Car-Parrinello simulations

The Car-Parrinello simulations were performed using the MOTECC-90 computer code [13]. All considered systems consist of 64 atoms in a cubic unit cell with a length of 23.4 a.u. and periodic boundary conditions. The plane-wave cut-off was chosen to be 6 Ryd. The atomic cores were described by the pseudopotentials of Bachelet et al. [14]. 

Quantum chemical methods are well established, accepted and of high potential for investigation of inorganic reaction mechanisms, especially if they can be applied as a fruitful interplay between theory and experiment. In the case of solvent exchange reactions their major deficiency is the limited possibility of including solvent effects. We demonstrated that with recent DFT-and ab initio methods, reaction mechanisms can be successfully explored. To obtain an idea about solvent effects, implicit solvent models can be used in the calculations, when their limitations are kept in mind. In future, more powerful computers will be available and will allow more sophisticated calculations to be performed. This will enable scientists to treat solvent molecules explicitly by ab initio molecular dynamics (e.g., Car-Parrinello simulations). The application of such methods will in turn complement the quantum chemical toolbox for the exploration of solvent and ligand exchange reactions. 

Rothlisberger U, 15 Years of Car-Parrinello Simulations in Physics, Chemistry and Biology In Computational Chemistry Reviews of Current Trends, Vol 6, edited by J Leszczynski (World Scientific, Singapore, 2001), pp 33-68... 

Rothlisberger U, P Carloni, K Doclo, M Parrinello (2000) A comparative study of galactose oxidase and active site analogs based on QM/MM Car Parrinello simulations. J. Biol. Inorg. Chem. 5 (2) 236-250... 

Hybrid QM/MM Car-Parrinello simulations in which the quantum part is treated at the AIMD level and the surrounding is described with a classical force field... 

Rational Design of Biomimetic Catalysts by Hybrid QM/MM Car-Parrinello Simulations of Galactose Oxidase... 

Similiar problems are known in classical MD simulations, where intramolecular and intermolecular dynamics evolve on different time scales. One possible solution to this problem is the method of multiple time scale propagators which is describede in section 5. Berne and co-workers [21] first used different time steps to integrate the intra- and intermolecular degrees of freedom in order to reduce the computational effort drastically. The method is based on a Trotter-factorization of the classical Liouville-operator for the time evolution of the classical system, resulting in a time reversible propagation scheme. The multiple time scale approach has also been used to speed up Car-Parrinello simulations [20] and ab initio molecular dynamics algorithms [21]. 

The analysis of such Car-Parrinello simulation is not limited to analysis of the distribution and d3mamics of the ions alone in Sect. 7 we will discuss the calculations of electronic properties (observables), like polarization, in the frame-work of DFT. We will also introduce the calculation of electronic response properties and excited states energies in DFT. 

B. Kirchner and J. Butter (2002) The structure of a DMSO/Water mixture from Car-Parrinello simulations. Chem. Phys. Lett. 364, p. 497... 

M. Colombo, L. Guidoni, A. Laio, A. Magistrate, P. Maurer, S. Piana, U. Rohrig, K. Spiegel, M. Sulpizi, J. VandeVondele, M. Zumstein, and U. Roth-lisberger (2002) Hybrid QM/MM Car-Parrinello Simulations of Catalytic and Enzymatic Reactions. CHIMIA 56, p. 13... 

F. A. Bornemann and C. Schutte (1999) Adaptive accuracy control for Car-Parrinello simulations. Numer. Math. 83, p. 179... 

P. Tangney and S. Scandolo (2002) How well do Car-Parrinello simulations reproduce the Born-Oppenheimer surface Theory and examples. J. Chem. Phys. 116, p. 14... 

M. Sulpizi, A. Laio, J. VandeVondele, U. Rothlisberger, A. Cattaneo, and P. Carloni (2003) Reaction Mechanism of Caspases Insights from Mixed QM/MM Car-Parrinello Simulations. Proteins-Structure, Function and Genetics 52, p. 212... 

Developments in first-principles simulations (FPMD) such as the Car-Parrinello (CPMD) method were the most important theoretical progress made in the last century [25], The reason for this is that the first-principles simulations approach is a combination of molecular-dynamics simulations with electronic structure calculations on the fly. In the Car-Parrinello simulation method the expensive QC part is... 

Years of Car-Parrinello Simulations in Physics, Chemistry and Biology (U. Rothlisberger)... 

In 1995, Marx and Parrinello performed an extensive ab initio electronic structure calculation (Car-Parrinello simulation ), which includes the quantum effects and showed that a preference for the Cj quantum ground state does exist. They also showed that there is a small but definite barrier for hydrogen equilibration. A study by Kutzelnigg et al. [high-level CCSD(T)-R12] with large basis sets on Cd Is" also reconfirmed the preferred Cj symmetrical struc-ture. ° An evaluation by Marx and Parrinello of results reported in the 1990s was disclosed in 1999. ... 

Moore s law, computational power has increased by a factor of 1000 since then. In addition, with the development of many computer codes that employ the Car-ParrineUo method, combined with the enhanced accuracy of density functionals that have been devised since 1985, there has been widespread use of the Car-Parrinello method. Between 1997 and the beginning of 2000, over 500 papers that incorporate results found using Car-Parrinello simulations have been published in major journals. Most of these papers have been published by groups considered primarily to be in the field of physics. On the other hand, the topics of these papers span the spectrum of disciplines as traditionally classified physics, industrial chemistry, catalysis, materials engineering, microelectronic materials, polymer science, biology, and geology. 

