AIMD simulation method electronic structure calculations

One very prominent development in DFT has been the coupling of electronic structure calculations (which, when the ground state is concerned, apply to zero temperature) with finite-temperature molecular dynamics simulations. The founding paper in this field was published by Carr and Parrinello in 1985 [13]. Carr and Parrinello formulate effective equations of motion for the electrons to be solved simultaneously with the classical equations of motion for the ions. The forces on the ions are calculated from first principles by use of the Hellman-Feynman theorem. An alternative to the Carr-Parrinello method is to solve the electronic structure self-consistently at every ionic time step. Both methods are referred to as ab initio molecular dynamics (AIMD) [14]. 

The difference from classical force field based simulations where the forces are calculated from pre-defined pair potentials is that the forces are derived from the global potential energy surface of an electronic structure theory. The vastly higher computational costs of an electronic structure calculation restrict the system size and the length of trajectories accessible by ab initio molecular dynamics simulations. However, it becomes clear that CPMD and AIMD are important steps towards general predictive methods, due to their independence from parameterizations. 

Due to the costs associated with the electronic structure calculations, AIMD simulations always suffer from short simulation times see also previous Sect. 3. In 2005, Iftimie and Tuckerman devised a method that allows well-converged results for IR spectra from small AIMD systems and short trajectories [72], The frequency-(v)-dependent Beer-Lambert absorptivity coefficient a(v) is given as... 

Molecular dynamics and Monte Carlo simulations have been used in the last decade to model ionic liquids. [4] Most of these simulations are classical as opp>osed to quantum mechanical the interactions between chemical species are modelled by emparical force fields, hence, the quality of these simulations is strongly dependent on the intermolecular potential employed. It has been proven that it is possible to find force fields accurate enough to describe ILs. [41] Long and large simulations using ab initio are impractical, however, ab initio molecular dynamics (AIMD) are somewhat less computer demanding and provide an accurate picture of ion-ion interactions of the liquid state, by combining electronic structure calculations with conventional Molecular Dynamic (MD) methods. 

The most common form of AIMD simulation employs DFT (see section First Principles Electronic Structure Methods ) to calculate atomic forces, in conjimction with periodic boundary conditions and a plane wave basis set. Using a plane wave basis has two major advantages over atom-centered basis functions (1) there is no basis set superposition error (Boys and Bernardi 1970 Marx and Hutter 2000) and (2) the Pulay correction (Pulay 1969,1987) to the HeUmann-Feynman force, due to basis set incompleteness, vanishes (Marx and Hutter 2000, 2009). 

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