Parrinello MD

Although in CP-MD the nuclei are still treated as classical particles, the choice of time step can no longer be based solely on the highest nuclear frequency We also need to consider the fictitious dynamics of the electronic degrees of freedom. In fact, the optimum simulation time step is closely linked to the value of the fictitious electron mass ft as we wiU see in the following. 

The fictitious mass has to be chosen small enough to guarantee adiabatic separation of electronic and nuclear motion. This means that the frequency spectrum of the electronic degrees of freedom (Marx and Hutter 2009 Pastore et al. 1991) 

The highest electronic frequency is determined by the plane-wave cutoff energy cut. 

Thus the maximum simulation time step, which is inversely proportional to w , thus obeys the relation  

According to O Eq. 7.107 the maximum time step can be increased by simply increasing ft. However, this would also result in a lowering of o)f (see O Eq. 7.105) and therefore in a smaller 

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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]. 

If we are interested in d3mamical quantities on the other side (vibrational density of states, infrared or Raman spectra), these quantities will then depend on the fictitious mass /x through the atomic mass renormalization. This dependence of the t3q)ical ionic frequency on fi will be linear at small /x. Thus, for extracting vibrational frequencies from Car-Parrinello MD, the criterium for choosing jj, should certainly be tighter than described in the previous paragraph. 

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. 

Classical force field MD, MC Embedded atomistic-quantum methods Car-Parrinello MD Quantum MC... 

Pantano et al used Car-Parrinello MD to compute the influence of thermal fluctuations on the proton hopping properties of a model substrate for enzymatic reactions, benzoylacetone. A plot showing the projection of ELF on the plane defined by the O-H-0 moiety unambiguously demonstrates the presence of electron pair density between the hydrogen and the two H-bond donors, suggesting the presence of a three-centre covalent bond. The character of the bond is o, as evidenced by analysing the Kohn-Sham one-electron wavefimction, in full agreement with AIM. 

Hybrid methods learn from the pros and cons of classical and quantum methods and try to combine the best features of both. These methods are of two categories (1) methods that are hybrid in a temporal sense, mixing electronic structure calculations with MD methods and (2) methods that are spatially hybrid, applying different methods in different physical regions of a molecule or computational domain. Car-Parrinello MD (CPMD) (Car and Parrinello 1985) and related methods such as... 

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. 

Higher hydrates of triflic acid were studied by Hayes, Paddison, and Tuckerman using path integral Car-Parrinello MD (Hayes et al., 2009, 2011). The larger amount of water available per acidic proton led to the formation of larger proton complexes and more versatile proton defect structures. Formation of such defects involves local proton transfer events. The observed defects correspond to local structures. They are energetically expensive to form, and it seems unlikely that they could propagate in the crystal. 

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. 

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... 

On the other hand, the FE of activation of the inverse reaction, AAjj, was 1.8 kcal moF (MP2) and is in good agreement with the estimation by the Car-Parrinello MD method ( 1.5 kcal moF [40]). On the contrary, the FE overestimation at the HF level could be understood mainly due to the incorrectness of the PE itself as shown in Fig. 8.8. It is understood that, for discussion of the FE stability of the proton transfer reaction of glycine in aqueous solution, it is essentially necessary to include the electron correlation effect at least by the MO calculation at the MP2 level. 

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... 

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