# Capabilities

A detailed explanation of the capabilities of each package within the suite can be found on the package page.

Where tutorials which explain a feature in some detail exist, this page will point to them. However, tutorials do not yet exist for many features.

As a stopgap, this page refers to a script in the source directory that tests the feature. For definiteness, we assume that the source directory is called *~/lm*.

### Table of Contents

- Drawing Energy Bands
- Drawing Fermi Surfaces
- Density-of-States, Partial DOS, Mulliken Analysis and Core Level Spectroscopy
- Spectral Functions
- Obtaining quasiparticle Energy Bands From 1-shot GW
- Obtaining a Self-Energy in Dynamical Mean Field Theory
- Dielectric Response and Optics
- Spin Susceptibility and Magnetic Exchange Interactions
- Properties of Disordered Materials and the Coherent Potential Approximation
- Molecular Statics
- Molecular Dynamics
- Noncollinear Magnetism
- Spin Statistics: Relaxation of Spin Quantization Axis
- Spin Orbit Coupling
- Fully Relativistic Dirac Equation
- Application of External Scalar Potential
- Fixed spin-moment
- Drawing Charge densities
- Application of External Zeeman B Field
- Using Functionals Other Than LDA
- LDA+U
- Adding a Homogenous Background Density
- Band Edge and Effective Mass Finder
- Building a Supercell
- Point Defects in Large Supercells
- Special Quasirandom Structures
- Spin Dynamics
- Phonons
- Other Notes

### Drawing Energy Bands

Energy bands can be drawn with the **lmf**, **lm**, **tbe**, **lmfgws**, **lmfdmft**, and **lmgf** codes.

This tutorial uses the ASA code **lm**; this one uses the full-potential code **lmf**, while this tutorial makes energy bands in the LDA and QS*GW*.

The Green’s function codes (**lmgf**, the *GW* and DMFT codes) are somewhat more complicated, as the bands are broadened, either through alloy scattering (CPA) or through many-body electron-electron interactions. Interacting energy bands for Fe generated by the fully dynamical self-energy are generated in this tutorial, and those for La_{2}CuO_{4} generated by DMFT are explained in this tutorial.

The **plbnds** utility is a very useful tool to render the bands generated by band codes in an easy-to read format for graphics packages to make figures with. It automatically makes a script for Questaal’s **fplot** (graphics utility). The **plbnds** documentation offers several examples.

### Drawing Fermi Surfaces

Fermi surfaces can be drawn with the **lmf** and **lm** codes. See this tutorial.

### Density-of-States, Partial DOS, Mulliken Analysis and Core Level Spectroscopy

All of the band codes (**lmf**, **lm**, and **tbe**) have the ability to generate the total Density of States (DOS). Total DOS are automatically generated when you set **BZ_SAVDOS**. DOS are written to file *dos.ext* (one DOS in the nonmagnetic case and two in the spin-polarized case). *Note:* this switch will not be active if **BZ_METAL** is zero. You can also make the DOS using the command-line switch **--dos** as described in this tutorial.

The **pldos** utility will render *dos.ext* into more user friendly formats, and perform other functions.

Questaal codes **lmf** and **lm** can resolve densities-of-states into partial contributions, either by projecting onto partial waves in augmentation spheres, or by Mulliken analysis. Questaal can also perform Core-Level Spectroscopy (CLS), also known as EELS, which is closely related to the DOS.

Accomplish these by adding one of following switches to the commmand-line:

**--dos**generates total DOS**--pdos**projects onto partial waves in augmentation spheres**--mull**projects onto basis functions.**--cls**performs core-level spectroscopy.

All the switches have several options; for **--pdos** and **--mull** see here; for **--cls** see here.

Tutorials for partial DOS, Mulliken analysis, and core-level spectroscopy, can be found on this page.

For *k*-resolved DOS, and as well as joint projection of *k* resolved and Mulliken resolved DOS onto orbitals, see this tutorial.

**lmgf** and **lmpg** can make partial DOS. They can either do it by Pade extrapolation to the real axis of the imaginary part of the Green’s function calculated on the contour in the complex plane, or you can choose a contour close to the real axis and generate DOS directly. The latter is more accurate, but more time consuming. For a demonstration, try

```
$ ~/lm/gf/test/test.gf nife
```

### Spectral Functions

DOS are equivalent to spectral functions, though generally spectral functions refer to DOS when there is some scattering to spread out the pole $\delta(E - E_0)$ in $Im(G)$ from a noninteracting eigenstate at energy $E_0$.

Codes calculate spectral functions for interacting electrons in several contexts:

- Calculated from
*GW*. See this tutorial. - Calculated in Dynamical Mean Field Theory. See the DMFT tutorial.
- The ASA Green’s function code
**lmgf**will calculate spectral functions in the context of the Coherent Potential Approximation, see this document. Electrons aren’t interacting in the many-body sense here; disorder causes scattering which has the same effect.

### Obtaining quasiparticle Energy Bands From 1-shot GW

The test case

```
$ gwd/test/test.gwd fe 1
```

demonstrates the method to obtain results for a metallic system.

### Obtaining a Self-Energy in Dynamical Mean Field Theory

See this document and this tutorial.

### Dielectric Response and Optics

See this document and this tutorial.

### Spin Susceptibility and Magnetic Exchange Interactions

For spin susceptibility in the ASA-Green’s function scheme, see this tutorial.

For a demonstration of the transverse magnetic susceptibility in the *GW* frameowork, try

```
$ gwd/test/test.gwd zbmnas 6
```

### Properties of Disordered Materials and the Coherent Potential Approximation

The ASA Green’s function code **lmgf** can treat chemical and spin disorder, and both at the same time, with the Coherent Potential approximation. It is documented here.

