Parrinello

Specific solute-solvent interactions involving the first solvation shell only can be treated in detail by discrete solvent models. The various approaches like point charge models, siipennoleciilar calculations, quantum theories of reactions in solution, and their implementations in Monte Carlo methods and molecular dynamics simulations like the Car-Parrinello method are discussed elsewhere in this encyclopedia. Here only some points will be briefly mentioned that seem of relevance for later sections. 

Car and Parrinello [202] proposed a teclmique for efficiently solving the Scluodinger equation which has had an enonuous impact on materials simulation (for reviews, see [203. 204. 205. 206]). The technique is an ab initio one, i.e., free of empirical parameters, and is based on the use of a quantum mechanical orthononual... 

Figure B3.3.12. Sulphur atoms in liquid iron at the Earth s core conditions, simnlated by first-principle Car-Parrinello molecular dynamics, (a) Initial conditions, showing a mannally-prepared initial cluster of snlphur atoms, (b) A short tune later, indicating spontaneous dispersal of the snlphur atoms, which mingle with the surroundmg iron atoms. Thanks are dne to D Alfe and M J Gillan for this figure. For fiirtlier details see [210. 211].

Parrinello M and Rahman A 1980 Crystal structure and pair potentials a molecular dynamics study Phys. Rev.L 45 1196-9... 

Parrinello M and Rahman A 1981 Polymorphic transitions In single crystals a new molecular dynamics method J. Appl. Phys. 52 7182-90... 

Car R and Parrinello M 1985 Unified approach for molecular dynamics and density-funotional theory Phys. Rev.L 55 2471-4... 

Remler D K and Madden P A 1990 Molecular dynamics without effective potentials via the Car-Parrinello approach Mol. Phys. 70 921-66... 

Rothlisberger U, Andreoni W and Parrinello M 1994 Struoture of nanosoale silioon olusters Phys. Rev. Lett. 72 665... 

While simulations reach into larger time spans, the inaccuracies of force fields become more apparent on the one hand properties based on free energies, which were never used for parametrization, are computed more accurately and discrepancies show up on the other hand longer simulations, particularly of proteins, show more subtle discrepancies that only appear after nanoseconds. Thus force fields are under constant revision as far as their parameters are concerned, and this process will continue. Unfortunately the form of the potentials is hardly considered and the refinement leads to an increasing number of distinct atom types with a proliferating number of parameters and a severe detoriation of transferability. The increased use of quantum mechanics to derive potentials will not really improve this situation ab initio quantum mechanics is not reliable enough on the level of kT, and on-the-fly use of quantum methods to derive forces, as in the Car-Parrinello method, is not likely to be applicable to very large systems in the foreseeable future. 

Car, R., Parrinello,M. Unified approach for molecular dynamics and density functional theory. Phys. Rev. Lett. 55 (1985) 2471-2474. 

Abstract. We present novel time integration schemes for Newtonian dynamics whose fastest oscillations are nearly harmonic, for constrained Newtonian dynamics including the Car-Parrinello equations of ab initio molecular dynamics, and for mixed quantum-classical molecular dynamics. The methods attain favorable properties by using matrix-function vector products which are computed via Lanczos method. This permits to take longer time steps than in standard integrators. 

Car-Parrinello Equations of Ab Initio Molecular Dynamics, Constrained Newtonian Dynamics... 

In the Car-Parrinello method [6] (and see, e.g., [24, 25, 16, 4]), the adiabatic time-dependent Born-Oppenheimer model is approximated by a fictitious Newtonian dynamics in which the electrons, represented by a set of... 

F. A. Bornemann and Ch. Schutte. A mathematical investigation of the Car-Parrinello method. Preprint SC 96-19, ZIB Berlin, 1996. To appear in Numer. Math. 

Abstract. This paper presents results from quantum molecular dynamics Simula tions applied to catalytic reactions, focusing on ethylene polymerization by metallocene catalysts. The entire reaction path could be monitored, showing the full molecular dynamics of the reaction. Detailed information on, e.g., the importance of the so-called agostic interaction could be obtained. Also presented are results of static simulations of the Car-Parrinello type, applied to orthorhombic crystalline polyethylene. These simulations for the first time led to a first principles value for the ultimate Young s modulus of a synthetic polymer with demonstrated basis set convergence, taking into account the full three-dimensional structure of the crystal. 

The Car-Parrinello quantum molecular dynamics technique, introduced by Car and Parrinello in 1985 [1], has been applied to a variety of problems, mainly in physics. The apparent efficiency of the technique, and the fact that it combines a description at the quantum mechanical level with explicit molecular dynamics, suggests that this technique might be ideally suited to study chemical reactions. The bond breaking and formation phenomena characteristic of chemical reactions require a quantum mechanical description, and these phenomena inherently involve molecular dynamics. In 1994 it was shown for the first time that this technique may indeed be applied efficiently to the study of, in that particular application catalytic, chemical reactions [2]. We will discuss the results from this and related studies we have performed. 

Secondly, the ultimate properties of polymers are of continuous interest. Ultimate properties are the properties of ideal, defect free, structures. So far, for polymer crystals the ultimate elastic modulus and the ultimate tensile strength have not been calculated at an appropriate level. In particular, convergence as a function of basis set size has not been demonstrated, and most calculations have been applied to a single isolated chain rather than a three-dimensional polymer crystal. Using the Car-Parrinello method, we have been able to achieve basis set convergence for the elastic modulus of a three-dimensional infinite polyethylene crystal. These results will also be fliscussed. 

The structure of the metallocene cation energy minimised with the Car-Parrinello method agrees well with the experimentally obtained crystal structures of related complexes. Typical features of the structure as obtained from X-ray diffraction on crystals of very similar neutral complexes (e.g., the dichlorides), such as small differences in distances between C atoms within a cyclopentadienyl (Cp) ring, as well as differences in distances between the C atoms of the Cp ring and the Zr atom, were revealed from the simulations. 

Regarding mechanical properties of polymers, the efficiency of the Car-Parrinello approach has enabled us to evaluate the ultimate Young s modulus of orthorhombic polyethylene, and demonstrate basis set convergence for that property. 

A key feature of the Car-Parrinello proposal was the use of molecular dynamics a simulated annealing to search for the values of the basis set coefficients that minimise I electronic energy. In this sense, their approach provides an alternative to the traditioi matrix diagonalisation methods. In the Car-Parrinello scheme, equations of motion ... 

An alternative to the Car-Parrinello method is the following scheme, which separates the electronic and nuclear motions ... 

Boero M, M Parrinello and K Terakura 1999. Ziegler-Natta Heterogeneous Catalysis by First Piincip Computer Experiments. Surface Science 438 1-8. 

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