Car-Parrinello MD simulations

The key step of the process corresponds to the H2 transfer from the Ru-based catalyst to the carbonyl group. Pavlova and Meijer studied this step by means of Car-Parrinello MD simulations using formaldehyde as the substrate, resulting in... 

With the development of GGA functionals, description of molecular systems with the Kohn-Sham method reached a precision similar to other quantum theory methods. It was quickly shown that the GGA s could also well reproduce the hydrogen bond properties. Short after, liquid water at ambient condition was first simulated by Car-Parrinello MD, with a sample of 32 water molecules with periodic boundary conditions [31]. Since then, many simulations of liquid water at different temperatures and pressures and of water solutions have been performed [32-39]. Nowadays, Car-Parrinello MD has become a major tool for the study of aqueous solutions [40-64]. 

A group of theoretical methods exists where the electronic wavefuntion is computed, and the atomic nuclei are propagated (using classical equations of motion). The Car-Parrinello MD method is one of this type [22-24]. These methods he between the extremes of the classical and ab initio methods, as they include some (quantum) electronic information and some (classical) dynamics information. These methods are called ah initio or first principles MD if you come from the classical community and semi-classical MD if you come firom the quantum community [9], Ah initio MD methods are far more expensive and cannot simulate as many molecules for as long as the classical simulations, but they are more flexible in that structures are not predetermined and information on the electronic structure is retained. Semi-classical MD can be carried out under periodic boundary conditions and thus the local liquid environment, and any extended bonding network, vyill be present. These methods hold a great deal of promise for the future study of ionic liquid systems, the first such calciilations on ionic liquids were reported in 2005 [21,25]. 

Frank and coworkers have employed a constrained distance method in conjunction with Car-Parrinello MD (CPMD) simuIatiOTis [99] to examine a variety of mechanochemical processes [33, 39-41, 100, 101]. During these simulations, F is applied by increasing the distance between a pair of atoms at a cmistant velocity. They have used this approach to explore the changes in electronic structure that occur when solvated polymers are stretched to the point of rupture [41]. Their studies showed that bond rupture occurred through a heterolytic process involving solvent molecules. Interestingly, their simuIatiOTis showed that the weakest bond does not necessarily correspond to the site of bond rupture. Rather, the bmid that is made most accessible to attack by solvent via E-induced changes in structure most ft equently corresponds to the site at which the polymer dissociates. 

Vienna ab initio Simulation Package (VASP) (Kresse and FurethmuUer 2000), and Car-Parrinello MD Program (CAMP-Atami) (Ohnishi 1994) combine molecular dynamics with DFT under a periodic boundary condition with the orbitals expanded in the plane wave. They have been routinely used in industrial applications such as heterogeneous catalysis. 

Initial optimization studies were performed with VASP (Vienna Ab Initio Simulation Protocol). Later on, optimization studies were repeated with Car-Parrinello MD (CPMD). With CPMD, the transition from upright to tilted shifts to a slightly larger value, dec 6.7 A. 

Exner and coworkers have used Af-methyl acetamide (NMA) as a test system for amide groups in protein backbones to calculate NMR chemical shifts with the Car-Parrinello MD method with explicit solvent molecules and quantum-chemical calculations of NMR parameters and compare with classical MD simulations. For example the C-P calculations give in general shorter solute-solvent H-bonds which in turn give a... 

A successful tool to describe and interpret experimental findings of liquids is to perform ab initio molecular dynamics (MD) simulations for the particular systems. We performed such simulations for 5 different compositions of NaSn - ranging from 20% to 80% of sodium - applying the Car-Parrinello technique [5]. 

An important advance in making explicit polarizable force fields computationally feasible for MD simulation was the development of the extended Lagrangian methods. This extended dynamics approach was first proposed by Sprik and Klein [91], in the sipirit of the work of Car and Parrinello for ab initio MD dynamics [168], A similar extended system was proposed by van Belle et al. for inducible point dipoles [90, 169], In this approach each dipole is treated as a dynamical variable in the MD simulation and given a mass, Mm, and velocity, p.. The dipoles thus have a kinetic energy, JT (A)2/2, and are propagated using the equations of motion just like the atomic coordinates [90, 91, 170, 171]. The equation of motion for the dipoles is... 

Another approach is that of including dynamics in the calculations. A dynamical formalism of DFT was first developed by Car and Parrinello [31], and has been employed in a wide range of areas, e.g. solvation problems, reactions on surfaces, solid-state interactions, and a variety of biochemical applications. In CP-MD one normally uses a plane wave basis to reduce the computational requirements and enable easy implementation of periodic boundary conditions. Nonetheless, CP-MD simulations are rather costly, and are normally not applied to systems larger than, say, 1-200 atoms, and over relatively short time frames. 

At several points in diis book, it has been emphasized that the prevalence of classical MC and MD simulations derives from die impracticality of carrying out fully QM dynamics. While diis is largely true, for systems of only modest size where short trajectories may be profitably analyzed, fully QM MD simulations using the so-called Car-Parrinello technique are a viable option (Car and Parrinello 1985). In its most widely used formulation, the Car-Parrinello method employs DFT as the electronic-structure method of choice. In... 

Figure 6.3 Three snapshots of MD and Car—Parrinello molecular dynamics simulations of the photoactive yellow protein, showing the entire protein (left), the pocket containing the chromophore (middle), and the chromophore itself (right). Thanks to Dr. Elske Leenders and Dr. Evert Jan Meijer for the simulation snapshots.

Hybrid multiscale models enable us to focus on the relevant part of a system. For example, Leenders et al. studied the proton transfer process in the photoactive yellow protein (Figure 6.3) [9], They used Car-Parrinello molecular dynamics [10], a QM method for dynamics simulations, to describe the chromophore and its hydrogen-bonded network in the protein pocket (middle and right-hand circles). This was combined with a traditional MD force field of 28 600 atoms, simulating the entire protein in water (left-hand circle). 

In order to overcome the limitations of currently available empirical force field param-eterizations, we performed Car-Parrinello (CP) Molecular Dynamic simulations [36]. In the framework of DFT, the Car-Parrinello method is well recognized as a powerful tool to investigate the dynamical behaviour of chemical systems. This method is based on an extended Lagrangian MD scheme, where the potential energy surface is evaluated at the DFT level and both the electronic and nuclear degrees of freedom are propagated as dynamical variables. Moreover, the implementation of such MD scheme with localized basis sets for expanding the electronic wavefunctions has provided the chance to perform effective and reliable simulations of liquid systems with more accurate hybrid density functionals and nonperiodic boundary conditions [37]. Here we present the results of the CPMD/QM/PCM approach for the three nitroxide derivatives sketched above details on computational parameters can be found in specific papers [13]. 

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]. 

Section 6 will deal with the core of the problem at hand, coupling of the electronic calculation with Molecular Dynamics for ions. We will describe in particular the Car-Parrinello method introduced in 1985 [2], which is really the starting point for combining on the fly electronic structure calculation to MD and statistical physics. This will be illustrated rapidly by a simulation of 32 water molecules at room temperature. 

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