# Characterization of BAND¶

**Functionality**

- Automatic geometry optimization
- Formation energy with respect to isolated atoms which are computed with a fully numerical Herman-Skillman type subprogram
- A choice of density functionals, including LDA (Local Density Approximation), GGA (Generalized Gradient Approximation), meta-GGA (with kinetic energy density dependence), and Hybrid (including exact exchange) functionals
- Time-dependent Current-DFT (TD-CDFT) for calculation of frequency-dependent dielectric functions of systems periodic in one, two and three dimensions.
- The ZORA method for scalar relativistic effects is available (also for the TD-CDFT option). Spin-orbit coupling can be taken into account, including non-collinear magnetization.
- Phonon spectrum.
- Electric field perpendicular to the periodic direction(s).
- Non-Equilibrium Green’s Function (NEGF) method for calculation of transmission and current plots.

**Analysis**

- Mulliken populations for basis functions, overlap populations between atoms or between basis functions.
- Hirshfeld charge analysis
- Densities-of-States: DOS, PDOS and OPWDOS/COOP
- Local Densities-of-States: LDOS (STM images)
- Form factors (X-ray structures)
- Charge analysis using Voronoi cells (yielding Voronoi Deformation Charges)
- Orbital plots
- Deformation density plots
- Band structure plots along the edges of the Brillouin zone
- One-electron energies and orbitals at the Brillouin Zone sample points
- Fragment orbitals and a Mulliken type population analysis in terms of the fragment orbitals
- Quantum Theory of Atoms In Molecules (QT-AIM). Atomic charges and critical points.
- Electron Localization Function (ELF).
- Fragment based Periodic Energy Decomposition Analysis (PEDA).
- PEDA combined with Natural Orbitals for Chemical Valency (NOCV) to decompose the orbital relaxation (PEDA-NOCV).

**Technical**

- Linear scaling techniques are used to speed up calculations on large unit cells
- SCF convergence based on a Direct Inversion of Iterative Subspace (DIIS) method. For problematic systems also LIST is available.
- The implementation is built upon a highly optimized numerical integration scheme for the evaluation of matrix elements of the Hamiltonian, property integrals involving the charge density, etc. This is the same numerical integration scheme as used in ADF.
- Basis functions are Slater-Type Orbitals (STOs) and/or Numerical Orbitals (NOs).
- The ZlmFit is used to fit the deformation density, which is the difference between the final density and the startup density. The deformation density has zero charge and will in general be small. The fitted deformation density is used for the calculation of the Coulomb potential and the derivatives of the total density (needed for the gradient corrections in the exchange-correlation functionals). In both cases the main part, due to the startup density, is calculated accurately by a numerical procedure, and only the small part from the deformation density is obtained via the fit.
- A frozen core facility is provided to allow efficient treatment of the inner atomic shells.
- Space group symmetry is used to reduce the computational effort in the integrals over the Brillouin zone.