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.

Theory of the isotope shift for zero-phonon optical transitions at traps in semiconductors

Most transition-metal magnets, although itinerant in nature, do not undergo large volume contractions on passing from the magnetic to the non-magnetic state Such a contraction might be expected because of the very large internal magnetic pressure which has been calculated to exist in these magnets at zero temperature By developing the theory of the spontaneous magnetovolume effect in greater generality than previously, the authors show that it is the local magnetic moment which dictates the pressure A positive pressure also arises from the energy of disordering the moments at high temperature, and a small net expansion from the coupling of magnetic fluctuations to the anharmonic part of the lattice potential The effects are related to the experimentally measurable specific heat and thermal coefficient of linear expansion They analyse the data to infer root-mean-square values of the atomic magnetic moments above the Curie (Neel) temperature TC(TN) in Fe, Ni and Cr, and find a remarkably small reduction from the saturation values at T=0 Even in the Invar alloys most of the atomic moment remains above Tc

Magnetic contributions to thermal expansion of transition metals: implications for local moments above Tc

The ordering of Al and Si in Mg cordierite Mg2Al4Si5O18 is considered using computer simulation. First the enthalpy of interaction J

 ij
 between sites is derived by computer modelling 101 different Al/Si configurations and analysing their energies. They are compared with similar results for three other minerals and with ab initio calculations to assess the whole approach. Secondly the ordering process is studied using Monte Carlo simulation applied to the J

 ij
 . The ordering phase transition temperature T
c is found as 1800°C in reasonable agreement with the experimental estimate of 1450° C. These are much lower than the estimate T
c(ABW)≈7600°C obtained from Bragg-Williams theory. Strong short-range order sets in below T
c(ABW), and the reasons for much lower temperature T
c of long-range ordering are discussed. Strong short-range also sets in very rapidly in a simulated anneal, in agreement with experiment. Thirdly an attempt is made to compare our calculated enthalpies directly with the results of NMR and calorimetry experiments, not completely successfully. A free energy ΔG≈4.6 eV for the activation barrier for ordering is suggested.

A computational study of Al/Si ordering in cordierite

Calculations of the rigid unit mode (RUM) spectrum of the high-temperature phase of SiO2 tridymite are used to explain the patterns of diffuse scattering seen in transmission electron microscopy experiments. These results show that RUM's can occur with wave vectors on curved surfaces in reciprocal space rather than being confined to symmetry points, lines or planes. The fact that the calculations reproduce the detail seen in the diffuse scattering provides a striking nontrivial confirmation of the validity of the rigid unit mode model.

Rigid unit modes in the high-temperature phase of SiO2 tridymite: calculations and electron diffraction

We have explicitly tested, using pseudopotential total-energy techniques, the effect of two representative embrittling impurities on the grain-boundary cohesion of a metal. We find that substitutional Ge and As impurities increase the Al[111] interlayer energy of cohesion both at the impurity-doped layer and one layer into the bulk. Our calculations do not support either the first-layer or the second-layer decohesion models of impurity-promoted grain-boundary embrittlement.

Volker Heine

Papers

Theory of the isotope shift for zero-phonon optical transitions at traps in semiconductors

Magnetic contributions to thermal expansion of transition metals: implications for local moments above Tc

A computational study of Al/Si ordering in cordierite

Rigid unit modes in the high-temperature phase of SiO2 tridymite: calculations and electron diffraction

Effect of impurity bonding on grain-boundary embrittlement.