Conventions in sisl

sisl is a joint effort to enable easy usage of electronic structure concepts in a scientific setting. Ranging between introductory levels up to, and including, full scientific employees.

There are certain conventions that we want to enforce in sisl, and we strive them as far as possible.

Units

All units in sisl are standardized to:

Length

All units internally and returned are in Angstrom.

Energy

All units internally and returned are in electron volts.

Mathematical notation

Here is a list of rules that sisl will strive to adhere to. If you find any inconsistencies in the documentation, please let us know!

• upper case characters such as \(I\) and \(J\) refer to atomic indices

• lower case characters such as \(i\) and \(j\) refer to orbital indices, e.g. \(i\in I\)

• scalars are represented via lower case italics, such as \(a\)

• vectors are represented via lower case bold faced, such as \(\mathbf a\)

  One may use \(\hat{\mathbf a}\) to signal normal vectors

  • dot-products between vectors should be explicit \(\mathbf a\cdot\mathbf b\)

• matrices are represented via upper case bold faced, such as \(\mathbf A\)

  • vector-matrix products are implicit \(\mathbf a\mathbf B\)

  • matrix-matrix products are implicit \(\mathbf A\mathbf B\)

• Greek letters are used for other indices, such as spin (\(\sigma\)), Cartesian or lattice vectors.

• range of indices are denoted with \(\{ \}\), such that, \(\{i\}\) is an orbital index range, \(\{I\}\) is an atomic index range and \(\{\alpha\}\) refers to some other range which should be inferred from the context

• the imaginary number is generally referred to as \(i\) in physics, its meaning should be implicit from the context.