With the words ab initio,  or first principles,we mean that no empirical input is used in the calculations, a part from the charge of the electron and the Plank's constant. We study the collection of electrons and nuclei using the laws of quantum mechanics (basically, solving the Shrodinger equation). However, a part from very elementary cases, the exact solution of the Shrodinger equation is impossible to find. You need some approximations, but in general this is not an obvious thing to do. About 35 years ago, Hohenberg and Kohn proposed a new formulation of quantum mechanics, Density Functional Theory (DFT), in which the only difficult quantity is concentrated in the so called "exchange-correlation"  (XC) energy. The exact form of XC is not known, but there are approximations that work very well for a lot of materials. Nowadays DFT is probably the most widely used ab initio technique.

A boost in first principles calculations was certainly due to Car and Parrinello, who 14 years ago invented a new method to unify DFT calculations and molecular dynamics simulation, allowing the study of finite temperature properties entirely from first principles. In their original work Car and Parrinello introduced Lagrangian containing the ionic degrees of freedom and new, fictitious, electronic ones. After an initial transient, where the electronic degree of freedom were brought to the ground state, the Car-Parrinello dynamics is switched on, and the electrons follow the motion of the ions adiabatically, remaining in their ground state.

After their work it was realized that there was also an other way to do ab initio molecular dynamics: each ionic dynamic step is followed by an electronic minimization, where the electrons are brought again in their ground state. In this procedure, straightforward in some sense, the crucial point that makes it a practical way to follow is a good guess for the starting electronic state after each ionic step, otherwise the electronic minimization is prohibitively too expensive.  A first solution to this problem was originally invented by Arias, Payne and Joannopoulos, who proposed a scheme to extrapolate the electronic wave-functions after a `subspace alignment', necessary between two successive time steps because the wavefunctions may be multiplied by an arbitrary phase factor. Recently, I found that it is very easy to improve substantially this scheme: I add an extrapolation of the charge density. Combining this with the extrapolation of the wave-functions I found that for some systems (liquid iron, for instance), the speed up is almost a factor of two. The reason for this improvement is that the electronic charge can be extrapolated much better than the wave-functions, because one can write:

n(t) = n_at(t) + dn(t)

where n(t) is the total electronic charge density at time t and n_at(t) is the sum of the atomic charge densities. The latter can be calculated exactly at each time step t, dn(t) is usually a small quantity and it is extrapolated. The result of the extrapolation of dn(t) plus n_at(t) provides a much better electronic charge than if the whole charge was extrapolated. This scheme is very easy to implement.



Page created 20 October 2000