About Questaal
Questaal is a suite of electronic structure programs. The codes can be used to model arbitrary materials, but they are mostly designed to answer condensedmatter theory questions about solid state (periodic) structures. The majority of the codes use an allelectron implementation of densityfunctional theory. This includes several forms (Hamiltonian and Green’s function) that serve different purposes. There is an allelectron implementation of GW theory, used most particularly in a quasiparticle selfconsistent form (QSGW). Tightbinding based on usersupplied empirical Hamiltonians is also supported. Recent development work includes Dynamic Mean Field Theory (DMFTQSGW), the Bethe Salpeter Equation (BSE), and direct (Green Function) solution of the Dirac equation.
These codes share a basis set of atomcentred functions. This basis is optimised to the problem. Compared to a plane wave basis, this results in a much more compact description, reducing run time and memory consumption. The cost is that the code is significantly more complex, and the user is involved in setting the basis for each problem.
The basis has its genesis in the Linear Muffin Tin Orbitals (LMTO) method of O. K. Andersen, who formulated the theory of linear methods in band theory. The LMTO and LAPW (Linear Augmented Plane Wave) methods are the most common direct forms of the linear methods, though most electronicstructure approaches (including those based on pseudopotentials) depend on a linearization as well. The present code is a descendent of the “tight binding linear method” that formed the mainstay of Andersen’s group in Stuttgart for many years.
Applications include modeling electronic structure, magnetic properties of materials, LandauerButtiker formulation of electronic transport, impurity effects in solids, and linear response.
Packages distributed in the Questaal suite include:

Full Potential LMTO: This is an allelectron implementation of densityfunctional theory using convolutions of Hankel functions and Gaussian orbitals as a basis set. This code also provides an interface to a GW package. It is a fairly accurate basis, and has been benchmarked against other allelectron schemes [XXX … check with Jerome]. You can also use Augmented Plane Waves as a basis, or a combination of the two, as described in this paper. A new, highly accurate tightbinding basis will soon be available, with the moniker “Jigsaw Puzzle Orbitals” (JPO’s). A basic tutorial for the main fullpotential program lmf. can be found here.

GW: A separate package contains an allelectron implementation of the GW approximation, using the fullpotential package to supply a front end with single particle quantities GW requires. The GW code uses a “mixed product basis” set for twoparticle quantities such as the bare and screened coulomb interaction. Its primary function is to calculate quasiparticle levels (or more generally energy band structure) within GW theory. Also part of this package is the ability to calculate optical and spin response functions, and spectral functions. See this paper for the theory corresponding to the present implementation. The present code is a descendent of the original ecalj package developed by Kotani, Faleev and van Schilfgaarde.

QSGW: GW is usually implemented as an extension to the LDA, i.e. G and W are generated from the LDA. The GW package also has the ability to carry out quasiparticle selfconsistency (QSGW). QSGW may be thought of as an optimised form of the GW approximation of Hedin. Selfconsistent calculations are more expensive than usual formulations of GW based on a perturbation of density functional theory, but it is much more accurate and systematic. Selfconsistency also removes dependence on the starting point and also makes it possible to generate ground state properties that are sensitive to selfconsistency, such as the magnetic moment.
Both GW and selfconsistent GW are executed through a family of scripts. The script for selfconsistent calculations is called lmgwsc; oneshot GW calculations use lmgw1shot; and other parts such as the dielectric function calculator and selfenergy maker use lmgw. lmfgws carries out postprocessing analysis of the dynamical self energy.
Once you have a converged QSGW selfenergy (an expensive and sometimes difficult calculation), most properties are calculated at the singleparticle (DFT) level.

LMTOASA: The original formulation of the LMTO method included the Atomic Spheres Approximation (ASA). Crystals are divided up into overlapping spheres, and only the l=0 component of the potential inside each sphere is kept. This approximation is very efficient — speeds rival those found in empirical tightbinding approaches, but its range of validity is limited. This is because sphere must fill space; hence there is a geometry violation that becomes severe if the spheres overlap too much. It works best for closepacked systems, and still remains today one of the best and most highly efficient approach to studying magnetic properties of reasonably closepacked systems. The ASA package can be used in a noncollinear framework. The executable binary is called lm.

Green’s Functions LMTO: An ASA based densityfunctional Green’s function formulation. The program, lmgf, calculates the Green’s function for a periodic system, and is a Green’s function counterpart to the lm code. It can be used to determine a range of properties including the density of states, energy band structure, and magnetic moment. It also has the ability to calculate magnetic exchange interactions and some other properties of linear response. This code can include spinorbit coupling perturbatively, and it also has a fully relativistic Dirac formulation. It also implements the Coherent Potential Approximation, for the study of alloys, or for disordered local moments, re a combination of the two.

Principal Layer Green’s Functions This code, lmpg, is an analog of lmgf for layered systems. Periodic boundary conditions are used in two dimensions, while the third dimension is treated in real space with a principal layer technique. This is advantageous because (1) semiinfinite boundary conditions are used this dimension, which correspond to the physical realisation of layered materials and (2) the computation time scales only linearly in the number of principal layers. lmpg can be used in a selfconsistent framework, and also to calculate transmission and reflection in the context of LandauerButtiker theory. There is a nonequilibrium Keldysh formulation of the ASA hamiltonian, as described in this paper.

QSGW + DMFT: When localised electronic orbitals (d or f type) participate in the states near the fermi level, the effect of electronic correlation can not be included as a small perturbation (RPA) and more accurate methods have to be invoked. The Questaal code has been interfaced with the Continuous Time Quantum Monte Carlo solver developed by K. Haule and coworkers. This couples the QSGW description of the lattice with stateoftheart Dynamical Mean Field Theory approaches. This code requires that Haule’s CTQMC be installed. The interface to that code is lmfdmft.

Empirical TightBinding The tbe code evaluates properties of the electronic structure from an empirical hamiltonian. The user supplies rules that defines the matrix elements of an atomcentred, tightbinding hamiltonian. It has various features, including selfconsistency for ionic systems, molecular dynamics, and implementation on GPU cards for fast execution.