### Molecular Statics

This tutorial shows how to use **lmf** to relax the crystal structure in Se to its equilibrium geometry.

### Molecular Dynamics

**lmf** can do molecular dynamics, but other DFT codes that use iterative diagonalization generally are more efficient.

The empirical tight-binding code **tbe** has an efficient implementation.

### Noncollinear Magnetism

This is available only in the ASA at present. There are no tutorials as yet. However, the source code has a number of tests that illustrate noncollinear magnetism. Try

```
$ ~/lm/nc/test/test.nc --list
```

### Spin Statistics: Relaxation of Spin Quantization Axis

**lm** and **lmgf** can perform “spin statics” — the analog of molecular statics where the spin quantization axis is relaxed to where the off-diagonal parts of the spin density matrix vanish.

There are no tutorials as yet. But try:

```
$ ~/lm/gf/test/test.gf nife
```

### Spin Orbit Coupling

There are no tutorials as yet. This test demonstrates the addition of $\lambda L \cdot S\rangle$ into the band code **lm**:

```
$ ~/lm/nc/test/test.so
```

Thistest combines CPA and spin orbit coupling in **lmgf**:

```
$ ~/lm/gf/test/test.gf fe2b
```

A basic test using **lmf**, comparing $\lambda L_z S_z\rangle$ to $\lambda L \cdot S\rangle$:

```
$ ~/lm/fp/test/test.fp felz 4
```

The following provides an extensive test of SO coupling, resolving contribution by site, and scaling $\lambda L \cdot S\rangle$ to extract the dependence on $\lambda$

```
$ ~/lm/fp/test/test.fp coptso
```

### Fully Relativistic Dirac Equation

The Dirac equation is implemented in the ASA, in codes **lm** and **lmgf**.

There is no tutorial as yet. See this demonstration:

```
$ ~/lm/gf/test/test.frgf ni
```

**lmfa** will generate core levels from the Dirac equation. See this tutorial.

### Application of External Scalar Potential

For the **lmf** code, try the following demonstration:

```
$ ~/lm/fp/test/test.fp mgo
```

### Fixed spin-moment

One technique stabilize self-consistency in difficut magnetic calculations, or to extract quantities such as the magnetic susceptibility, you can imposed a fixed magnetic moment by imposing distinct Fermi levels for each spin. This is equivalent to imposing a static, $q >= 0$ Zeeman field.

The following tests demonstrate the fixed-spin moment technique

```
$ fp/test/test.fp felz
$ fp/test/test.fp ni
```

### Drawing Charge densities

There is no tutorial at present. Try

```
~/lm/fp/test/test.fp bzt 3
```

### Application of External Zeeman B Field

In the ASA, try the following demonstrations

```
$ ~/lm/nc/test/test.nc 5 6
```

In the FP code, try the following demonstration

```
$ ~/lm/fp/test/test.fp gdn
```

### Using Functionals Other Than LDA

**lmf** demonstrates the PBE functional with this test:

The ASA code demonstrates the PBE functional with this test:

```
$ ~/lm/fp/test/test.fp te
```

The ASA code **lm** demonstrates the PBE functional with this test:

```
$ ~/lm/testing/test.lm kfese
```

### LDA+U

The following tests illustrate LDA+U in the **lmf** code:

```
$ ~/lm/fp/test/test.fp cdte
$ ~/lm/fp/test/test.fp gdn
$ ~/lm/fp/test/test.fp eras
$ ~/lm/fp/test/test.fp er
```

In the ASA, try

```
$ ~/lm/testing/test.lm er
```

### Adding a Homogenous Background Density

Try the following demonstration:

```
$ ~/lm/fp/test/test.fp c
```

### Band Edge and Effective Mass Finder

Finding band edges in complex semiconductors and insulators can be a tedious exercise. This tutorial explains a tool that automates the process and also gives effective mass tensors around band extrema.

### Building a Supercell

For now, look at these tests:

```
$ ~/lm/testing/test.lmscell --list
```

### Point Defects in Large Supercells

Tutorials are in progress. If you are interested contact us.

### Special Quasirandom Structures

For now, do this test for an SQS structure of NiO

```
$ ~/lm/testing/test.lmscell 4
```

### Spin Dynamics

No tutorials yet, sorry.

### Phonons

No tutorials yet, sorry.

### Other Notes

#### Techniques for Brillouin Zone Integration

Techniques for Brillouin zone integration are described some detail here.

#### How to Make Integer Lists in Various Contexts

The syntax for integer lists is described here. In some contexts lists can consist of real numbers. The same rules apply.

#### How to Define Rotations in Various Contexts

Rotations are used for crystal axes, spin quantization axes, and in a few other contexts. They are constructed by a succession of angles around specified axes. This page explains how to specify rotations.

#### How Site Positions are Read by the Input File

Lattice data (lattice vectors and site positions) can be read in different ways. See this page.

#### Angular Momentum in the Questaal suite

Questaal codes use real harmonics $Y_{lm}$ by default, which are real linear combination of spherical harmonics $Y_{lm}$. The ASA codes will, however, use true spherical harmonics if you set **OPTIONS_SHARM** to true.

The $Y_{lm}$ are functions of solid angle, while $Y_{lm}r^l$ are polynomials in $x$, $y$, and $z$. This page documents Questaal’s conventions for real and spherical harmonics and shows the polynomial forms of hte $Y_{lm}$ for $l = 0...3$.

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