Wave function fictitious mass

The first term in this Lagrangian contains the fictitious mass of the wave-function, /1. This fictitious kinetic energy term should not be confused with the real kinetic energy of electrons included in the electronic Hamiltonian. 

Figure 4-3. A comparison of the Car-Parinello and Bom-Oppenheimer molecular dynamics the potential energy (top) and temperature (kinetic energy, bottom) from the CP-MD and BO-MD simulations for ethylene, started from the same geometry and wave function. The results obtained form the simulations with the CPMD program13 (Troullier-Martins pseudopotentials,1415 time step of 4 a.u., fictitious mass 400 a.u., cut-off energy 70 Ry, unit cell 12 A x 12 A xl2 A)...

The Car-Parinello equations of motion (Eq. 3) contain the basic parameter of the method, i.e the fictitious mass of the wave function, p. 

In the Car and Parrinello (1985) scheme, ion dynamics is combined with a fictitious classical electron dynamics, with nuclei assigned real masses and the electron wave functions arbitrary fictitious masses. One starts the molecular-dynamics simulation at high temperature and cools progressively to zero temperature to find the ground state of both electrons and ions simultaneously. Although this approach at first seems strange and unphysical, it has yielded excellent results for amorphous Si (Car and Parrinello, 1988) and recently for SiOj (Allan and Teter, 1987) and S clusters (Hohl et al., 1988) and will probably play an important role in the future development of the field. 

It was shown by Car and Parrinello that classical MD (CPMD, Car-Parrinello molecular dynamics) can be performed in the framework of ab initio electronic theory. In CPMD, coefficients of the electronic basis functions (q ) are treated as dynamical variables with associate mass (//). The trajectories of these fictitious particles representing the electronic wave function ) of the system can propagate simultaneously with the dynamics... 

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