Principles of the Car-Parrinello method

The central concept of AIMD as introduced by Car and Parrinello [1] lies in the idea to treat the electronic degrees of freedom, as described by e.g. one-electron wavefunctions ipi, as dynamical classical variables. The mixed system of nuclei and electrons is then described in terms of the extended classical Lagrangian Cex.  

The claissical equations of motion (EOM) of this system are given by the Euler-Lagrange equations  

For finite values of p, the system moves within a given thickness of jE above the Born-Oppenheimer surface. Adiabacity is ensured if the highest frequency of the nuclear motion 

Most of the current implementations use the original Car-Parrinello scheme based on DFT. The system is treated within periodic boundary conditions and the Kohn-Sham one-electron orbitals V are expanded in a basis set of plane waves (with wave vectors 

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