# Bands and occupation numbers for metals and insulators

### This page gives hints on how to to specify bands and occupation numbers, for metals or insulators with the ABINIT package.

##### Copyright (C) 2016-2017 ABINIT group (FJ)

Mentioned in topic_k-points, help_features#2.2.

### Table of content:

- 1. Introduction.
- 2. Related lesson(s) of the tutorial.
- 3. Related input variables.
- 4. Selected input files.

### 1. Introduction.

Metallic as well as insulating systems can be treated, depending on the value of occopt. The default value of occopt corresponds to an insulator (or finite molecule): the number of bands (or states for a molecule) is deduced from the number of electrons brought by each pseudopotential ion, and then all the bands are occupied (by two electrons in case of a non-spin-polarized system, or by 1 electron in the cas of a spin-polarized system), and a small number of empty bands are added, e.g. to obtain the band gap.

For a metallic system, use a value of occopt between 3 and 7. ABINIT will compute a default number of bands, including some nearly unoccupied ones, and find the occupation numbers. The different values of occopt correspond to different smearing schemes (smearning defined by tsmear for defining the occupation numbers, e.g. Fermi broadening, the Gaussian broadening, the Gaussian-Hermite broadening, as well as the modifications proposed by Marzari. Finite temperatures can also be treated thanks to a smearing scheme (Verstraete scheme) using tphysel.

It is possible to define manually the number of bands (input variable nband) as well as the occupation numbers (input variable occ). This might be useful to perform a Δ-SCF calculation for excited states.
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### 2. Related lesson(s) of the tutorial.

- The lesson 1 deals with the H2 molecule : get the total energy, the electronic energies, the charge density, the bond length, the atomisation energy
- The lesson 2 deals again with the H2 molecule: convergence studies, LDA versus GGA
- The lesson 3 deals with crystalline silicon (an insulator): the definition of a k-point grid, the smearing of the cut-off energy, the computation of a band structure, and again, convergence studies ...
- The lesson 4 deals with crystalline aluminum (a metal), and its surface: occupation numbers, smearing the Fermi-Dirac distribution, the surface energy, and again, convergence studies ...
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### 3. Related input variables.

Basic input variables:

... nband [Number of BANDs]
... occ [OCCupation numbers]
... occopt [OCCupation OPTion]
... tsmear [Temperature of SMEARing]

Useful input variables:

... fband [Factor for the number of BANDs]
... nbdbuf [Number of BanDs for the BUFfer]
... tphysel [Temperature (PHYSical) of the ELectrons]

Relevant internal variables:

... %mband [Maximum number of BANDs]
... %nelect [Number of ELECTrons]
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### 4. Selected input files.

WARNING : as of ABINITv8.6.x, the list of input files provided in the specific section of the topics Web pages is still to be reviewed/tuned. In some cases, it will be adequate, and in other cases, it might be incomplete, or perhaps even useless.
The user can find some related example input files in the ABINIT package in the directory /tests, or on the Web:

tests/v1/Input: t02.in t04.in

tests/v2/Input: t45.in t46.in
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