Car-Parinello method

The Car-Parinello method can be extended into a mixed QM/ MM scheme by use of a mixed Lagrangian of the form [10-12] ... 

Car-Parinello method In ordinary simulations the electronic structure of the particles is taken as fixed, and the molecules interact through given potentials. In the Car-Parinello method [16], at each step of the simulation the electronic structure of the system is recalculated, usually through density-functional methods [17, 18], and from these the forces on the particles are obtained. In principle, this is the most exact but also the most time-consuming method, so that only small ensembles can be considered. Sometimes this method is simplified by restricting the electronic structure calculations to a part of the ensemble. 

In the simulations reported above the interactions between the various components were mostly based on semiempir-ical potentials. In contrast, Price, Halley, and their collaborators attempt to model the whole interface in the spirit of the Car-Parinello method [16]. One of the first systems investigated was the interface between a copper electrode and water [67]. For this purpose these authors set up a simulation cell with approximate dimensions of 42 A X 15 A X 15 A. Each cell contained a slab of copper atoms that were five-layers thick, the two surfaces having (100) structure. The remaining space was filled with water molecules. CycKc boundary conditions were applied in all directions. Obviously, an ab initio, all electrons calculation is quite impossible for such a system, and may not even be desirable. Instead, Halley and collaborators used a mixture of pseudopotentials... 

The Car-Parinello method is an alternative to Bom-Oppenheimer. Optimization of geometry and calcnlation of wave function occur simultaneously. Forces on the nnclei are calcnlated from the charges as in the Hellman-Feynman approximation. The nnclei are moving classically and their kinetic energy is decreased until the eqnUibrinm for that particular electronic density is found. The electronic charge density is recalculated and a new equilibrinm position found. 

The main purpose of this chapter is to present the basics of ab initio molecular dynamics, focusing on the practical aspects of the simulations, and in particular, on modeling chemical reactions. Although CP-MD is a general molecular dynamics scheme which potentially can be applied in combination with any electronic structure method, the Car-Parinello MD is usually implemented within the framework of density functional theory with plane-waves as the basis set. Such an approach is conceptually quite distant from the commonly applied static approaches of quantum-chemistry with atom-centered basis sets. Therefore, a main... 

The Car-Parinello MD approach is usually applied in combination with plane wave based electronic structure methods. Use of plane waves in Car-Parinello MD is in many ways easier than the atom-centered basis sets (Gaussian-type or Slater-type... 

Another method of controlling the temperature that can be used in CP MD is the stochastic thermostat of Andersen.27 In this approach the velocity of randomly selected nucleus is rescaled this corresponds in a way to the stochastic collisions with other particles in the system. Therefore, this approach is often called a stochastic collision method. The Andersen thermostat has recently been shown28 to perform very well in the Car-Parinello molecular dynamic simulations of bimolecular chemical reactions. 

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 a very recent calculation by Markwick et al. targeted molecular dynamics methods were implemented in the framework of Car-Parinello molecular dynamics to study the nature of the double proton transfer [48]. They predict a concerted proton transfer reaction. In the very early stages of this reaction the system enters a vibrationally excited pretransitional state. Whereas in the global minima large amplitude fluctuations have been found in the pretransitional region, the frequency of these fluctuations is found to increase dramatically while the amplitude of the oscillation decreases when approaching the transition state. 

Two methods, identified as Car-Parinello [113] and Born-Oppenheimer [114], have been advanced for performing direct dynamics simulations. For the former, the motions of the electrons are determined simultaneously as the nuclear classical equations of motion are integrated, to determine the change in the electronic wave function as the nuclei move. For the second method the electronic wave function is optimized during the numerical integration of the classical trajectory. 

The ah initio methods can be used in developing approximate classical expressions for the interactions present in these systems. The way in which this is done is the subject of this section. We note in passing that recent work on so-called ab initio molecular dynamics such as Car-Parinello MD [22-24] is blurring the distinction between purely ab initio methods and the classical simulation methods described below. In fact, the first ab initio M D simulation study of an ionic liquid was reported recently [21]. 

Hamiltonian models are classified according to then-level of approximation. The features of Schroedinger (S), Born-Oppenheimer (BO), and McMillan-Mayer (MM) level Hamiltonian models are exemplified in Table I by a solution of NaCl in H2O. The majority of investigations on electrolyte solutions are carried out at the MM level. BO-Level calculations are a precious tool for Monte Carlo and molecular dynamics simulations as well as for integral equation approaches. However, their importance is widely limited to stractural investigations. They, as well as the S-level models, have not yet obtained importance in electrochemical engineering. S-Level quantum-mechanical calculations mainly follow the Car-Parinello ab initio molecular dynamics method. 

In this chapter we will review recent developments in modelling proton transport in different media. We will thereby narrow the topic to atomistic modelling of transport properties and processes only. The majority of studies in this area employ molecular dynamics (MD) to get insight into the mechanisms. For large systems classical force fields are used, small systems are often studied with ab-initio molecular dynamics, especially with Car-Parinello MD simulations. These methods are well known and documented, including their drawbacks, as e.g. finite-size effects in periodic simulations." Therefore, we will abandon explicit comments on the computational details, and refer the interested reader to the cited references or ordinary textbooks. 

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