Classical MD simulations

The principal idea behind the CSP approach is to use input from Classical Molecular Dynamics simulations, carried out for the process of interest as a first preliminary step, in order to simplify a quantum mechanical calculation, implemented in a subsequent, second step. This takes advantage of the fact that classical dynamics offers a reasonable description of many properties of molecular systems, in particular of average quantities. More specifically, the method uses classical MD simulations in order to determine effective... 

AVcorr can be evaluated readily from the classical MD simulation for any choice of coordinate system, and it may be possible to determine the modes that give the smallest AVcorr- These should be optimal CSP modes. Work along these lines is in ])rogress in our group. So far, however, the coordi-... 

Elliott et al.i applied classical MD simulations to study the dynamics of small molecules in a model Nafion membrane for A= 1, 3.8, and 9.7. They observed wafer segregafion info "bound" water associated with the sulfonate groups and more loosely attached "free" water. 

To conclude our brief overview of ab initio MD, we note that the dynamics defined by Eq. (9.16) define a microcanonical ensemble. That is, trajectories defined by this Lagrangian will conserve the total energy of the system. Similar to the situation for classical MD simulations, it is often more useful to calculate trajectories associated with dynamics at a constant temperature. One common and effective way to do this is to add additional terms to the Lagrangian so that calculations can be done in the canonical ensemble (constant N, V, and T) using the Nose-Hoover thermostat introduced in Section 9.1.2. 

Even for purely adiabatic reactions, the inadequacies of classical MD simulations are well known. The inability to keep zero-point energy in all of the oscillators of a molecule leads to unphysical behavior of classical trajectories after more than about a picosecond of their time evolution." It also means that some important physical organic phenomena, such as isotope effects, which are easily explained in a TST model, cannot be reproduced with classical molecular dynamics. So it is clear that there is much room for improvement of both the computational and experimental methods currently employed by those of us interested in reaction dynamics of organic molecules. Perhaps some of the readers of this book will be provide some of the solutions to these problems. 

Valence bond (VB) theories or empirical valence bond (EVB) methods have been developed in order to solve this problem with bond potential functions that (i) allow the change of the valence bond network over time and (ii) are simple enough to be used efficiently in an otherwise classical MD simulation code. In an EVB scheme, the chemical bond in a dissociating molecule is described as the superposition of two states a less-polar bonded state and an ionic dissociated state. One of the descriptions is given by Walbran and Kornyshev in modeling of the water dissociation process.4,5 As... 

An introduction to the modeling methods can be found in refs. [22,231. The classical MD simulations reported here were performed with the modified AMBER software/241 in which the potential energy consists of harmonic deformations of bond and angles, dihedral energies, plus non-bonded interactions represented by a sum of pair wise additive coulombic and van der Waals contributions ... 

It is now interesting to check if this picture is either confirmed or modified by changing the description of the solvent. This check is here realized introducing diazine-water clusters extracted from classical MD simulations and comparing their NMR properties calculated once again with PCM or with the QM/MM(pol) model we have introduced in the previous section with the acronym DPM. 

In order to generate an appropriate number of solute-solvent clusters to be used in the NMR calculations a series of classical MD simulations of pyrazine, pyrimidine or pyridazine in aqueous solution has been carried out. All the details of the force fields used for the diazines and water as well as computational details of the MD simulation can be found in Ref. [31]. Every 1 ps an MD configuration was dumped so as to obtain 600 different molecular configurations. Then, a spherical cut-off distance equal to 12 A was applied so as to obtain the final cluster including 230-240 water molecules together with the solute. 

Table 13-2. Vertical electronic n —> 7T transition energy of acetone in gas phase, Egas, and aqueous solution, Ewat, in units of eV. Excitation energy in aqueous solution was obtained from the combined QM/MM calculations treating acetone molecule at the quantum mechanical level of theory as indicated in the first column and using the polarizable potential for water molecules as a statistical average over 1200 molecular configurations extracted from classical MD simulation. The solvent shift in excitation energy, AE (in cm-1), is evaluated as a difference between excitation energies in water and in vacuum...

In this first task, each excess proton is permanently attached to a hydronium ion. This assumption prohibits stractural diffusion of the proton. However, for the purposes of the first task, namely the generation of molecular-level stmcture of the hydrated membrane and its interfaces, this approximation is adequate. For the second task, namely the generation of transport properties, this limitation is removed. Although, the classical MD simulations in task I cannot quantitatively characterize the stmctural diffusion mechanism, from the analysis of the hydration structure of the hydronium ions in these simulations the characteristics of Zundel and Eigen ion (which are necessary for structural diffusion) can be studied. 

The distribution of the first peak from the g(r) of classical MD simulations where the system of hydronium ions and water molecules are treated classically. 

The vehicular diffusion components from the non-reactive system, RSt and RStt are plotted in Fig. 26. Diffusivities from the classical MD simulation, Dy h can be used as the reference value for comparison. The expected vehicular component, can also be generated based on the experimental total diffusivity and the... 

The classical MD simulations performed in task I provide self-diffusion coefficients for water and also for hydronium ions, which is strictly the vehicular component of the proton diffusivity. These diffusion coefficients are calculated from the mean square displacement of H2O and HsO using the Einstein relation. The numerical values for Nation and SSC membranes at the four hydration levels are hsted in Table 5 along with the experimental values. ... 

The diffusion coefficients of water calculated from the MD simulations exhibited good agreement with experiment both in terms of the trend with respect to increasing water content as well as the trend with respect to length of the side chain. The diffusivity of the hydronium ions calculated from classical MD simulation agreed with experiment in terms of the trend with respect to increasing water content, but were consistently too low and did not reflect the experimental dependence on length of the side chain,... 

The introduction of the Cm-Parrinello method has not only extended the range of classical MD simulations based on empirical potentials but at the same time, it has also significantly increased the capabilities of conventional electronic structure calculations. Through the combination with a MD method a generalization to finite temperature and condensed phase systems was achieved. Furthermore, a whole set of simulation tools based on statistical mechanics can be apphed in this way in the context of an electronic structure method. Consequently, many dynamic as well as thermodynamic properties can be described within the accuracy of a first-principles method. 

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]. 

MD simulations based on first principles quantum mechanical forces will become more and more widespread. These methods are dramatically more expensive than classical MD simulations. F increases several orders of magnitude, while N and T have to be decreased in these simulations in order to make them feasible)... 

In classical MD simulations it is often assumed that the nuclei move on a potential energy surface. Implicit in this assumption is that the Born-Oppenheimer approximation applies that electronic and nuclear motion can... 

A nonconventional view of membrane microstructure, which neither conforms with the solution nor with the porous rock picture, was recently suggested in Ref. 84. Classical MDs simulations on microstructure and molecular mobility in swollen Nation membranes revealed a picture of a rather dynamic structure of water clusters with temporary formation and break-up of water bridges between them. The frequency of intercluster bridge formation was found to be consistent with the experimental transport coefficients through the membrane. 

In this chapter, we provide a brief overview of GPU hardware and programming techniques and then review the progress that has been made in using GPU hardware to accelerate classical MD simulations of condensed-phase biological systems we review some of the challenges and limitations that have faced those trying to... 

---