About Questaal
Questaal is a suite of first-principles electronic structure programs. The codes can be used to model arbitrary materials, but they are mostly designed to answer condensed-matter theory questions about solid state (periodic) structures. The majority of the codes use an all-electron implementation of density-functional theory. This includes several forms (Hamiltonian and Green’s function) that serve different purposes. The feature that distinguishes Questaal from other implementations of electronic structure, is its all-electron implementation of many-body perturbation theory, especially its implementation of a quasiparticle self-consistent form of GW, (QSGW). A tight-binding based on user-supplied empirical Hamiltonians is also supported. Other features include the ability to perform calculations in Dynamical Mean Field Theory in conjunction with QSGW (DMFT-QSGW), the Bethe Salpeter Equation (BSE), and direct (Green Function) solution of the Dirac equation.
This page offers a brief comparative survey of the different flavors of first principles methods in the literature, and see this page for a comparison of the advantages different methods offer, and why the QSGW approximation can be particularly advantageous.
Questaal codes share a basis set of atom-centred functions. This basis is optimised to the potential of the chemical and lattice structure under investigation. 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 electronic-structure 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, Landauer-Buttiker formulation of electronic transport, impurity effects in solids, and linear response. There is a peer-reviewed methods paper. This news highlight describes some of Questaal’s unique features, in particular the ability to combine QSGW and dynamical mean field theory; while this psi-k highlight makes an argument for why Questaal is optimally designed for future developments in electronic structure.
Packages distributed in the Questaal suite that solve for the electronic structure include:
- Full Potential LMTO: This is an all-electron implementation of density-functional 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 all-electron schemes; see Sec 3.13 of this Computer Physics Communications. 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 tight-binding basis will soon be available, with the moniker “ Jigsaw Puzzle Orbital” (JPO’s). A basic tutorial for the main full-potential program lmf can be found here.
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 self-consistency (QSGW). QSGW may be thought of as a n optimised form of the GW approximation of Hedin. Self-consistent 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. Self-consistency also removes dependence on the starting point and also makes it possible to generate ground state properties that are sensitive to self-consistency, such as the magnetic moment. Usually QSGW is launched through a script lmgw.sh.
DMFT: Dynamical Mean Field Theory is an approach designed to handle strong correlations in a small subspace of a system, for example when localized 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. Such an environment gives rise to interesting many-body phenomena such as superconductivity. DMFT is a local theory, in which the hilbert space is partitioned into a correlated part and the remainder. The local theory couples the QSGW (or DFT) description of the lattice with an essentially exact solver of the local problem. It is particularly good for spin fluctuations, which are generally low-energy and the vertex that controles their correlations is mostly confined to atomic-like orbitals such as transition metal 3d states or 4f states. Questaal has an interface to two DFMT codes, the CTQMC solver developed by K. Haule and coworkers, and a hybridization-expansion solver in the Triqs package. These codes are not part of Questaal and must be installed separately. The interface to the Questaal suite and the DMFT solver is called lmfdmft. The steps to run it are explained in this tutorial. The process is a bit complicated, however and the tutorial has not been updated for some time.
lmfgws: Once you have a converged QSGW self-energy (an expensive and sometimes difficult calculation), properties are normally calculated from the single-particle potential generated by quasiparticlization of the dynamical GW self-energy. To analyze the dynamical self-energy, lmfgws reads a dynamical self-energy, generated with from GW or from DMFT to generate spectral information. Its use is explained in this tutorial. TheBrillouin zone unfolding scheme can also use lmfgws.
LMTO-ASA: 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 tight-binding 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 close-packed systems, and still remains today one of the best and most highly efficient approach to studying magnetic properties of reasonably close-packed systems. The ASA suite is described here. An important functionality is its implementation a non-collinear framework and also a fully relativistic framework. The executable binary is called lm.
Green’s Functions LMTO: An ASA based density-functional 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 spin-orbit 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) semi-infinite 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 self-consistent framework, and also to calculate transmission and reflection in the context of Landauer-Buttiker theory. There is a non-equilibrium Keldysh formulation of the ASA hamiltonian, as described in this paper.
Empirical Tight-Binding The tbe code evaluates properties of the electronic structure from an empirical hamiltonian. The user supplies rules that defines the matrix elements of an atom-centred, tight-binding hamiltonian. It has various features, including self-consistency for ionic systems, molecular dynamics, and implementation on GPU cards for fast execution.
See this page for a summary of the main executables.