Molecular dynamics Car-Parrinello

At this point, all the ingredients are in place for introducing ab initio MD. If we assumes we have minimized the functional E[p] for a given set [Rj] of nuclear coordinates, we can write the Hamiltonian governing the time evolution of the atomic positions as 

The wide acceptance and successful application of DFT-MD relies on a different point of view, described in the seminal paper by Car and Parrinello [8], see also [82]. In Eq. (23), we rnade the dependence of U on the expansion coefficients [a] explicit for the KS orbitals. Strictly speaking, this notation is redundant, because these coefficients are those minimizing the functional E[p] and, therefore, the only independent variables 

HOMO and LUMO occupation, and thus leaves the Bom-Oppenheimer surface. Needless to say, this problem is especially relevant for metal clusters, because these systems have a comparatively smaller HOMO-LUMO gap than other clusters or molecules. Nevertheless, for finite systems a vanishing HOMO-LUMO gap is the exception and not the rule, even for metallic elements, and experience based on many computations has shown that extensive adiabatic simulations can be performed for metal clusters. 

A few details on the basic algorithms used to integrate the equations of motion are collected in Appendix B. 

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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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