By far the major computational quantum mechanical method used to compute the electronic state in Car-Parrinello simulations is density-functional theory (DFT) (Hohenberg and Kohn, 1964 Kohn and Sham, 1965 Parr and Yang, 1989). It is the method used originally by Roberto Car and Michele Parrinello in 1985, and it provides the highest level of accuracy for the computational cost. For these reasons, in this section the only computational quantum mechanical method discussed is DFT. Section A consists of a brief review of classical molecular dynamics methods. Following this is a description of DFT in general (Section B) and then a description of practical DFT computations of chemical systems using the plane-wave pseudopotential method (Section C). The section ends with a description of the Car-Parrinello method and some basic issues involved in its use (Section D). 

To avoid using a predefined form for the interaction potential in molecular dynamics simulations, the quantum mechanical state of the many-electron system can be determined for a given nuclear configuration. From this quantum mechanical state, all properties of the system can be determined, in particular, the total electronic energy and the force on each of the nuclei. The quantum mechanically derived forces can then be used in place of the classically derived forces to propagate the atomic nuclei. This section describes the most widely used quantum mechanical method for computing these forces used in Car-Parrinello simulations. 

The form of the basis set expansion is chosen to be convenient to model the system and to perform the integrals needed to solve the coupled Eqs. (13). Examples of convenient forms are Gaussians, numerical grids, and plane waves. Plane waves have often (but not exclusively) been chosen as the basis set expansion used in Car-Parrinello simulations for two reasons (i) It is generally desired to simulate extended systems, such as bulk materials, surfaces, and hquids, and plane waves provide a convenient way to model these systems using periodic boundary conditions (ii) forces on atomic nuclei can be calculated very efficiently if the electrons are described by plane waves by making use of the Heilman-Feynman theorem (yide infra). 

The methodology described above provides the ability to perform molecular dynamics simulations without choosing forms and parameters for interaction potentials. Because Car-Parrinello simulations are molecular... 

The downside to the power of Car-Parrinello calculations is that they are computationally costly. Typically, the largest systems that can be treated are of the order of 100 atoms, and the time scale of the simulations is of the order of picoseconds. The purposes of Car-Parrinello simulations generally fall under three main categories (i) simulations as a means of optimization to determine structural properties, (ii) direct simulations of processes occurring over short time scales, and (iii) simulations to sample equilibrium properties. 

Studies under categories ii and iii provide more poignant examples of the power of Car-Parrinello methods. Because of the magnitude of the literature on applications of Car-Parrinello simulations, 1 have chosen to focus on a few case studies to iUustrate the potential of simulations under these categories for problems of interest to chemical engineers. The areas that 1 have chosen are (A) gas-phase processes (B) processes in bulk materials (C) properties of liquids, solvation, and reactions in liquids (D) heterogeneous reactions and processes on surfaces (E) phase transitions and (F) processes in biological systems. 

Fig. 10. Pair correlation functions obtained both from Car-Parrinello simulations and from experiments. The thick solid lines are simulation results obtained using a supercell with 64 water molecules. The thin solid lines are for the 32-water molecule simulation. The short-dashed line is from experimental neutron scattering results (Soper et al., 1997), and the long-dashed line is from an X-ray study. Reprinted with permission from Silvestrelli and Parrinello (1999).

The structure of a water/silicon interface was studied (Ursenbach et al, 1997), in addition to a water/copper interface (Halley et al, 1998) and a water/palladium interface (Klesingeza/., 1998). Finally, two studies have used Car-Parrinello simulations in conjunction with the Green-Kubo relations to calculate viscosities in liquid metals (Alfe and Gillan, 1998 Stadler et al, 1999). 

There has been a variety of studies using Car-Parrinello simulations to determine the structure and energetics of adsorbates on semiconductor and insulating surfaces. Studies on metal surfaces are much rarer, and as far as I know, first-principles molecular dynamics simulations have not yet been used to study reactive processes on metals. The reason is primarily one of computational expense, because metals require the inclusion of a large number of k-points. Tliere is, of course, a substantial body of work which uses static quantum mechanical calculations to study reactions on metal surfaces. 

Boero et al. (1998) used Car-Parrinello molecular dynamics to study the polymerization of ethylene at titanium sites in MgCl2-supported Ziegler-Natta catalysts. Their objectives were to evaluate the reaction mechanism, in addition to determining the free energy profile of the polymerization process. Obviously, the characteristic time scale of this process is much greater than the picosecond time scale directly accessible by the simulation. Thus, it is not possible to observe the polymerization process via a straightforward Car-Parrinello simulation. 

Initially, Boero et al. (1998) performed an optimization of their entire system on a sixfold coordinated Ti site called the Corradini site. They then varied the values of their reaction coordinate, decreasing it by increments of 0.2 to 0.1 A. At each value of the reaction coordinate, they performed Car-Parrinello simulations to obtain f rc-c- The temperature of the simulations was 323 K. 

Car-Parrinello simulations present powerful ways to study phase diagrams and to find new phases of materials, particularly at high pressures. Typically, (N,T,P) simulations are performed using deformable supercells. Methodology can be found in the following references Focher et al. (1994),... 

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