Car-Parrinello direct QM simulation

Let us consider a system for which the BO approximation holds and for which the motion of the nuclei ean be deseribed by classieal mechanics. The interaction potential is given 

In order to use eq. [8.89] in a MD simulation, ealeulations of /o for a number of configurations of the order of lO are needed. Obviously this is eomputationally very demanding, so that the use of certain very accurate QM methods (for example, the configuration interaction (Cl)) is precluded. A practical alternative is the use of DFT. Following Kohn and Sham, the eleetron density p(r) can be written in terms of oecupied single-particle orthonormal orbitals  

A point on the BO potential energy surfaee (PES) is then given by the minimum with re-speet to the /j of the energy funetional  

In the eonventional approach, the minimization of the energy functional (eq. [8.91]) with respect to the orbitals /i subject to the orthonormalization constraint leads to a set of self-consistent equations (the Kohn-Sham equations), i.e.  

It is possible to use an alternative approach, regarding the minimization of the functional as an optimization problem, which can be solved by means of the simulated annealing procedure. A simulated annealing technique based on MD can be efficiently applied to minimize the KS functional the resulting technique, called dynamical simulated annealing allows the study of finite temperature properties. 

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Mixed QM/MM Car-Parrinello simulation techniques are among the most powerful computational methods for exact numerical calculations of macroscopic and microscopic properties at finite temperatures of a large variety of condensed matter systems of current theoretical and experimental interest. Physical quantities that may be computed exactly and compared directly to experimental results, where available, include the kinetic, potential, and total energy, the radial distribution function, neutron scattering cross-sections, and so on. 

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