Parrinello Molecular Dynamics

In order to further increase computational efficiency. Car and Parrinello have introduced a technique to bypass the need for wavefunction optimization at each molecular dynamics step (Car and Parrinello 1985 Marx and Hutter 2000). Instead, the molecular wavefunction is dynamically propagated along with the atomic nuclei according to the equations of motion 

This equation describes the motion of a particle of mass Mi along one dimension (Xj), where Fx, is the force on the particle in that dimension. The solution of these differential equations 

Molecular Dynamics Simulation From Ab Initio to Coarse Grained  

In realistic models of intermolecular interactions, the force on particle I changes whenever particle I changes its position or whenever another atom with which particle I interacts changes its position. Therefore the motions of all the particles are coupled together, which results in a many-body problem that cannot be solved analytically. Therefore finite difference methods are used to integrate the equations of motion. 

Generally, the integration of O Eq. 7.17 is broken into consecutive steps that are conducted at different times t that are separated by increments of 6t, which is generally referred to as the time step. First, the total force on each particle in the system at time t is calculated as the vector sum of its interactions with other particles. 

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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].

Thar J, Reckien W, Kirchner B (2007) Car-Parrinello Molecular Dynamics Simulations and Biological Systems. 268 133-171... 

Markwick PRL, Doltsinis NL, Schlitter J (2007) Probing irradiation induced DNA damage mechanisms using excited state Car-Parrinello molecular dynamics. J Chem Phys 126 045104... 

Iannuzzi, M. Laio, A. Parrinello, M., Efficient exploration of reactive potential energy surfaces using Car-Parrinello molecular dynamics, Phys. Rev. Lett. 2003, 90, 238302-238304... 

Laio, A. VandeVondele, J. Rothlisberger, U., A Hamiltonian electrostatic coupling scheme for hybrid Car-Parrinello molecular dynamics simulations, J. Chem. Phys. 2002,116, 6941-6947... 

Applications of Car-Parrinello Molecular Dynamics in Biochemistry - Binding of Ligands in Myoglobin... 

Figure 26 Car-Parrinello Molecular Dynamics of CH4 (a) and C2H6 (b) in SbFs/HF 50 mol % SbF5. (from reference72)...

In this section we focused our attention to a rationalization of the factors determining the stereoselectivity through ab initio mixed quantum/classical (QM/MM) Car-Parrinello molecular dynamic simulations. We have used the same basic computational approach used in Section 3 to explore the potential energy surface of the reaction. Since the catalyst system, 1, is relatively large, we have used the combined QM/MM model system B as shown in Figure 3 and described in subsections 2.1 and 3.1. 

Figure 3. Proton conduction mechanism in iiquid imida-zoie, as revealed by a Car—Parrinello molecular dynamics (CPMD) simulation.3 Note the similarities with the proton conduction mechanism in water (see Figure 1).

Bhargava, B.L., and Balasubramanian, S., Intermolecular structure and dynamics in an ionic liquid A Car-Parrinello molecular dynamics simulation study of 1,3-dimethylimidazolium chloride, Chem. Phys. Lett., 417, 486-491, 2006. 

The first way has been followed in what has become known as Car-Parrinello molecular dynamics (CPMD) (9). A solute and 60-90 solvent molecules are considered to represent the system, and the QM calculations are performed with density functionals, usually of generalised gradient approximation type (GGA), such as the Becke-Lee-Young-Parr (BLYP) (10) or the Perdew-Burke-Enzerhofer (PBE) (11,12) functionals. It is clear that the semiempirical character of concurrent density functional theory (DFT) methods and the use of these simple functionals imply a number of error sources and do not really provide a method-inherent control procedure to test the reliability of results. Recently it has been shown that these functionals even do not enable a correct description of the solvent water itself, as at ambient temperature they will describe water not as liquid but as supercooled system... 

The mechanistic borderline between E2 and ElcB mechanisms has been studied under various conditions.1,2 The mechanism of the elimination reaction of 2-(2-fluoroethyl)-1-methylpyridinium has been explored explored by Car-Parrinello molecular dynamics in aqueous solution.3 The results indicated that the reaction mechanism effectively evolves through the potential energy region of the carbanion the carbon-fluoride bond breaks only after the carbon-hydrogen bond. 

Chen, B., Ivanov, I., Park, J. M., Parrinello, M., Klein, M. L. (2002), Solvation Structure and Mobility Mechansims of OH" A Car-Parrinello Molecular Dynamics Investigation of Alkaline Solutions, J. Phys. chem. B 106, 12006-12016. 

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.

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