Section 2.2.11.7. CP (Car–Parrinello) method

Conventional quantum-mechanical calculations are done using the Born–Oppenheimer approximation, in which one assumes (in most cases to a very good approximation) that the electrons are decoupled from the nuclear motion. Therefore the electronic structure is calculated for fixed atomic (nuclear) positions. Car & Parrinello (1985) suggested a new method in which they combined the motion of the nuclei (at finite temperature) with the electronic degrees of freedom. They started with a fictitious Lagrangian in which the wavefunctions follow a dynamics equation of motion. Therefore, the CP method combines the motion of the nuclei (following Newton's equation) with the electrons (described within DFT) into one formalism by solving equations of motion for both subsystems. This simplifies the computational effort and allows ab initio molecular dynamics calculations to be performed in which the forces acting on the atoms are calculated from the wavefunctions within DFT. The CP method has attracted much interest and is widely used, with a plane-wave basis, extended with pseudo-potentials and recently enhanced into an all-electron method using the projector augmented wave (PAW) method (Blöchl, 1994). Such CP schemes can also be used to find equilibrium structures and to explore the electronic structure.