length of this tail has often been ignored. Some estimates of its length are made and its consequences pointed out. A semiquantitative discussion is given of various recent data, including the effect of an oxide layer on barrier height, the variation of barrier height with the metal, the work function of a free surface at high doping, and the effect of a cesium layer on the work function.

Theory of Surface States

Some new methods are presented for calculating the density of states n(E) and other aspects of electronic structure in a tight-binding band, without use of Bloch's theorem or the band structure E(k). The methods are therefore applicable to calculating the local density of states at surfaces, impurities etc. and relate the electronic structure to the local atomic environment. They depend on developing the Green function as an infinite continued fraction. There is no difficulty in obtaining n(E) in a few minutes computing time correct to the first 50 moments for an s-band and 10 moments for d-bands. The present paper discusses the methods and ideas, with specific applications to follow.

https://iopscience.iop.org/article/10.1088/0022-3719/5/20/004/pdf

Electronic structure based on the local atomic environment for tight-binding bands

The purpose of the present work is to obtain a better atomic pseudopotential with respect to convergence and computational efficiency while retaining reasonable transferability in the context of electronic-structure calculations for solids using a plane-wave basis set. We introduce a systematic procedure for generating optimized nonlocal pseudopotentials by minimizing the high Fourier components of the pseudo-wave-functions with the constraints of normalization and continuity of first and second derivatives of the wave function at the core radius. This is based on the recent ideas of Rappe et al. (RRKJ) [Phys. Rev. B 41, 1227 (1990)], but overcomes certain difficulties which we have found with the RRKJ scheme. For computational efficiency this optimized nonlocal pseudopotential is transformed into a Kleinman-Bylander (KB) form. To ensure the transferability we first compare the logarithmic derivative of the all-electron wave function with that of the final KB form of the optimized nonlocal pseudopotential over a wide range of energies. We then test the KB form of the potential in a number of atomic environments. The structural properties of ZnS are calculated to demonstrate the reliability of our optimized nonlocal separable ab initio pseudopotential and its total-energy convergence.

Optimized and transferable nonlocal separable ab initio pseudopotentials

The Fourier transform of the self-consistent screened model potential has been calculated for 25 elements. The results are presented in a form applicable to the potential in the solid or liquid metal or semiconductor, or to the electron-phonon interaction. They are reliable to about 0.01 ryd. The calculations are a continuation of the work by Heine and Abarenkov (1964), using the screening theory of Animalu (1965 a). The behaviour at high wave numbers and other points of detail are discussed much more thoroughly than before. Some average band effective masses are also calculated.

Volker Heine

Papers

Theory of Surface States

Electronic structure based on the local atomic environment for tight-binding bands

Optimized and transferable nonlocal separable ab initio pseudopotentials

Theory of Surface States

The screened model potential for 25 elements