Molecular dynamics simulation finite-field

Force field calculations often truncate the non bonded potential energy of a molecular system at some finite distance. Truncation (nonbonded cutoff) saves computing resources. Also, periodic boxes and boundary conditions require it. However, this approximation is too crude for some calculations. For example, a molecular dynamic simulation with an abruptly truncated potential produces anomalous and nonphysical behavior. One symptom is that the solute (for example, a protein) cools and the solvent (water) heats rapidly. The temperatures of system components then slowly converge until the system appears to be in equilibrium, but it is not. 

One very prominent development in DFT has been the coupling of electronic structure calculations (which, when the ground state is concerned, apply to zero temperature) with finite-temperature molecular dynamics simulations. The founding paper in this field was published by Carr and Parrinello in 1985 [13]. Carr and Parrinello formulate effective equations of motion for the electrons to be solved simultaneously with the classical equations of motion for the ions. The forces on the ions are calculated from first principles by use of the Hellman-Feynman theorem. An alternative to the Carr-Parrinello method is to solve the electronic structure self-consistently at every ionic time step. Both methods are referred to as ab initio molecular dynamics (AIMD) [14]. 

Twenty years ago Car and Parrinello introduced an efficient method to perform Molecular Dynamics simulation for classical nuclei with forces computed on the fly by a Density Functional Theory (DFT) based electronic calculation [1], Because the method allowed study of the statistical mechanics of classical nuclei with many-body electronic interactions, it opened the way for the use of simulation methods for realistic systems with an accuracy well beyond the limits of available effective force fields. In the last twenty years, the number of applications of the Car-Parrinello ab-initio molecular d3mam-ics has ranged from simple covalent bonded solids, to high pressure physics, material science and biological systems. There have also been extensions of the original algorithm to simulate systems at constant temperature and constant pressure [2], finite temperature effects for the electrons [3], and quantum nuclei [4]. 

Some of the systems where the symmetry is low and the number of atoms relatively high are those occurring in the field of heterogeneous catalysis. The combination of a surface of a (in the ideal case, semi-infinite) crystal and one or more finite molecules (maybe even together with the presence of some medium) makes the study of the chemical reactions on the surfaces of crystals very complicated. In Section 6 we saw that such studies are becoming possible but still only for the simplest reactions on fairly idealized surfaces. Moreover, the calculations explore mainly energetical aspects and not kinetic aspects of the reactions. This means also that the time scales that can be treated with quantum-mechanical molecular-dynamics simulations are much too small (10 -10 s) compared with those that often are relevant for chemical reactions. 

Any of the methods used in classical Monte Carlo and molecular dynamics simulations may be borrowed in the combined QM/MM approach. However, the use of a finite system in condensed phase simulations is always a severe approximation, even when appropriate periodic or stochastic boundary conditions are employed. A further complication is the use of potential function truncation schemes, particular in ionic aqueous solutions where the long-range Coulombic interactions are significant beyond the cutoff distance.Thus, it is alluring to embed a continuum reaction field model in the quantum mechanical calculations in addition to the explicit solute—solvent interaaions to include the dielectric effect beyond the cutoff distance. - uch an onion shell arrangement has been used in spherical systems, whereas Lee and Warshel introduced an innovative local reaction field method for evaluation of long-... 

These apparent restrictions in size and length of simulation time of the fully quantum-mechanical methods or molecular-dynamics methods with continuous degrees of freedom in real space are the basic reason why the direct simulation of lattice models of the Ising type or of solid-on-solid type is still the most popular technique to simulate crystal growth processes. Consequently, a substantial part of this article will deal with scientific problems on those time and length scales which are simultaneously accessible by the experimental STM methods on one hand and by Monte Carlo lattice simulations on the other hand. Even these methods, however, are too microscopic to incorporate the boundary conditions from the laboratory set-up into the models in a reahstic way. Therefore one uses phenomenological models of the phase-field or sharp-interface type, and finally even finite-element methods, to treat the diffusion transport and hydrodynamic convections which control a reahstic crystal growth process from the melt on an industrial scale. 

The reported results for equilibrium properties were obtained by means of the standard Monte Carlo (MC), molecular dynamics (MD), and Gibbs ensemble (GE) simulation methods [23, 24], For the trial systems of a finite range the simple spherical cutoff was used, whereas in simulations of the full systems either the Ewald summation or the reaction field method were used. For further technical details we refer the reader to the original papers. 

Complementarily, several numerical approaches have also been proposed either at the molecular scale, using molecular dynamics [17], or at larger mesoscopic scales using finite element methods, lattice-Boltzmann simulations, or phase-field... 

In this chapter we will review recent developments in modelling proton transport in different media. We will thereby narrow the topic to atomistic modelling of transport properties and processes only. The majority of studies in this area employ molecular dynamics (MD) to get insight into the mechanisms. For large systems classical force fields are used, small systems are often studied with ab-initio molecular dynamics, especially with Car-Parinello MD simulations. These methods are well known and documented, including their drawbacks, as e.g. finite-size effects in periodic simulations." Therefore, we will abandon explicit comments on the computational details, and refer the interested reader to the cited references or ordinary textbooks. 

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