Car-Parinello

J.3 Mixed Quantum Mechanical/Molecular Mechanical Car-Parinello Simulations 15... 

Mixed Quantum Mechanical/Molecular Mechanical (QM/MM) Car-Parinello Simulations... 

By use of parallel computers Car-Parinello simulations can currently be performed for systems containing a few hundred to a few thousand atoms. However impressive, this is still too limited a size for most biologically relevant applications. One possible solution for the modeling of systems of several tens of thousands... 

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

In this way, efficient and consistent QM/MM Car-Parinello simulations of complex extended systems of several tens of thousands to several hundred thousand atoms can be performed in which the steric and electrostatic effects of the surrounding are taken explicitly into account. 

As a simple example of a QM/MM Car-Parinello study, we present here results from a mixed simulation of the zwitterionic form of Gly-Ala dipeptide in aqueous solution [12]. In this case, the dipeptide itself was described at the DFT (BLYP [88, 89 a]) level in a classical solvent of SPC water molecules [89b]. The quantum solute was placed in a periodically repeated simple cubic box of edge 21 au and the one-particle wavefunctions were expanded in plane waves up to a kinetic energy cutoff of 70 Ry. After initial equilibration, a simulation at 300 K was performed for 10 ps. 

According to CASSCF (and nonhybrid functionals), the spin population on the Fe atom is close to 1.0, whereas the NO moiety does not carry a significant amount of spin density. Based on that, the Fe(I)-NO+ electronic structure was assigned to the FeP-NO complex. Earlier, (147) based on Car-Parinello MD simulations, the Fe(III)-NO electronic structure was suggested for the FeP-NO complex. Additional complications came from the comparison of N-0 bond length while the experimentally measured bond... 

Mundy CJ, Colvin ME, Quong AA (2002) Irradiated guanine a Car-Parinello molecular dynamics study of dehydrogenation in the presence of an OH radical. J Phys Chem A 106 10063-10071 Murata-Kamiya N, Kamiya H, Muraoka M, Kaji H, Kasai H (1998) Comparison of oxidation products from DNA components byy-irradiation and Fenton-type reactions. J Radiat Res 38 121-131 Nabben FJ, van der Stroom HA, Loman H (1983) Inactivation of biologically active DNA by isopropanol and formate radicals. Int J Radiat Biol 43 495-504 Nakashima M, Hayon E (1979) Rates of reaction of inorganic phosphate radicals in solution. J Phys Chem 74 3290-3291... 

The terms of this type must be summed over all bonds between the heavy atoms. The formulae eqs. (3.100), (3.101) represent the potential energy of the molecular system as a quadratic function on small variations of the variables wf. This may be used either in a frame of a linear response analysis of reaction of the system of hybridization tetrahedra to various perturbations or (if the hybridization tetrahedra are supplied by fictitious inertia momenta) as potential energy of the system of the tetrahedra in a frame of a Car-Parinello-like [46] procedure. 

Keywords First-Principle Molecular Dynamics, Car-Parinello Molecular Dynamics, Density... 

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... 

In this section we will briefly present the basic concepts of ab initio molecular dynamics within the Born-Oppenheimer and Car-Parinello approach. It is not our intention to cover the theoretical background of the Car-Parinello MD scheme in details. Instead we would like to concentrate on the practical aspects of the simulation and only briefly comment on the physical meaning of the basic parameters that must be specified in the input for a simulation. A more detailed discussion of the theoretical basis for the CP MD can be found in an excellent review article by Marx and Hutter.2... 

The Euler-Lagrange equation leads to the Car-Parinello equations of motion of the form ... 

Thus, in the Car-Parinello MD scheme the initially converged wave function is propagated according to Eq. (2), and does not need to be re-optimized at every timestep (see Figure 4-1). 

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... 

Figure 4-3. A comparison of the Car-Parinello and Bom-Oppenheimer molecular dynamics the potential energy (top) and temperature (kinetic energy, bottom) from the CP-MD and BO-MD simulations for ethylene, started from the same geometry and wave function. The results obtained form the simulations with the CPMD program13 (Troullier-Martins pseudopotentials,1415 time step of 4 a.u., fictitious mass 400 a.u., cut-off energy 70 Ry, unit cell 12 A x 12 A xl2 A)...

The most popular way to control the temperature in the CP MD simulation was introduced by Nose and Hoover.23,24 This approach includes an extra friction term (velocity dependent) into the Car-Parinello equations of motions (cf. Eq. 3) ... 

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. 

The typical time scale for the Car-Parinello MD simulation is presently of the order of picoseconds. This time scale is usually not sufficient to directly observe a chemical reaction in a single free dynamics simulation, due to relatively high activation-energy barriers. Thus, many approaches have been proposed to simulate such rare reactive events. 

Some attempts to inclnde structural diffusion exist. The mechanism of proton transport in bulk water has been studied by various molecular modeling techniques like the Car-Parinello ab initio molecnlar dynamics simnlations (CPAIMD), mixed quan-tnm and classical mechanics technique (QM/MM), E " ... 

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