Introduction and basic definitions

In this chapter the implementation of plane wave/pseudopotential ab initio molecular dynamics methods within the CPMD computer code [696] is explained. We concentrate on the basics, thus leaving advanced methods to later chapters and in addition all formulas are given for the spin-unpolarized or restricted case for simplicity. This allows us to highlight the essential features of a plane wave code, as well as the reasons for its high performance, in detail. The implementation of more sophisticated versions of the presented algorithms, as well as of the more advanced techniques in Chapter 5 is, in most cases, very similar to what is introduced here.

There are many reviews on the plane wave/pseudopotential method as such, or in connection with the Car–Parrinello algorithm. Older articles [335, 673, 1149, 1391], as well as the book by Singh [1365], concentrate on the electronic structure problem, whereas the review by Jones and Gunnarsson [716] as well as the textbooks by Martin [913] and Kohanoff [762], provide a glimpse of Car–Parrinello molecular dynamics as well. Other reviews [485, 486, 1123, 1209, 1498] introduce the plane wave/pseudopotential method with the aim of connecting it to the molecular dynamics technique.

Supercells and plane wave basis

The unit cell of a periodically repeated system is defined by the Bravais lattice vectors a1, a2, and a3 (see e.g. Ref. [48] for a general discussion). The Bravais vectors can be combined into a 3×3 matrix h = [a1, a2, a3] [48, 1105].